google scholar problem solving

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Review Article
• Open access
• Published: 11 January 2023

The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature

• Enwei Xu   ORCID: orcid.org/0000-0001-6424-8169 1 ,
• Wei Wang 1 &
• Qingxia Wang 1  

Humanities and Social Sciences Communications volume  10 , Article number:  16 ( 2023 ) Cite this article

19k Accesses

21 Citations

3 Altmetric

Metrics details

• Science, technology and society

Collaborative problem-solving has been widely embraced in the classroom instruction of critical thinking, which is regarded as the core of curriculum reform based on key competencies in the field of education as well as a key competence for learners in the 21st century. However, the effectiveness of collaborative problem-solving in promoting students’ critical thinking remains uncertain. This current research presents the major findings of a meta-analysis of 36 pieces of the literature revealed in worldwide educational periodicals during the 21st century to identify the effectiveness of collaborative problem-solving in promoting students’ critical thinking and to determine, based on evidence, whether and to what extent collaborative problem solving can result in a rise or decrease in critical thinking. The findings show that (1) collaborative problem solving is an effective teaching approach to foster students’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]); (2) in respect to the dimensions of critical thinking, collaborative problem solving can significantly and successfully enhance students’ attitudinal tendencies (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI[0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI[0.58, 0.82]); and (3) the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have an impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. On the basis of these results, recommendations are made for further study and instruction to better support students’ critical thinking in the context of collaborative problem-solving.

Similar content being viewed by others

A meta-analysis of the effects of design thinking on student learning

Fostering twenty-first century skills among primary school students through math project-based learning

A meta-analysis to gauge the impact of pedagogies employed in mixed-ability high school biology classrooms

Introduction.

Although critical thinking has a long history in research, the concept of critical thinking, which is regarded as an essential competence for learners in the 21st century, has recently attracted more attention from researchers and teaching practitioners (National Research Council, 2012 ). Critical thinking should be the core of curriculum reform based on key competencies in the field of education (Peng and Deng, 2017 ) because students with critical thinking can not only understand the meaning of knowledge but also effectively solve practical problems in real life even after knowledge is forgotten (Kek and Huijser, 2011 ). The definition of critical thinking is not universal (Ennis, 1989 ; Castle, 2009 ; Niu et al., 2013 ). In general, the definition of critical thinking is a self-aware and self-regulated thought process (Facione, 1990 ; Niu et al., 2013 ). It refers to the cognitive skills needed to interpret, analyze, synthesize, reason, and evaluate information as well as the attitudinal tendency to apply these abilities (Halpern, 2001 ). The view that critical thinking can be taught and learned through curriculum teaching has been widely supported by many researchers (e.g., Kuncel, 2011 ; Leng and Lu, 2020 ), leading to educators’ efforts to foster it among students. In the field of teaching practice, there are three types of courses for teaching critical thinking (Ennis, 1989 ). The first is an independent curriculum in which critical thinking is taught and cultivated without involving the knowledge of specific disciplines; the second is an integrated curriculum in which critical thinking is integrated into the teaching of other disciplines as a clear teaching goal; and the third is a mixed curriculum in which critical thinking is taught in parallel to the teaching of other disciplines for mixed teaching training. Furthermore, numerous measuring tools have been developed by researchers and educators to measure critical thinking in the context of teaching practice. These include standardized measurement tools, such as WGCTA, CCTST, CCTT, and CCTDI, which have been verified by repeated experiments and are considered effective and reliable by international scholars (Facione and Facione, 1992 ). In short, descriptions of critical thinking, including its two dimensions of attitudinal tendency and cognitive skills, different types of teaching courses, and standardized measurement tools provide a complex normative framework for understanding, teaching, and evaluating critical thinking.

Cultivating critical thinking in curriculum teaching can start with a problem, and one of the most popular critical thinking instructional approaches is problem-based learning (Liu et al., 2020 ). Duch et al. ( 2001 ) noted that problem-based learning in group collaboration is progressive active learning, which can improve students’ critical thinking and problem-solving skills. Collaborative problem-solving is the organic integration of collaborative learning and problem-based learning, which takes learners as the center of the learning process and uses problems with poor structure in real-world situations as the starting point for the learning process (Liang et al., 2017 ). Students learn the knowledge needed to solve problems in a collaborative group, reach a consensus on problems in the field, and form solutions through social cooperation methods, such as dialogue, interpretation, questioning, debate, negotiation, and reflection, thus promoting the development of learners’ domain knowledge and critical thinking (Cindy, 2004 ; Liang et al., 2017 ).

Collaborative problem-solving has been widely used in the teaching practice of critical thinking, and several studies have attempted to conduct a systematic review and meta-analysis of the empirical literature on critical thinking from various perspectives. However, little attention has been paid to the impact of collaborative problem-solving on critical thinking. Therefore, the best approach for developing and enhancing critical thinking throughout collaborative problem-solving is to examine how to implement critical thinking instruction; however, this issue is still unexplored, which means that many teachers are incapable of better instructing critical thinking (Leng and Lu, 2020 ; Niu et al., 2013 ). For example, Huber ( 2016 ) provided the meta-analysis findings of 71 publications on gaining critical thinking over various time frames in college with the aim of determining whether critical thinking was truly teachable. These authors found that learners significantly improve their critical thinking while in college and that critical thinking differs with factors such as teaching strategies, intervention duration, subject area, and teaching type. The usefulness of collaborative problem-solving in fostering students’ critical thinking, however, was not determined by this study, nor did it reveal whether there existed significant variations among the different elements. A meta-analysis of 31 pieces of educational literature was conducted by Liu et al. ( 2020 ) to assess the impact of problem-solving on college students’ critical thinking. These authors found that problem-solving could promote the development of critical thinking among college students and proposed establishing a reasonable group structure for problem-solving in a follow-up study to improve students’ critical thinking. Additionally, previous empirical studies have reached inconclusive and even contradictory conclusions about whether and to what extent collaborative problem-solving increases or decreases critical thinking levels. As an illustration, Yang et al. ( 2008 ) carried out an experiment on the integrated curriculum teaching of college students based on a web bulletin board with the goal of fostering participants’ critical thinking in the context of collaborative problem-solving. These authors’ research revealed that through sharing, debating, examining, and reflecting on various experiences and ideas, collaborative problem-solving can considerably enhance students’ critical thinking in real-life problem situations. In contrast, collaborative problem-solving had a positive impact on learners’ interaction and could improve learning interest and motivation but could not significantly improve students’ critical thinking when compared to traditional classroom teaching, according to research by Naber and Wyatt ( 2014 ) and Sendag and Odabasi ( 2009 ) on undergraduate and high school students, respectively.

The above studies show that there is inconsistency regarding the effectiveness of collaborative problem-solving in promoting students’ critical thinking. Therefore, it is essential to conduct a thorough and trustworthy review to detect and decide whether and to what degree collaborative problem-solving can result in a rise or decrease in critical thinking. Meta-analysis is a quantitative analysis approach that is utilized to examine quantitative data from various separate studies that are all focused on the same research topic. This approach characterizes the effectiveness of its impact by averaging the effect sizes of numerous qualitative studies in an effort to reduce the uncertainty brought on by independent research and produce more conclusive findings (Lipsey and Wilson, 2001 ).

This paper used a meta-analytic approach and carried out a meta-analysis to examine the effectiveness of collaborative problem-solving in promoting students’ critical thinking in order to make a contribution to both research and practice. The following research questions were addressed by this meta-analysis:

What is the overall effect size of collaborative problem-solving in promoting students’ critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills)?

How are the disparities between the study conclusions impacted by various moderating variables if the impacts of various experimental designs in the included studies are heterogeneous?

This research followed the strict procedures (e.g., database searching, identification, screening, eligibility, merging, duplicate removal, and analysis of included studies) of Cooper’s ( 2010 ) proposed meta-analysis approach for examining quantitative data from various separate studies that are all focused on the same research topic. The relevant empirical research that appeared in worldwide educational periodicals within the 21st century was subjected to this meta-analysis using Rev-Man 5.4. The consistency of the data extracted separately by two researchers was tested using Cohen’s kappa coefficient, and a publication bias test and a heterogeneity test were run on the sample data to ascertain the quality of this meta-analysis.

Data sources and search strategies

There were three stages to the data collection process for this meta-analysis, as shown in Fig. 1 , which shows the number of articles included and eliminated during the selection process based on the statement and study eligibility criteria.

This flowchart shows the number of records identified, included and excluded in the article.

First, the databases used to systematically search for relevant articles were the journal papers of the Web of Science Core Collection and the Chinese Core source journal, as well as the Chinese Social Science Citation Index (CSSCI) source journal papers included in CNKI. These databases were selected because they are credible platforms that are sources of scholarly and peer-reviewed information with advanced search tools and contain literature relevant to the subject of our topic from reliable researchers and experts. The search string with the Boolean operator used in the Web of Science was “TS = (((“critical thinking” or “ct” and “pretest” or “posttest”) or (“critical thinking” or “ct” and “control group” or “quasi experiment” or “experiment”)) and (“collaboration” or “collaborative learning” or “CSCL”) and (“problem solving” or “problem-based learning” or “PBL”))”. The research area was “Education Educational Research”, and the search period was “January 1, 2000, to December 30, 2021”. A total of 412 papers were obtained. The search string with the Boolean operator used in the CNKI was “SU = (‘critical thinking’*‘collaboration’ + ‘critical thinking’*‘collaborative learning’ + ‘critical thinking’*‘CSCL’ + ‘critical thinking’*‘problem solving’ + ‘critical thinking’*‘problem-based learning’ + ‘critical thinking’*‘PBL’ + ‘critical thinking’*‘problem oriented’) AND FT = (‘experiment’ + ‘quasi experiment’ + ‘pretest’ + ‘posttest’ + ‘empirical study’)” (translated into Chinese when searching). A total of 56 studies were found throughout the search period of “January 2000 to December 2021”. From the databases, all duplicates and retractions were eliminated before exporting the references into Endnote, a program for managing bibliographic references. In all, 466 studies were found.

Second, the studies that matched the inclusion and exclusion criteria for the meta-analysis were chosen by two researchers after they had reviewed the abstracts and titles of the gathered articles, yielding a total of 126 studies.

Third, two researchers thoroughly reviewed each included article’s whole text in accordance with the inclusion and exclusion criteria. Meanwhile, a snowball search was performed using the references and citations of the included articles to ensure complete coverage of the articles. Ultimately, 36 articles were kept.

Two researchers worked together to carry out this entire process, and a consensus rate of almost 94.7% was reached after discussion and negotiation to clarify any emerging differences.

Eligibility criteria

Since not all the retrieved studies matched the criteria for this meta-analysis, eligibility criteria for both inclusion and exclusion were developed as follows:

The publication language of the included studies was limited to English and Chinese, and the full text could be obtained. Articles that did not meet the publication language and articles not published between 2000 and 2021 were excluded.

The research design of the included studies must be empirical and quantitative studies that can assess the effect of collaborative problem-solving on the development of critical thinking. Articles that could not identify the causal mechanisms by which collaborative problem-solving affects critical thinking, such as review articles and theoretical articles, were excluded.

The research method of the included studies must feature a randomized control experiment or a quasi-experiment, or a natural experiment, which have a higher degree of internal validity with strong experimental designs and can all plausibly provide evidence that critical thinking and collaborative problem-solving are causally related. Articles with non-experimental research methods, such as purely correlational or observational studies, were excluded.

The participants of the included studies were only students in school, including K-12 students and college students. Articles in which the participants were non-school students, such as social workers or adult learners, were excluded.

The research results of the included studies must mention definite signs that may be utilized to gauge critical thinking’s impact (e.g., sample size, mean value, or standard deviation). Articles that lacked specific measurement indicators for critical thinking and could not calculate the effect size were excluded.

Data coding design

In order to perform a meta-analysis, it is necessary to collect the most important information from the articles, codify that information’s properties, and convert descriptive data into quantitative data. Therefore, this study designed a data coding template (see Table 1 ). Ultimately, 16 coding fields were retained.

The designed data-coding template consisted of three pieces of information. Basic information about the papers was included in the descriptive information: the publishing year, author, serial number, and title of the paper.

The variable information for the experimental design had three variables: the independent variable (instruction method), the dependent variable (critical thinking), and the moderating variable (learning stage, teaching type, intervention duration, learning scaffold, group size, measuring tool, and subject area). Depending on the topic of this study, the intervention strategy, as the independent variable, was coded into collaborative and non-collaborative problem-solving. The dependent variable, critical thinking, was coded as a cognitive skill and an attitudinal tendency. And seven moderating variables were created by grouping and combining the experimental design variables discovered within the 36 studies (see Table 1 ), where learning stages were encoded as higher education, high school, middle school, and primary school or lower; teaching types were encoded as mixed courses, integrated courses, and independent courses; intervention durations were encoded as 0–1 weeks, 1–4 weeks, 4–12 weeks, and more than 12 weeks; group sizes were encoded as 2–3 persons, 4–6 persons, 7–10 persons, and more than 10 persons; learning scaffolds were encoded as teacher-supported learning scaffold, technique-supported learning scaffold, and resource-supported learning scaffold; measuring tools were encoded as standardized measurement tools (e.g., WGCTA, CCTT, CCTST, and CCTDI) and self-adapting measurement tools (e.g., modified or made by researchers); and subject areas were encoded according to the specific subjects used in the 36 included studies.

The data information contained three metrics for measuring critical thinking: sample size, average value, and standard deviation. It is vital to remember that studies with various experimental designs frequently adopt various formulas to determine the effect size. And this paper used Morris’ proposed standardized mean difference (SMD) calculation formula ( 2008 , p. 369; see Supplementary Table S3 ).

Procedure for extracting and coding data

According to the data coding template (see Table 1 ), the 36 papers’ information was retrieved by two researchers, who then entered them into Excel (see Supplementary Table S1 ). The results of each study were extracted separately in the data extraction procedure if an article contained numerous studies on critical thinking, or if a study assessed different critical thinking dimensions. For instance, Tiwari et al. ( 2010 ) used four time points, which were viewed as numerous different studies, to examine the outcomes of critical thinking, and Chen ( 2013 ) included the two outcome variables of attitudinal tendency and cognitive skills, which were regarded as two studies. After discussion and negotiation during data extraction, the two researchers’ consistency test coefficients were roughly 93.27%. Supplementary Table S2 details the key characteristics of the 36 included articles with 79 effect quantities, including descriptive information (e.g., the publishing year, author, serial number, and title of the paper), variable information (e.g., independent variables, dependent variables, and moderating variables), and data information (e.g., mean values, standard deviations, and sample size). Following that, testing for publication bias and heterogeneity was done on the sample data using the Rev-Man 5.4 software, and then the test results were used to conduct a meta-analysis.

Publication bias test

When the sample of studies included in a meta-analysis does not accurately reflect the general status of research on the relevant subject, publication bias is said to be exhibited in this research. The reliability and accuracy of the meta-analysis may be impacted by publication bias. Due to this, the meta-analysis needs to check the sample data for publication bias (Stewart et al., 2006 ). A popular method to check for publication bias is the funnel plot; and it is unlikely that there will be publishing bias when the data are equally dispersed on either side of the average effect size and targeted within the higher region. The data are equally dispersed within the higher portion of the efficient zone, consistent with the funnel plot connected with this analysis (see Fig. 2 ), indicating that publication bias is unlikely in this situation.

This funnel plot shows the result of publication bias of 79 effect quantities across 36 studies.

Heterogeneity test

To select the appropriate effect models for the meta-analysis, one might use the results of a heterogeneity test on the data effect sizes. In a meta-analysis, it is common practice to gauge the degree of data heterogeneity using the I 2 value, and I 2  ≥ 50% is typically understood to denote medium-high heterogeneity, which calls for the adoption of a random effect model; if not, a fixed effect model ought to be applied (Lipsey and Wilson, 2001 ). The findings of the heterogeneity test in this paper (see Table 2 ) revealed that I 2 was 86% and displayed significant heterogeneity ( P  < 0.01). To ensure accuracy and reliability, the overall effect size ought to be calculated utilizing the random effect model.

The analysis of the overall effect size

This meta-analysis utilized a random effect model to examine 79 effect quantities from 36 studies after eliminating heterogeneity. In accordance with Cohen’s criterion (Cohen, 1992 ), it is abundantly clear from the analysis results, which are shown in the forest plot of the overall effect (see Fig. 3 ), that the cumulative impact size of cooperative problem-solving is 0.82, which is statistically significant ( z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]), and can encourage learners to practice critical thinking.

This forest plot shows the analysis result of the overall effect size across 36 studies.

In addition, this study examined two distinct dimensions of critical thinking to better understand the precise contributions that collaborative problem-solving makes to the growth of critical thinking. The findings (see Table 3 ) indicate that collaborative problem-solving improves cognitive skills (ES = 0.70) and attitudinal tendency (ES = 1.17), with significant intergroup differences (chi 2  = 7.95, P  < 0.01). Although collaborative problem-solving improves both dimensions of critical thinking, it is essential to point out that the improvements in students’ attitudinal tendency are much more pronounced and have a significant comprehensive effect (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]), whereas gains in learners’ cognitive skill are slightly improved and are just above average. (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

The analysis of moderator effect size

The whole forest plot’s 79 effect quantities underwent a two-tailed test, which revealed significant heterogeneity ( I 2  = 86%, z  = 12.78, P  < 0.01), indicating differences between various effect sizes that may have been influenced by moderating factors other than sampling error. Therefore, exploring possible moderating factors that might produce considerable heterogeneity was done using subgroup analysis, such as the learning stage, learning scaffold, teaching type, group size, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, in order to further explore the key factors that influence critical thinking. The findings (see Table 4 ) indicate that various moderating factors have advantageous effects on critical thinking. In this situation, the subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), learning scaffold (chi 2  = 9.03, P  < 0.01), and teaching type (chi 2  = 7.20, P  < 0.05) are all significant moderators that can be applied to support the cultivation of critical thinking. However, since the learning stage and the measuring tools did not significantly differ among intergroup (chi 2  = 3.15, P  = 0.21 > 0.05, and chi 2  = 0.08, P  = 0.78 > 0.05), we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving. These are the precise outcomes, as follows:

Various learning stages influenced critical thinking positively, without significant intergroup differences (chi 2  = 3.15, P  = 0.21 > 0.05). High school was first on the list of effect sizes (ES = 1.36, P  < 0.01), then higher education (ES = 0.78, P  < 0.01), and middle school (ES = 0.73, P  < 0.01). These results show that, despite the learning stage’s beneficial influence on cultivating learners’ critical thinking, we are unable to explain why it is essential for cultivating critical thinking in the context of collaborative problem-solving.

Different teaching types had varying degrees of positive impact on critical thinking, with significant intergroup differences (chi 2  = 7.20, P  < 0.05). The effect size was ranked as follows: mixed courses (ES = 1.34, P  < 0.01), integrated courses (ES = 0.81, P  < 0.01), and independent courses (ES = 0.27, P  < 0.01). These results indicate that the most effective approach to cultivate critical thinking utilizing collaborative problem solving is through the teaching type of mixed courses.

Various intervention durations significantly improved critical thinking, and there were significant intergroup differences (chi 2  = 12.18, P  < 0.01). The effect sizes related to this variable showed a tendency to increase with longer intervention durations. The improvement in critical thinking reached a significant level (ES = 0.85, P  < 0.01) after more than 12 weeks of training. These findings indicate that the intervention duration and critical thinking’s impact are positively correlated, with a longer intervention duration having a greater effect.

Different learning scaffolds influenced critical thinking positively, with significant intergroup differences (chi 2  = 9.03, P  < 0.01). The resource-supported learning scaffold (ES = 0.69, P  < 0.01) acquired a medium-to-higher level of impact, the technique-supported learning scaffold (ES = 0.63, P  < 0.01) also attained a medium-to-higher level of impact, and the teacher-supported learning scaffold (ES = 0.92, P  < 0.01) displayed a high level of significant impact. These results show that the learning scaffold with teacher support has the greatest impact on cultivating critical thinking.

Various group sizes influenced critical thinking positively, and the intergroup differences were statistically significant (chi 2  = 8.77, P  < 0.05). Critical thinking showed a general declining trend with increasing group size. The overall effect size of 2–3 people in this situation was the biggest (ES = 0.99, P  < 0.01), and when the group size was greater than 7 people, the improvement in critical thinking was at the lower-middle level (ES < 0.5, P  < 0.01). These results show that the impact on critical thinking is positively connected with group size, and as group size grows, so does the overall impact.

Various measuring tools influenced critical thinking positively, with significant intergroup differences (chi 2  = 0.08, P  = 0.78 > 0.05). In this situation, the self-adapting measurement tools obtained an upper-medium level of effect (ES = 0.78), whereas the complete effect size of the standardized measurement tools was the largest, achieving a significant level of effect (ES = 0.84, P  < 0.01). These results show that, despite the beneficial influence of the measuring tool on cultivating critical thinking, we are unable to explain why it is crucial in fostering the growth of critical thinking by utilizing the approach of collaborative problem-solving.

Different subject areas had a greater impact on critical thinking, and the intergroup differences were statistically significant (chi 2  = 13.36, P  < 0.05). Mathematics had the greatest overall impact, achieving a significant level of effect (ES = 1.68, P  < 0.01), followed by science (ES = 1.25, P  < 0.01) and medical science (ES = 0.87, P  < 0.01), both of which also achieved a significant level of effect. Programming technology was the least effective (ES = 0.39, P  < 0.01), only having a medium-low degree of effect compared to education (ES = 0.72, P  < 0.01) and other fields (such as language, art, and social sciences) (ES = 0.58, P  < 0.01). These results suggest that scientific fields (e.g., mathematics, science) may be the most effective subject areas for cultivating critical thinking utilizing the approach of collaborative problem-solving.

The effectiveness of collaborative problem solving with regard to teaching critical thinking

According to this meta-analysis, using collaborative problem-solving as an intervention strategy in critical thinking teaching has a considerable amount of impact on cultivating learners’ critical thinking as a whole and has a favorable promotional effect on the two dimensions of critical thinking. According to certain studies, collaborative problem solving, the most frequently used critical thinking teaching strategy in curriculum instruction can considerably enhance students’ critical thinking (e.g., Liang et al., 2017 ; Liu et al., 2020 ; Cindy, 2004 ). This meta-analysis provides convergent data support for the above research views. Thus, the findings of this meta-analysis not only effectively address the first research query regarding the overall effect of cultivating critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills) utilizing the approach of collaborative problem-solving, but also enhance our confidence in cultivating critical thinking by using collaborative problem-solving intervention approach in the context of classroom teaching.

Furthermore, the associated improvements in attitudinal tendency are much stronger, but the corresponding improvements in cognitive skill are only marginally better. According to certain studies, cognitive skill differs from the attitudinal tendency in classroom instruction; the cultivation and development of the former as a key ability is a process of gradual accumulation, while the latter as an attitude is affected by the context of the teaching situation (e.g., a novel and exciting teaching approach, challenging and rewarding tasks) (Halpern, 2001 ; Wei and Hong, 2022 ). Collaborative problem-solving as a teaching approach is exciting and interesting, as well as rewarding and challenging; because it takes the learners as the focus and examines problems with poor structure in real situations, and it can inspire students to fully realize their potential for problem-solving, which will significantly improve their attitudinal tendency toward solving problems (Liu et al., 2020 ). Similar to how collaborative problem-solving influences attitudinal tendency, attitudinal tendency impacts cognitive skill when attempting to solve a problem (Liu et al., 2020 ; Zhang et al., 2022 ), and stronger attitudinal tendencies are associated with improved learning achievement and cognitive ability in students (Sison, 2008 ; Zhang et al., 2022 ). It can be seen that the two specific dimensions of critical thinking as well as critical thinking as a whole are affected by collaborative problem-solving, and this study illuminates the nuanced links between cognitive skills and attitudinal tendencies with regard to these two dimensions of critical thinking. To fully develop students’ capacity for critical thinking, future empirical research should pay closer attention to cognitive skills.

The moderating effects of collaborative problem solving with regard to teaching critical thinking

In order to further explore the key factors that influence critical thinking, exploring possible moderating effects that might produce considerable heterogeneity was done using subgroup analysis. The findings show that the moderating factors, such as the teaching type, learning stage, group size, learning scaffold, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, could all support the cultivation of collaborative problem-solving in critical thinking. Among them, the effect size differences between the learning stage and measuring tool are not significant, which does not explain why these two factors are crucial in supporting the cultivation of critical thinking utilizing the approach of collaborative problem-solving.

In terms of the learning stage, various learning stages influenced critical thinking positively without significant intergroup differences, indicating that we are unable to explain why it is crucial in fostering the growth of critical thinking.

Although high education accounts for 70.89% of all empirical studies performed by researchers, high school may be the appropriate learning stage to foster students’ critical thinking by utilizing the approach of collaborative problem-solving since it has the largest overall effect size. This phenomenon may be related to student’s cognitive development, which needs to be further studied in follow-up research.

With regard to teaching type, mixed course teaching may be the best teaching method to cultivate students’ critical thinking. Relevant studies have shown that in the actual teaching process if students are trained in thinking methods alone, the methods they learn are isolated and divorced from subject knowledge, which is not conducive to their transfer of thinking methods; therefore, if students’ thinking is trained only in subject teaching without systematic method training, it is challenging to apply to real-world circumstances (Ruggiero, 2012 ; Hu and Liu, 2015 ). Teaching critical thinking as mixed course teaching in parallel to other subject teachings can achieve the best effect on learners’ critical thinking, and explicit critical thinking instruction is more effective than less explicit critical thinking instruction (Bensley and Spero, 2014 ).

In terms of the intervention duration, with longer intervention times, the overall effect size shows an upward tendency. Thus, the intervention duration and critical thinking’s impact are positively correlated. Critical thinking, as a key competency for students in the 21st century, is difficult to get a meaningful improvement in a brief intervention duration. Instead, it could be developed over a lengthy period of time through consistent teaching and the progressive accumulation of knowledge (Halpern, 2001 ; Hu and Liu, 2015 ). Therefore, future empirical studies ought to take these restrictions into account throughout a longer period of critical thinking instruction.

With regard to group size, a group size of 2–3 persons has the highest effect size, and the comprehensive effect size decreases with increasing group size in general. This outcome is in line with some research findings; as an example, a group composed of two to four members is most appropriate for collaborative learning (Schellens and Valcke, 2006 ). However, the meta-analysis results also indicate that once the group size exceeds 7 people, small groups cannot produce better interaction and performance than large groups. This may be because the learning scaffolds of technique support, resource support, and teacher support improve the frequency and effectiveness of interaction among group members, and a collaborative group with more members may increase the diversity of views, which is helpful to cultivate critical thinking utilizing the approach of collaborative problem-solving.

With regard to the learning scaffold, the three different kinds of learning scaffolds can all enhance critical thinking. Among them, the teacher-supported learning scaffold has the largest overall effect size, demonstrating the interdependence of effective learning scaffolds and collaborative problem-solving. This outcome is in line with some research findings; as an example, a successful strategy is to encourage learners to collaborate, come up with solutions, and develop critical thinking skills by using learning scaffolds (Reiser, 2004 ; Xu et al., 2022 ); learning scaffolds can lower task complexity and unpleasant feelings while also enticing students to engage in learning activities (Wood et al., 2006 ); learning scaffolds are designed to assist students in using learning approaches more successfully to adapt the collaborative problem-solving process, and the teacher-supported learning scaffolds have the greatest influence on critical thinking in this process because they are more targeted, informative, and timely (Xu et al., 2022 ).

With respect to the measuring tool, despite the fact that standardized measurement tools (such as the WGCTA, CCTT, and CCTST) have been acknowledged as trustworthy and effective by worldwide experts, only 54.43% of the research included in this meta-analysis adopted them for assessment, and the results indicated no intergroup differences. These results suggest that not all teaching circumstances are appropriate for measuring critical thinking using standardized measurement tools. “The measuring tools for measuring thinking ability have limits in assessing learners in educational situations and should be adapted appropriately to accurately assess the changes in learners’ critical thinking.”, according to Simpson and Courtney ( 2002 , p. 91). As a result, in order to more fully and precisely gauge how learners’ critical thinking has evolved, we must properly modify standardized measuring tools based on collaborative problem-solving learning contexts.

With regard to the subject area, the comprehensive effect size of science departments (e.g., mathematics, science, medical science) is larger than that of language arts and social sciences. Some recent international education reforms have noted that critical thinking is a basic part of scientific literacy. Students with scientific literacy can prove the rationality of their judgment according to accurate evidence and reasonable standards when they face challenges or poorly structured problems (Kyndt et al., 2013 ), which makes critical thinking crucial for developing scientific understanding and applying this understanding to practical problem solving for problems related to science, technology, and society (Yore et al., 2007 ).

Suggestions for critical thinking teaching

Other than those stated in the discussion above, the following suggestions are offered for critical thinking instruction utilizing the approach of collaborative problem-solving.

First, teachers should put a special emphasis on the two core elements, which are collaboration and problem-solving, to design real problems based on collaborative situations. This meta-analysis provides evidence to support the view that collaborative problem-solving has a strong synergistic effect on promoting students’ critical thinking. Asking questions about real situations and allowing learners to take part in critical discussions on real problems during class instruction are key ways to teach critical thinking rather than simply reading speculative articles without practice (Mulnix, 2012 ). Furthermore, the improvement of students’ critical thinking is realized through cognitive conflict with other learners in the problem situation (Yang et al., 2008 ). Consequently, it is essential for teachers to put a special emphasis on the two core elements, which are collaboration and problem-solving, and design real problems and encourage students to discuss, negotiate, and argue based on collaborative problem-solving situations.

Second, teachers should design and implement mixed courses to cultivate learners’ critical thinking, utilizing the approach of collaborative problem-solving. Critical thinking can be taught through curriculum instruction (Kuncel, 2011 ; Leng and Lu, 2020 ), with the goal of cultivating learners’ critical thinking for flexible transfer and application in real problem-solving situations. This meta-analysis shows that mixed course teaching has a highly substantial impact on the cultivation and promotion of learners’ critical thinking. Therefore, teachers should design and implement mixed course teaching with real collaborative problem-solving situations in combination with the knowledge content of specific disciplines in conventional teaching, teach methods and strategies of critical thinking based on poorly structured problems to help students master critical thinking, and provide practical activities in which students can interact with each other to develop knowledge construction and critical thinking utilizing the approach of collaborative problem-solving.

Third, teachers should be more trained in critical thinking, particularly preservice teachers, and they also should be conscious of the ways in which teachers’ support for learning scaffolds can promote critical thinking. The learning scaffold supported by teachers had the greatest impact on learners’ critical thinking, in addition to being more directive, targeted, and timely (Wood et al., 2006 ). Critical thinking can only be effectively taught when teachers recognize the significance of critical thinking for students’ growth and use the proper approaches while designing instructional activities (Forawi, 2016 ). Therefore, with the intention of enabling teachers to create learning scaffolds to cultivate learners’ critical thinking utilizing the approach of collaborative problem solving, it is essential to concentrate on the teacher-supported learning scaffolds and enhance the instruction for teaching critical thinking to teachers, especially preservice teachers.

Implications and limitations

There are certain limitations in this meta-analysis, but future research can correct them. First, the search languages were restricted to English and Chinese, so it is possible that pertinent studies that were written in other languages were overlooked, resulting in an inadequate number of articles for review. Second, these data provided by the included studies are partially missing, such as whether teachers were trained in the theory and practice of critical thinking, the average age and gender of learners, and the differences in critical thinking among learners of various ages and genders. Third, as is typical for review articles, more studies were released while this meta-analysis was being done; therefore, it had a time limit. With the development of relevant research, future studies focusing on these issues are highly relevant and needed.

Conclusions

The subject of the magnitude of collaborative problem-solving’s impact on fostering students’ critical thinking, which received scant attention from other studies, was successfully addressed by this study. The question of the effectiveness of collaborative problem-solving in promoting students’ critical thinking was addressed in this study, which addressed a topic that had gotten little attention in earlier research. The following conclusions can be made:

Regarding the results obtained, collaborative problem solving is an effective teaching approach to foster learners’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]). With respect to the dimensions of critical thinking, collaborative problem-solving can significantly and effectively improve students’ attitudinal tendency, and the comprehensive effect is significant (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

As demonstrated by both the results and the discussion, there are varying degrees of beneficial effects on students’ critical thinking from all seven moderating factors, which were found across 36 studies. In this context, the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have a positive impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. Since the learning stage (chi 2  = 3.15, P  = 0.21 > 0.05) and measuring tools (chi 2  = 0.08, P  = 0.78 > 0.05) did not demonstrate any significant intergroup differences, we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving.

Data availability

All data generated or analyzed during this study are included within the article and its supplementary information files, and the supplementary information files are available in the Dataverse repository: https://doi.org/10.7910/DVN/IPFJO6 .

Bensley DA, Spero RA (2014) Improving critical thinking skills and meta-cognitive monitoring through direct infusion. Think Skills Creat 12:55–68. https://doi.org/10.1016/j.tsc.2014.02.001

Article   Google Scholar  

Castle A (2009) Defining and assessing critical thinking skills for student radiographers. Radiography 15(1):70–76. https://doi.org/10.1016/j.radi.2007.10.007

Chen XD (2013) An empirical study on the influence of PBL teaching model on critical thinking ability of non-English majors. J PLA Foreign Lang College 36 (04):68–72

Google Scholar  

Cohen A (1992) Antecedents of organizational commitment across occupational groups: a meta-analysis. J Organ Behav. https://doi.org/10.1002/job.4030130602

Cooper H (2010) Research synthesis and meta-analysis: a step-by-step approach, 4th edn. Sage, London, England

Cindy HS (2004) Problem-based learning: what and how do students learn? Educ Psychol Rev 51(1):31–39

Duch BJ, Gron SD, Allen DE (2001) The power of problem-based learning: a practical “how to” for teaching undergraduate courses in any discipline. Stylus Educ Sci 2:190–198

Ennis RH (1989) Critical thinking and subject specificity: clarification and needed research. Educ Res 18(3):4–10. https://doi.org/10.3102/0013189x018003004

Facione PA (1990) Critical thinking: a statement of expert consensus for purposes of educational assessment and instruction. Research findings and recommendations. Eric document reproduction service. https://eric.ed.gov/?id=ed315423

Facione PA, Facione NC (1992) The California Critical Thinking Dispositions Inventory (CCTDI) and the CCTDI test manual. California Academic Press, Millbrae, CA

Forawi SA (2016) Standard-based science education and critical thinking. Think Skills Creat 20:52–62. https://doi.org/10.1016/j.tsc.2016.02.005

Halpern DF (2001) Assessing the effectiveness of critical thinking instruction. J Gen Educ 50(4):270–286. https://doi.org/10.2307/27797889

Hu WP, Liu J (2015) Cultivation of pupils’ thinking ability: a five-year follow-up study. Psychol Behav Res 13(05):648–654. https://doi.org/10.3969/j.issn.1672-0628.2015.05.010

Huber K (2016) Does college teach critical thinking? A meta-analysis. Rev Educ Res 86(2):431–468. https://doi.org/10.3102/0034654315605917

Kek MYCA, Huijser H (2011) The power of problem-based learning in developing critical thinking skills: preparing students for tomorrow’s digital futures in today’s classrooms. High Educ Res Dev 30(3):329–341. https://doi.org/10.1080/07294360.2010.501074

Kuncel NR (2011) Measurement and meaning of critical thinking (Research report for the NRC 21st Century Skills Workshop). National Research Council, Washington, DC

Kyndt E, Raes E, Lismont B, Timmers F, Cascallar E, Dochy F (2013) A meta-analysis of the effects of face-to-face cooperative learning. Do recent studies falsify or verify earlier findings? Educ Res Rev 10(2):133–149. https://doi.org/10.1016/j.edurev.2013.02.002

Leng J, Lu XX (2020) Is critical thinking really teachable?—A meta-analysis based on 79 experimental or quasi experimental studies. Open Educ Res 26(06):110–118. https://doi.org/10.13966/j.cnki.kfjyyj.2020.06.011

Liang YZ, Zhu K, Zhao CL (2017) An empirical study on the depth of interaction promoted by collaborative problem solving learning activities. J E-educ Res 38(10):87–92. https://doi.org/10.13811/j.cnki.eer.2017.10.014

Lipsey M, Wilson D (2001) Practical meta-analysis. International Educational and Professional, London, pp. 92–160

Liu Z, Wu W, Jiang Q (2020) A study on the influence of problem based learning on college students’ critical thinking-based on a meta-analysis of 31 studies. Explor High Educ 03:43–49

Morris SB (2008) Estimating effect sizes from pretest-posttest-control group designs. Organ Res Methods 11(2):364–386. https://doi.org/10.1177/1094428106291059

Article   ADS   Google Scholar  

Mulnix JW (2012) Thinking critically about critical thinking. Educ Philos Theory 44(5):464–479. https://doi.org/10.1111/j.1469-5812.2010.00673.x

Naber J, Wyatt TH (2014) The effect of reflective writing interventions on the critical thinking skills and dispositions of baccalaureate nursing students. Nurse Educ Today 34(1):67–72. https://doi.org/10.1016/j.nedt.2013.04.002

National Research Council (2012) Education for life and work: developing transferable knowledge and skills in the 21st century. The National Academies Press, Washington, DC

Niu L, Behar HLS, Garvan CW (2013) Do instructional interventions influence college students’ critical thinking skills? A meta-analysis. Educ Res Rev 9(12):114–128. https://doi.org/10.1016/j.edurev.2012.12.002

Peng ZM, Deng L (2017) Towards the core of education reform: cultivating critical thinking skills as the core of skills in the 21st century. Res Educ Dev 24:57–63. https://doi.org/10.14121/j.cnki.1008-3855.2017.24.011

Reiser BJ (2004) Scaffolding complex learning: the mechanisms of structuring and problematizing student work. J Learn Sci 13(3):273–304. https://doi.org/10.1207/s15327809jls1303_2

Ruggiero VR (2012) The art of thinking: a guide to critical and creative thought, 4th edn. Harper Collins College Publishers, New York

Schellens T, Valcke M (2006) Fostering knowledge construction in university students through asynchronous discussion groups. Comput Educ 46(4):349–370. https://doi.org/10.1016/j.compedu.2004.07.010

Sendag S, Odabasi HF (2009) Effects of an online problem based learning course on content knowledge acquisition and critical thinking skills. Comput Educ 53(1):132–141. https://doi.org/10.1016/j.compedu.2009.01.008

Sison R (2008) Investigating Pair Programming in a Software Engineering Course in an Asian Setting. 2008 15th Asia-Pacific Software Engineering Conference, pp. 325–331. https://doi.org/10.1109/APSEC.2008.61

Simpson E, Courtney M (2002) Critical thinking in nursing education: literature review. Mary Courtney 8(2):89–98

Stewart L, Tierney J, Burdett S (2006) Do systematic reviews based on individual patient data offer a means of circumventing biases associated with trial publications? Publication bias in meta-analysis. John Wiley and Sons Inc, New York, pp. 261–286

Tiwari A, Lai P, So M, Yuen K (2010) A comparison of the effects of problem-based learning and lecturing on the development of students’ critical thinking. Med Educ 40(6):547–554. https://doi.org/10.1111/j.1365-2929.2006.02481.x

Wood D, Bruner JS, Ross G (2006) The role of tutoring in problem solving. J Child Psychol Psychiatry 17(2):89–100. https://doi.org/10.1111/j.1469-7610.1976.tb00381.x

Wei T, Hong S (2022) The meaning and realization of teachable critical thinking. Educ Theory Practice 10:51–57

Xu EW, Wang W, Wang QX (2022) A meta-analysis of the effectiveness of programming teaching in promoting K-12 students’ computational thinking. Educ Inf Technol. https://doi.org/10.1007/s10639-022-11445-2

Yang YC, Newby T, Bill R (2008) Facilitating interactions through structured web-based bulletin boards: a quasi-experimental study on promoting learners’ critical thinking skills. Comput Educ 50(4):1572–1585. https://doi.org/10.1016/j.compedu.2007.04.006

Yore LD, Pimm D, Tuan HL (2007) The literacy component of mathematical and scientific literacy. Int J Sci Math Educ 5(4):559–589. https://doi.org/10.1007/s10763-007-9089-4

Zhang T, Zhang S, Gao QQ, Wang JH (2022) Research on the development of learners’ critical thinking in online peer review. Audio Visual Educ Res 6:53–60. https://doi.org/10.13811/j.cnki.eer.2022.06.08

Download references

Acknowledgements

This research was supported by the graduate scientific research and innovation project of Xinjiang Uygur Autonomous Region named “Research on in-depth learning of high school information technology courses for the cultivation of computing thinking” (No. XJ2022G190) and the independent innovation fund project for doctoral students of the College of Educational Science of Xinjiang Normal University named “Research on project-based teaching of high school information technology courses from the perspective of discipline core literacy” (No. XJNUJKYA2003).

Author information

Authors and affiliations.

College of Educational Science, Xinjiang Normal University, 830017, Urumqi, Xinjiang, China

Enwei Xu, Wei Wang & Qingxia Wang

You can also search for this author in PubMed   Google Scholar

Corresponding authors

Correspondence to Enwei Xu or Wei Wang .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Informed consent

Additional information.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary tables, rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Xu, E., Wang, W. & Wang, Q. The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature. Humanit Soc Sci Commun 10 , 16 (2023). https://doi.org/10.1057/s41599-023-01508-1

Download citation

Received : 07 August 2022

Accepted : 04 January 2023

Published : 11 January 2023

DOI : https://doi.org/10.1057/s41599-023-01508-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

Impacts of online collaborative learning on students’ intercultural communication apprehension and intercultural communicative competence.

• Hoa Thi Hoang Chau
• Hung Phu Bui
• Quynh Thi Huong Dinh

Education and Information Technologies (2024)

Exploring the effects of digital technology on deep learning: a meta-analysis

The impacts of computer-supported collaborative learning on students’ critical thinking: a meta-analysis.

• Yoseph Gebrehiwot Tedla
• Hsiu-Ling Chen

Sustainable electricity generation and farm-grid utilization from photovoltaic aquaculture: a bibliometric analysis

• A. A. Amusa
• M. Alhassan

International Journal of Environmental Science and Technology (2024)

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Problem-Solving in Mathematics Education

• Reference work entry
• First Online: 01 January 2020
• Cite this reference work entry

• Manuel Santos-Trigo 2  

1483 Accesses

9 Citations

Introduction

Problem-solving approaches appear in all human endeavors. In mathematics, activities such as posing or defining problems and looking for different ways to solve them are central to the development of the discipline. In mathematics education, the systematic study of what the process of formulating and solving problems entails and the ways to structure problem-solving approaches to learn mathematics has been part of the research agenda in mathematics education. How have research and practicing problem-solving approaches changed and evolved in mathematics education, and what themes are currently investigated? Two communities have significantly contributed to the characterization and development of the research and practicing agenda in mathematical problem-solving: mathematicians who recognize that the process of formulating, representing, and solving problems is essential in the development of mathematical knowledge (Polya 1945 ; Hadamard 1945 ; Halmos 1980 ) and mathematics...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime
• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Durable hardcover edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Artigue M, Houdement C (2007) Problem solving in France: didactic and curricular perspectives. ZDM Int J Math Educ 39(5–6):365–382

Article   Google Scholar  

Cai J, Nie B (2007) Problem solving in Chinese mathematics education: research and practice. ZDM Int J Math Educ 39(5–6):459–473

Common Core State Standards for Mathematics (CCSS) (2010) Common Core State Standards initiative. http://www.corestandards.org/

Devlin K (2002) The millennium problems. The seven greatest unsolved mathematical puzzles of our time. Granta Publications, London

Google Scholar  

Dick TP, Hollebrands K (2011) Focus in high school mathematics: technology to support reasoning and sense making. The National Council of Teachers of Mathematics, Reston

Doorman M, Drijvers P, Dekker T, Van den Heuvel-Panhuizen M, de Lange J, Wijers M (2007) Problem solving as a challenge for mathematics education in the Netherlands. ZDM Int J Math Educ 39(5–6):405–418

English LD, Gainsburg J (2016) Problem solving in a 21st-century mathematics curriculum. In: English LD, Kirshner D (eds) Handbook of international research in mathematics education. Routledge, New York, pp 313–335

Hadamard J (1945) An essay on the psychology of invention in the mathematical field. Dover Publications, New York

Halmos PR (1980) The heart of mathematics. Am Math Mon 87(7):519–524

Halmos PR (1994) What is teaching. Am Math Mon 101(9):848–854

Hilbert D (1902) Mathematical problems. Bulletin of the American Mathematical Society, 8:437–479

Hoyles C, Lagrange J-B (eds) (2010) Mathematics education and technology: rethinking the terrain. The 17th ICMI study. Springer, New York

Krutestkii VA (1976) The psychology of mathematical abilities in school children. University of Chicago Press, Chicago

Lester FK, Kehle PE (1994) From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In: Lesh R, Doerr HM (ed) Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahawah: New Jersey, pp 501–517

Lesh R, Zawojewski JS (2007) Problem solving and modeling. In: Lester FK Jr (ed) The second handbook of research on mathematics teaching and learning. National Council of Teachers of Mathematics. Information Age Publishing, Charlotte, pp 763–804

Lester F, Kehle PE (2003) From problem solving to modeling: the evolution of thinking about research on complex mathematical activity. In: Lesh R, Doerr H (eds) Beyond constructivism: models and modeling perspectives on mathematics problem solving, learning and teaching. Lawrence Erlbaum, Mahwah, pp 501–518

Liljedahl P, Santos-Trigo M (2019) Mathematical problem solving. Current themes, trends and research, https://doi.org/10.1007/978-3-030-10472-6 Cham, Switzerland: Springer

NCTM (1989) Curriculum and evaluation standards for school mathematics. NCTM, Reston

NCTM (2000) Principles and standards for school mathematics. National Council of Teachers of Mathematics, Reston

NCTM (2009) Focus in high school mathematics. Reasoning and sense making. NCTM, Reston

Perkins DN, Simmons R (1988) Patterns of misunderstanding: An integrative model of science, math, and programming. Rev of Edu Res 58(3):303–326

Polya G (1945) How to solve it. Princeton University Press, Princeton

Book   Google Scholar  

Santos-Trigo M (2007) Mathematical problem solving: an evolving research and practice domain. ZDM Int J Math Educ 39(5, 6):523–536

Santos-Trigo M, Reyes-Martínez I (2018) High school prospective teachers’ problem-solving reasoning that involves the coordinated use of digital technologies. Int J Math Educ Sci Technol. https://doi.org/10.1080/0020739X.2018.1489075

Santos-Trigo M, Reyes-Rodriguez, A (2016) The use of digital technology in finding multiple paths to solve and extend an equilateral triangle task, International. Journal of Mathematical Education in Science and Technology 47:1:58–81. https://doi.org/10.1080/0020739X.2015.1049228

Schoenfeld AH (1985) Mathematical problem solving. Academic, New York

Schoenfeld AH (1992) Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In: Grows DA (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp 334–370

Schoenfeld AH (2015) How we think: a theory of human decision-making, with a focus on teaching. In: Cho SJ (ed) The proceedings of the 12th international congress on mathematical education. Springer, Cham, pp 229–243. https://doi.org/10.1007/978-3-319-12688-3_16

Chapter   Google Scholar  

Selden J, Mason A, Selden A (1989) Can average calculus students solve nonroutine problems? J Math Behav 8:45–50

Wertheimer M (1945) Productive thinking. Harper, New York

Download references

Author information

Authors and affiliations.

Centre for Research and Advanced Studies, Mathematics Education Department, Cinvestav-IPN, Mexico City, Mexico

Manuel Santos-Trigo

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Manuel Santos-Trigo .

Editor information

Editors and affiliations.

Department of Education, Centre for Mathematics Education, London South Bank University, London, UK

Stephen Lerman

Section Editor information

Department of Science Teaching, The Weizmann Institute of Science, Rehovot, Israel

Ruhama Even

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this entry

Cite this entry.

Santos-Trigo, M. (2020). Problem-Solving in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_129

Download citation

DOI : https://doi.org/10.1007/978-3-030-15789-0_129

Published : 23 February 2020

Publisher Name : Springer, Cham

Print ISBN : 978-3-030-15788-3

Online ISBN : 978-3-030-15789-0

eBook Packages : Education Reference Module Humanities and Social Sciences Reference Module Education

Share this entry

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List

Analysing Complex Problem-Solving Strategies from a Cognitive Perspective: The Role of Thinking Skills

1 MTA-SZTE Digital Learning Technologies Research Group, Center for Learning and Instruction, University of Szeged, 6722 Szeged, Hungary

Gyöngyvér Molnár

2 MTA-SZTE Digital Learning Technologies Research Group, Institute of Education, University of Szeged, 6722 Szeged, Hungary; uh.degezs-u.yspde@ranlomyg

Associated Data

The data used to support the findings cannot be shared at this time as it also forms part of an ongoing study.

Complex problem solving (CPS) is considered to be one of the most important skills for successful learning. In an effort to explore the nature of CPS, this study aims to investigate the role of inductive reasoning (IR) and combinatorial reasoning (CR) in the problem-solving process of students using statistically distinguishable exploration strategies in the CPS environment. The sample was drawn from a group of university students (N = 1343). The tests were delivered via the eDia online assessment platform. Latent class analyses were employed to seek students whose problem-solving strategies showed similar patterns. Four qualitatively different class profiles were identified: (1) 84.3% of the students were proficient strategy users, (2) 6.2% were rapid learners, (3) 3.1% were non-persistent explorers, and (4) 6.5% were non-performing explorers. Better exploration strategy users showed greater development in thinking skills, and the roles of IR and CR in the CPS process were varied for each type of strategy user. To sum up, the analysis identified students’ problem-solving behaviours in respect of exploration strategy in the CPS environment and detected a number of remarkable differences in terms of the use of thinking skills between students with different exploration strategies.

1. Introduction

Problem solving is part and parcel of our daily activities, for instance, in determining what to wear in the morning, how to use our new electronic devices, how to reach a restaurant by public transport, how to arrange our schedule to achieve the greatest work efficiency and how to communicate with people in a foreign country. In most cases, it is essential to solve the problems that recur in our study, work and daily lives. These situations require problem solving. Generally, problem solving is the thinking that occurs if we want “to overcome barriers between a given state and a desired goal state by means of behavioural and/or cognitive, multistep activities” ( Frensch and Funke 1995, p. 18 ). It has also been considered as one of the most important skills for successful learning in the 21st century. This study focuses on one specific kind of problem solving, complex problem solving (CPS). (Numerous other terms are also used ( Funke et al. 2018 ), such as interactive problem solving ( Greiff et al. 2013 ; Wu and Molnár 2018 ), and creative problem solving ( OECD 2010 ), etc.).

CPS is a transversal skill ( Greiff et al. 2014 ), operating several mental activities and thinking skills (see Molnár et al. 2013 ). In order to explore the nature of CPS, some studies have focused on detecting its component skills ( Wu and Molnár 2018 ), whereas others have analysed students’ behaviour during the problem-solving process ( Greiff et al. 2018 ; Wu and Molnár 2021 ). This study aims to link these two fields by investigating the role of thinking skills in learning by examining students’ use of statistically distinguishable exploration strategies in the CPS environment.

1.1. Complex Problem Solving: Definition, Assessment and Relations to Intelligence

According to a widely accepted definition proposed by Buchner ( 1995 ), CPS is “the successful interaction with task environments that are dynamic (i.e., change as a function of users’ intervention and/or as a function of time) and in which some, if not all, of the environment’s regularities can only be revealed by successful exploration and integration of the information gained in that process” ( Buchner 1995, p. 14 ). A CPS process is split into two phases, knowledge acquisition and knowledge application. In the knowledge acquisition (KAC) phase of CPS, the problem solver understands the problem itself and stores the acquired information ( Funke 2001 ; Novick and Bassok 2005 ). In the knowledge application (KAP) phase, the problem solver applies the acquired knowledge to bring about the transition from a given state to a goal state ( Novick and Bassok 2005 ).

Problem solving, especially CPS, has frequently been compared or linked to intelligence in previous studies (e.g., Beckmann and Guthke 1995 ; Stadler et al. 2015 ; Wenke et al. 2005 ). Lotz et al. ( 2017 ) observed that “intelligence and [CPS] are two strongly overlapping constructs” (p. 98). There are many similarities and commonalities that can be detected between CPS and intelligence. For instance, CPS and intelligence share some of the same key features, such as the integration of information ( Stadler et al. 2015 ). Furthermore, Wenke et al. ( 2005 ) stated that “the ability to solve problems has featured prominently in virtually every definition of human intelligence” (p. 9); meanwhile, from the opposite perspective, intelligence has also been considered as one of the most important predictors of the ability to solve problems ( Wenke et al. 2005 ). Moreover, the relation between CPS and intelligence has also been discussed from an empirical perspective. A meta-analysis conducted by Stadler et al. ( 2015 ) selected 47 empirical studies (total sample size N = 13,740) which focused on the correlation between CPS and intelligence. The results of their analysis confirmed that a correlation between CPS and intelligence exists with a moderate effect size of M(g) = 0.43.

Due to the strong link between CPS and intelligence, assessments of these two domains have been connected and have overlapped to a certain extent. For instance, Beckmann and Guthke ( 1995 ) observed that some of the intelligence tests “capture something akin to an individual’s general ability to solve problems (e.g., Sternberg 1982 )” (p. 184). Nowadays, some widely used CPS assessment methods are related to intelligence but still constitute a distinct construct ( Schweizer et al. 2013 ), such as the MicroDYN approach ( Greiff and Funke 2009 ; Greiff et al. 2012 ; Schweizer et al. 2013 ). This approach uses the minimal complex system to simulate simplistic, artificial but still complex problems following certain construction rules ( Greiff and Funke 2009 ; Greiff et al. 2012 ).

The MicroDYN approach has been widely employed to measure problem solving in a well-defined problem context (i.e., “problems have a clear set of means for reaching a precisely described goal state”, Dörner and Funke 2017, p. 1 ). To complete a task based on the MicroDYN approach, the problem solver engages in dynamic interaction with the task to acquire relevant knowledge. It is not possible to create this kind of test environment with the traditional paper-and-pencil-based method. Therefore, it is currently only possible to conduct a MicroDYN-based CPS assessment within the computer-based assessment framework. In the context of computer-based assessment, the problem-solvers’ operations were recorded and logged by the assessment platform. Thus, except for regular achievement-focused result data, logfile data are also available for analysis. This provides the option of exploring and monitoring problem solvers’ behaviour and thinking processes, specifically, their exploration strategies, during the problem-solving process (see, e.g., Chen et al. 2019 ; Greiff et al. 2015a ; Molnár and Csapó 2018 ; Molnár et al. 2022 ; Wu and Molnár 2021 ).

Problem solving, in the context of an ill-defined problem (i.e., “problems have no clear problem definition, their goal state is not defined clearly, and the means of moving towards the (diffusely described) goal state are not clear”, Dörner and Funke 2017, p. 1), involved a different cognitive process than that in the context of a well-defined problem ( Funke 2010 ; Schraw et al. 1995 ), and it cannot be measured with the MicroDYN approach. The nature of ill-defined problem solving has been explored and discussed in numerous studies (e.g., Dörner and Funke 2017 ; Hołda et al. 2020 ; Schraw et al. 1995 ; Welter et al. 2017 ). This will not be discussed here as this study focuses on well-defined problem solving.

1.2. Inductive and Combinatorial Reasoning as Component Skills of Complex Problem Solving

Frensch and Funke ( 1995 ) constructed a theoretical framework that summarizes the basic components of CPS and the interrelations among the components. The framework contains three separate components: problem solver, task and environment. The impact of the problem solver is mainly relevant to three main categories, which are memory contents, dynamic information processing and non-cognitive variables. Some thinking skills have been reported to play an important role in dynamic information processing. We can thus describe them as component skills of CPS. Inductive reasoning (IR) and combinatorial reasoning (CR) are the two thinking skills that have been most frequently discussed as component skills of CPS.

IR is the reasoning skill that has been covered most commonly in the literature. Currently, there is no universally accepted definition. Molnár et al. ( 2013 ) described it as the cognitive process of acquiring general regularities by generalizing single and specific observations and experiences, whereas Klauer ( 1990 ) defined it as the discovery of regularities that relies upon the detection of similarities and/or dissimilarities as concerns attributes of or relations to or between objects. Sandberg and McCullough ( 2010 ) provided a general conclusion of the definitions of IR: it is the process of moving from the specific to the general.

Csapó ( 1997 ) pointed out that IR is a basic component of thinking and that it forms a central aspect of intellectual functioning. Some studies have also discussed the role of IR in a problem-solving environment. For instance, Mayer ( 1998 ) stated that IR will be applied in information processing during the process of solving general problems. Gilhooly ( 1982 ) also pointed out that IR plays a key role in some activities in the problem-solving process, such as hypothesis generation and hypothesis testing. Moreover, the influence of IR on both KAC and KAP has been analysed and demonstrated in previous studies ( Molnár et al. 2013 ).

Empirical studies have also provided evidence that IR and CPS are related. Based on the results of a large-scale assessment (N = 2769), Molnár et al. ( 2013 ) showed that IR significantly correlated with 9–17-year-old students’ domain-general problem-solving achievement (r = 0.44–0.52). Greiff et al. ( 2015b ) conducted a large-scale assessment project (N = 2021) in Finland to explore the links between fluid reasoning skills and domain-general CPS. The study measured fluid reasoning as a two-dimensional model which consisted of deductive reasoning and scientific reasoning and included inductive thinking processes ( Greiff et al. 2015b ). The results drawing on structural equation modelling indicated that fluid reasoning which was partly based on IR had significant and strong predictive effects on both KAC (β = 0.51) and KAP (β = 0.55), the two phases of problem solving. Such studies have suggested that IR is one of the component skills of CPS.

According to Adey and Csapó ’s ( 2012 ) definition, CR is the process of creating complex constructions out of a set of given elements that satisfy the conditions explicitly given in or inferred from the situation. In this process, some cognitive operations, such as combinations, arrangements, permutations, notations and formulae, will be employed ( English 2005 ). CR is one of the basic components of formal thinking ( Batanero et al. 1997 ). The relationship between CR and CPS has frequently been discussed. English ( 2005 ) demonstrated that CR has an essential meaning in several types of problem situations, such as problems requiring the systematic testing of alternative solutions. Moreover, Newell ( 1993 ) pointed out that CR is applied in some key activities of problem-solving information processing, such as strategy generation and application. Its functions include, but are not limited to, helping problem solvers to discover relationships between certain elements and concepts, promoting their fluency of thinking when they are considering different strategies ( Csapó 1999 ) and identifying all possible alternatives ( OECD 2014 ). Moreover, Wu and Molnár ’s ( 2018 ) empirical study drew on a sample (N = 187) of 11–13-year-old primary school students in China. Their study built a structural equation model between CPS, IR and CR, and the result indicated that CR showed a strong and statistically significant predictive power for CPS (β = 0.55). Thus, the results of the empirical study also support the argument that CR is one of the component skills of CPS.

1.3. Behaviours and Strategies in a Complex Problem-Solving Environment

Wüstenberg et al. ( 2012 ) stated that the creation and implementation of strategic exploration are core actions of the problem-solving task. Exploring and generating effective information are key to successfully solving a problem. Wittmann and Hattrup ( 2004 ) illustrated that “riskier strategies [create] a learning environment with greater opportunities to discover and master the rules and boundaries [of a problem]” (p. 406). Thus, when gathering information about a complex problem, there may be differences between exploration strategies in terms of efficacy. The MicroDYN scenarios, a simplification and simulation of the real-world problem-solving context, will also be influenced by the adoption and implementation of exploration strategies.

The effectiveness of the isolated variation strategy (or “Vary-One-Thing-At-A-Time” strategy—VOTAT; Vollmeyer et al. 1996 ) in a CPS environment has been hotly debated ( Chen et al. 2019 ; Greiff et al. 2018 ; Molnár and Csapó 2018 ; Molnár et al. 2022 ; Wu and Molnár 2021 ; Wüstenberg et al. 2014 ). To use the VOTAT strategy, a problem solver “systematically varies only one input variable, whereas the others remain unchanged. This way, the effect of the variable that has just been changed can be observed directly by monitoring the changes in the output variables” ( Molnár and Csapó 2018, p. 2 ). Understanding and using VOTAT effectively is the foundation for developing more complex strategies for coordinating multiple variables and the basis for some phases of scientific thinking (i.e., inquiry, analysis, inference and argument; Kuhn 2010 ; Kuhn et al. 1995 ).

Some previous studies have indicated that students who are able to apply VOTAT are more likely to achieve higher performance in a CPS assessment ( Greiff et al. 2018 ), especially if the problem is a well-defined minimal complex system (such as MicroDYN) ( Fischer et al. 2012 ; Molnár and Csapó 2018 ; Wu and Molnár 2021 ). For instance, Molnár and Csapó ( 2018 ) conducted an empirical study to explore how students’ exploration strategies influence their performance in an interactive problem-solving environment. They measured a group (N = 4371) of 3rd- to 12th-grade (aged 9–18) Hungarian students’ problem-solving achievement and modelled students’ exploration strategies. This result confirmed that students’ exploration strategies influence their problem-solving performance. For example, conscious VOTAT strategy users proved to be the best problem-solvers. Furthermore, other empirical studies (e.g., Molnár et al. 2022 ; Wu and Molnár 2021 ) achieved similar results, thus confirming the importance of VOTAT in a MicroDYN-based CPS environment.

Lotz et al. ( 2017 ) illustrated that effective use of VOTAT is associated with higher levels of intelligence. Their study also pointed out that intelligence has the potential to facilitate successful exploration behaviour. Reasoning skills are an important component of general intelligence. Based on Lotz et al. ’s ( 2017 ) statements, the roles IR and CR play in the CPS process might vary due to students’ different strategy usage patterns. However, there is still a lack of empirical studies in this regard.

2. Research Aims and Questions

Numerous studies have explored the nature of CPS, some of them discussing and analysing it from behavioural or cognitive perspectives. However, there have barely been any that have merged these two perspectives. From the cognitive perspective, this study explores the role of thinking skills (including IR and CR) in the cognition process of CPS. From the behavioural perspective, the study focuses on students’ behaviour (i.e., their exploration strategy) in the CPS assessment process. More specifically, the research aims to fill this gap and examine students’ use of statistically distinguishable exploration strategies in CPS environments and to detect the connection between the level of students’ thinking skills and their behaviour strategies in the CPS environment. The following research questions were thus formed.

• (RQ1) What exploration strategy profiles characterise the various problem-solvers at the university level?
• (RQ2) Can developmental differences in CPS, IR and CR be detected among students with different exploration strategy profiles?
• (RQ3) What are the similarities and differences in the roles IR and CR play in the CPS process as well as in the two phases of CPS (i.e., KAC and KAP) among students with different exploration strategy profiles?

3.1. Participants and Procedure

The sample was drawn from one of the largest universities in Hungary. Participation was voluntary, but students were able to earn one course credit for taking part in the assessment. The participants were students who had just started their studies there (N = 1671). 43.4% of the first-year students took part in the assessment. 50.9% of the participants were female, and 49.1% were male. We filtered the sample and excluded those who had more than 80% missing data on any of the tests. After the data were cleaned, data from 1343 students were available for analysis. The test was designed and delivered via the eDia online assessment system ( Csapó and Molnár 2019 ). The assessment was held in the university ICT room and divided into two sessions. The first session involved the CPS test, whereas the second session entailed the IR and CR tests. Each session lasted 45 min. The language of the tests was Hungarian, the mother tongue of the students.

3.2. Instruments

3.2.1. complex problem solving (cps).

The CPS assessment instrument adopted the MicroDYN approach. It contains a total of twelve scenarios, and each scenario consisted of two items (one item in the KAC phase and one item in the KAP phase in each problem scenario). Twelve KAC items and twelve KAP items were therefore delivered on the CPS test for a total of twenty-four items. Each scenario has a fictional cover story. For instance, students found a sick cat in front of their house, and they were expected to feed the cat with two different kinds of cat food to help it recover.

Each item contains up to three input and three output variables. The relations between the input and output variables were formulated with linear structural equations ( Funke 2001 ). Figure 1 shows a MicroDYN sample structure containing three input variables (A, B and C), three output variables (X, Y and Z) and a number of possible relations between the variables. The complexity of the item was defined by the number of input and output variables, and the number of relations between the variables. The test began with the item with the lowest complexity. The complexity of each item gradually increased as the test progressed.

A typical MicroDYN structure with three input variables and three output variables ( Greiff and Funke 2009 ).

The interface of each item displays the value of each variable in both numerical and figural forms (See Figure 2 ). Each of the input variables has a controller, which makes it possible to vary and set the value between +2 (+ +) and −2 (− −). To operate the system, students need to click the “+” or “−” button or use the slider directly to select the value they want to be added to or subtracted from the current value of the input variable. After clicking the “Apply” button in the interface, the input variables will add or subtract the selected value, and the output variables will show the corresponding changes. The history of the values for the input and output variables within the same problem scenario is displayed on screen. If students want to withdraw all the changes and set all the variables to their original status, they can click the “Reset” button.

Screenshot of the MicroDYN item Cat—first phase (knowledge acquisition). (The items were administered in Hungarian.)

In the first phase of the problem-solving process, the KAC phase, students are asked to interact with the system by changing the value of the input variables and observing and analysing the corresponding changes in the output variables. They are then expected to determine the relationship between the input and output variables and draw it in the form of (an) arrow(s) on the concept map at the bottom of the interface. To avoid item dependence in the second phase of the problem-solving process, the students are provided with a concept map during the KAP phase (see Figure 3 ), which shows the correct connections between the input and output variables. The students are expected to interact with the system by manipulating the input variables to make the output variables reach the given target values in four steps or less. That is, they cannot click on the “Apply” button more than four times. The first phase had a 180 s time limit, whereas the second had a 90 s time limit.

Screenshot of the MicroDYN item Cat—second phase (knowledge application). (The items were administered in Hungarian).

3.2.2. Inductive Reasoning (IR)

The IR instrument (see Figure 4 ) was originally designed and developed in Hungary ( Csapó 1997 ). In the last 25 years, the instrument has been further developed and scaled for a wide age range ( Molnár and Csapó 2011 ). In addition, figural items have been added, and the assessment method has evolved from paper-and-pencil to computer-based ( Pásztor 2016 ). Currently, the instrument is widely employed in a number of countries (see, e.g., Mousa and Molnár 2020 ; Pásztor et al. 2018 ; Wu et al. 2022 ; Wu and Molnár 2018 ). In the present study, four types of items were included after test adaptation: figural series, figural analogies, number analogies and number series. Students were expected to ascertain the correct relationship between the given figures and numbers and select a suitable figure or number as their answer. Students used the drag-and-drop operation to provide their answers. In total, 49 inductive reasoning items were delivered to the participating students.

Sample items for the IR test. (The items were administered in Hungarian.).

3.2.3. Combinatorial Reasoning (CR)

The CR instrument (see Figure 5 ) was originally designed by Csapó ( 1988 ). The instrument was first developed in paper-and-pencil format and then modified for computer use ( Pásztor and Csapó 2014 ). Each item contained figural or verbal elements and a clear requirement for combing through the elements. Students were asked to list every single combination based on a given rule they could find. For the figural items, students provided their answers using the drag-and-drop operation; for the verbal items, they were asked to type their answers in a text box provided on screen. The test consisted of eight combinatorial reasoning items in total.

Sample item for the CR test. (The items were administered in Hungarian).

3.3. Scoring

Students’ performance was automatically scored via the eDia platform. Items on the CPS and IR tests were scored dichotomously. In the first phase (KAC) of the CPS test, if a student drew all the correct relations on the concept map provided on screen within the given timeframe, his/her performance was assigned a score of 1 or otherwise a score of 0. In the second phase (KAP) of the CPS test, if the student successfully reached the given target values of the output variables by manipulating the level of the input variables within no more than four steps and the given timeframe, then his/her performance earned a score of 1 or otherwise a score of 0. On the IR test items, if a student selected the correct figure or number as his/her answer, then he or she received a score of 1; otherwise, the score was 0.

Students’ performance on the CR test items was scored according to a special J index, which was developed by Csapó ( 1988 ). The J index ranges from 0 to 1, where 1 means that the student provided all the correct combinations without any redundant combinations on the task. The formula for computing the J index is the following:

x stands for the number of correct combinations in the student’s answer,

T stands for the number of all possible correct combinations, and

y stands for the number of redundant combinations in the student’s answer.

Furthermore, according to Csapó ’s ( 1988 ) design, if y is higher than T, then the J index will be counted as 0.

3.4. Coding and Labelling the Logfile Data

Beyond concrete answer data, students’ interaction and manipulation behaviour were also logged in the assessment system. This made it possible to analyse students’ exploration behaviour in the first phase of the CPS process (KAC phase). Toward this aim, we adopted a labelling system developed by Molnár and Csapó ( 2018 ) to transfer the raw logfile data to structured data files for analysis. Based on the system, each trial (i.e., the sum of manipulations within the same problem scenario which was applied and tested by clicking the “Apply” button) was modelled as a single data entity. The sum of these trials within the same problem was defined as a strategy. In our study, we only consider the trials which were able to provide useful and new information for the problem-solvers, whereas the redundant or operations trials were excluded.

In this study, we analysed students’ trials to determine the extent to which they used the VOTAT strategy: fully, partially or not at all. This strategy is the most successful exploration strategy for such problems; it is the easiest to interpret and provides direct information about the given variable without any mediation effects ( Fischer et al. 2012 ; Greiff et al. 2018 ; Molnár and Csapó 2018 ; Wüstenberg et al. 2014 ; Wu and Molnár 2021 ). Based on the definition of VOTAT noted in Section 1.3 , we checked students’ trials to ascertain if they systematically varied one input variable while keeping the others unchanged, or applied a different, less successful strategy. We considered the following three types of trials:

• “Only one single input variable was manipulated, whose relationship to the output variables was unknown (we considered a relationship unknown if its effect cannot be known from previous settings), while the other variables were set at a neutral value like zero […]
• One single input variable was changed, whose relationship to the output variables was unknown. The others were not at zero, but at a setting used earlier. […]
• One single input variable was changed, whose relationship to the output variables was unknown, and the others were not at zero; however, the effect of the other input variable(s) was known from earlier settings. Even so, this combination was not attempted earlier” ( Molnár and Csapó 2018, p. 8 )

We used the numbers 0, 1 and 2 to distinguish the level of students’ use of the most effective exploration strategy (i.e., VOTAT). If a student applied one or more of the above trials for every input variable within the same scenario, we considered that they had used the full VOTAT strategy and labelled this behaviour 2. If a student had only employed VOTAT on some but not all of the input variables, we concluded that they had used a partial VOTAT strategy for that problem scenario and labelled it 1. If a student had used none of the trials noted above in their problem exploration, then we determined that they had not used VOTAT at all and thus gave them a label of 0.

3.5. Data Analysis Plan

We used LCA (latent class analysis) to explore students’ exploration strategy profiles. LCA is a latent variable modelling approach that can be used to identify unmeasured (latent) classes of samples with similarly observed variables. LCA has been widely used in analysing logfile data for CPS assessment and in exploring students’ behaviour patterns (see, e.g., Gnaldi et al. 2020 ; Greiff et al. 2018 ; Molnár et al. 2022 ; Molnár and Csapó 2018 ; Mustafić et al. 2019 ; Wu and Molnár 2021 ). The scores for the use of VOTAT in the KAC phase (0, 1, 2; see Section 3.4 ) were used for the LCA analysis. We used Mplus ( Muthén and Muthén 2010 ) to run the LCA analysis. Several indices were used to measure the model fit: AIC (Akaike information criterion), BIC (Bayesian information criterion) and aBIC (adjusted Bayesian information criterion). With these three indicators, lower values indicate a better model fit. Entropy (ranging from 0 to 1, with values close to 1 indicating high certainty in the classification). The Lo–Mendell–Rubin adjusted likelihood ratio was used to compare the model containing n latent classes with the model containing n − 1 latent classes, and the p value was the indicator for whether a significant difference could be detected ( Lo et al. 2001 ). The results of the Lo–Mendell–Rubin adjusted likelihood ratio analysis were used to decide the correct number of latent classes in LCA models.

ANOVA was used to analyse the performance differences for CPS, IR and CR across the students from the different class profiles. The analysis was run using SPSS. A path analysis (PA) was employed in the structural equation modelling (SEM) framework to investigate the roles of CR and IR in CPS and the similarities and differences across the students from the different exploration strategy profiles. The PA models were carried out with Mplus. The Tucker–Lewis index (TLI), the comparative fit index (CFI) and the root-mean-square error of approximation (RMSEA) were used as indicators for the model fit. A TLI and CFI larger than 0.90 paired with a RMSEA less than 0.08 are commonly considered as an acceptable model fit ( van de Schoot et al. 2012 ).

4.1. Descriptive Results

All three tests showed good reliability (Cronbach’s α: CPS: 0.89; IR: 0.87; CR: 0.79). Furthermore, the two sub-dimensions of the CPS test, KAC and KAP, also showed satisfactory reliability (Cronbach’s α: KAC: 0.86; KAP: 0.78). The tests thus proved to be reliable. The means and standard deviations of students’ performance (in percentage) on each test are provided in Table 1 .

The means and standard deviations of students’ performance on each test.

4.2. Four Qualitatively Different Exploration Strategy Profiles Can Be Distinguished in CPS

Based on the labelled logfile data for CPS, we applied latent class analyses to identify the behaviour patterns of the students in the exploration phase of the problem-solving process. The model fits for the LCA analysis are listed in Table 2 . Compared with the 2 or 3 latent class models, the 4 latent class model has a lower AIC, BIC and aBIC, and the likelihood ratio statistical test (the Lo–Mendell–Rubin adjusted likelihood ratio test) confirmed it has a significantly better model fit. The 5 and 6 latent class models did not show a better model fit than the 4 latent class model. Therefore, based on the results, four qualitatively different exploration strategy profiles can be distinguished, which covered 96% of the students.

Fit indices for latent class analyses.

The patterns for the four qualitatively different exploration strategy profiles are shown in Figure 6 . In total, 84.3% of the students were proficient exploration strategy users, who were able to use VOTAT in each problem scenario independent of its difficulty level (represented by the red line in Figure 5 ). In total, 6.2% of the students were rapid learners. They were not able to apply VOTAT at the beginning of the test on the easiest problems but managed to learn quickly, and, after a rapid learning curve by the end of the test, they reached the level of proficient exploration strategy users, even though the problems became much more complex (represented by the blue line). In total, 3.1% of the students proved to be non-persistent explorers, and they employed VOTAT on the easiest problems but did not transfer this knowledge to the more complex problems. Finally, they were no longer able to apply VOTAT when the complexity of the problems increased (represented by the green line). In total, 6.5% of the students were non-performing explorers; they barely used any VOTAT strategy during the whole test (represented by the pink line) independent of problem complexity.

Four qualitatively different exploration strategy profiles.

4.3. Better Exploration Strategy Users Showed Better Performance in Reasoning Skills

Students with different exploration strategy profiles showed different kinds of performance in each reasoning skill under investigation. Results (see Table 3 ) showed that more proficient strategy users tended to have higher achievement in all the domains assessed as well as in the two sub-dimensions in CPS (i.e., KAC and KAP; ANOVA: CPS: F(3, 1339) = 187.28, p < 0.001; KAC: F(3, 1339) = 237.15, p < 0.001; KAP: F(3, 1339) = 74.91, p < 0.001; IR: F(3, 1339) = 48.10, p < 0.001; CR: F(3, 1339) = 28.72, p < 0.001); specifically, students identified as “proficient exploration strategy users” achieved the highest level on the reasoning skills tests independent of the domains. On average, they were followed by rapid learners, non-persistent explorers and, finally, non-performing explorers. Tukey’s post hoc tests revealed more details on the performance differences of students with different exploration profiles in each of the domains being measured. Proficient strategy users proved to be significantly more skilled in each of the reasoning domains. They were followed by rapid learners, who outperformed non-persistent explorers and non-performing explorers in CPS. In the domains of IR and CR, there were no achievement differences between rapid learners and non-persistent explorers, who significantly outperformed non-performing strategy explorers.

Students’ performance on each test—grouped according to the different exploration strategy profiles.

4.4. The Roles of IR and CR in CPS and Its Processes Were Different for Each Type of Exploration Strategy User

Path analysis was used to explore the predictive power of IR and CR for CPS and its processes, knowledge acquisition and knowledge application, for each group of students with different exploration strategy profiles. That is, four path analysis models were built to indicate the predictive power of IR and CR for CPS (see Figure 7 ), and another four path analyses models were developed to monitor the predictive power of IR and CR for the two empirically distinguishable phases of CPS (i.e., KAC and KAP) (see Figure 8 ). All eight models had good model fits, the fit indices TLI and CFI were above 0.90, and RMSEA was less than 0.08.

Path analysis models (with CPS, IR and CR) for each type of strategy user; * significant at 0.05 ( p   <  0.05); ** significant at 0.01 ( p   <  0.01); N.S.: no significant effect can be found.

Path analysis models (with KAC, KAP, IR and CR) for each type of strategy user; * significant at 0.05 ( p  <  0.05); ** significant at 0.01 ( p  <  0.01); N.S.: no significant effect can be found.

Students’ level of IR significantly predicted their level of CPS in all four path analysis models independent of their exploration strategy profile ( Figure 7 ; proficient strategy users: β = 0.432, p < 0.01; rapid learners: β = 0.350, p < 0.01; non-persistent explorers: β = 0.309, p < 0.05; and non-performing explorers: β = 0.386, p < 0.01). This was not the case for CR, which only proved to have predictive power for CPS among proficient strategy users (β = 0.104, p < 0.01). IR and CR were significantly correlated in all four models.

After examining the roles of IR and CR in the CPS process, we went further to explore the roles of these two reasoning skills in the distinguishable phases of CPS. The path analysis models ( Figure 8 ) showed that the predictive power of IR and CR for KAC and KAP was varied in each group. Levels of IR and CR among non-persistent explorers and non-performing explorers failed to predict their achievement in the KAC phase of the CPS process. Moreover, rapid learners’ level of IR significantly predicted their achievement in the KAC phase (β = 0.327, p < 0.01), but their level of CR did not have the same predictive power. Furthermore, the proficient strategy users’ levels of both reasoning skills had significant predictive power for KAC (IR: β = 0.363, p < 0.01; CR: β = 0.132, p < 0.01). In addition, in the KAP phase of the CPS problems, IR played a significant role for all types of strategy users, although with different power (proficient strategy users: β = 0.408, p < 0.01; rapid learners: β = 0.339, p < 0.01; non-persistent explorers: β = 0.361, p < 0.01; and non-performing explorers: β = 0.447, p < 0.01); by contrast, CR did not have significant predictive power for the KAP phase in any of the models.

5. Discussion

The study aims to investigate the role of IR and CR in CPS and its phases among students using statistically distinguishable exploration strategies in different CPS environments. We examined 1343 Hungarian university students and assessed their CPS, IR and CR skills. Both achievement data and logfile data were used in the analysis. The traditional achievement indicators formed the foundation for analysing the students’ CPS, CR and IR performance, whereas process data extracted from logfile data were used to explore students’ exploration behaviour in various CPS environments.

Four qualitatively different exploration strategy profiles were distinguished: proficient strategy users, rapid learners, non-persistent explorers and non-performing explorers (RQ1). The four profiles were consistent with the result of another study conducted at university level (see Molnár et al. 2022 ), and the frequencies of these four profiles in these two studies were very similar. The two studies therefore corroborate and validate each other’s results. The majority of the participants were identified as proficient strategy users. More than 80% of the university students were able to employ effective exploration strategies in various CPS environments. Of the remaining students, some performed poorly in exploration strategy use in the early part of the test (rapid learners), some in the last part (non-persistent explorers) and some throughout the test (non-performing explorers). However, students with these three exploration strategy profiles only constituted small portions of the total sample (with proportions ranging from 3.1% to 6.5%). The university students therefore exhibited generally good performance in terms of exploration strategy use in a CPS environment, especially compared with previous results among younger students (e.g., primary school students, see Greiff et al. 2018 ; Wu and Molnár 2021 ; primary to secondary students, see Molnár and Csapó 2018 ).

The results have indicated that better exploration strategy users achieved higher CPS performance and had better development levels of IR and CR (RQ2). First, the results have confirmed the importance of VOTAT in a CPS environment. This finding is consistent with previous studies (e.g., Greiff et al. 2015a ; Molnár and Csapó 2018 ; Mustafić et al. 2019 ; Wu and Molnár 2021 ). Second, the results have confirmed that effective use of VOTAT is strongly tied to the level of IR and CR development. Reasoning forms an important component of human intelligence, and the level of development in reasoning was an indicator of the level of intelligence ( Klauer et al. 2002 ; Sternberg and Kaufman 2011 ). Therefore, this finding has supplemented empirical evidence for the argument that effective use of VOTAT is associated with levels of intelligence to a certain extent.

The roles of IR and CR proved to be varied for each type of exploration strategy user (RQ3). For instance, the level of CPS among the best exploration strategy users (i.e., the proficient strategy users) was predicted by both the levels of IR and CR, but this was not the case for students with other profiles. In addition, the results have indicated that IR played important roles in both the KAC and KAP phases for the students with relatively good exploration strategy profiles (i.e., proficient strategy users and rapid learners) but only in the KAP phase for the rest of the students (non-persistent explorers and non-performing explorers); moreover, the predictive power of CR can only be detected in the KAC phase of the proficient strategy users. To sum up, the results suggest a general trend of IR and CR playing more important roles in the CPS process among better exploration strategy users.

Combining the answers to RQ2 and RQ3, we can gain further insights into students’ exploration strategy use in a CPS environment. Our results have confirmed that the use of VOTAT is associated with the level of IR and CR development and that the importance of IR and CR increases with proficiency in exploration strategy use. Based on these findings, we can make a reasonable argument that IR and CR are essential skills for using VOTAT and that underdeveloped IR and CR will prevent students from using effective strategies in a CPS environment. Therefore, if we want to encourage students to become better exploration strategy users, it is important to first enhance their IR and CR skills. Previous studies have suggested that establishing explicit training in using effective strategies in a CPS environment is important for students’ CPS development ( Molnár et al. 2022 ). Our findings have identified the importance of IR and CR in exploration strategy use, which has important implications for designing training programmes.

The results have also provided a basis for further studies. Future studies have been suggested to further link the behavioural and cognitive perspectives in CPS research. For instance, IR and CR were considered as component skills of CPS (see Section 1.2 ). The results of the study have indicated the possibility of not only discussing the roles of IR and CR in the cognitive process of CPS, but also exploration behaviour in a CPS environment. The results have thus provided a new perspective for exploring the component skills of CPS.

6. Limitations

There are some limitations in the study. All the tests were low stake; therefore, students might not be sufficiently motivated to do their best. This feature might have produced the missing values detected in the sample. In addition, some students’ exploration behaviour shown in this study might theoretically be below their true level. However, considering that data cleaning was adopted in this study (see Section 3.1 ), we believe this phenomenon will not have a remarkable influence on the results. Moreover, the CPS test in this study was based on the MicroDYN approach, which is a well-established and widely used artificial model with a limited number of variables and relations. However, it does not have the power to cover all kinds of complex and dynamic problems in real life. For instance, the MicroDYN approach cannot measure ill-defined problem solving. Thus, this study can only demonstrate the influence of IR and CR on problem solving in well-defined MicroDYN-simulated problems. Furthermore, VOTAT is helpful with minimally complex problems under well-defined laboratory conditions, but it may not be that helpful with real-world, ill-defined complex problems ( Dörner and Funke 2017 ; Funke 2021 ). Therefore, the generalizability of the findings is limited.

7. Conclusions

In general, the results have shed new light on students’ problem-solving behaviours in respect of exploration strategy in a CPS environment and explored differences in terms of the use of thinking skills between students with different exploration strategies. Most studies discuss students’ problem-solving strategies from a behavioural perspective. By contrast, this paper discusses them from both behavioural and cognitive perspectives, thus expanding our understanding in this area. As for educational implications, the study contributes to designing and revising training methods for CPS by identifying the importance of IR and CR in exploration behaviour in a CPS environment. To sum up, the study has investigated the nature of CPS from a fresh angle and provided a sound basis for future studies.

Funding Statement

This study has been conducted with support provided by the National Research, Development and Innovation Fund of Hungary, financed under the OTKA K135727 funding scheme and supported by the Research Programme for Public Education Development, Hungarian Academy of Sciences (KOZOKT2021-16).

Author Contributions

Conceptualization, H.W. and G.M.; methodology, H.W. and G.M.; formal analysis, H.W.; writing—original draft preparation, H.W.; writing—review and editing, G.M.; project administration, G.M.; funding acquisition, G.M. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Ethical approval was not required for this study in accordance with the national and institutional guidelines. The assessments which provided data for this study were integrated parts of the educational processes of the participating university. The participation was voluntary.

Informed Consent Statement

All of the students in the assessment turned 18, that is, it was not required or possible to request and obtain written informed parental consent from the participants.

Data Availability Statement

Conflicts of interest.

Authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

• Adey Philip, Csapó Benő. Developing and Assessing Scientific Reasoning. In: Csapó Benő, Szabó Gábor., editors. Framework for Diagnostic Assessment of Science. Nemzeti Tankönyvkiadó; Budapest: 2012. pp. 17–53. [ Google Scholar ]
• Batanero Carmen, Navarro-Pelayo Virginia, Godino Juan D. Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils. Educational Studies in Mathematics. 1997; 32 :181–99. doi: 10.1023/A:1002954428327. [ CrossRef ] [ Google Scholar ]
• Beckmann Jens F., Guthke Jürgen. Complex problem solving, intelligence, and learning ability. In: Frensch Peter A., Funke Joachim., editors. Complex Problem Solving: The European Perspective. Erlbaum; Hillsdale: 1995. pp. 177–200. [ Google Scholar ]
• Buchner Axel. Basic topics and approaches to the study of complex problem solving. In: Frensch Peter A., Funke Joachim., editors. Complex Problem Solving: The European Perspective. Erlbaum; Hillsdale: 1995. pp. 27–63. [ Google Scholar ]
• Chen Yunxiao, Li Xiaoou, Liu Jincheng, Ying Zhiliang. Statistical analysis of complex problem-solving process data: An event history analysis approach. Frontiers in Psychology. 2019; 10 :486. doi: 10.3389/fpsyg.2019.00486. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Csapó Benő. A kombinatív képesség struktúrája és fejlődése. Akadémiai Kiadó; Budapest: 1988. [ Google Scholar ]
• Csapó Benő. The development of inductive reasoning: Cross-sectional assessments in an educational context. International Journal of Behavioral Development. 1997; 20 :609–26. doi: 10.1080/016502597385081. [ CrossRef ] [ Google Scholar ]
• Csapó Benő. Teaching and Learning Thinking Skills. Swets & Zeitlinger; Lisse: 1999. Improving thinking through the content of teaching; pp. 37–62. [ Google Scholar ]
• Csapó Benő, Molnár Gyöngyvér. Online diagnostic assessment in support of personalized teaching and learning: The eDia System. Frontiers in Psychology. 2019; 10 :1522. doi: 10.3389/fpsyg.2019.01522. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Dörner Dietrich, Funke Joachim. Complex problem solving: What it is and what it is not. Frontiers in Psychology. 2017; 8 :1153. doi: 10.3389/fpsyg.2017.01153. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• English Lyn D. Combinatorics and the development of children’s combinatorial reasoning. In: Jones Graham A., editor. Exploring Probability in School: Challenges for Teaching and Learning. Springer; New York: 2005. pp. 121–41. [ Google Scholar ]
• Fischer Andreas, Greiff Samuel, Funke Joachim. The process of solving complex problems. Journal of Problem Solving. 2012; 4 :19–42. doi: 10.7771/1932-6246.1118. [ CrossRef ] [ Google Scholar ]
• Frensch Peter A., Funke Joachim. Complex Problem Solving: The European Perspective. Psychology Press; New York: 1995. [ Google Scholar ]
• Funke Joachim. Dynamic systems as tools for analysing human judgement. Thinking and Reasoning. 2001; 7 :69–89. doi: 10.1080/13546780042000046. [ CrossRef ] [ Google Scholar ]
• Funke Joachim. Complex problem solving: A case for complex cognition? Cognitive Processing. 2010; 11 :133–42. doi: 10.1007/s10339-009-0345-0. [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Funke Joachim. It Requires More Than Intelligence to Solve Consequential World Problems. Journal of Intelligence. 2021; 9 :38. doi: 10.3390/jintelligence9030038. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Funke Joachim, Fischer Andreas, Holt Daniel V. Competencies for complexity: Problem solving in the twenty-first century. In: Care Esther, Griffin Patrick, Wilson Mark., editors. Assessment and Teaching of 21st Century Skills. Springer; Dordrecht: 2018. pp. 41–53. [ Google Scholar ]
• Gilhooly Kenneth J. Thinking: Directed, Undirected and Creative. Academic Press; London: 1982. [ Google Scholar ]
• Gnaldi Michela, Bacci Silvia, Kunze Thiemo, Greiff Samuel. Students’ complex problem solving profiles. Psychometrika. 2020; 85 :469–501. doi: 10.1007/s11336-020-09709-2. [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Greiff Samuel, Funke Joachim. Measuring complex problem solving-the MicroDYN approach. In: Scheuermann Friedrich, Björnsson Julius., editors. The Transition to Computer-Based Assessment. Office for Official Publications of the European Communities; Luxembourg: 2009. pp. 157–63. [ Google Scholar ]
• Greiff Samuel, Holt Daniel V., Funke Joachim. Perspectives on problem solving in educational assessment: Analytical, interactive, and collaborative problem solving. Journal of Problem Solving. 2013; 5 :71–91. doi: 10.7771/1932-6246.1153. [ CrossRef ] [ Google Scholar ]
• Greiff Samuel, Molnár Gyöngyvér, Martina Romain, Zimmermann Johannes, Csapó Benő. Students’ exploration strategies in computer-simulated complex problem environments: A latent class approach. Computers & Education. 2018; 126 :248–63. [ Google Scholar ]
• Greiff Samuel, Wüstenberg Sascha, Avvisati Francesco. Computer-generated log-file analyses as a window into students’ minds? A showcase study based on the PISA 2012 assessment of problem solving. Computers & Education. 2015a; 91 :92–105. [ Google Scholar ]
• Greiff Samuel, Wüstenberg Sascha, Funke Joachim. Dynamic problem solving: A new measurement perspective. Applied Psychological Measurement. 2012; 36 :189–213. doi: 10.1177/0146621612439620. [ CrossRef ] [ Google Scholar ]
• Greiff Samuel, Wüstenberg Sascha, Csapó Benő, Demetriou Andreas, Hautamäki Jarkko, Graesser Arthur C., Martin Romain. Domain-general problem solving skills and education in the 21st century. Educational Research Review. 2014; 13 :74–83. doi: 10.1016/j.edurev.2014.10.002. [ CrossRef ] [ Google Scholar ]
• Greiff Samuel, Wüstenberg Sascha, Goetz Thomas, Vainikainen Mari-Pauliina, Hautamäki Jarkko, Bornstein Marc H. A longitudinal study of higher-order thinking skills: Working memory and fluid reasoning in childhood enhance complex problem solving in adolescence. Frontiers in Psychology. 2015b; 6 :1060. doi: 10.3389/fpsyg.2015.01060. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Hołda Małgorzata, Głodek Anna, Dankiewicz-Berger Malwina, Skrzypińska Dagna, Szmigielska Barbara. Ill-defined problem solving does not benefit from daytime napping. Frontiers in Psychology. 2020; 11 :559. doi: 10.3389/fpsyg.2020.00559. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Klauer Karl Josef. Paradigmatic teaching of inductive thinking. Learning and Instruction. 1990; 2 :23–45. [ Google Scholar ]
• Klauer Karl Josef, Willmes Klaus, Phye Gary D. Inducing inductive reasoning: Does it transfer to fluid intelligence? Contemporary Educational Psychology. 2002; 27 :1–25. doi: 10.1006/ceps.2001.1079. [ CrossRef ] [ Google Scholar ]
• Kuhn Deanna. What is scientific thinking and how does it develop? In: Goswami Usha., editor. The Wiley-Blackwell Handbook of Childhood Cognitive Development. Wiley-Blackwell; Oxford: 2010. pp. 371–93. [ Google Scholar ]
• Kuhn Deanna, Garcia-Mila Merce, Zohar Anat, Andersen Christopher, Sheldon H. White, Klahr David, Carver Sharon M. Strategies of knowledge acquisition. Monographs of the Society for Research in Child Development. 1995; 60 :1–157. doi: 10.2307/1166059. [ CrossRef ] [ Google Scholar ]
• Lo Yungtai, Mendell Nancy R., Rubin Donald B. Testing the number of components in a normal mixture. Biometrika. 2001; 88 :767–78. doi: 10.1093/biomet/88.3.767. [ CrossRef ] [ Google Scholar ]
• Lotz Christin, Scherer Ronny, Greiff Samuel, Sparfeldt Jörn R. Intelligence in action—Effective strategic behaviors while solving complex problems. Intelligence. 2017; 64 :98–112. doi: 10.1016/j.intell.2017.08.002. [ CrossRef ] [ Google Scholar ]
• Mayer Richard E. Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science. 1998; 26 :49–63. doi: 10.1023/A:1003088013286. [ CrossRef ] [ Google Scholar ]
• Molnár Gyöngyvér, Csapó Benő. Az 1–11 évfolyamot átfogó induktív gondolkodás kompetenciaskála készítése a valószínűségi tesztelmélet alkalmazásával. Magyar Pedagógia. 2011; 111 :127–40. [ Google Scholar ]
• Molnár Gyöngyvér, Csapó Benő. The efficacy and development of students’ problem-solving strategies during compulsory schooling: Logfile analyses. Frontiers in Psychology. 2018; 9 :302. doi: 10.3389/fpsyg.2018.00302. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Molnár Gyöngyvér, Alrababah Saleh Ahmad, Greiff Samuel. How we explore, interpret, and solve complex problems: A cross-national study of problem-solving processes. Heliyon. 2022; 8 :e08775. doi: 10.1016/j.heliyon.2022.e08775. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Molnár Gyöngyvér, Greiff Samuel, Csapó Benő. Inductive reasoning, domain specific and complex problem solving: Relations and development. Thinking Skills and Creativity. 2013; 9 :35–45. doi: 10.1016/j.tsc.2013.03.002. [ CrossRef ] [ Google Scholar ]
• Mousa Mojahed, Molnár Gyöngyvér. Computer-based training in math improves inductive reasoning of 9- to 11-year-old children. Thinking Skills and Creativity. 2020; 37 :100687. doi: 10.1016/j.tsc.2020.100687. [ CrossRef ] [ Google Scholar ]
• Mustafić Maida, Yu Jing, Stadler Matthias, Vainikainen Mari-Pauliina, Bornstein Marc H., Putnick Diane L., Greiff Samuel. Complex problem solving: Profiles and developmental paths revealed via latent transition analysis. Developmental Psychology. 2019; 55 :2090–101. doi: 10.1037/dev0000764. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Muthén Linda K., Muthén Bengt O. Mplus User’s Guide. Muthén & Muthén; Los Angeles: 2010. [ Google Scholar ]
• Newell Allen. Reasoning, Problem Solving, and Decision Processes: The Problem Space as a Fundamental Category. MIT Press; Boston: 1993. [ Google Scholar ]
• Novick Laura R., Bassok Miriam. Problem solving. In: Holyoak Keith James, Morrison Robert G., editors. The Cambridge Handbook of Thinking and Reasoning. Cambridge University Press; New York: 2005. pp. 321–49. [ Google Scholar ]
• OECD . PISA 2012 Field Trial Problem Solving Framework. OECD Publishing; Paris: 2010. [ Google Scholar ]
• OECD . Results: Creative Problem Solving—Students’ Skills in Tackling Real-Life Problems (Volume V) OECD Publishing; Paris: 2014. [ Google Scholar ]
• Pásztor Attila. Ph.D. thesis. Doctoral School of Education, University of Szeged; Szeged, Hungary: 2016. Technology-Based Assessment and Development of Inductive Reasoning. [ Google Scholar ]
• Pásztor Attila, Csapó Benő. Improving Combinatorial Reasoning through Inquiry-Based Science Learning; Paper presented at the Science and Mathematics Education Conference; Dublin, Ireland. June 24–25; 2014. [ Google Scholar ]
• Pásztor Attila, Kupiainen Sirkku, Hotulainen Risto, Molnár Gyöngyvér, Csapó Benő. Comparing Finnish and Hungarian Fourth Grade Students’ Inductive Reasoning Skills; Paper presented at the EARLI SIG 1 Conference; Helsinki, Finland. August 29–31; 2018. [ Google Scholar ]
• Sandberg Elisabeth Hollister, McCullough Mary Beth. The development of reasoning skills. In: Sandberg Elisabeth Hollister, Spritz Becky L., editors. A Clinician’s Guide to Normal Cognitive Development in Childhood. Routledge; New York: 2010. pp. 179–89. [ Google Scholar ]
• Schraw Gregory, Dunkle Michael E., Bendixen Lisa D. Cognitive processes in well-defined and ill-defined problem solving. Applied Cognitive Psychology. 1995; 9 :523–38. doi: 10.1002/acp.2350090605. [ CrossRef ] [ Google Scholar ]
• Schweizer Fabian, Wüstenberg Sascha, Greiff Samuel. Validity of the MicroDYN approach: Complex problem solving predicts school grades beyond working memory capacity. Learning and Individual Differences. 2013; 24 :42–52. doi: 10.1016/j.lindif.2012.12.011. [ CrossRef ] [ Google Scholar ]
• Stadler Matthias, Becker Nicolas, Gödker Markus, Leutner Detlev, Greiff Samuel. Complex problem solving and intelligence: A meta-analysis. Intelligence. 2015; 53 :92–101. doi: 10.1016/j.intell.2015.09.005. [ CrossRef ] [ Google Scholar ]
• Sternberg Robert J. Handbook of Human Intelligence. Cambridge University Press; New York: 1982. [ Google Scholar ]
• Sternberg Robert J., Kaufman Scott Barry. The Cambridge Handbook of Intelligence. Cambridge University Press; New York: 2011. [ Google Scholar ]
• van de Schoot Rens, Lugtig Peter, Hox Joop. A checklist for testing measurement invariance. European Journal of Developmental Psychology. 2012; 9 :486–92. doi: 10.1080/17405629.2012.686740. [ CrossRef ] [ Google Scholar ]
• Vollmeyer Regina, Burns Bruce D., Holyoak Keith J. The impact of goal specificity on strategy use and the acquisition of problem structure. Cognitive Science. 1996; 20 :75–100. doi: 10.1207/s15516709cog2001_3. [ CrossRef ] [ Google Scholar ]
• Welter Marisete Maria, Jaarsveld Saskia, Lachmann Thomas. Problem space matters: The development of creativity and intelligence in primary school children. Creativity Research Journal. 2017; 29 :125–32. doi: 10.1080/10400419.2017.1302769. [ CrossRef ] [ Google Scholar ]
• Wenke Dorit, Frensch Peter A., Funke Joachim. Complex Problem Solving and intelligence: Empirical relation and causal direction. In: Sternberg Robert J., Pretz Jean E., editors. Cognition and Intelligence: Identifying the Mechanisms of the Mind. Cambridge University Press; New York: 2005. pp. 160–87. [ Google Scholar ]
• Wittmann Werner W., Hattrup Keith. The relationship between performance in dynamic systems and intelligence. Systems Research and Behavioral Science. 2004; 21 :393–409. doi: 10.1002/sres.653. [ CrossRef ] [ Google Scholar ]
• Wu Hao, Molnár Gyöngyvér. Interactive problem solving: Assessment and relations to combinatorial and inductive reasoning. Journal of Psychological and Educational Research. 2018; 26 :90–105. [ Google Scholar ]
• Wu Hao, Molnár Gyöngyvér. Logfile analyses of successful and unsuccessful strategy use in complex problem-solving: A cross-national comparison study. European Journal of Psychology of Education. 2021; 36 :1009–32. doi: 10.1007/s10212-020-00516-y. [ CrossRef ] [ Google Scholar ]
• Wu Hao, Saleh Andi Rahmat, Molnár Gyöngyvér. Inductive and combinatorial reasoning in international educational context: Assessment, measurement invariance, and latent mean differences. Asia Pacific Education Review. 2022; 23 :297–310. doi: 10.1007/s12564-022-09750-z. [ CrossRef ] [ Google Scholar ]
• Wüstenberg Sascha, Greiff Samuel, Funke Joachim. Complex problem solving—More than reasoning? Intelligence. 2012; 40 :1–14. doi: 10.1016/j.intell.2011.11.003. [ CrossRef ] [ Google Scholar ]
• Wüstenberg Sascha, Greiff Samuel, Molnár Gyöngyvér, Funke Joachim. Cross-national gender differences in complex problem solving and their determinants. Learning and Individual Differences. 2014; 29 :18–29. doi: 10.1016/j.lindif.2013.10.006. [ CrossRef ] [ Google Scholar ]

• Open access
• Published: 05 February 2018

The role of problem solving ability on innovative behavior and opportunity recognition in university students

• Ji Young Kim 1 ,
• Dae Soo Choi 1 ,
• Chang-Soo Sung 1 &
• Joo Y. Park 2  

Journal of Open Innovation: Technology, Market, and Complexity volume  4 , Article number:  4 ( 2018 ) Cite this article

25k Accesses

31 Citations

1 Altmetric

Metrics details

Universities engage in entrepreneurship education to increase social value creation, through students’ new opportunities recognition. However, there are not enough of empirical researches on whether the current entrepreneurship education can be differentiated from other curriculum to improve the opportunity recognition process. This study argues that it is very important for cognitive abilities to be manifested as behavior when students in university are new opportunities recognition. For this purpose, the relationship between problem solving ability, innovation behavior, and opportunity perception was verified empirically. This study was conducted on 203 students who took entrepreneurship education courses at Korean universities. The results of this study showed that problem solving ability positively influenced innovation behavior and opportunity perception. Innovation behavior was identified as a key parameter that partially mediated the relationship between problem solving ability and innovation behavior. The implication of this study is to prove the relationship between individual ‘s problem - solving ability considering the characteristics of education in Korea and the opportunity through innovative behavior and various learning strategies to help entrepreneurship education to design better courses for the future It has important implications for strategic pedagogy that can enhance behavioral elements in development.

It is the new opportunity recognition that all firms focus on for a new economic paradigm (Ancona and Caldwell, 1992 ). Recognizing high opportunities can significantly improve profit, growth, and / or competitive positioning. And this new opportunity leads to innovation. From a conceptual point of view, research is continuing on the question of ‘what is opportunity’ and ‘where is opportunity’ (Gartner and Carter, 2003 ; Venkataraman & Sarasvathy, 2001 ). Research on the discovery and realization of new opportunities is a very important research area that suggests how to discover and utilize creative opportunities that create new value and profit for pre-service workers, and is the ultimate goal of entrepreneurship education. (Kim et al., 2016 ). Particularly, there is a lot of debate about the relationship between opportunity perception and personal characteristics. Despite many arguments, however, research on individual characteristics and opportunity perceptions is still insufficient, and a unified opinion has not been created due to differences between cognitive and behavioral theories (Ko & Butler, 2003 ). In particular, there is much controversy over the relationship between opportunity recognition and personal traits, and research has been continuing to demonstrate that organizational learning in organizations can influence opportunity recognition (Shane & Venkataraman, 2000 ). In particular, learning enhances cognitive ability, which is an opportunity that leads to opportunity recognition through the manifestation of behavior (Lumpkin and Dess, 2004 ). Many studies have also demonstrated the difference in behavior that successful entrepreneurs see as contributing to their ability to recognize opportunities and create innovative business ideas (Dyer et al., 2008 ; Kim et al., 2017 ). For example, Alvarez and Barney ( 2005 ) argue for mountain climbing and mountain building to understand the implications of entrepreneurial behavior in relation to these theories. In other words, a new opportunity for entrepreneurs is not a passive case that is generally found and climbed by climbers such as mountains, but rather by the actions of entrepreneurs, creating competition for the market, creating another market, Is the same. Therefore, in order for a person’s cognitive ability to recognize a new opportunity, it must focus on manifesting an action that can realize an innovative idea. In this regard, Kanter ( 1988 ) proved the relationship between new opportunity recognition and those with innovative tendencies and regarded this new opportunity recognition as innovation activity through organizational education. Scott and Bruce ( 1994 ) have integrated a number of research flows into innovation pioneers to develop and test individual innovative behavioral models. In particular, they argued that individual problem-solving styles are very important to induce innovative behavior. Although there are a number of studies on problem solving ability, innovation behavior, and new opportunities, most of the opportunistic researches have been conducted in organizational units of companies. Is still insufficient. Furthermore, unified opinions were not created due to differences between cognitive theory and behavioral theory (Ko & Butler, 2003 ). It is also true that the effects of entrepreneurship education in university have not been studied empirically because they are mainly focused on promoting cognitive ability and applied to various kinds of teaching methods.

This study argues that it is very important for cognitive abilities to be manifested as behavior that. “Through” courses, In other words, it is very important to induce students to act through ‘learning through process’ learning through behavioral learning by providing students with some (virtual or real) business to start doing some of the actions of the entrepreneur. When students in university are new opportunity recognition. Especially, entrepreneurship education, which ultimately focuses on whether it is a new opportunity, is very important to induce behavior through behavior learning beyond the cognitive ability as the general education curriculum. Particularly, innovative behaviors that create and realize innovative ideas are very important for new opportunity recognition (Paine & Organ, 2000 ).In order to achieve this, various kinds of teaching methods are being pursued in the university, but studies on the effectiveness of behavioral learning have not been studied yet. In this study, we are based on team-based learning among various teaching methods for behavior learning that leads to innovative behaviors. Team learning instructional activity sequence designed by Michaelsen and Sweet ( 2008 ), the most well known team-based learning in entrepreneurship education as in class-primarily group work and outside class-primarily individual work. In this way, we demonstrate empirically the relationship between individual problem solving ability and opportunity through innovative behavior, and develop a variety of learning strategies that help entrepreneurship education to design better courses for the future. I would like to point out some implications for strategic pedagogy to increase the element.

The paper proceeds as follows: Initially we present the theory of innovative behavior with individual problem-solving ability, innovative behavior and opportunity recognition. We develop hypotheses to confirm its basic predictions in the student context. Finally, we link the findings with the wider social effect of entrepreneurship literature and highlight the theoretical contributions and practical implications.

Theoretical background

‘opportunity recognition’ as entrepreneurship education unit of analysis.

A commonly focused analysis in entrepreneurship research over the last 30 years has been the ‘opportunity’, most simply defined as any situation in which new products or services can be development of production (Casson, 1982 ; Shane & Venkataraman, 2000 ; Venkataraman, 1997 ). The definition of opportunity recognition is defined in many ways, but opportunity is defined as a perceived means of generating economic value (ie, profit) that has not been exploited previously and is not currently exploited by others. If opportunity is defined in this way, opportunity recognition can be defined as a cognitive process (or process) that concludes that an individual has identified an opportunity (Baron and Ensley, 2006 ). Kirzner ( 1997 ) pointed out that the distribution of information in society affects the discovery of entrepreneurial opportunities and that only a few individuals can identify and recognize specific opportunities in the market. The process of finding opportunities also depends on the individual’s ability and discovery (Stevenson & Gumpert, 1985 ). For example, people may miss opportunities due to a lack of cognitive ability to change external environments (Stevenson & Gumpert, 1985 ). Only those who recognize and value the existence of opportunity can benefit from new opportunities (Ardichvili et al., 2003a , b ; Shane & Venkataraman, 2000 ). Opportunity recognition is an early step in transforming value into a business concept that creates value and generates revenue and distinguishes it from the aggressive stages of detailed assessment and development of recognized opportunities and potential economic value. The focus of the new venture business is also an innovative opportunity to create new opportunities rather than merely expanding or repeating existing business models (Gaglio & Katz, 2001 ). As a result, universities need to make use of a variety of initiatives to educate students to recognize innovative opportunities. Therefore, entrepreneurship education aimed at a new opportunity recognition should be able to provide learning opportunities based on various theories of favorable conditions for new business creation and the types of traits required for new ventures (Garavan & O’Cinne’ide, 1994 ).

Based on these considerations, we also define opportunity recognition as the formation of beliefs that can be translated into actions in order to understand the signals of change (new information on new conditions) and respond to these changes.

Problem-solving ability and innovative behavior of education for students

Problem-solving abilities have been proven to be one of the key factors for success in organizations and personal careers (Anderson & Anderson 1995 ). Through decades of research data, organizations and schools have studied factors that affect improvement. Problem-solving abilities are defined in a number of prior studies, and problem-solving abilities in a volatile and sophisticated knowledge- and technology-based industry are an important ability to drive innovation and sustainable growth and development in the industry. Table  1 show the concept of problem solving ability defined in previous research.

There have been a number of previous studies, emphasis has been placed on the importance and meaning of rational problem-solving processes in order to improve problem-solving abilities, and research has focused on individual problem solving styles (Woodman et al., 1993 ; Scott & Bruce, 1994 ). According to the personal innovation behavior model of Scott and Bruce ( 1994 ), climate has shown individual innovative behavior as a result of individuals signaling the organization’s expectations of behavior and the potential consequences of action. Innovative organizations are, last but not least, equipment, facilities and time, including the direction of creativity and innovative change (Kanter, 1983 ; Siegel & Kaemmerer, 1978 ) Proper supply of such resources is important to innovation (Amabile, 1988 ; Van de Ven & Angle, 1989 ; Dubickis & Gaile-Sarkane, 2017 ). Based on a study of Koestler’s ( 1964 ) creative thinking, Jabri conceptualized a problem-solving style consisting of two independent thinking styles. He uses a structured problem-solving styles that is based on associative thinking, follows a set of rules, resolves reasonably logically, and uses an intuitive problem-solving ability that focuses on problem-solving, not tied to existing rules with multiple ideas. Intuitive problem solving styles tend to process information from different paradigms simultaneously. It is therefore more likely to create new problem solutions as possible (Isaksen, 1987 ; Kirton, 1976 ). However, style assessment is not desirable because the style of problem solving affects style differently depending on the individual problem-solving situations (Scott & Bruce, 1994 ). We are proposing a role for the University to encourage innovative behavior based on the individuality of our students in order to recognize new opportunities through education about Scott and Bruce’s innovative behavioral models and diverse entrepreneurship education approaches. And involvement of resources, such as entrepreneurship awareness programs, ultimately leads to the identification of individual characteristics and innovation. In addition, current Korean entrepreneurship education is mainly focused on cognitive learning to improve problem solving ability, and one aspect of cognitive learning plays an important role in learning process of new venture firms. This study has a more direct focus on behavior learning such as team-based learning.

Hypothesis development

Problem-solving ability and innovative behavior.

Problem solving is to discover knowledge and skills that reach the target country by interfering with a set of processes and goals where the solution is unknown, unfamiliar, or reaching a new state of goal (Jonassen, 2004 ; Inkinen, 2015 ). There are various approaches to solve this problem. To solve problems and improve problem solving with a successful solution experience, you should adopt the method that best suits your problem solution. You need to select the appropriate inputs for the solution elements and a flexible process structure. Problem solving ability has been recognized as a key element of innovative behavior in responding to rapid changes with the ability to find various alternatives and predict outcomes from these alternatives to maximize positive results, minimize negative consequences, and select solutions to problems (Barron & Harrington, 1981 ; Jabri, 1991 ; Kirton, 1976 ). We pose the following hypotheses:

Hypothesis 1: Individual problem-solving ability has an effect on the innovative behavior of students.

Innovative behavior and opportunity recognition

Innovation involves introducing ideas from outside the organization, through creative processes, and linking these ideas to products or processes. Many scholars studying innovation recognize that designing ideas is only one step in the innovation process (Kanter, 1988 ). Innovation is changing at the organizational or individual level. Kanter, Scott and Bruce defined personal innovation. In other words, an innovation act starts with recognition of a problem, adoption of a new idea, or creation of a solution, and an individual with an innovative tendency wants to create a realistically realizable group with the sympathy of such an idea. Innovative individuals create prototypes for innovations that enable ideas to be realized specifically with goods or services and become productive use and social day merchandising. According to previous studies, opportunity perception can be seen as an individual’s corporate strategy that focuses on the perception and exploitation of individuals about potential business ideas and opportunities and finds resources to create innovative outcomes (Manev et al., 2005 ). New Venture Ideas (NVI) are imaginary combinations of product/service offerings; potential markets or users, and means of bringing these offerings into existence (Davidsson, 2015 ). From the viewpoint of a potential entrepreneur like a university student, entrepreneurship starts with an idea. This process continues with a range of practices including attractiveness and feasibility of an idea, gathering information to minimize value-related uncertainty and possibility and perhaps the main idea’s conformity ratio in terms of newly discovered needs (Hayton & Cholakova, 2012 ). Earlier we proposed that the program as a whole increases the students’ innovative behavior and that innovative performance is the new venture ideas. Since it is logical to assume that the relationship between innovative behavior and opportunity recognition. We pose the following hypotheses:

Hypothesis 2: Innovative behavior will be a more potent inducer of opportunity recognition.

Problem-solving ability and opportunity recognition

Among the many factors influencing opportunity perception, the problems that arise in the fourth industry, the knowledge-based industry of the twenty-first century, are unpredictable and unstructured; they cannot be solved with existing solutions and require creative problem-solving skills. In order to determine how to solve problem situations that are different from the current situation and have unknown results, problems are solved through the process of adjusting previous experience, knowledge, and intuition (Charles & Lester, 1982 ). Experience, knowledge, and intuition are applied simultaneously to a single problem, not individually or collectively, and the intellectual and creative results that can be quickly and effectively solved in problem solving are seen as problem solving abilities (Ardichvili et al., 2003a , b ). Empirical studies of problem-solving abilities and opportunity perceptions have provided strong evidence that there is a positive relationship between theoretical integrative processes and corporate opportunity recognition (Ucbasaran et al., 2009 ). Therefore, we hypothesized that:

Hypothesis 3: Problem solving ability has an effect on the opportunity recognition.

The respondents for this study were randomly selected from three universities in Korea. Most of the respondents in this study were Korean university students who experienced team-based learning during behavioral learning through entrepreneurship education. Since then, we have been guided by two main criteria when choosing these universities. First, students who take entrepreneurship courses are critical to their innovation behavior. This led us to realize that innovative behavior is an important factor in an individual’s survival and growth. The second is that the parallel process of theoretical and behavioral learning is highly satisfied. A pilot study was conducted to verify the reliability and validity of the research measurements with 28 students at a university. The results of the pilot study showed high clarity and reliability (Cronbach ‘s alphas were all above 0.70) ​​of the research measurements. The sample of the pilot study was not incorporated in the present study.

This study was conducted in a four - year undergraduate course (various majors) that took entrepreneurship courses in Korea university programs. Students in this course have a mix of students who have previously experienced entrepreneurship and those who have not. During the course, students were taught the theoretical lessons for 8 weeks and the team for the 8 weeks. The questionnaire was administered during the last week of the course.

The data were analyzed from 203 participants, out of a total of 209, of which 7 were not appropriate. Of the 203 participants, 27% were female and 73% were male and the grade distribution was 3% for freshmen, 12% for grade 2, 26% for grade 2, and 59% for grade 2. The main distribution is 26% in social science, 16% in business and economics, 39% in engineering, 11% in music and athletics and 7% in others (see Table  2 ).

Measurement

The structure of the model was measured by questionnaires (problem-solving ability, innovation behavior and opportunity recognition questionnaire) consisting of the scale taken from questionnaires verified in previous studies. Tool selection was performed on two criteria. First, the selected tool should measure the same structure (ie, the original measured structure had to be conceptually identical to the way the structure was defined in this study model). Secondly, the psychometric qualities of the instrument for the student had to be high.

Assessment of the factors was carried out through principal component analyses (varimax rotation with eigenvalues of 1.0 or above) of the scales connected to the same level of the model to confirm the uniqueness of the scales with respect to each other. This was supplemented by the computation of the internal consistency reliability of the scales (Cronbach’s α). These analyses were executed using the individual participants’ responses (Nunnally & Bernstein, 1994 ).

Problem- solving ability was measured on a 7-point Likert-scale (1 = ‘completely disagree’; 7 = ‘completely agree’). Jabri ( 1991 ) used a measurement tool to measure individual problem solving ability.

Innovative behavior was measured on a 7-point Likert-scale (1 = ‘completely disagree’; 7 = ‘completely agree’). In order to measure innovation behavior, we modified the questionnaire items to fit the intention of this study among the questionnaire items used by Scott and Bruce ( 1994 ) and Kim and Rho ( 2010 ).

Opportunity recognition was measured on a 7-point Likert-scale (1 = ‘completely disagree’; 7 = ‘completely agree’). In order to measure opportunity recognition, we modified the questionnaire items to fit the intention of this study among the questionnaire items used by Kim and Rho ( 2010 ).

Methods of analysis

The first two parts of the analysis were primarily based on (multiple) regression analyses. The last part of the analysis was informed through the path analyses. The adequacy of the models was assessed by AMOS 18(Arbuckle & Wothke, 2003 ). Models were all tested with standardized coefficients obtained from the Principal Component Analysis. To ascertain the model fit, we analyzed the comparative fit index (CFI), the normed fit index (NFI), the Root Mean Square Err of Approximation (RMSEA), the standardized root mean square residual (SRMR) and the chi-square test statistic.

Reliability and validity are essential psychometrics to be reported. The first step to evaluate those aspects was to use the Cronbach’s alpha and the composite reliability to test reliability of the proposed scales. The usual threshold level is 0.7 for newly developed measures (Fornell and Larcker, 1981 ). Values range from 0.69 to 0.79 in the case of Cronbach’s alpha, and from 0.85 to 0.92 in the case of composite reliability (see Table  3 ). Therefore, these scales may be considered as reliable. Next, we estimated the research model, displayed in Fig.  1 , using structural equation modeling (SEM) and AMOS 18 (Arbuckle & Wothke, 2003 ). Our analysis revealed an adequate measurement model with high factor loadings for all the items on the expected factors and communalities of each item exceeding 0.50. We discuss three fit indices that are generally considered as important (Hu & Bentler, 1998 ). First, the CFI-value represents the overall difference between observed and predicted correlations. A value of 0.04 which is situated well below the cut-off value of 0.08, suggests that the hypothesized model resembles the actual correlations. Secondly, Bentler’s CFI (comparative fit index) greater than 0.90 and 0.95 which is above the cut-off of 0.90 (Schumacker & Lomax, 1996 ). Thirdly, NFI greater greater than 0.90 and 0.95 which is above the cut-off of 0.90 (Schumacker & Lomax, 1996 ). Fourthly, the standardized root mean square residual (SRMR) value of 0.0392 which is situated well below the cut-off value of 0.05(Hu & Bentler, 1998 ), and the chi-square value of 3581.622 which is situated well below the cut-off value of 0.0005. Finally, the RMSEA (root mean square error of approximation) equals 0.04 with a 90% confidence interval between 0.03 and 0.05.

Analysis of mediation effect

The value and confidence interval are situated over but below the cut-off value of 0.1 which suggests not a great but a good fit. Factor analysis was verified by factor analysis using principal component analysis and only factors with an eigenvalue of 1 or more by orthogonal rotation method were selected. Factor loading was considered to be significant at 0.5 or more (Hair et al., 2006a , b ). As a result of the analysis, cumulative explanation for 72.4% of the total variance. Confirmatory factor analysis thus supported the differentiation of the three components Also we tested the confirmatory validity of the construct by testing whether the structural linkage of each square is greater than the mean variance extraction (AVE) of each structure. The AVE ranged from 0.52 to 0.53, reaching the recommended level of .50 for both Fornell and Larcker ( 1981 ). Therefore, all constructs showed sufficient convergent validity (see Table 3 ).

As shown in Table  4 , the AVE value of each variable has a higher value than that of other factors. Therefore, the discriminant validity of the proposed model can be judged as appropriate.

Means, standard deviations, and correlations among the study variables are shown in Table  5 .

The mean scores for the conceptual model were as follows for problem-solving ability (MD. 5.20, SD.1.08), innovative behavior (MD.5.20, SD.1.03), and opportunity recognition (MD. 5.14, SD. 1.06) conditions. The means of problem-solving ability, innovative behavior, and opportunity recognition were high. Furthermore, those variables correlated positively with each other.

Figure  1 showed that all paths and their significance levels are presented in Table  6 . The path between the latent variables problem-solving ability and innovative behavior was significant (p, 0.001), consistent with Hypotheses 1. In addition, there was innovative behavior and opportunity recognition (p, 0.01), this result provide empirical support for Hypothesis 2.

H3 proposed that Problem-solving ability is positively related to opportunity recognition. The results of the correlation analysis: The coefficient of problem solving and opportunity perception weakened from .717 to .444, but it is still partly mediated because it is still significant (C. R  = 7.604 ***). This supports H3 (see Table 6 ).

In order to verify the significance of the indirect effect, the bootstrapping must be performed in AMOS, and the actual significance test should be identified using two-tailed significance. As a result, the significance of indirect effect is 0.04 ( p  < 0.05), which is statistically significant (see Table  7 ).

Discussion and conclusion

We have tried to demonstrate the effects of behavior and its significance by differentiating from the general curriculum emphasizing cognitive effects as a model of problem solving ability emerging as innovative behavior through opportunity of university entrepreneurship education.. This supports the premise that entrepreneurship education can improve opportunities or processes through behavioral learning. The results of this study support the role of entrepreneurship education in creating opportunities for innovative behavior and problem solving abilities. Entrepreneurship education should provide different types of learning for new opportunities and focus on what is manifested in behavior.

In addition, based on previous research, we propose whether the following contents are well followed and whether it is effective. First, the emergence of innovative behavior in problem-solving abilities increases as the cognitive diversity of students with diverse majors and diverse backgrounds increases. Second, the more entrepreneurial learning experiences, the greater the chance of new opportunities. Third, it is necessary to investigate students’ problem solving style and problem-solving ability first, and then a teaching strategy based on this combination of systematic and effective theory and practice is needed. Of course, as demonstrated by many studies, it may be easier to enhance the effectiveness of opportunity recognition through cognitive learning. This is because it emphasizes the achievement of knowledge and understanding with acquiring skills and competence. This process, however, is not enough for entrepreneurship education. However, we do not support full team-based behavioral learning in the class designed by Michaelsen and Sweet ( 2008 ). As with the results of this study, problem solving ability is positively related to opportunity perception directly. As previously demonstrated in previous studies, problem solving ability can be enhanced by cognitive learning (Anderson et al., 2001 ; Charles & Lester, 1982 ).

Therefore, it has been demonstrated that it is more efficient to balance a certain level of cognitive learning and behavior learning in consideration of the level of students in a course. Also this study satisfies the need for empirical research by Lumpkin and Lichtenstein ( 2005 ) and Robinson et al. ( 2016 ) and others. This will help to improve understanding of how entrepreneurship training is linked to various learning models and their effectiveness and to design better courses for the future. Finally, this study sought to provide an awareness of entrepreneurship education as the best curriculum for solutions that evolved into innovative behaviors that create new values and ultimately represent new opportunities. This study shows that it can positively influence the social effect of creating new value, that is, not only the cognitive effect of general pedagogy, but also the innovation behavior. By providing this awareness, we have laid the groundwork for empirical research on entrepreneurship education in order to create more opportunities for prospective students in education through education and to expand their capabilities.

Limitation and future research

Indeed, the concepts presented here and the limitations of this study have important implications that can fruitfully be addressed in future research. First, we selected a sample of college students taking entrepreneurship training. However, since it is not the whole of Korean university students, it is difficult to extend the research results to all college students in Korea. Second, there is no precedent research on the role of innovation behavior as intermedia in college students. Therefore, we were forced to proceed as an exploratory study.

The ability to recognize opportunities can provide significant benefits that can remain firm and competitive in an ever-changing environment. Future research should therefore expand these insights and try to empirically test more ways in which entrepreneurship pedagogy teaches how learning methods can be integrated into venture creation and growth processes to help new process opportunities. By providing this study, we will help entrepreneurship education in the university to create more opportunities and expand the capacity of prospective members.

Alvarez, S. A., & Barney, J. B. (2005). How do entrepreneurs organize firms under conditions of uncertainty? Journal of Management, 31 (5), 776–793.

Article   Google Scholar  

Amabile, T. M. (1988). A model of creativity and innovation in organizations. Research in Organizational Behavior, 10 (1), 123–167.

Google Scholar  

Ancona, D. G., & Caldwell, D. F. (1992). Demography and design: Predictors of new product team performance. Organization Science, 3 (3), 321–341.

Anderson, P. M., & Anderson, P. M. (1995). Analysis of faulted power systems (Vol. 445). New York: IEEE press.

Anderson, L. W., Krathwohl, D. R., Airasian, P., Cruikshank, K., Mayer, R., Pintrich, P., & Wittrock, M. (2001). A taxonomy for learning, teaching and assessing: A revision of Bloom’s taxonomy . New York: Longman Publishing.

Arbuckle, J. L., & Wothke, W. (2003). AMOS 5 user’s guide . Chicago: Smallwaters.

Ardichvili, A., Cardozo, R., & Ray, S. (2003a). A theory of entrepreneurial opportunity identification and development. Journal of Business Venturing, 18 (1), 105–123.

Ardichvili, A., Cardozo, R., & Ray, S. (2003b). A theory of entrepreneurial opportunity identification and development. Journal of Business Venturing, 18 (1), 105–123.

Baron, R. A., & Ensley, M. D. (2006). Opportunity recognition as the detection of meaningful patterns: Evidence from comparisons of novice and experienced entrepreneurs. Management Science, 52 (9), 1331–1344.

Barron, F., & Harrington, D. M. (1981). Creativity, intelligence, and personality. Annual review of psychology, 32 (1), 439–476.

Casson, M. (1982). The entrepreneur: An economic theory . Lanham: Rowman & Littlefield.

Charles, R., & Lester, F. (1982). Teaching problem solving: What, why & how . Palo Alto: Dale Seymour Publications.

Davidsson, P. (2015). Entrepreneurial opportunities and the entrepreneurship nexus: A re-conceptualization. Journal of Business Venturing, 30 (5), 674–695.

Dubickis, M., & Gaile-Sarkane, E. (2017). Transfer of know-how based on learning outcomes for development of open innovation. Journal of Open Innovation : Technology, market, and complexity , 3 (1), 4.

Dyer, J. H., Gregersen, H. B., & Christensen, C. (2008). Entrepreneur behaviors, opportunity recognition, and the origins of innovative ventures. Strategic Entrepreneurship Journal, 2 (4), 317–338.

D'zurilla, T. J., & Nezu, A. M. (1990). Development and preliminary evaluation of the social problem-solving inventory. Psychological Assessment: A Journal of Consulting and Clinical Psychology, 2 (2), 156.

Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research , 39–50.

Gaglio, C. M., & Katz, J. A. (2001). The psychological basis of opportunity identification: Entrepreneurial alertness. Small Business Economics, 16 (2), 95–111.

Garavan, T. N., & O’Cinneide, B. (1994). Entrepreneurship education and training programmes: A review and evaluation-part 1. Journal of European Industrial Training, 18 (8), 3–12.

Gartner, W. B., & Carter, N. M. (2003). Entrepreneurial behavior and firm organizing processes. In Handbook of entrepreneurship research (pp. 195–221). New Mexico: Springer US.

Hair, E., Halle, T., Terry-Humen, E., Lavelle, B., & Calkins, J. (2006a). Children's school readiness in the ECLS-K: Predictions to academic, health, and social outcomes in first grade. Early Childhood Research Quarterly, 21 (4), 431–454.

Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2006b). Multivariate Data Analysis (6th ed.). Upper Saddle River: Pearson Education, Inc..

Hayton, J. C., & Cholakova, M. (2012). The role of affect in the creation and intentional pursuit of entrepreneurial ideas. Entrepreneurship Theory and Practice, 36 (1), 41–68.

Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3 (4), 424.

Inkinen, T. (2015). Reflections on the innovative city: Examining three innovative locations in a knowledge bases framework. Journal of Open Innovation : Technolodgy, market. Complexity, 1 (1), 8.

Isaksen, S. G. (1987). Frontiers of creativity research: Beyond the basics. Bearly Ltd.

Jabri, M. M. (1991). The development of conceptually independent subscales in the measurement of modes of problem solving. Educational and Psychological Measurement, 51 (4), 975–983.

Jonassen, D. H. (2004). Learning to solve problems: An instructional design guide (Vol. 6). Hoboken: John Wiley & Sons.

Kanter, R. M. (1983). The change masters: Binnovation and entrepreneturship in the American corporation. Touchstone Book.

Kanter, R. M. (1988). Three tiers for innovation research. Communication Research, 15 (5), 509–523.

Kim, H. C., Song, C. H., & An, B. R. (2016). A study on effects of personal characteristics on start-up opportunity and entrepreneurial intention of start-up. Korean Management Consulting review, 16 (3), 75–87.

Kim, S. A., Ryoo, H. Y., & Ahn, H. J. (2017). Student customized creative education model based on open innovation. Journal of Open Innovation : Technology, Market, and Complexity , 3 (1), 6.

Kim, T. H., & Roh, J. H. (2010). A Study of the Impact of Public Service Motivation on Innovative Behavior of Organizational Members. Korean Journal of Public Administration, 48(3).

Kirton, M. (1976). Adaptors and innovators: A description and measure. Journal of Applied Psychology, 61 (5), 622.

Kirzner, I. M. (1997). Entrepreneurial discovery and the competitive market process: An Austrian approach. Journal of Economic Literature, 35 (1), 60–85.

Ko, S., & Butler, J. E. (2003). Alertness, bisociative thinking ability, and discovery of entrepreneurial opportunities in Asian hi-tech firms.

Koestler, A. (1964). The act of creation: A study of the conscious and unconscious processes of humor, scientific discovery and art.

Lumpkin, G. T., & Dess, G. G. (2004). E-Business Strategies and Internet Business Models: How the Internet Adds Value. Organizational Dynamics, 33 (2), 161–173.

Lumpkin, G. T., & Lichtenstein, B. B. (2005). The role of organizational learning in the opportunity-recognition process. Entrepreneurship Theory and Practice, 29 (4), 451–472.

Manev, I. M., Gyoshev, B. S., & Manolova, T. S. (2005). The role of human and social capital and entrepreneurial orientation for small business performance in a transitional economy. International Journal of Entrepreneurship and Innovation Management, 5 (3–4), 298–318.

Michaelsen, L. K., & Sweet, M. (2008). The essential elements of team-based learning. New directions for teaching and learning, 2008 (116), 7–27.

Nunnally, J. C., & Bernstein, I. H. (1994). Validity. Psychometric theory, 99–132.

Paine, J. B., & Organ, D. W. (2000). The cultural matrix of organizational citizenship behavior: Some preliminary conceptual and empirical observations. Human Resource Management Review, 10 (1), 45–59.

Robinson, S., Neergaard, H., Tanggaard, L., & Krueger, N. F. (2016). New horizons in entrepreneurship education: from teacher-led to student-centered learning. Education+ Training, 58(7/8), 661–683.

Schumacker, R. E., & Lomax, R. G. (1996). A beginner's guide to structural equation modeling . Mahwah: Laurence Erlbaum Google Scholar.

Scott, S. G., & Bruce, R. A. (1994). Determinants of innovative behavior: A path model of individual innovation in the workplace. Academy of Management Journal, 37 (3), 580–607.

Shane, S. A. (2003). A general theory of entrepreneurship: The individual-opportunity nexus . Cheltenham: Edward Elgar Publishing.

Book   Google Scholar  

Shane, S., & Venkataraman, S. (2000). The promise of entrepreneurship as a field of research. Academy of Management Review, 25 (1), 217–226.

Siegel, S. M., & Kaemmerer, W. F. (1978). Measuring the perceived support for innovation in organizations. Journal of Applied Psychology, 63 (5), 553–562.

Spivack, G., Platt, J. J., & Shure, M. B. (1976). The problem-solving approach to adjustment . San Francisco: Jossey-Bass.

Stevenson, H., & Gumpert, D. (1985). The heart of entrepreneurship.

Stevenson, H. H. & J. C. Jarillo (1990). 'A paradigm of entrepreneurship: Entrepreneurial management', Strategic Management Journal, 11, pp. 17–27.

Ucbasaran, D., Westhead, P., & Wright, M. (2009). The extent and nature of opportunity identification by experienced entrepreneurs. Journal of Business Venturing, 24 (2), 99–115.

Van de Ven, A. H., & Angle, H. L. (1989). Suggestions for managing the innovation journey (No. 9). Strategic Management Research Center, University of Minnesota.

Venkataraman, S. (1997). The distinctive domain of entrepreneurship research. Advances in entrepreneurship, firm emergence and growth, 3 (1), 119–138.

Venkataraman, S., & Sarasvathy, S. D. (2001). Strategy and entrepreneurship: Outlines of an untold story.

Warner, M. (2002). Publics and counterpublics. Public Culture, 14 (1), 49–90.

Woodman, R. W., Sawyer, J. E., & Griffin, R. W. (1993). Toward a theory of organizational creativity. Academy of Management Review, 18 (2), 293–321.

Download references

Author information

Authors and affiliations.

Dept. of Technology Entrepreneurship (Graduate School), Dongguk University, 904 Chungmurogwn, Toegye-ro 36Gil, Jung-gu, Seoul, 100-272, South Korea

Ji Young Kim, Dae Soo Choi & Chang-Soo Sung

Yonsei School of Business, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 120-749, South Korea

Joo Y. Park

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Joo Y. Park .

Ethics declarations

Publisher’s note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and permissions

About this article

Cite this article.

Kim, J.Y., Choi, D.S., Sung, CS. et al. The role of problem solving ability on innovative behavior and opportunity recognition in university students. J. open innov. 4 , 4 (2018). https://doi.org/10.1186/s40852-018-0085-4

Download citation

Received : 12 September 2017

Accepted : 22 January 2018

Published : 05 February 2018

DOI : https://doi.org/10.1186/s40852-018-0085-4

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Problem-solving ability
• Innovative behavior
• Opportunity recognition
• Entrepreneurship education