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Cognitive load during problem solving: Effects on learning

1988, Cognitive science

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Cognitive load during problem solving: Effects on learning

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Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching

Discipline-based education research: understanding and improving learning in, multimodal interfaces, discipline-based education research: understanding and improving learning in undergraduate science and engineering., levels of expertise and instructional design, soar: an architecture for general intelligence, individual differences in solving physics problems (1978), development of expertise in mathematical problem solving., effects of prior knowledge on use of cognitive capacity in three complex cognitive tasks., use of cognitive capacity in reading identical texts with different amounts of discourse level meaning., related papers (5), cognitive architecture and instructional design, cognitive load theory and the format of instruction, cognitive load measurement as a means to advance cognitive load theory, nine ways to reduce cognitive load in multimedia learning, multimedia learning.

John Sweller's Cognitive Load Theory

COGNITIVE SCIENCE 12, 257-285 (1988)

Cognitive Load During Problem Solving : Effects on Learning

JOHN SWELLER University of New South Wales

Considerable evidence indicates that domain specific knowledge in the form of schemes is the primary factor distinguishing experts from novices in problem- solving skill. Evidence that conventional problem-solving activity is not effective in schema acquisition is also accumulating. It is suggested that a major reason for the ineffectiveness of problem solving as a learning device, is that the cognitive processes required by the two activities overlap insufficiently, and that conven- tional problem solving in the form of means-ends analysis requires a relatively large amount of cognitive processing capacity which is consequently unavail- able for schema acquisition. A computational model and experimental evidence provide support for this contention. Theoretical and practical implications are discussed.

Problem-solving skill is highly valued. For most of this century, many theo- rists and educational institutions have placed a heavy emphasison this abil- ity, especially in mathematics and science (seeDewey, 1910, 1916). Entire movements such as “ discovery learning ” (e.g., Bruner, 1961)were spawned, at least in part, by the perceived importance of fostering problem-solving skills. This emphasison problem solving was not associatedwith a commen- surate knowledge of its characteristics and consequences.In the last few years, this state of affairs has begun to changewith our knowledge of rele- vant mechanismsincreasing markedly. Thesemechanisms have implications for learning, as well as problem solving. The purpose of the present paper is to suggest that contrary to current practice and many cognitive theories, some forms of problem solving interfere with learning.

This research was supported by a grant from the Australian ResearchGrants Scheme. The computational model was constructed while the author was on leave at the Learning Research and Development Center, University of Pittsburgh. I wish to thank J. Green0 and H. Simon for discussing aspects of the model with me. I also wish to thank E. Reesfor assistancewith the PRISM language, and T. Cahn for research assistance.The cooperation the New South Wales Department of Education and of D. Brown, Principal, F. Navin, Deputy Principal, and also J. Kopp, Mathematics Master, South Sydney High School is gratefully acknowledged. Correspondence and requests for reprints should be sent to J. Sweller, School of Educa- tion, University of New South Wales, P.O. Box 1. Kensington, NSW 2033, Australia.

257 258 SWELLER

EXPERT-NOVICE DISTINCTIONS

Several findings derived from the extensive research in recent years on expert-novice distinctions need to be noted. They can be sectioned into 3 categories: Memory of problem state configurations; Problem solving strat- egies; and Features used in categorizing problems.

Memory of Problem-State Configurations The forerunner of work on memory of problem-state configurations came from research on chess. De Groot (1966) investigated distinctions between chess masters and less experienced players. He failed to find differences in breadth or depth of search. The only major difference occurred in memory of realistic chess,positions. This difference was not replicated using random board configurations indicating that the superiority of masters was not due to general short-term memory factors. Chase and Simon (1973a, 1973b) found that while both novices and masters rememberedboth realistic chess configurations and sequencesof moves in chunks, the number of chunks did not differ appreciably. Differences did occur in chunk size with masters’ chunks being far larger than those of novices. In recent years these results have been replicated in a wide variety of domains. For example, Egan and Schwartz (1979) using electronic circuit diagrams, Jeffries, Turner, Polson, and Atwood (1981) using computer pro- grams, Sweller and Cooper (1985) and Cooper and Sweller (1987) using algebra and Voss, Vesonder, and Spilich (1980) using baseball sequencesall found superior recall by experts of presented material.

Problem-Solving Strategies Most mathematics and mathematics-related problems can be classified as transformation problems (Greeno, 1978).which consist of an initial state, a goal state, and legal problem-solving operators. Theseproblems can be solved using search techniquessuch as means-endsanalysis which involves attempt- ing to reduce differences between each problem state encountered and the goal state using the operators. Not all problem solvers use this strategy. Larkin, McDermott, Simon, and Simon (1980) and Simon and Simon (1978) using physics problems, found that the strategiesused by expert and novice problem solvers differed. Novices used means-endsanalysis. They worked backward from the goal setting subgoals. This procedure continued until equations containing no unknowns other than a desired subgoal were encountered. The procedure was then essentially reversedand a forward-working sequencefollowed. Ex- perts in contrast, eliminated the backward-working phase. They began by choosing an equation which allowed a value for an unknown to be calculated. This allowed other unknowns to be calculated which led to the goal. COGNITIVE LOAD DURING PROBLEM SOLVING 259

These results can be closely integrated with those on memory of problem states. Experts are able to work forward immediately by choosing appropri- ate equations leading to the goal becausethey recognize each problem and each problem state from previous experienceand know which moves are ap- propriate. The same cognitive structures which allow experts to accurately recall the configuration of a given problem state also allow immediate moves toward the goal from the givens. These cognitive structures will be called schemaswhere a schemais defined as a structure which allows problem solvers to recognize a problem state as belonging to a particular category of problem states that normally require particular moves. This means, in effect, that the problem solver knows that certain problem states can be grouped, at least in part, by their similarity and the similarity of the moves that can be made from those states. Novices, not possessingappropriate schemas, are not able to recognize and memorize problem configurations and are forced to use general problem-solving strategies such as means-endsanalysis when faced with a problem.

Features Used in Categorizing Problems Hinsley, Hayes, and Simon (1977) found that competent problem solvers could readily categorize algebra word problems with a high degreeof inter- subject agreement. In related research, Chi, Glaser, and Rees (1982) found that expert physicists, when asked to categorize a series of physics prob- lems, tended to group them on the basis of solution mode. Problems soluble by a basic principle of physics such as conservation of energy tended to be placed in the same category. In contrast, novices preferred to group prob- lems according to surface structures such as the inclusion of shared objects in the problem statement. For example, problems mentioning an inclined plane tended to be placed in the same category. The same basic principles leading to expert-novice distinctions in problem- solving strategies and memory of realistic problem-state configurations may also be instrumental in determining modes of problem categorization. Ex- perts, possessing schemas allowing them to distinguish between problem states and their associated moves, may categorize problems according to those schemas. If an expert has a schema which suggeststhat conservation of energy should be used to solve a particular problem, then that problem is likely to be categorized with other problems to which the same schema can apply. Novices, not having sophisticated schemasof this type must resort to surface structures when classifying problems. In summary, the expert-novice research suggests that domain specific knowledge, in the form of schemas, is a major factor distinguishing experts from novices in problem-solving skill. Differences in memory of problem states, strategies used and categories into which problems are placed can all be explained by assuming that experts have acquired schemas which play a crucial role in the way in which they approach and solve problems. 260 SWELLER

LEARNING In the previous section it was suggestedthat schema acquisition constitutes a primary factor determining problem solving skill. The manner in which this skill is best acquired is an important question with both theoretical and practical ramifications. Surprisingly, little research has been carried out on this issue. It is commonly assumedby both theoreticians and those concerned with practical problem-solving issues that practice on a large number of conventional problems is the best way of gaining problem-solving skill. Given the domain-specific, knowledge-based nature of problem-solving skill discussed in the last section, there is reason to doubt this assumption. There are also theoretical reasons which will be discussed in the next section for supposing that conventional problem-solving is an inefficient way of ac- quiring schemas. In the last few years, my collaborators and I have obtained experimental evidence supporting the same conclusion. These results are summarized below.

Evidence of Interference Between Conventional Problem Solving and Schema Acquisition The initial findings were obtained using puzzle problems. Mawer and Sweller (1982), Sweller (1983), and Sweller, Mawer, and Howe (1982) presented subjects with a variety of puzzle problems which could be solved either by means-endsanalysis or by inducing a rule based on the problem structure. Over many experiments it was found that while subjects had little difficulty solving these problems, they tended not to induce the relevant rules. This aspect of the problem structure could only be readily induced if consider- able additional information was implicitly or explicitly provided. It was concluded that conventional, goal-directed search heuristics such as means- ends analysis, while facilitating problem solution, could frequently prevent problem solvers from learning essentialaspects of a problem’s structure. Evi- dence supporting this conclusion has been obtained by Lewis and Anderson (1985). Sweller and Levine (1982) obtained direct evidence for this suggestion using maze problems. For some subjects the position of the goal was known. A conventional means-ends strategy of attempting to reduce differences between a given problem state and the goal state could be employed. Other subjects were not shown the goal position. They had to find both the goal and the route to the goal. Under these circumstances, it is not possible to reduce differences between a given problem state and the goal state because the goal state is not known until it is attained. Subjects given a conven- tional goal, in most casesfailed to induce essential structural features of the problems which under some circumstances prevented them from even solv- ing relatively simple problems. In contrast, the use of nonspecific goals per- mitted rapid learning of essential structural characteristics. These results COGNITIVE LOAD DURING PROBLEM SOLVING 261 provided further evidence of the negative effects of means-endsanalysis on learning.

PROBLEM-SOLVING SEARCH VIA MEANS-ENDS ANALYSIS AND SCHEMA ACQUISITION: CONTRARY GOALS? Why should some forms of problem-solving search such as means-ends analysis interfere with learning? There are two related mechanisms which may be particularly important when considering learning and problem solv- ing: selective attention and limited cognitive processing capacity.

Selective Attention Solving a problem and acquiring schemas may require largely unrelated cognitive processes. In order to solve a problem by means-endsanalysis, a problem solver must attend to differences between a current problem state and the goal state. Previously used problem-solving operators and the rela- tions between problem states and operators can be totally ignored by prob- lem solvers using this strategy under most conditions. Previous states and operators needto be noted only to prevent retracing steps during solution. We may contrast thesemechanisms with those required by schemaacquisi- tion. In order to acquire a schema, a problem solver must learn to recognize a problem state as belonging to a particular category of problem states that require particular moves. As a consequence, we might expect attention to problem states previously arrived at and the moves associated with those states to be important components of schema acquisition.

Cognitive Processing Capacity The cognitive load imposed on a person using a complex problem solving strategy such as means-endsanalysis may be an even more important factor in interfering with learning during problem solving. Under most circum- stances, means-ends analysis will result in fewer dead-ends being reached than any other general strategy which does not rely on prior domain-specific knowledge for its operation. One price paid for this efficiency may be a heavy use of limited cognitive-processing capacity. In order to use the strat- egy, a problem solver must simultaneously consider the current problem state, the goal state, the relation between the current problem state and the goal state, the relations between problem-solving operators and lastly, if subgoals have been used, a goal stack must be maintained. The cognitive- processing capacity needed to handle this information may be of such a magnitude as to leave little for schema acquisition, even if the problem is solved. While selective attention and limited cognitive processing capacity mecha- nisms have been treated independently in the previous discussions, they are 262 SWELLER related. Indeed, for practical purposes, under some conditions it may not be useful to distinguish between the two processes.Assume a problem solver whose entire cognitive processing capacity is devoted to goal attainment. It was suggestedin the previous section that this leaves no capacity to be de- voted to schemaacquisition. Rather than using cognitive processingcapacity terms, we could just as easily describe these circumstances in attentional terms. A problem solver whose cognitive processing capacity is entirely devoted to goal attainment is attending to this aspect of the problem to the exclusion of those features of the problem necessaryfor schemaacquisition.

CATEGORIES OF FORWARD-WORKING STRATEGIES It was suggestedpreviously that backward working could provide an indica- tor of a means-endstrategy. In contrast, a problem solver may work forward when using any one of several distinct strategies. First, the schema-driven approach used by experts will proceed forward from the givens becausea schema encodes a series of problem states and their associated moves. All states encounteredhave schemasassociated with them indicating appropriate forward moves. Second, forward working may occur during means-endanal- ysis either becausethe problem solver chooses to attempt to reduce differ- ences between a current problem state and the goal state by working from the current problem state, or becausethe problem does not contain a suffi- ciently well specified goal to allow backward working. As well as these two previously discussed strategies, there is a third forward-working strategy. Problem solvers may work forward without being controlled either by a schema or by a problem goal. They may simply explore the problem space in order to see what moves are possible. The practicality of the third strategy is dependent on the problem struc- ture. Many problems have extensive state spaces.An uncontrolled search of a space containing thousands of paths is clearly unlikely to be productive. Mathematics or mathematically based problems presented to students tend not to be of this type. Most contain very limited state spaceswhich can be explored fully in a few minutes by anyone familiar with the problem-solving operators. A kinematics or geometry problem is likely to contain no more than about a dozen (and probably far fewer) unknowns and even fewer equa- tions or theorems which can serve as problem solving operators. Because mathematics problems are of primary interest in this paper, it is appropriate to place a heavy emphasison a nonspecific goal, schemafree approach both as an experimental tool and, rn,ore importantly, as a tool able to assist in theory building. We might expect a nonspecific goal strategy to substantially decrease cognitive load. Using this strategy, a problem solver merely has to find an equation allowing the calculation of any unknown rather than assessdiffer- COGNITIVE LOAD DURING PROBLEhh SOLVING 263 ences between a current problem state and the goal. This, in turn, should allow schema acquisition to occur more readily. Subsequent sections pro- vide both experimental and theoretical (via a computational model) evidence for these contentions.

CONSEQUENCES OF A NONSPECIFIC GOAL STRATEGY ON MATHEMATICAL PROBLEM SOLVING- EXPERIMENTAL EVIDENCE Sweller, Mawer, and Ward (1983) presented problem solvers with simple physics or geometry problems which had beenmodified in order to eliminate the conventional, specific goal. This was done by replacing a conventional goal such as “What is the racing car’s acceleration” by the statement “Cal- culate the value of as many variables as you can.” It was suggestedthat this may be analogous to Sweller and Levine’s (1982) replacement of a specific by a nonspecific goal using maze problems. In the case of physics and geometry problems, the same theoretical rationale can be used to hypothe- size that reducing goal specificity will enhance schema acquisition: A non- specific goal eliminates the possibility of using a means-ends strategy to solve the problems. The results of these experiments indicated that the development of problem-solving expertise was enhancedmore rapidly using a reduced goal specificity procedure. While these experiments provided evi- dencethat means-endsanalysis interferes with learning, they do not indicate the mechanisms by which it might do so. The model described in the next section provides support for the suggestion that cognitive processing load is an important factor reducing learning during means-ends analysis.

RELATIVE COGNITIVE LOAD IMPOSED BY MEANS-ENDS ANALYSIS AND FORWARD WORKING- A COMPUTATIONAL MODEL A direct measure of the cognitive load imposed by a particular strategy or procedure is not available currently. Any potential measuremust be capable of simultaneously accounting for problem difficulty, subject knowledge, and strategy used. Computational models do this naturally. Programs which model problem solving using means-endsor alternatively, nonspecific goal strategies can be analyzed in order to obtain an indicator of the relative information-processing capacity required by the two strategies. This section describes such a procedure. Separate forward- and backward-oriented models have been described by Larkin, McDermott, Simon, and Simon (1980). The backward-working system solves physics problems using a means-endsstrategy. This model is 244 SWELLER designed to model novice behavior. The other works forward and was de- signed to model expert behavior. The model to be described here is a single system designedto work backward or forward depending on whether a spe- cific goal is included in the problem statement. Because it is designed to model backward or forward strategies, it bears some conceptual similarities to Larkin et al.‘s models. One difference is due to the fact that it is designed only to model novice behavior when confronted with either goal-specific or goal nonspecific problems rather than novice-expert differences. For this reason it consists of a single program which must determine the type of problem faced. The major differences between the current and previous models are due to the highly specific function of the current model. The primary purpose for constructing the program was to provide evidence for the suggestion that means-endsanalysis imposesa greater cognitive load than a nonspecific goal procedure. Consequently, care had to be taken to ensure that the model’s mechanisms (especially the means-ends mechanisms) were basic, with no possibly unnecessaryfeatures that might increase cognitive load. In this sense, the model is “minimal.” It contains the minimal essentials of means-endsand nonspecific goal strategies. This facilitates a comparison of the capacity required by both strategies that reduces the risk that either strategy has been burdened by unnecessary factors. Thus, in contrast to previous work, the model is not intended as a detailed description of prob- lem solving behavior. Such details could distort its function. The model was constructed using PRISM, a production system language designedto model cognitive processes(see Langley & Neches, 1981). A pro- duction systemis a set of inference rules that have conditions for applications and actions to be taken if the conditions are satisfied. The model permitted the conditions of a single set of productions to be matched with the elements of a single- working memory . Decisions concerning the order in which pro- ductions fired were determined by three factors. The initial decision was basedon the relative strengths of the relevant productions. Each production was allocated an initial strength based on psychological assumptions. This could remain constant or alter during a run. If there were several produc- tions with an equal strength which exceededthat of the remaining produc- tions, an additional decision rule was used to break the tie. The “activation” of the statements in working memory that can match the condition side of each production was used for this purpose. The activation of statementscan be considered analogous to the extent that those statements are known or familiar. For relevant productions, this activation was summed and the production with the highest activation fired. If, after this procedure, there was still a tie between productions, one of them was chosen at random to fire. In addition, a production which fired on one cycle could not match the same elements and fire again. COGNITIVE LOAD DURING PROBLEM SOLVING 265

Measuring Cognitive Load Using a Production System While a production system is not specifically designedto measure cognitive load, there are several aspects of production systems which could provide suitable measures. First, we might expect cognitive load to be correlated with the number of statements in working memory. We know that human short-term memory is severely limited and any problem that requires a large number of items to be stored in short-term memory may contribute to an excessive cognitive load. In so far as short-term memory corresponds to a production system’s working memory, it is reasonableto supposethat an in- creased number of statements in working memory increases cognitive load. The number of productions and the number of conditions that need to match statements in working memory should also provide measuresof cog- nitive load. In order to make progress on a transformation problem by choosing a move, a production system must determine which of its various productions should fire, using the mechanisms described previously. The first and critical step, is to find those productions which match elements in working memory. It seems plausible to suggest that the more productions that need to be considered at each step in the problem and the more state- ments that need to be matched in order to decide between productions, the greater is the “cognitive load.” The analogy between a production system determining which production should fire and a person deciding what to do next, may be quite close. In both cases, the elements of the problem and the knowledge brought to bear on the problem must be coordinated. A production system with many pro- ductions each containing many statements, may be analogous to a person using a complex problem-solving strategy involving many choice points with each choice requiring a large amount of information. It also should be noted that the general argument applies irrespective of the specific assumptions concerning the system’s architecture. For example, a parallel system should require more routes or channels (communication bandwidth) to handle complex rather than simple search mechanisms. These routes or channels should no longer be available for learning. In other words, while the precise measurement will depend on the architecture of the system, the general principle that a more complex search mechanism will require increased capacity which may interfere with learning, should not.

PRODUCTION SYSTEM DETAILS This section provides details of a production system designedto allow esti- mates of the relative cognitive load imposed while solving conventional problems by means-ends analysis, compared to nonspecific goalproblems otherwise identical in structure. The program is essentially an equation 266 SWELLER chaining system. As such, it can be used to solve problems which in essence, require the construction of a chain of previously given equations connecting the givens to the goal. Geometry, trigonometry, and kinematics problems provide examples of this category. To solve a kinematics problem for example, a chain (or chains) consisting of equations of motion must be constructed. One end of the chain must contain the givens and allow the calculation of values for new variables. These new variables can be used in other equations which become intermediate links in the chain. The end of the chain must contain the goal which can be calculated using the previous links. With limitations to be discussedbelow, the system to be described will solve all problems of this type as well as structurally identical problems with nonspecified goals.

Working Memory The system commenceswith the following information in working memory: (a) A list of the equations that might potentially be used in attempting to solve the problem; (b) A list indicating which of the variables found in any of the equations are known; (c) A similar list indicating which of the varia- bles are unknown. A statement indicating the goal variable was included in the case of conventional problems with a specific goal. These lists are a combination of the relevant information that subjects must extract from a problem statement and the problem-solving operators (equations) needed to solve the problem. We assume that problem solvers have this information immediately prior to attempting their first move. This only leavesthe problem solving strategies that might be used to attain solu- tion. The list of productions specifies these and by eliminating all else from this list, we have a clear delineation betweenthe cognitive processesbrought into play before and after the first move. Working memory can be used to measure cognitive processing capacity required before the first move while the production list can be used similarly for processing that occurs during and after the first move.

Description and Justification of Means-Ends Productions Since it has been hypothesized that a means-endsstrategy imposes a heavy cognitive load, the productions required to describe the strategy must be minimal in number in order to avoid artificially increasing this load. Table 1 contains a list of four such productions which are considered essential to a means-endsstrategy. The elimination of any one of these productions will prevent equation chaining problems from being solved by a means-ends strategy. Furthermore, they are sufficient to allow solution of all equation chaining problems which do not require the processing of more than one equation at a time. Problems requiring the use of more sophisticated algebraic procedures such as simultaneous equations can not be solved by these productions. It COGNITIVE LOAD DURING PROBLEM SOLVING 267

TABLE 1 Set of Means-Ends and NonSpecific Goal Equation-Chaining Productions

Means-ends Productions Conditions Actions Strength

1 If a problem has a specified then the goal becomes known 1.2 goal and if an equation is known in which the goal is the only unknown

2 If a problem has a specified then the unknowns not 1.0 goal and if an equation is previously set as subgoals known which contains the and other than the goal goal and one or more become subgoals unknowns not previously set as subgoals

3 If an equation is known which then the unknowns not 1 .o contains subgoals and one previously set as subgoals or or more unknowns not become subgools previously set as subgoals

4 If an equation is known in then the subgoal becomes 1.1 which a subgoal is the only a known unknown

Nonspecific goal Production 5 If a problem does not hove a then the unknown becomes 1.0 specified goal and if on a known equation can be found with only one unknown should neverthelessbe noted in this context, that a new set of equations can always be derived from the sets of simultaneous equations and this will allow any problem to be solved without the use of the simultaneous equa- tions. In this sense,the four productions are sufficient to allow the solution of all equation chaining problems. Any failures can be rectified by deriving the relevant set of equations. For example, if a body is uniformly accelerated from rest, and if acceleration and distance travelled are known, then time travelled can be calculated using the equations; s=vt, v= .5V and V= at. To solve this problem, simultaneous equations can be used to derive the equation s = Sat*, assuming this is not known. The problem can then be solved in a single move using this equation. (Of course, the equations = .5at’ is normally taught. If all possible equations in a system are learned, then all possible problems can be solved in one move.) The condition side of the first means-endsproduction in Table 1 tests whether the problem has a specific goal and whether an equation is known in which that goal is the only unknown. If these conditions are met, the ac- tion side of the production states that the goal is now known.,The relative 268 SWELLER strength of this production ensures that it will fire prior to any alternative productions whose conditions are also met. (The relative strengths of pro- ductions reflect ordinal relations only.) Nevertheless, becauseits conditions are restrictive-under most problem conditions there are more equations with several unknowns than equations in which the goal is the only unknown -this production is always the last to fire. Before it fires, the values of other unknowns normally need to be found using other productions (unless it is the only production to fire). Once the first production fires, the system comes to a halt. Without this production, a value fer the goal cannot be found. If the first production cannot fire, then the second production must fire. It does not require the goal to be the only unknown in an equation. If any equation is known containing the goal, then this production will fire. The action side specifies that all unknowns other than the goal will become sub- goals. These subgoals are thus added to working memory. Despite its rela- tively low strength, normally, this production is the first to fire becausein a soluble problem, its conditions can always be met immediately. Basically, it only requires an equation containing the goal variable. It might also be noted, that if this production fires repeatedly (which may not necessarily occur), the system is engaging in a breadth first search. It is attempting to find as many questions as possible containing the goal. This production is essential for the initial setting of subgoals. Once subgoals have been added to working memory by the actions of the second production, the third and fourth productions can fire. The condi- tions of these include subgoals rather than goals and in the caseof the third production, include statements preventing previous subgoals from being reset as subgoals. The third production allows a search in depth rather than the search in breadth of the second production. If used repeatedly, this production can construct a chain of subgoals with a chain of equations. Nevertheless, it is not constrained to a search in depth. It can also conduct a search in breadth, finding as many equations as possible containing a particular subgoal and adding all unknowns as additional subgoals in working memory. Without this production, a chain of subgoals linking equations from the goal to the givens cannot be constructed. The fourth production has a higher strength than the third but under most problem conditions will fire later becauseof its more restrictive condi- tions. In order to fire, this production must find an equation containing a subgoal as the only unknown. This contrasts with the third production which can fire after finding an equation with unknowns other than the subgoal. The fourth production can fire only after the second has fired becauseprior to this, working memory contains no subgoals. This is a working-forward production. Without it, the system could not calculate values which allow chaining from the givens to the goal. COGNITIVE LOAD DURING PROBLEM SOLVING 269

Example of Means-Ends Operation These four productions appear to be sufficient to solve all equation chain- ing problems provided suitable equations are known. Figure 1 indicates the flow of control. A kinematics problem discussedin detail will be used to provide a simple example of the system’s operation. The problem states: A car that starts from rest and acceleratesuniformly at 2 meters/s/s in a straight line has an averagevelocity of 17 meters/s. How far has it travelled? It can be solved using the three equations, s=vt, v= SV and V=at. As noted above, these equations can be used to solve all problems in which an object is uniformly acceleratedfrom rest in a straight line. In order to solve this problem, the system must have the three equations in working memory, a list of the variables in the equations which are known (a, v), a similar list of the unknowns (t; V) and a statement indicating the goal variable (s). This is assumedto be equivalent to a person who has read

Figure 1. Flow of Control Under Means-Ends Production. (System halts either when the problem is solved or when no production can fire because no new subgoals can be generated and no equation can be solved.) 270 SWELLER the problem statement, assumed a set of equations which might be relevant to solution, and determined with respect to each variable whether it is known, unknown or the goal. Translation and other processesleading to this repre- sentation of the problem are not reflected in the system. Only the end result is fed into working memory becauseonly subsequent problem-solving pro- cessesare of concern when comparing conventional and goal-free problems. This is because translation processes are assumed to be identical in both cases and do not need to be compared.

Working Backward The system will first attempt to solve this problem in a single step using the first production becausethis production has the highest strength. It will at- tempt to find an equation containing a, v, and s. Since such an equation is not available, the first production cannot fire. The fourth production has the next highest strength but this cannot fire becausethere are no subgoals in working memory. For the same reason, the third production cannot fire either. The second production can fire. An equation (s = vt) is known which contains :he goal and unknown(s). Time (t) becomes a subgoal. The third and fourth productions now can be considered since subgoals are included in their conditions. The fourth production has a higher strength but cannot fire becauseno equation can be found in which t is the only unknown. The third production can fire using V=at. Final velocity is now a subgoal.

Working Forward To this point, the system has been working backward from the goal, setting up subgoals. With final velocity as a subgoal, it can solve an equation and attempt to work forward. The conditions of the second, third, and fourth productions are all met at this juncture but the fourth production has the greatest strength. The equation v= SV contains the subgoal V and the known v. The action side of the production will add V as a known and delete it as a subgoal. The same production will now fire again, matched to differ- ent elements. The equation V=at contains the subgoal t and the knowns a and V. Subgoal t is converted into a known. The conditions of the first pro- duction, which is the strongest, are now met. The equation s=vt contains the goal s with v and t as knowns. Once this production fires, a value for s is obtained.

A Production to Solve Nonspecific Goal Problems A single production is sufficient to solve problems in which the goal is not specified. The fifth production of Table 1 provides a description. It is de- signed to search for equations containing a single unknown and solve for that unknown with no referenceto a goal. By firing repeatedly, all unknowns that can be derived from the givens of a problem statement will be found. Figure 2 diagrams the flow of control. Problem statement and

equations in

working memory

stop search

Solve equation and

convert unknown

Figure 2. Flow of Control Under a NonSpecific Goal Production

271 272 SWELLER

Assume the last sentenceof the previous kinematics problem is replaced by the statement “Calculate the value of as many variables as you can.” The problem is now representedin working memory by the same equations and same knowns as the conventional problem. The only difference is that the previous goal (distance) is now listed as an unknown. Becauseno goal or subgoal is listed in working memory, none of the means-endsproductions can fire. Each time the nonspecific goal production fires, it essentiallyduplicates the forward-working actions of the means-ends productions but’does so in a nondirected fashion. While the means-ends productions continually attempt to work forward due to the strength of the forward working productions (1 and 4), they are not able to do so until a suitable set of goals and subgoalshave been added to working memory. The nonspecific goal production works forward automatically. On our kinemat- ics example, it will fire three times, successivelyfinding V using v = SV, t using V = at and s using s = vt. The samevariables were found by the means- ends productions.

MEASURES OF COGNITIVE LOAD Cognitive load can be measured in several ways. We will consider: (1) the number of statements in working memory; (2) the number of productions; (3) the number of cycles to solution; (4) the total number of conditions matched. Table 2 allows a comparison of these measureswhen the system solves a conventional and nonspecific goal version of the previously dis- cussedkinematics problem. Both the means-endsand the analogous nonspecific goal problems com- mence with an equal number of statements in working memory-14. The only difference is that the conventional problems contain a statement speci- fying a goal while the non-specific goal problems have the goal variable listed as another unknown. The equal number of statements reflects the assumption that the translation and general representation processesare

TABLE 2 Simulation Data Under Conventional and Nonspecific Goal Conditions When Solving o 3-Step Equation Choining Problem

Conventional Nonspecific Goal

Average working memory 15.5 14 Peak working memory 16 14 Number of active productions 4 1 Number of cycles 5 3 Total number of conditions matched 29 17 Note. See text for an example problem. COGNITIVE LOAD DURING PROBLEM SOLVING 273 similar in terms of cognitive load for conventional and nonspecific goal problems. A means-ends strategy requires the addition of subgoals to working memory during solution. A nonspecific goal strategy has no net additions resulting in identical average and peak working memory loads. In so far as working memory corresponds to human short-term memory, this can be im- portant due to the severe limitations of short-term memory. A small addi- tional load could be critical. It must neverthelessbe pointed out, that most problem solvers faced with the need to remember subgoals, are likely to use an external memory source such as pencil and paper. Differences in working memory may not be critical under these circumstances. There are more substantial differences on all other measuresof cognitive load. It might be noted that the ratio of cycles to conditions matched is ap- proximately equal for both the conventional and nonspecific goal problems. This is reflected by the approximately equal number (7-9) of statements in each production. The organization of the current system clearly requires more active pro- ductions, cycles, and conditions matched for a means-ends strategy than a nonspecific goal strategy. The major difference is in the number of produc- tions and it is this difference that requires emphasis. If these productions reflect human cognitive processes, then they provide strong evidence for the contention that a means-ends strategy imposes a relatively high cognitive load. The plausibility of this claim rests heavily on the suggestion that the means-ends system is minimal. If it is minimal, then attempts to provide more realistic models of cognitive processes would result in expansions rather than contractions of the system. The means-endsmodel of Larkin, McDermott, Simon, and Simon (1980) provides an example of a system that has many more productions than the current model. There are several classes of these productions omitted from the current system. For example, Larkin et al.‘s model has productions which assign symbols to appropriate statements of the problem description rather than have the symbols and their status (known, unknown, goal) placed ini- tially in working memory. As another example, productions are used to generate equations rather than assuming, as does the current model, that the relevant set of equations is known and in working memory. The inclu- sion of productions such as these is reasonable in a system designed to model as many aspects as possible of problem-solving performance. They are not nevertheless, essential and for this reason had to be excluded from a model pared to the bare minimum. The nonspecific goal subsystem is of course, also minimal. It is neverthe- less, plausible. Problem solvers faced with a nonspecific goal problem do simply search for equations that can be applied to a given problem state to enable solution of an unknown (see Sweller, Mawer, & Ward, 1983). The goal-free production mimics this activity. 274 SWELLER

Relations Between Cognitive Load and Number of Productions Why should the number of productions (and elements that require match- ing) provide a measureof cognitive load? A qualitative analysis of the means- ends subsystem provides some evidence for the suggestion that it imposes a heavy cognitive load. A problem solver who is processing information in a manner similar to the means-ends subsystem, must at any given problem state decide whether there is an equation providing a single step solution (first production), whether the value for a desired subgoal can be calculated (fourth production), whether a chain of subgoals should be constructed (search in depth using the third production) or whether a series of unrelated subgoals should be established (search in breadth using the second and/or third productions). Each of these decisions must be determined by the rela- tion between the current problem state and the goal, keeping in mind the available problem-solving operators (the equations). The four productions may accurately represent the difficulties faced by a problem solver using a means-ends strategy. It seems improbable that these complex decisions are automated and can run without a considerable strain on cognitive resources. The issue may be examined in terms of a “human production system.” At each choice point, he or she must attempt to match the known values with equations containing the goal to see if a solution is available; decide whether this is a futile exercise at this point; decide on the basis of available unknowns whether subgoals should be set up; decide on the basis of the knowns, unknowns, and equations which subgoal track should be followed; decide on the basis of the known values and available equations whether a value for a subgoal can be calculated; decide whether this is a futile exercise. It may not be surprising that under these circumstances the “system” fre- quently collapses (the problem solver gives up). Furthermore, none of these processesappears to be related to schema acquisition. Any learning processes must be imposed as additional mechanisms requiring additional cognitive capacity. These processes may be contrasted with those imposed by a nonspecific goal problem. There is only one decision that needsto be made. Can a value be found for an unknown? It may be reasonable to suggest that this simple process poses little impediment to learning. It may not be surprising that the complex means-ends process can block learning. A diagrammatic representation of the differences between the two strate- gies may be obtained by comparing Figure 1, which diagrams the flow of control under a means-ends strategy, with Figure 2, which diagrams the flow of control under a nonspecific goal strategy. The differences between the two diagrams may well reflect the differences in cognitive capacity re- quired by the two processes. It may be argued that in order to demonstrate that a heavy cognitive load during problem solving interferes with learning, it is important that learning COGNITIVE LOAD DURING PROBLEM SOLVING 275 mechanisms be included in the model. In fact, such interference is inevitable assuming that: (a) the system (or person) has a fixed cognitive capacity; (b) both problem solving and learning require some of that capacity; (c) the problem solving and learning mechanisms differ. As indicated previously, these assumptions can explain the data. Under these assumptions, any in- creasein resourcesrequired during problem solving must inevitably decrease resources available for learning. Consequently, only the first step-evidence that required processing capacity may be relatively heavy during the means- ends analysis-is necessary. Consequencesfor learning follow inevitably. In summary, a production system approach was used to provide some in- dication of the relative cognitive load of a means-endscompared to a non- specific goal strategy. Analysis of a system consisting of no more than the bare essentials needed to operate the strategies revealed that means-ends analysis required somewhat more information in working memory and a substantially more complex production system than a nonspecific goal strat- egy. This could be interpreted as suggesting that means-ends analysis re- quires more cognitive capacity than a nonspecific goal strategy’

EXPERIMENTAL EVIDENCE In previous sections, experimental results were discussed which suggested that means-ends analysis could impose a relatively heavy cognitive load. This evidence was indirect, consisting primarily of performance characteris- tics such as strategies used, categorization of solutions, speed of solution and errors on subsequent problems. Additional, stronger evidence for the contention was obtained by formal modelling techniques. There also is some relatively direct experimental evidence which is available. If means-endsanalysis imposes a heavy cognitive load, we might expect its use to simultaneously influence aspects of performance such as number of errors. In a mathematical task, novice problem solvers who do not have a substantial facility in the use of essential problem-solving operators-nor- mally mathematical principles, equations, theorems, etc.-may be more likely to commit mathematical errors when using means-endsanalysis than

I It should be noted that the implemented system required separate productions to handle equations containing two variables (e.g., v = SV) and three variables (e.g., s = vt). Thus, each of the productions listed in Table 1 consisted of two productions in the implemented system. Furthermore, in the case of means-ends productions dealing with equations containing three variables, separate productions were required to generate subgoals where only one unknown existed as opposed to two unknowns. These variations resulted in ten means-ends productions and two goal-free productions. Additional productions, similar in structure to the existing ones, would need to be added to handle equations with more than three variables. The varia- tions were necessitated by purely computational considerations and were not thought to have psychological significance. For this reason they have not been discussed in detail. 276 SWELLER when using a nonspecific goal strategy. We might expect that if a strategy re- quires a large amount of cognitive processing capacity, less will be available for other, competing aspects of the task. Errorless use of, for example, equations, is one such aspect. Results bearing directly on this issue have been obtained by Owen and Sweller (1985) in a series of studies. We used nonspecific goal trigonometry problems in which subjects were required to find the lengths of all the sides of a given diagram. This could be contrasted with the performance of sub- jects presentedwith a conventional problem consisting of the same diagram of which a specific side had to be found. Unlike previous experiments employing this paradigm (e;g. Sweller, Mawer, 8c Ward, 1983), the prob- lems were not specifically structured to ensure that nonspecific goal subjects calculated the lengths of the same sides as those presented with the conven- tional problems. The groups were matched with respect to time spent on the problems rather than number of problems. This meant that while both groups spend a fixed amount of time solving problems, both the number of problems and number of sides calculated could vary. Over several experiments, the major finding was that the conventional group made significantly more mathematical errors (e.g., misuseof the equa- tion sine = opposite/hypotenuse) per side calculated as the nonspecific goal group. Four to six times as many mathematical errors were made by the con- ventional group. In fact, the total number of errors made by the conventional groups were consistently greater despitethe fact that thesegroups consistently found fewer sides. As was the case in previous experiments, the advantage of nonspecific goal problems transferred to subsequentproblems with fewer errors and faster performance in later problem solving. The most obvious explanation for these results is in terms of the pr-vi- ously outlined model. Problem solvers organizing a problem according +o means-endsprinciples, suffer from a cognitive overload which leaves little capacity for other aspects of the task. This overload can be manifested by an increase in the number of mathematical errors made. The results of the Owen and Sweller (1985) experiments, in conjunction with the prior theoretical analysis, suggest that simultaneously solving a problem by means-endsanalysis and attempting to acquire schemas asso- ciated with the problem, may be analogous to a dual task. Attempting to solve the problem may be consideredthe primary task. Acquiring knowledge of the problem structure and of elementswhich might facilitate subsequent solution attempts may be considered the secondary task. A considerable volume of work has been carried out using a dual-task paradigm. Britton and his colleagues (Britton, Glyrm, Meyer, 8c Penland, 1982; Britten, Holdredge, Curry, & Westbrook, 1979; Britton & Tesser, 1982)have used reaction times to a click as the secondary task with a variety of complex cognitive tasks as the primary task. They found that the second- COGNITIVE LOAD DURING PROBLEM SOLVING 277 ary task could be used to indicate the cognitive capacity required by the primary task. Lansman and Hunt (1982) found that a secondary, reaction time task could be used to measure how much spare capacity was available while engagedon an easy primary task. This, in turn, could be used to pre- dict performance on a subsequent, more difficult task. Fisk and Schneider (1984) obtained results indicating that increasing the extent to which subjects were required to attend to one task during controlled processing reduced the extent to which items were stored in long-term memory on a second task. Book and Garling (1980) and Lindberg and Garling (1982) found that knowl- edge concerning a traversed path was interfered with if subjects had to count backward while traversing the path. All of these findings suggeststrongly that a secondary task can be used as an indicator of the cognitive load imposed by a primary task. If, as sug- gested above, problem solving search via means-ends analysis and schema acquisition are independent tasks, then they may be considered as primary and secondary tasks respectively, within a dual task paradigm. Under these circumstances, if a strategy such as means-ends analysis is used to accom- plish the primary task (attain the problem goal), then becausethe strategy imposes a heavy cognitive load, fewer resources may be available for the secondary task. Performance on aspectsof the secondary task such as correct use of mathematical rules may be used to indicate the cognitive load imposed by the primary task. The Owen and Sweller (1985) experiments, in effect, used this procedure. Nevertheless, a direct use of the dual task paradigm may provide more evidence for the hypothesis that means-endsanalysis im- poses a heavy cognitive load. An indication of the relative cognitive load imposed by means-endsand nonspecific goal strategies may be obtained by explicitly requiring subjects to engagein a secondary task while solving conventional or nonspecific goal problems. In the current experiment the secondary task was memory of the givens and the solution of a previously solved problem. This secondary task was chosen becauseit was thought that enhanced memory of these charac- teristics could provide some evidence of schema acquisition. If a schema allows subjects to classify a problem and indicates which moves are appro- priate, then we might expect that enhanced memory of problem givens and solutions indicates enhanced schema acquisition. (Although it must, of course, be recognized that a schema requires more than just memory of givens and solutions. Nevertheless, these may be prerequisites for schema acquisition.) Unlike previous experiments employing a nonspecific goal procedure (Owen & Sweller, 1985; Sweller, Mawer, & Ward, 1983) the current experi- ment was not designedto test whether a nonspecific goal procedure enhanced subsequent problem-solving performance. It was designed solely to test whether reducing cognitive load by reducing problem-solving search activity 278 SWELLER using means-ends analysis could allow subjects to learn more of specific aspects of the problem. Problem solving search activity was reduced by presenting subjects with nonspecific goal trigonometry problems. Subjects were required to find the lengths of all but those sides not neededto solve equivalent conventional problems with conventional goals. The sides not re- quired were indicated. A second group was presented with the equivalent conventional problems. Both groups were required to memorize and later reproduce the givens and solutions of the problems as a secondary task. Two opposing hypotheses can be considered. First, as argued above, an increased cognitive load imposed by the conventional problems may de- crease performance on the secondary task. Second, because the primary task requires subjects to deal with all of the elements of the secondary task, it can be hypothesized that increased cognitive load on the primary task, by strengthening those elements, should improve performance on the secondary task.

METHOD Subjects The subjects were 24 students from a Year 10 (age 15-16 years) class of a Sydney high school. All had been introduced previously to the sine, cosine, and tangent ratios.

Procedure All subjects, tested individually, were presented a sheet explaining and giv- ing examples of the use of the sine, cosine, and tangent ratios. When sub- jects were satisfied that the material was understood they were informed that they would be required to solve 6 problems. They were also told that after each problem was solved they would be required to precisely reproduce the original diagram and the correct solution of the problem pre- ceding the one that had just been solved. There was no reproduction phase after the first problem (since there was no preceding problem to reproduce) and the fifth problem was the last requiring reproduction. Subjects were also told that their major task was to solve the problem. The problem state- ment and diagram were removed immediately after the last solution step had been taken. If on any problem the solution had not been obtained within 5 minutes, the experimenter provided the correct solution. There was no time limit on the reproduction phases. Each phase ended when subjects were satisfied that they could not improve their reproduction any further. Pencil and paper were used for both the problem solving and reproduction phases. Time and. errors for each of the solution and reproduction . phases were recorded. A conventional and nonspecific goal group of 12 subjects each were used. Figure 3 provides an example of a conventional problem. In order to solve COGNITIVE LOAD DURING PROBLEM SOLVING 279

Figure 3. Example Trigonometry Problem (If the goal of the problem is to find the length of CB, the solution is CA=sine 3W4.4; CB=CA/cosine 49.) this problem the sine ratio needs to be used followed by the cosine ratio. The two trigonometric ratios neededto solve the remaining 5 problems were sine-sine, cosine-cosine,cosine-tangent, sine-tangent, and tangent-tangent, respectively. Each problem was identical in diagrammatic configuration to Figure 3 but.the line segmentlabels (vertices)and the anglesvaried. The non- specific goal problems were identical except that subjects were told to find the lengths of as many sides as possible and the two sides not neededto solve the conventional problems were marked to indicate that they should not be solved for. No numerical values were required with subjects merely being asked to indicate the equations neededto solve the problems.

Results and Discussion Table 3 indicates mean time to solve eachproblem for the two groups. (Non- solvers were allocated a time of 300 s.) There was no difference in total time to solve the 6 problems between groups, F(1,22) = .17. (The .05 level of sig- nificance is used throughout this article.) Nevertheless, it might be noted that on each of the 6 problems the goal-free group required marginally less time than the conventional group and the probability of this occurring by chance is .016. Trend analysis indicated a significant linear trend with later problems being solved more rapidly than earlier ones,F(1,22) =49.38. There SWELLER

TABLE 3 Mean Seconds to Problem Solution (Mean mathematical errors are in brackets.)

Group Problem 1 2 3 4 5 6

Conventional 274 (1.2) 239 (1.0) 170 (0.3) 188 (0.5) 193 (0.5) 138 (0.6) NonSpecific Go01 272 (1.2) 227 (1 .l) 156 (0.25) 170 (0.7) 191 (0.75) 126 (0.2) was no group X problem interaction suggestingthat both groups improved at approximately the same rate, F(1,22) = .Ol. Table 3 also indicates the number of mathematical errors made where mathematical errors include algebraic errors or trigonometric errors such as defining the sine ratio as adjacent/hypotenuse. The results duplicate those for solution times with no difference betweengroups, F(1,22) =0, a signifi- cant linear trend with fewer errors being made on later problems, F(1,22) = 19.97, and no group X problem interaction, F(1,22) = .37. Table 4 indicates the number of subjects who were able to solve each problem within the allotted 5 minutes per problem. (Subjects who could not solve a problem were given the solution by the experimenter.) Most subjects could not solve the first problem but improved rapidly thereafter. Table 4 also indicates the mean number of sides calculated by each group on each problem. Table 5 indicates mean reproduction times for the two groups on each of the 5 reproductions. There was no difference betweenthe two groups in total time, F(1,22) = .Ol. A significant linear trend was obtained, F(1,22) =4.76

TABLE 4 Number of Subjects Reaching Problem ,Solution Within 5 Minutes, IMean number of sides calculated in oarentheses.)

Conventional 4 (1.08) 5 (1.42) 10 (1.83) 9 (1.75) 9 (1.67) 11 (1.83) Nonspecific Goal 2 (1.25) a (1.75) 11 (1.92) 11 (1.92) 0 (1.58) 10 (1.83)

TABLE 5 Mean Seconds for Reproduction

Group Problem 1 2 :! 4 5

Convention01 232 202 206 166 143 Nonspecific Goal 209 175 166 199 192 COGNITIVE LOAD DURING PROBLEM SOLVING 281 indicating increasedspeed in reproduction over problems. A nonsignificant group X problem interaction was obtained, F(1,22) = 3.83. Errors on the reproduction task are the major focus of this experiment. Six categories of errors were used. 1, A segment-labellingerror was scored if any of the line segmentswas in- correctly labelled-e.g., if line AB was labelled CD, 2. Angle-position errors occurred when an angle was incorrectly stated as a given or an unknown. 3. Angle-value errors occurred when a numerical value was incorrect. (If a new angle value appearedin a new position which had previously been an unknown, then both an angle-value and angle-position error was scored.) 4. Side-position errors occurred when an unknown side was labelled as known or vice-versa. 5. Side-value errors were scored when the given side was given the wrong length. (Side-position and side-value errors were scored when a value which had not appeared in the original was given to an originally unknown side.) 6. Solution errors were incorrect reproductions of the solution. Each reproduction by each subject was given a score of 1 or 0 on each of these 6 criteria for each of the 5 problems. Any error on any of the criteria resulted in a score of 1 on that criterion. By adding acrossproblems, a total score out of 5 could be obtained for each subject. Table 6 provides mean scores on each of the criteria for the two groups. Becauseall scores fell in the limited range O-5, severefloor or ceiling ef- fects were obtained resulting in grossly skeweddistributions. For this reason, nonparametric techniques were used to analysethis data. Mann-Whitney U tests were used to analysedifferences betweengroups on either the segment- labelling errors, U(12,12) = 55, or the angle-value errors, U(12,12) = 63. The nonspecific goal group made significantly fewer angle-position errors, U(12,12)=29, side-valueerrors, U(12,12)=27, side-position errors, U(12,12) =41, and solution errors, U(12,12)= 17.5. The nature of the secondary task allowed 2 opposing hypothesesto be tested. Depending on the cognitive mechanismsthat operate, a heavy cogni-

TABLE 6 Mean Reproduction Error Scores for Each Category

Group Error Type Segment- Angle- Angie- Side- Side- labels value position value position Solution

Conventional 2.9 3.6 2.4 2.6 1.6 3.4 Nonspecific Goal 2.4 3.4 1.1 1.3 1.2 1 .S 282 SWELLER tive load during conventionalproblem solving relative to a nonspecificgoal task, couldeither facilitate or inhibit memoryof the problemstructure. The resultsprovide no evidencethat an increasedload during conventionalprob- lem solvingassists problem solvers in assimilatinginformation concerning the initial problemstructure or the solutionsteps. Instead, the resultscon- form to thoseobtained in moreconventional dual task experimentswith the cognitiveload imposedby one task interfering with performanceon the other. .More excesscapacity appears to be availableafter solving a non- specificgoal problemthan a conventionalproblem. The patternof differencesbetween the conventionaland nonspecificgoal problemsalso is of interest,A schemawas defined above as a structurethat permitsproblem solvers to categorizea problemas one which allows certain movesfor solution.If a nonspecificgoal problem enhances schema acquisi- tion, we might expectsubjects solving nonspecific goal problemsto have superiorrecall of structural aspectsof the problemsuch as the characteris- tics of the givensand the solution moves.In the current experiment,this shouldtranslate into superiorperform~ce on the angle-position,side-posi- tion, and solutionmeasures since these are requiredto constructa schema. The nonspecificgoal group wassuperior on all of these.The other measures -segment-labelling,angle-value and side-value-are presumablyirrelevant to schemaacquisition since a schemacould be inducedwithout reference to thesedetails. Side-value was the only one of thesemeasures providing a sig~~c~t differencebetween groups. This may provide limited evidence that subjectsfollowed instructions to concentrateon problemsolution rather than the recalltask. In the process,where cognitive capacity was available, they may have learnedmore of those characteristicsneeded to facilitate schemaacquisition rather than irrelevantaspects of the problem.Thus the particularpattern of resultsmay also be usedto supportthe generalhypoth- esisthat cognitiveload under conv~tion~ problem-solvingconditions in- terfereswith schemaacquisition. It might be noted, the resultson the primary task (problemsolution) do not replicatethose obtained by Owenand Sweller(1985) or Sweller,Mawer, and Ward (1983) who repeatedlyobtained improved performanceunder nonspecificgoal as opposedto conventionalconditions. Nevertheless,it should be noted that the previous studiesdid not use a secondarytask. Assuminga fixed cognitivecapacity for eachsubject, an advantagedue to reducedcognitive load canbe distributedover both tasksin a dualtask exer- ciseor concentratedover oneor the other of the two tasks,To someextent, this distributionof cognitiveresources is at the discretionof the subjects.In the presentexperiment, it appearsthat mostsubjects allocated excess capacity to the secondtask resultingin the usualperformance difference occurring on that task rather than the primary one. In theseterms, the resultsare in accordwith previousfindings. Nonspecific goal conditionshave facilitated COGNITIVE LOAD DURING PROBLEM SOLVING 283

performance. The only difference from previous experiments is that the major facilitation has been transferred from the primary to the secondary task. (In this context, it should be noted that the goal-modified group took less time to solve each of the 6 problems than the conventional group and this is unlikely to be a chance effect.)

THEORETICAL AND PRACTICAL IMPLICATIONS Two general inferences can be drawn. First, it may be tentatively suggested that the use of computational models as measuring devicescould have a more general applicability. Currently, there is no a priori method for determining the difficulty problem solvers will have in solving specific problems. Present- ing the problem is the only viable technique. Inability to determine something as fundamental as problem difficulty may be a major impediment to pro- gress. This gap in our basic technical repertoire is neverthelessunderstand- able. A measure which simultaneously accounts for problem and problem solver characteristics is bound to be complex. By using minimal computa- tional models it may be possible to simultaneously isolate and measurethose aspects of a problem and a problem solver’s strategy and knowledge that govern important aspects of performance. The second conclusion, based partly on using a computational model as a measuring device, may be put more strongly. Conventional problem solv- ing activity via means-endsanalysis normally leads to problem-solution, not to schema acquisition. Both theoretical and practical implications flow from this conclusion. The theoretical points made in the present paper suggest that cognitive effort expended during conventional problem solving leads to the problem goal, not to learning. Goal attainment and schema acquisition may be two largely unrelated and even incompatible processes. This may be relevant to all learning through problem-solving theories (e.g., see Anderson, 1982; Laird, Newell, & Rosenbloom, 1987). The suggestions made in this article have clear applications, especially in an educational context. Most mathematics and mathematics-basedcurricula place a heavy emphasis on conventional problem solving as a learning device. Once basic principles have been explained and a limited number of worked examples demonstrated, students are normally required to solve substantial numbers of problems. Much time tends to be devoted to problem solving and as a consequence, considerable learning probably occurs during this period. The emphasis on problem solving is nevertheless, based more on tradition than on research findings. There seemsto be no clear evidencethat conventional problem solving is an efficient learning device and .consider- able evidence that it is not. If, as suggestedhere, conventional problems im- pose a heavy cognitive load which does not assist in learning, they may be 284 SWELLER better replacedby nonspecific goal problems or worked examples(see Sweller & Cooper, 1985). The use of conventional problems should be reserved for tests and perhaps as a motivational device.

CONCLUSIONS In summary we may conclude: (1) Both experimental evidenceand theoreti- cal analysis suggestthat conventional problem solving through means-ends analysis may impose a heavy cognitive load; (2) The mechanisms required for problem solving and schema acquisition may be substantially distinct; (3) As a consequence,the cognitive effort required by conventional problem solving may not assist in schemaacquisition; (4) Since schemaacquisition is possibly the most important component of problem solving expertise, the development of expertise may be retarded by a heavy emphasison problem solving; (5) Current theories and practice frequently assumeproblem solving is an effective meansof learning and consequentlymay require modification.

H Original SubmissionDate: ???.

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Cognitive Load During Problem Solving: Effects on Leaming

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Cognitive Load Theory – The Definitive Guide

Understanding Cognitive Load theory is essential if teachers are going to help students learn topics and concepts efficiently.

What is Cognitive Load Theory? Cognitive Load Theory explains that working (or short-term) memory has a limited capacity and that overloading it reduces the effectiveness of teaching. There are 3 types of cognitive load; Intrinsic (how complex the task is), Extraneous (distractions that increase load, and Germane (linking new information with the already stored in the long term memory).

If only we knew how students mentally process new information?

Oh, wait…We do!

Why it isn’t the first thing taught to new teachers bewilders me!

Wanna know all about it?

I thought so, let’s dive in.

What is Cognitive Load Theory?

Cognitive load theory builds on the premise that working (or short-term) memory has a limited capacity and that overloading it reduces the effectiveness of teaching. Much in the same way that having too many windows open on your computer, reduces its capability to work properly.

Given that the goal of learning is to move new information from the working memory into the long term memory, Cognitive load theory suggests that instructional materials and environments should be designed to reduce this load, thus removing distractions enables a more efficient passage of the desired learning from working memory to the long term memory.

Cognitive Load Theory was initially developed by Psychologist, John Sweller in 1988 ( Cognitive Load During Problem Solving: Effects on Learning ), with further work done in 1998 ( Cognitive Architecture and Instructional Design ).

What is Working Memory?

The working memory is responsible for rapid perceptual and linguistic processing. Put simply, it works out what the new information is all about and whether to store it in long term memory or discard it.

What are Schemas?

When a student (or anyone for that matter) is subjected to new information, their brain gives it a classification and stores it in the long term memory, this classification is known as schemas.

Schemas are like folders in your memory where you store similar information, i.e. you may have a file for all things to do with clothes or things to do with pasta etc. You also have behavioral schemas. Those that store all things to do with driving a car, making a sandwich or ice skating.

The more you use these schemas (practice) the easier the retrieval of the knowledge. Schemas are a very big part of cognitive load theory.

What is Cognitive Load?

Cognitive load refers to the amount of information the working memory can hold at any one given time. Most people can handle a cognitive load of between 3 and 7 separate pieces of information.

Cognitive load theory differentiates the types of cognitive load into 3 types; Intrinsic, Extraneous and Germane.

What are the 3 Types of Cognitive Load?

The three types of cognitive load build upon each other, too much of each of the first two (Intrinsic and Extraneoous) may not leave enough working memory to deal with the third (Germane).

Intrinsic Cognitive Load

Intrinsic cognitive load refers to the innate difficulty of the task. For example, recalling that Clownfish live in anemones would be low intrinsic load, whereas, explaining why both species benefit from this would be a higher level of intrinsic load.

Teachers can match the intrinsic load of a topic to the experience of the learner but can’t do much to reduce the complexity of the topic.

We can, however, reduce extraneous load.

Extraneous Cognitive Load

Extraneous cognitive load is where we as teachers have the most control.

Extraneous cognitive load is concerned with the material and environment we subject the students to.

Poorly constructed materials and busy classroom environments can lead to the split-attention effect and add to extraneous cognitive load, it is our job to reduce this with the way we present our lessons.

Simply stated the split-attention effect is the distraction generated by using too many conflicting principles. It is detrimental to cognitive load.

Reducing the materials down to only contain the elements that are required is crucial.

Irrelevant images, distracting sounds or animations or even fonts that are difficult to read, a monotone voice and complicated vocabulary all add to the extraneous load.

If you don’t manage the first two correctly, the next one can’t happen…

…and that’s a BIG problem!

I bet you’re wondering how you can reduce extraneous load right?

Don’t worry we’ll get to that in a bit.

Germane Cognitive Load

Germane load is what we actually want to happen, it is the capacity of the working memory to link new ideas with information in the long term memory (It’s the moment we’ve all seen, the “a-ha” lightbulb when a student finally gets it!).

The more prior knowledge a student has, the more effective the germane loading stage. Germane load is where metacognitive strategies come into play, it is where students are aware of their thinking processes and able to adapt new information accordingly.

Teaching students the prerequisite skills prior to having them undertake a more complicated task will help them construct new schemas that strengthen their working memory.

This means that pre-training, or teaching people prerequisite skills before introducing a more complex topic, will help them establish schemas that extend their working memory; and this then means that they can understand and learn more difficult information.

If we overload a student’s working memory with intrinsic load (making the task too difficult to comprehend or carry out) or extraneous load (giving too many distracting stimuli), we don’t leave enough to achieve the goal, the successful germane load.

This results in frustration (in both the student and the teacher) and a reduction in engagement in future tasks. How many times have you heard “I just don’t get it, it won’t stay in my head”?

Maybe analyzing the intrinsic and extraneous load you are putting the students under needs a rethink.

What are the 5 Principles of Reducing Cognitive Load?

I told you earlier when talking about extraneous load that I’d show you the best ways of reducing it. Well, as promised, here we go. (I’d never let you down!)

In his 2002 paper, Richard E. Mayer described five principles that teachers can use to help reduce cognitive load and thus, increase retention and progress by our students.

As an exercise, take a look through a few of your lessons and ask yourself, “Do my lesson designs to follow these principles?”.

The Coherence Principle

Quite simply, the coherence principle involves reducing the amount of information on each slide/page/worksheet to only that that is necessary.

Images, sounds and words that are not essential, add to cognitive load.

Giving the student’s working memory fewer stimuli to focus on enables more processing power to be used by the germane load (remember this is our goal).

The Signalling Principle

The signalling principle tells us to help our students focus on the information we are talking about by highlighting the important details.

We can do this via arrows or rings around the information. This reduces cognitive load by taking the work of scanning this visual away from the working memory.

This results in more juice for the germane load!

The Redundancy Principle

Students learn best from images and narration, rather than text and narration. Images (visual) and narration (audio) do not compete with each other, therefore they use less cognitive load.

This is known as the “Modality Effect”.

Basically, don’t put lots of text on your resources and definitely don’t just read out the text word for word (you might as well tell your students to go to sleep, they’re going to be doing that anyway!).

In John Sweller’s original paper “ Cognitive Load Theory ” he concludes that, “Working memory capacity can be effectively increased, and learning improved, by using a dual-mode presentation.” (Cognitive Load Theory, 2011, Sweller, Ayres & Kalyuga).

Dual coding theory suggests that images, a small amount of text and narration (visual and verbal stimuli) are the most efficient way of reducing extraneous load. Just look at the two examples below that I have taken from Oliver Caviglioli’s brilliant book “ Dual Coding with Teachers “

Spatial Contiguity

Placing labels next to the thing they are describing, so students don’t have to waste cognitive load juice working anything out.

It’s all about making the working memory’s job easier in terms of intrinsic and extraneous load so students have more use of germane load, the ability to make those connections with previously learned information.

Temporal Contiguity

Last but not least is temporal contiguity. This one is achieved simply by presenting the visual images and their labels at the same time. By doing this, the working memory knows they should be treated as an individual unit rather than separate entities.

Now you see why I’m convinced Cognitive Load Theory should be taught to all trainee teachers. It literally teaches us how to teach!

Along with Rosenshine’s Principles of Instruction , Metacognition and Dual Coding Theory , Cognitive Load Theory, in my opinion, should be the basis of all teacher training.

What do you think? Comment below with your thoughts.

But first, there’s a bonus poster at the bottom of this post from Oliver Caviglioli .

Cognitive Load Theory FAQ

Cognitive Load Theory was initially developed by Psychologist, John Sweller in 1988 (Cognitive Load During Problem Solving: Effects on Learning), with further work done in 1998 (Cognitive Architecture and Instructional Design)

Intrinsic: The complexity of the task at hand. Extraneous: This is concerned with the material and environment we subject the students to. Excessive distractions lead to an increase in extraneous load. Germane: The capacity of the working memory to link new ideas with information in the long term memory (It’s the moment we’ve all seen, the “ a-ha ” lightbulb when a student finally gets it!).

1. The Coherence Principle. 2. The Signalling Principle. 3. The Redundancy Principle. 4. Spatial Contiguity. 5. Temporal Contiguity. For an explanation of each of these, read “ The 5 Principles of Reducing Cognitive Load “

Cognitive Analysis of Medical Decision-Making: An Extended MULTIMOORA-Based Multigranulation Probabilistic Model with Evidential Reasoning

Published: 20 August 2024

Cite this article

cognitive load during problem solving effects on learning sweller

Wenhui Bai 1 ,
Chao Zhang ORCID: orcid.org/0000-0001-6248-9962 1 , 2 ,
Yanhui Zhai 1 , 2 ,
Arun Kumar Sangaiah 3 , 4 , 5 ,
Baoli Wang 6 &
Wentao Li 1 , 7

Cognitive computation has leveraged the capabilities of computer algorithms, rendering it an exceptionally efficient approach for addressing multi-attribute group decision-making (MAGDM) problems. Due to the stability of MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) and the capability of evidential reasoning (ER) to combine information from multiple sources, the technique of multigranulation probabilistic rough sets (MG PRSs) holds great promise for solving MAGDM problems. Thus, a new and stable method for MAGDM is proposed. Initially, three forms of multigranulation Pythagorean fuzzy probabilistic rough sets (MG PF PRSs) are constructed using MULTIMOORA approaches. Next, the hierarchical clustering method is employed to cluster similar decision information and consolidate the decision-makers’ preferences. Representatives are chosen from each category to simplify information fusion calculations and reduce complexity by reducing the model’s dimensionality. Following that, the rankings obtained from the three methods are fused using ER. Ultimately, the validity of our method is revealed via a case analysis on chickenpox cases from the UCI data set by employing cognitive analysis. The paper outlines a method for MAGDM that provides significant advantages. Specifically, the use of MULTIMOORA improves the stability of decision results, while the incorporation of ER reduces the overall uncertainty of entire decision processes.

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Data Availability

The data sets generated during and/or analyzed during the current study are available in the UCI repository .

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This paper was supported by the National Natural Science Foundation of China (62272284, 61972238, 12201518, 62072294, 61703363), the Special Fund for Science and Technology Innovation Teams of Shanxi (202204051001015), the China Postdoctoral Science Foundation (2023T160401), the Cultivate Scientific Research Excellence Programs of Higher Education Institutions in Shanxi (CSREP) (2019SK036), the Natural Science Foundation of Chongqing (CSTB2023NSCQ-MSX0152), the Science and Technology Research Program of Chongqing Education Commission (KJQN202100205, KJQN202100206), the Training Program for Young Scientific Resear-chers of Higher Education Institutions in Shanxi, and the Graduate Education Innovation Programs of Shanxi Province (2024KY034), and Wenying Young Scholars of Shanxi University.

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Bai, W., Zhang, C., Zhai, Y. et al. Cognitive Analysis of Medical Decision-Making: An Extended MULTIMOORA-Based Multigranulation Probabilistic Model with Evidential Reasoning. Cogn Comput (2024). https://doi.org/10.1007/s12559-024-10340-x

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DOI: 10.1037/0022-0663.91.2.334
Corpus ID: 54592195

A comparison of cognitive load associated with discovery learning and worked examples

J. Tuovinen , J. Sweller
Published 1 June 1999
Computer Science, Education
Journal of Educational Psychology

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Learner experience and efficiency of instructional guidance, when problem solving is superior to studying worked examples., the effects of early schema acquisition on mathematical problem solving, instructional heuristics for the use of worked examples to manage instructional designers’ cognitive load while problem-solving, the expertise reversal effect, the influence of domain knowledge on strategy use during simulation-based inquiry learning, the inﬂuence of domain knowledge on strategy use during simulation-based inquiry learning, the influence of the order and congruency of correct and erroneous worked examples on learning and (meta-)cognitive load, empirical evidence on the relative efficiency of worked examples versus problem‐solving exercises in accounting principles instruction, 49 references, the use of worked examples as a substitute for problem solving in learning algebra, exploratory learning with a computer simulation for control theory: learning processes and instructional support, variability of worked examples and transfer of geometrical problem-solving skills: a cognitive-load approach, goal setting and procedure selection in acquiring computer skills: a comparison of tutorials, problem solving, and learner exploration, training strategies for attaining transfer of problem-solving skill in statistics: a cognitive-load approach., training by exploration: facilitating the transfer of procedural knowledge through analogical reasoning, cognitive architecture and instructional design, cognitive load during problem solving: effects on learning, using worked examples as an instructional support in the algebra classroom., strategy guidance and memory aiding in learning a problem-solving skill, related papers.

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The cognitive load theory

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Cognitive load during problem solving: Effects on learning☆
In order to solve COGNITIVE LOAD DURING PROBLEM SOLVING 279 C 49` 4 35' D A B Figure 3. Example Trigonometry Problem (If the goal of the problem is to find the length of CB, the solution is CA=sine 35/4.4; CB=CA/cosine 49.) this problem the sine ratio needs to be used followed by the cosine ratio.
Cognitive Load During Problem Solving: Effects on Learning
Cognitive Load During Problem Solving: Effects on Learning. John Sweller, Corresponding Author. John Sweller. University of New South Wales. School of Education, University of New South Wales, P.O. Box 1. ... It is suggested that a major reason for the ineffectiveness of problem solving as a learning device, is that the cognitive processes ...
Cognitive load during problem solving: Effects on learning.
Contends that domain-specific knowledge in the form of schemas is the primary factor distinguishing experts from novices in problem-solving (PS) skill. Evidence that conventional PS activity is not effective in schema acquisition is accumulating. It is suggested that a major reason for the ineffectiveness of PS as a learning device is that the cognitive processes required by the 2 activities ...
Cognitive Load During Problem Solving: Effects on Learning
Cognitive Load During Problem Solving: Effects on Learning. J. Sweller. Published in Cognitive Sciences 1 April 1988. Psychology. TLDR. It is suggested that a major reason for the ineffectiveness of problem solving as a learning device, is that the cognitive processes required by the two activities overlap insufficiently, and that conventional ...
Cognitive load during problem solving: Effects on learning☆
Evidence that conventional problem-solving activity is not effective in schema acquisition is also accumulating. It is suggested that a major reason for the ineffectiveness of problem solving as a learning device, is that the cognitive processes required by the two activities overlap insufficiently, and that conventional problem solving in the ...
Cognitive Load During Problem Solving: Effects on Learning
Cognitive Load During Problem Solving: Effects on Learning. John Sweller - 1988 - Cognitive Science 12 (2):257-285. Observation Can Be as Effective as Action in Problem Solving. Magda Osman - 2008 - Cognitive Science 32 (1):162-183. Problem Solving in a Foreign Language: A Study in Content and Language Integrated Learning.
Cognitive load during problem solving: Effects on learning
See Full PDFDownload PDF. COGNITIVE SCIENCE 12, 257-285 (1988) Cognitive Load During ProblemSolving: Effects on Learning JOHN SWELLER University of New South Wales Considerable evidence indicates that domain specific knowledge in the form of schemes is the primary factor distinguishing experts from novices in problemsolving skill.
Cognitive Load During Problem Solving: Effects on Learning
Considerable evidence indicates that domain specific knowledge in the form of schemas is the primary factor distinguishing experts from novices in problem-solving skill. Evidence that conventional pr...
Cognitive load during problem solving: Effects on learning
TL;DR: It is suggested that a major reason for the ineffectiveness of problem solving as a learning device, is that the cognitive processes required by the two activities overlap insufficiently, and that conventional problem solving in the form of means-ends analysis requires a relatively large amount of cognitive processing capacity which is consequently unavailable for schema acquisition.
John Sweller's Cognitive Load Theory
Principles of Sweller's cognitive load theory. The specific recommendations regarding the design of instructional material that John Sweller proposes in his cognitive load theory include: Change problem-solving methods by using problems without goals or solved examples. The goal is to avoid approaches that impose a heavy working memory load.
Cognitive Load Theory: New Conceptualizations, Specifications, and
During the past two decades, cognitive load theory (CLT: Paas et al.2003a, 2004; Sweller 1988; Sweller et al. 1998; Van Merriënboer and Sweller 2005) has become an influential theory in the fields of educational psychology and instructional design.Evidence for that influence comes from Ozcinar (), who, examining research publications and trends in instructional design during the period 1980 ...
Cognitive Load Theory (John Sweller)
Sweller's theories are best applied in the area of instructional design of cognitively complex or technically challenging material. His concentration is on the reasons that people have difficulty learning material of this nature. Cognitive load theory has many implications in the design of learning materials which must, if they are to be ...
Cognitive Load During Problem Solving: Effects on Learning
Figure 1. Flow of Control Under Means-Ends Production. (System halts either when the problem is solved or when no production can fire because no new subgoals can be generated - "Cognitive Load During Problem Solving: Effects on Learning"
Cognitive-Load Theory: Methods to Manage Working Memory Load in the
When learning a new task by problem solving, learners use most of their WM resources for applying the problem-solving strategy, which imposes a very high extraneous cognitive load and consequently leaves no resources for learning. In contrast, when learning through studying worked examples, all resources can be spent on learning.
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Cognitive load theory places a primary emphasis on the cognitive mechanisms involved in learning when designing instructional presentations, and suggests that information presented to learners and the activities required of them should be structured to eliminate any avoidable load on working memory. Expand. 2.
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Cognitive load theory (Sweller 1988, ... Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12, 257-285. ... G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2, 59-89. Article Google Scholar
Cognitive Load During Problem Solving: Effects on Learning
COGNITIVE SCIENCE 12, 257-285 (1988) Cognitive Load During Problem Solving: Effects on Learning JOHN SWELLER University of New South Wales
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John Sweller - 1988 - Cognitive Science 12 (2):257-285. Increasing information access cost to protect against interruption effects during problem solving. Phillip L. Morgan, John Patrick & Tanya Patrick - 2010 - In S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society.
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Cognitive Load Theory
Cognitive Load Theory was initially developed by Psychologist, John Sweller in 1988 (Cognitive Load During Problem Solving: Effects on Learning), with further work done in 1998 (Cognitive Architecture and Instructional Design). What is Working Memory? The working memory is responsible for rapid perceptual and linguistic processing.
Cognitive Analysis of Medical Decision-Making: An Extended ...
Cognitive computation has leveraged the capabilities of computer algorithms, rendering it an exceptionally efficient approach for addressing multi-attribute group decision-making (MAGDM) problems. Due to the stability of MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) and the capability of evidential reasoning (ER) to combine information from ...
[PDF] A comparison of cognitive load associated with discovery learning
The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra. J. Sweller Graham Cooper. Mathematics. ... Cognitive Load During Problem Solving: Effects on Learning. J. Sweller. Psychology. Cogn. Sci. 1988; TLDR. It is suggested that a major reason for the ineffectiveness of problem solving as a learning device, is that the ...

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