Impact of reducing intrinsic cognitive load on learning in a mathematical domain

Impact of Reducing Intrinsic Cognitive Load on Learningin a Mathematical Domain

PAUL AYRES*

School of Education, University of New South Wales, Sydney, Australia

SUMMARY

This paper examines the effectiveness of instructional strategies that lower cognitive load by reducingtask complexity (intrinsic cognitive load). Three groups of 13-year-old students were required to learnamathematical task under different conditions. One group (Isolated) followed a strategy that used part-tasks where the constituent elements were isolated from each other (element isolation). A secondgroup (Integrated) received whole tasks where all elements were fully integrated, and a third group(Mixed) followed a mixed strategy progressing from part-tasks to whole-tasks. Results indicated thatthe part-task strategy was effective in lowering cognitive load for all students, but only benefittedlearning for students with low prior knowledge. In contrast, students with a higher prior knowledgelearned significantly more having studied whole tasks during instruction compared with part-tasks.The mixed-mode method proved to be ineffective for both levels of prior knowledge. These results arediscussed in terms of cognitive load theory. Copyright # 2006 John Wiley & Sons, Ltd.

How can we make complex tasks easier to learn? Recent advances in cognitive load theory

(CLT) may provide some clues. A key tenet of CLT is that overloading working memory

inhibits learning and therefore in order to facilitate learning, cognitive load (working

memory load) must be kept at a manageable level. The main aim of this study was to

investigate the impact of lowering cognitive load by directly reducing problem complexity

(intrinsic cognitive load).

CLT researchers have identified three sources of cognitive load that occur during

learning: Intrinsic, extraneous and germane. Intrinsic cognitive load is the load placed on

working memory by the intrinsic nature of the materials to be learned. Extraneous

cognitive load is created by the instructional mode and conditions, while germane

cognitive load is the load required for schema formation and automation (see Paas, Renkl,

& Sweller, 2003; Sweller, van Merrienboer, & Paas, 1998). Whereas germane cognitive

load has a positive influence as working memory resources are directly engaged in

learning, the other two forms of cognitive load can have a negative effect. If either intrinsic

and/ or extraneous load is high then working memory can become overloaded and

adversely affect learning.

APPLIED COGNITIVE PSYCHOLOGYAppl. Cognit. Psychol. 20: 287–298 (2006)

Published online in Wiley InterScience(www.interscience.wiley.com). DOI: 10.1002/acp.1245

*Correspondence to: P. Ayres, School of Education, University of New South Wales, Sydney NSW 2052,Australia. E-mail: [email protected].

Contract/grant sponsor: Faculty of Arts and Social Sciences at the University of New South Wales, SydneyAustralia.

Copyright # 2006 John Wiley & Sons, Ltd.

It is argued that the three sources of cognitive load are additive (see Sweller, in press) and

the total cognitive load is given by the sum of the three. If intrinsic load and/or extraneous

load is reduced then there is the potential to increase germane load without overloading

working memory. From this perspective, instructional designers have a potential incentive

to lower either or both of these two loads. Whereas strategies to lower extraneous load are

well documented (see Sweller, 1999; van Merrienboer & Ayres, 2005), methods to lower

intrinsic load have only more recently been investigated. The present study continues this

recent research trend by testing the effectiveness of a strategy (element isolation) to lower

intrinsic cognitive load and facilitate learning in a mathematical domain (algebra).

INTRINSIC COGNITIVE LOAD

This section examines intrinsic cognitive load in more detail and discusses some of the

strategies researchers have employed to reduce it.

Element interactivity

It is argued that element interactivity is the main generator of intrinsic cognitive load (Paas

et al., 2003; Sweller & Chandler, 1994). Element interactivity refers to the way the

individual elements of a task interact with other. Tasks low in element interactivity contain

elements that do not react with each other, can be learnt in isolation, and require relatively

low working memory load. In contrast, tasks high in element interactivity contain

interacting elements that cannot be learnt in isolation, and therefore require a higher

working memory load. Consequently a task is difficult to learn because of the number of

elements that have to be assimilated simultaneously rather than the number of elements the

task contains (Sweller, 1999; Sweller & Chandler, 1994). Element interactivity is innate to

a task, dependent only upon the number of interacting elements present, and cannot be

manipulated by instructional design without changing the nature of the task or

compromising understanding (see Chandler & Sweller, 1996; Paas et al., 2003; Pollock,

Chandler, & Sweller, 2002). However, as expertise develops in a domain, the intrinsic load

caused by a specific task decreases as the interactions become learned and incorporated

into schemas (Kalyuga, Ayres, Chandler, & Sweller, 2003; Renkl & Atkinson, 2003). By

possessing domain-specific schemas, the learner is able to treat interacting elements as

single elements (chunks), thus reducing intrinsic cognitive load.

Lowering intrinsic load through instructional design

Researchers have often used the principle of schema acquisition in their strategies to reduce

intrinsic cognitive load. One method is pre-training (see Mayer & Moreno, 2003), where

learners initially develop specific prior knowledge before the final materials are presented.

For example, Mayer, Mathias, and Wetzell (2002), using a multimedia environment, found

that learning was enhanced when learners received an initial pre-training phase on

individual components of a mechanical system, before learning about the full causal model

(all components together). Similarly, Clarke, Ayres, and Sweller (2005) found that

spreadsheet novices benefited from pre-training in spreadsheet skills before using them to

learn mathematical concepts. In contrast, learning was not as effective with an integrated

approach that required both mathematical concepts and spreadsheet skills to be learned

Copyright # 2006 John Wiley & Sons, Ltd. Appl. Cognit. Psychol. 20: 287–298 (2006)

288 P. Ayres

simultaneously. Simple-to-complex sequencing has also been recommended as an

effective strategy to reduce intrinsic cognitive load (see also van Merrienboer, Kester, &

Paas, 2006). In particular, the initial presentation of part-tasks helps consolidate procedures

or rules, which can be applied to whole tasks at a later stage (van Merrienboer, Clark, & de

Croock, 2002). Other similar techniques, such as focusing on subgoals (Catrambone, 1998)

or segmenting materials (Mayer & Chandler, 2001) before the full tasks are presented, have

also been found to be effective.

The strategies outlined above rely on a sequential approach to lower intrinsic cognitive

load. As Gerjets, Scheiter, and Catrambone (2004) observe, such approaches do not change

the intrinsic load of the tasks directly, but change the tasks themselves in the initial

instructional phase. Furthermore, vanMerrienboer, Kirschner, and Kester (2003) argue that

a part-task approach may not be that effective for complex learning environments that

require the integration of a number of skills, knowledge and attitudes. In such

circumstances, it is proposed that whole tasks should be presented initially, although in a

more simplified (reduced intrinsic load) format before progressing to full complexity.

Using whole tasks and directly reducing intrinsic load is a strategy also proposed by Gerjets

et al. (2004) who argue the case for a modular approach. In a modular approach solution

procedures are subdivided into smaller meaningful units.

A further study by Pollock, Chandler, and Sweller (2002) combined both a sequential

approach with a strategy to directly reduce intrinsic cognitive load. A notable feature of the

Pollock et al. design was to deliberately reduce element interactivity, rather than merely

create simpler part-tasks. Pollock et al. argued that novices, with little schema acquisition

in the domain, find learning new complex skills difficult because of high element

interactivity. As a solution to this problem Pollock et al. proposed a two stage learning

experience for novices. The first phase requires the tasks to be de-constructed in such a way

as to reduce the simultaneous processing of elements. During this phase learning is

conducted element-by-element, which reduces working memory load, and allows some

partial schemas to be acquired but with reduced understanding. In the second phase the

integrated tasks are introduced; and, with the aid of partial schemas, learners have an

increased working memory capacity to cope with the interacting elements. This strategy

was called the isolated-elements procedure and in two experiments (1 and 3), Pollock et al.

demonstrated that novices did indeed learn more (about electronics) using this technique

than learners who received an equivalent two-stage approach with materials consisting of

only fully integrated elements. Furthermore, it was also found (experiments 2 and 4) that

learners with more knowledge in the domain did not benefit from an isolated-elements

approach compared with a fully integrated approach because of prior knowledge.

AIMS OF THE STUDY

Amain of this study was to extend the research on the isolated- elements strategy and to test

its effectiveness in a mathematical domain. Although Pollock et al. (2002) found different

effects according to the knowledge base of the learners these differences were not directly

compared. Previous CLT research has identified the expertise reversal effect (see Kalyuga,

Ayres, Chandler, & Sweller, 2003, for a review) as a major phenomenon in instructional

design: Instructional strategies that are effective for novices may be ineffective for more-

expert learners. Consequently, the influence of expertise was an additional focus in this

study.


Impact of reducing intrinsic cognitive load 289

Algebraic tasks of the type 5(3x� 4)� 2(4x� 7), where students are required to

multiply out the brackets, were chosen as the mathematical learning domain for two

reasons. Firstly, the types of errors made and their causes have been mapped previously by

Ayres (2001, in press) and are not considered an easy task for many school-aged children.

In particular, students often make errors due to high working memory loads, rather than

through lack of knowledge. Secondly they are a very suitable medium to isolate elements

and reduce interactivity. To complete bracket expansion tasks (described in more detail

later in the paper) four successive calculations need to be made. However, when learners

are presented with the whole task, learners need to decide which terms and operators

(elements) need to be combined to identify the four calculations. Consequently, these tasks,

like many tasks in mathematics (Sweller & Chandler, 1994) are high in element

interactivity because of the total number of combinations (interactions) that need to be

considered simultaneously. However, if the learner is guided to focus on individual

calculations rather than the whole task, the number of combining elements is reduced

significantly. Thus an isolated-elements strategy was achieved in this study by requiring

students to learn and practice calculations individually, rather than as a sequence of

interacting calculations.

EXPERIMENT 1

In this experiment the effectiveness of the proposed isolated-elements strategy was

evaluated. Two sets of bracket tasks were devised. One set (Integrated) required all four

calculations to be completed per problem, whereas the second set (Isolated) required only a

single calculation to be made (isolated-elements). However, the second set was designed in

such a way that it was equivalent to the first set, requiring identical calculations to be made

overall. It was expected that the isolated set of problems would be easier to solve than the

integrated set because element interactivity was significantly reduced in the former. To test

this hypothesis, errors rates and self-rating measures of cognitive load were directly

compared on both sets of problems.

Method

Participants and design

Thirty-four eighth grade girls (mean age of 13.8 years) of average mathematical ability

from a Sydney Girls high school were assigned at random to either a group receiving the

isolated set of problems (the Isolated group, N¼ 17) or the integrated set (the Integrated

group, N¼ 17). All students had received some experience on the given tasks as part of

their normal school curriculum prior to completing this experiment.

Materials

A booklet was designed for each group (Isolated and Integrated), containing worked

examples, test problems and a subjective rating task of cognitive load. The booklets

consisted of A4 sheets of paper with sufficient space for students to write their answers. For

the test phase, a problem set of eight bracket problems, as described above, was created. In

the Integrated booklet, the eight problems were presented as whole tasks, with each

problem requiring four separate calculations to be made. In the Isolated Booklet, the same

eight problems were presented but repeated in groups of four, with each problem requiring


290 P. Ayres

exactly one calculation. The required calculation was indicated by an arrow, which was

drawn under the relevant within-bracket term (see Appendix A for examples). To ensure an

equivalence of materials, all problems in the Isolated set required single calculations,

which exactly matched the four calculations (including position) of an equivalent bracket

problem in the Integrated set. For example the first four test problems (see Appendix A) in

the Isolated booklet required the calculation of �3�2x, �3�� 4, 9�4, and 9�� 2x,

respectively which matched the four calculations needed to expand the first test problem in

the Integrated booklet. This design was repeated for all eight original bracket problems.

Consequently problems in the Integrated set required a total of 32 calculations presented as

eight whole tasks, whereas problems in the Isolated set required the same 32 calculations

but presented in 32 part-tasks.

In order to ensure that the participants understood what was required and to provide a

limited review on the topic, as well as model solutions, both booklets contained worked-

examples. The Integrated booklet contained two fully worked-examples (four calculations

each), whereas the Isolated booklet contained the same two problems but desegregated into

eight matched partially worked-examples (single calculations each) as previously

described. Consequently, both groups received an equivalent introduction involving a total

of eight calculations. These worked examples were presented on the first pages of the

answer booklets. Appendix B illustrates a worked-example for each group.

To ascertain the cognitive load demands of the test problems, a self-rating scale of

mental effort was used (see Paas & vanMerrienboer, 1994; Paas, Tuovinen, Tabbers, & van

Gerven, 2003), consisting of a nine-point scale: 1 (extremely easy), 2 (very easy), 3 (easy),

4 (quite easy), 5 (neither easy or difficult), 6 (quite difficult), 7 (difficult), 8 (very difficult),

and 9 (extremely difficult). Each of these choices was presented in the answer booklets

immediately following the last test task.

Procedure

All students were given one of the two booklets at random in their regular mathematics

class at school. They were told to study the worked examples given, complete the problem

sets and rate how easy or difficult they found the test problems. All students were given

sufficient time to finish all tasks. All answers were written in the booklets and calculators

were not used.

Results and discussion

The self-rating measure and the number of errors made by each student on the test

problems were recorded. The Isolated group had a mean error rate of 1.0 (SD¼ 1.7) and

mean cognitive load rating of 2.5 (SD¼ 1.3); whereas the Integrated group had a mean

error rate of 2.8 (SD¼ 2.9) and mean cognitive load rating of 3.6 (SD¼ 1.7). It was notable

that all students in the Isolated group completed individual calculations as indicated by the

arrows. No misinterpretations were evident, indicating that the arrow strategy was

effective. Two-tailed t-tests revealed significant differences for errors, t (32)¼ 2.16,

p< 0.05, Cohen’s d¼ 0.8, and cognitive load, t (32)¼ 2.11, p< 0.05, d¼ 0.7. Both these

results, with medium to large effect sizes, are consistent with each other–the group that

received the brackets in the form requiring single calculations, made fewer errors and rated

the task easier than students who received the brackets in the traditional format. These

results support the prediction that a single-calculation strategy (isolated-elements) reduces

element interactivity and consequently overall cognitive load in this domain. It should be



noted that a Cohen’s d effect size is used throughout this paper, where 0.2. 0.5 and 0.8

represent low, medium and large effects, respectively (see Cohen, 1988).

EXPERIMENT 2

The results of Experiment 1 indicated that an isolated-elements strategy reduces both the

error rate and cognitive load in this domain. In this experiment, the effectiveness of

isolated-elements as an instructional strategy was examined. Three strategies were directly

compared. The first strategy (Integrated) was based on whole problem instruction,

consistent with the traditional teaching approach in this domain. The second strategy

(Isolated) consisted of an instructional format based on individual calculations (isolated-

elements). The third strategy (Mixed), based on the principles of a sequential strategy (see

Mayer & Chandler, 2001; Mayer et al., 2002; Pollock et al., 2002), combined the previous

two strategies by switching from an isolated to an integrated mode. All three strategies

utilised worked examples (see Atkinson, Derry, Renkl, & Wortham, 2000, for a summary)

to keep additional extraneous cognitive load to a minimum. It was hypothesised that if

learners, particularly those with little expertise in the domain, were presented instructional

materials in an isolated-elements format, learning would be enhanced as a result of reduced

intrinsic cognitive load. However, it was also predicted that learners with expertise in the

domain would be able to learn without a reduction in intrinsic load. To test these

predictions, a measure of the learner’s mathematical ability was collected.

Method

Participants and design

The participants were 78 eighth grade girls (mean age of 13.1 years) from a Sydney Girls

high school. School-based assessments in the form of end-of-year examinations of general

mathematical ability including algebra were used to rank the students as either at or above

the median level, or below the median for this school grade. Two groups of differing

mathematical ability were therefore identified and classified as above average (N¼ 41) or

below average (N¼ 37). It should be noted that the ‘above’ and ‘below’ ability labels used

throughout this paper represent only relative differences of the cohort. These students were

randomly assigned to either the Isolated (Above N¼ 14, Below N¼ 12), Mixed (Above

N¼ 13, Below N¼ 13) or Integrated (Above N¼ 14, Below N ¼11) groups.

Materials

Two booklets were designed for each group corresponding to an acquisition and learning

phase. The booklets consisted of A4 sheets of paper with sufficient space for students to

write their answers. For the acquisition phase, four pairs of bracket problems similar to

those used in Experiment 1 were created as a basis for all three instructional strategies. The

first problem in each pair was designed as a worked example to study while the second

problem had to be solved. For example, the worked solution to �3 (2x� 4)þ 9 (4� 2x)

would be given (see Appendix B) and then a problem with similar features, such as �5

(3x� 6)þ 7 (2� 8x), was presented as a problem to be solved. In the Integrated booklet all

problems were presented as whole tasks, requiring learners to study four worked-solutions

and solve four problems requiring a total of 16 calculations to be made. In contrast,

problems in the Isolated booklet were presented as part-tasks, desegregated from the full


292 P. Ayres

tasks, as previously described in Experiment 1, with arrows identifying specific

calculations. As a result of this design, 16 (part-task) problem pairs were presented in the

Isolated booklet, corresponding to the same four problem pairs in the Integrated booklet. In

the Mixed booklet, the acquisition phase consisted of the first eight problem pairs (part-

tasks) presented in the Isolated booklet, followed by the last two problem pairs (whole-

tasks) presented in the Integrated booklet. The same 16 calculations were required as in the

other two booklets. To assess cognitive load during instruction, the subjective instrument

used in Experiment 1 was again employed. This task was presented immediately following

the acquisition phase in each booklet.

For the test phase, an identical test booklet was constructed for all three groups. These

booklets contained eight problems consisting of bracket expansion tasks similar to those

studied in the acquisition phase. All problems were presented in a fully integrated (whole-

task) format requiring the four calculations to be made. To ensure that the task was

understood, a worked practice example was positioned on the first page before the problem

set was commenced. This was particularly important for the Isolated group who had not

experienced such a task in their acquisition period.

Procedure

The acquisition and test phases were administered on consecutive days during the students’

normal mathematics classes at school. Calculators were not used and sufficient time was

given for all students to complete both phases. No feedback was given and students did not

have access to their acquisition booklets while completing the test phase.

Results

In both phases the errors made by each student were recorded. For each of the six groups,

means and standard deviations of errors made and cognitive load scores are reported in

Table 1. For the test phase 3 students were absent from school and did not participate,

adjusting numbers in each group to: Isolated (Above N¼ 14, Below N¼ 13), Mixed

(Above N¼ 12, Below N¼ 12) or Integrated (Above N¼ 13, Below N¼ 11).

Acquisition phase

A 3� 2 ANOVAwas conducted on the cognitive load measures and the errors made during

the acquisition period. For the self-rating measures there was a significant main effect for

Table 1. Mean (standard deviations) cognitive load measures and error scores for acquisition and testphases in Experiment 2

AbilityInstructional

methodCognitive

load measuresAcquisitionphase errors

Test phaseerrors

Above Average Isolated 2.29 (1.14) 0.86 (1.17) 4.57 (3.34)Mixed 3.46 (1.05) 1.31 (1.11) 3.42 (4.38)

Integrated 3.64 (1.45) 1.71 (1.59) 1.14 (1.70)Combined groups 3.54 (1.27) 1.29 (1.33) 3.03 (3.50)

Below average Isolated 3.54 (1.27) 1.17 (1.40) 3.22 (3.15)Mixed 3.71 (1.51) 2.75 (1.96) 5.25 (3.31)

Integrated 4.55 (1.04) 2.45 (1.57) 5.09 (3.53)Combined groups 3.91 (1.33) 2.11 (1.76) 4.58 (3.32)



instruction strategy, F(2, 70)¼ 5.59, MSE¼ 8.87, p< 0.01, d¼ 0.8. A post hoc Fisher’s

LSD test (used throughout the paper at the 0.05 level) revealed that students rated the

Isolated strategy significantly less demanding than either the Integrated or Mixed strategy.

There was also a significant main effect of ability, F(1, 70)¼ 7.64,MSE¼ 12.12, p< 0.01,

d¼ 0.6. Students with above average mathematical ability found the tasks required less

mental effort than below average students. There was no interaction between the two, F(2,

70)¼ 1.05, MSE¼ 1.66, p¼ 0.36. For the number of errors made there was a significant

main effect for instructional strategy, F(2, 70)¼ 4.22, MSE¼ 9.29, p< 0.05, d¼ 0.7. The

post hoc test revealed that students made significantly fewer errors using an Isolated

strategy compared with both the Integrated and Mixed strategies. There was a significant

main effect of ability, F(1, 70)¼ 5.91, MSE¼ 13.01, p< 0.05, d¼ 0.5, with higher ability

students making fewer errors. There was no significant interaction, F(2, 70)¼ 0.94,

MSE¼ 2.07, p¼ 0.40. Overall the results, with medium to large effect sizes, from the error

analysis matched the cognitive load ratings. Error rates and cognitive load levels were

lowest for the Isolated group.

Because it was predicted that the knowledge base of the learner would impact on the

effectiveness of the instructional mode, planned contrasts for both low and high ability

students were conducted on instructional strategy throughout this experiment. For students

with the lower ability there was no significant result for cognitive load, but a close to

significant result for acquisition errors, F(2,32)¼ 3.05,MSE¼ 8.45, p¼ 0.06, d¼ 0.8. The

post hoc test revealed that the Isolated group made significantly less errors than the Mixed

group. For the higher ability groups there was no significant difference for acquisition

errors, but a significant effect for cognitive load measures, F(2, 38)¼ 5.00, MSE¼ 7.54,

p¼ 0.01, d¼ 1.0. Post hoc comparisons revealed that the Isolated strategy was rated

significantly easier than both the Integrated and Mixed strategies.

Test phase

A 3� 2 ANOVA was conducted on the errors made during the test phase. A significant

result was found for ability, F(1, 66)¼ 3.53, MSE¼ 38.4, p¼ 0.06, d¼ 0.5, but no

significant main effect was found for instructional strategy F(2, 66)¼ 0.86, MSE¼ 9.24,

p¼ 0.43. However a significant strategy-ability interaction was found, F(2, 66)¼ 3.76,

MSE¼ 40.97, p< 0.05, d¼ 0.7 (see Figure 1). A simple main effects test revealed a

significant difference between the three strategies, F(2, 37)¼ 3.99,MSE¼ 42.46, p< 0.05,

d¼ 1.0, for the higher ability group, with the Integrated strategy superior to the Isolated

strategy under the post hoc test. No significant simple main effects were found for the lower

ability students.

GENERAL DISCUSSION

The interaction found on the test results in Experiment 2 is consistent with an expertise

reversal effect (Kalyuga et al., 2003). The effectiveness of the instructional strategy was

dependent upon the mathematical knowledge base of the learner. Clearly the higher ability

group performed better with a fully integrated strategy compared with an isolated-elements

approach. Although no significant differences for the lower ability group during the test

phase were found, the lowest error rates for both the test and acquisition phases, as well as

the lowest cognitive load rating were obtained by an isolated strategy. All of which support

the prediction that the isolated mode is more beneficial for the lower ability students.


294 P. Ayres

Of great theoretical interest were the overall results for the higher ability students.

Although tests results showed that the integrated-elements strategy was superior, during

acquisition the isolated strategy was rated the least cognitively demanding mode and the

least number of errors were made (see Table 1). This raises an interesting question—why

did a strategy that reduced cognitive load significantly and lowered error rates

appreciatively not transfer as well to learning? The answer may well lie with germane

cognitive load. The results suggest that germane cognitive load was also low for these

students in the isolated group otherwise more learning would have been expected. It is

therefore feasible that this particularly learning strategy failed to engage these students

sufficiently in the learning process—it was perhaps too simple. In such situations learners

may need to be engaged more directly in cognitive processing linked to schema

acquisition. In contrast for lower ability students, the reduction in intrinsic cognitive load

may have made it easier to understand the mathematical processes and invest more mental

effort in learning (germane cognitive load).

Previous explanations of the expertise reversal effect have pinpointed redundancy as the

main cause (see Kalyuga et al., 2003). However in this study, even though the isolated-

elements mode may have been redundant for the high knowledge students, any such

redundancy did not increase cognitive load. A lack of germane cognitive load is therefore a

more likely cause of the expertise reversal effect in this case, an explanation previously

promoted by Renkl and Atkinson (2003). Consequently an important conclusion follows

from this analysis—reducing cognitive load will not automatically facilitate learning if

germane load is also lowered.

Limitations and future directions

This study was limited to some degree by the small number of participants, the restricted

mathematical domain and some design features. Firstly the number of students in each

Figure 1. Strategy-ability interaction for errors made during the test phase of Experiment 2



treatment cell was quite small and consequently the study may have lacked power.

Nevertheless, all effect sizes for the main results connected to the effectiveness of

instructional strategies and the levels of cognitive load were generally quite large

(minimum d value of 0.7) and may compensate for the small n. Secondly, only 13 year-old

girls were included in the study. Although previous research in the domain by Ayres (2001)

found no gender differences, future research should include both, as well as larger cell sizes

and different age groups. One reason the domain was chosen was that the elements of

the tasks were easily isolated due to the sequential nature of the problems. However, these

tasks are somewhat limited mathematically. Consequently, in order to generalize the

findings further other mathematical domains need to be considered. Fourthly, no

instructional times were collected in the study as sufficient timewas allowed for students to

finish all tasks. Such a measure may have provided further insights into the instructional

modes in terms of efficiencies. Again future research might include this measure.

Lastly, it was surprising, considering the research support for a two-phase model (see

Mayer et al., 2002; Pollock et al., 2002; van Merrienboer et al., 2003) the mixed strategy

did not appear to be effective for either of the ability groupings. Whereas the higher ability

students could learn from the integrated mode alone and did not need a mixed strategy, the

lower ability students also did not benefit from a sequenced approach. It is not possible to

explain this latter result from the data collected, but it’s feasible that the lower ability

students may have needed a greater exposure to the isolated mode before switching. Future

research could investigate the conditions under which a two-phase model could be

effective.

ACKNOWLEDGEMENTS

This research was supported by a grant from the Faculty of Arts and Social Sciences at the

University of New South Wales, Sydney Australia. I also thank the reviewers.

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APPENDIX A

APPENDIX B

Examples of test problems per group given in Experiment 1

Test problem for the integrated group Test problems for the isolated group

For each problem expand the bracketsQ.1 �3 (2x� 4)þ 9 (4� 2x)

¼

For each problem expand onlythe calculations indicated by the arrows

Q1. �3 (2x� 4)þ 9 (4� 2x)#

¼Q2. �3 (2x� 4)þ 9 (4� 2x)

#¼

Q3. �3 (2x� 4)þ 9 (4� 2x)#

¼Q4. �3 (2x� 4)þ 9 (4� 2x)

#¼

Examples of worked examples provided in Experiment 1

Worked-example for the integrated group Worked-example for the isolated group

�3 (5x� 2)þ 9 (7� 2x) �3 (5x� 2)þ 9 (7� 2x)¼�3� 5x� 3� �2þ 9 � 7þ 9 � �2x #¼�15xþ 6þ 63� 18x. # ¼�3 � 5x

¼�15x

#Note: students were required to stop at this stage, and not group the terms together further, thus emphasizing theconcept of bracket expansion only.


298 P. Ayres

Impact of reducing intrinsic cognitive load on learning in a mathematical domain

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