Cognitive Load in Solving Mathematics Problems: Validating the Role of Motivation and the Interaction Among Prior Knowledge, Worked Examples, and Task Difficulty — TEI-tagged view

Gupta, Zheng · 2020 · psychology · doi:10.20897/ejsteme/9252 · full text at the source · TEI xml · tagged edition · index · concepts · authors
Where this record's text came from. faceted 2026-08 by reading the locally held text (pdftext); every evidence string verified as an exact substring of that text before merging. Replication status 'replicated' records the paper's own statement that its prior-knowledge findings confirm Kalyuga et al. and Pollock et al.; it is not an independent verdict on this study, which has not itself been replicated. What the facets cannot capture: the headline three-way interaction is small (ŋ2 = .04) and holds only for the posttest, not for any cognitive-load measure, and one half of the key prior-knowledge x worked-example contrast (higher-prior-knowledge learners doing better with completion examples) did not reach significance (p = .22) even though the abstract and conclusion state it without that qualification - the paper reports this openly in the results but does not list it under limitations, so it is not recorded there. The extraction joins some line-broken words ('threeway', 'lowprior'); quotes preserve them. 2026-08-14 and 2026-08-15 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node.
5 quotes on this page break a word across a line. The PDF this text was extracted from hyphenated those words at the end of a printed line — adversar- ial, repre- sentations — and the extractor kept the hyphen and the space. The quotes keep them because a quote is reproduced exactly or it proves nothing: the break is the typesetter’s, not the author’s. A search of this page will not find the affected words.
Other fields define these differently the same word, defined another way in another discipline
performance 5 fields · cognitive load 3 fields · standard deviation 3 fields · statistical-significance 2 fields
Tags on this paper every tag the record carries, whether or not the words occur in the text below — a number is how many papers in the corpus carry that tag; a tag with no number is unique to this paper
cognitive load7 intrinsic cognitive load3 extraneous cognitive load3 behavioural-experiment117

Our tag layer for this paper

Cross-disciplinary analysis
content-tags & facets: phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text
phenomenoncognitive load in mathematical problem solving— “Cognitive load can play a key role in learners’ abilities to solve complex problems like mathematics.”
claim-typemechanism— “It was found that higher-prior knowledge learners performed better with completion-worked examples than full-worked examples whereas lower-prior knowledge learners performed better with full-worked examples than completion-worked examples.”
method — evidence— “One hundred and sixty participants were recruited who were randomly assigned into one of eight learning conditions.”
mechanismWhen extraneous load is suppressed, working memory resources are freed and become available to the germane and intrinsic load involved in solving the problem— “In other words, with the influence of extraneous cognitive load abated, the cognitive resources in the working memory become available for the efforts to solve complex mathematics problems that were related to germane (efforts) and intrinsic (content complexity) cognitive load.”mechanisms[0]
mechanismHigh extraneous load consumes the limited working memory resources, leaving too few for germane load, which is why extraneous load lowers both germane load and the felt probability of success— “This is further supported by the findings of negative correlation between extraneous cognitive load and probability of success in the current study, suggesting with high extraneous cognitive load the learners would have few cognitive resources left in working memory, hence making little room for germane cognitive load in learning.”mechanisms[1]
replicates expertise reversal effect findings of Kalyuga (2007), Kalyuga et al. (1998) and Pollock et al. (2002)— “Further, the significant main effects for prior knowledge indicated that high- and low-prior knowledge learners differed significantly in intrinsic cognitive load and germane cognitive load when solving complex algebraic problems with different worked examples suggesting an expertise reversal effect, which confirmed the findings in previous…claim_relations[0]
builds-on Sweller, Van Merriënboer and Paas (1998) hypothesis of a negative relationship between extraneous and germane cognitive load— “A negative correlation between extraneous cognitive load and germane cognitive load (r = -.264, p < .01) was detected which confirms Sweller et al.’s (1998) hypothesis about the negative relationship between extraneous and germane cognitive load.”claim_relations[1]
sensecognitive load - AS MEASURED: three subscales of one ten-item self-report questionnaire, intrinsic on items 1-3, extraneous on 4-6, germane on 7-10— “The instrument measures three aspects of cognitive load: intrinsic (items 1-3), extraneous (items 4-6), and germane (items 7-10)”senses[0]
senseintrinsic cognitive load - defined by the difficulty of the material itself, which the paper says CANNOT be changed or altered— “Intrinsic cognitive load is defined by the difficulty of the instructional materials that cannot be changed or altered.”senses[1]
senseextraneous cognitive load - defined by the instructional design rather than by the material: load caused by improper design such as redundant information— “Extraneous cognitive load refers to the mental load caused by improper instructional design like imposing redundant information in learning materials that requires learners’ additional processing effort.”senses[2]
controla control condition whose learners studied the same problems WITHOUT worked examples, against a group shown half the examples first — held — rules out time on the problems, and exposure to the problem material, as the explanation of the difference - both groups meet the same problems, and only the worked examples differ— “The learners in control condition studied the problem without worked examples.”controls[0]
edgeintrinsic cognitive load —is-a→ cognitive load— “Three types of cognitive load exist in learning. They are: intrinsic, extraneous and germane cognitive load.”concept_edges[0]
edgeextraneous cognitive load —is-a→ cognitive load— “Three types of cognitive load exist in learning. They are: intrinsic, extraneous and germane cognitive load.”concept_edges[1]
outcome (stated by the tagger, no quotation)control — heldcontrols[0]
for which uselimitation — the cognitive-load analysis specifically: THE FAILURE TO OBTAIN A SIGNIFICANT THREE-WAY INTERACTION BY COGNITIVE LOAD INDICATES THAT MORE WORK IS NEEDED— “The failure to obtain a significant threeway interaction by cognitive load indicates that more work is needed to help learners understand the types of cognitive load when responding to the questionnaire.”limitations[0]
for which uselimitation — every null in the paper: ANOTHER LIMITATION IS THE POWER OF THE STUDY— “Another limitation is the power of the study.”limitations[1]
for which uselimitation — the prior-knowledge grouping: THE CURRENT STUDY USED THE TRI-SPLIT METHODS IN DEFINING HIGH- AND LOW PRIOR KNOWLEDGE LEARNERS WHICH COULD WEAKEN THE POWER - the middle third is discarded and the groups are constructed— “More participants may be needed, especially the current study used the tri-split methods in defining high- and lowprior knowledge learners which could weaken the power of the study.”limitations[2]
for which uselimitation — reading a cognitive-load score as a predictor of performance: the paper states high load does not necessarily produce low performance and low load does not guarantee good performance— “However, high cognitive load does not necessarily end up in low performance and low cognitive load does not mean learners will always perform well in learning.”limitations[3]
for which uselimitation — the cognitive-load values in this study: all three types are scored from one 10-item self-report questionnaire on a 0-10 Likert scale— “It is a 10-item self-report questionnaire with a Likert scale from 0 (Not at all the case) to 10 (Completely the case). The instrument measures three aspects of cognitive load”limitations[4]
for which uselimitation — these results as evidence about learning: the study explored immediate effects, with retention and transfer named as future work— “The current study explored the immediate effects of worked examples in relation to prior knowledge and task difficulty. Future research may examine the long-term effect by inviting participants back after a period of time to study learners’ knowledge retention and transfer.”limitations[5]
replicationreplicated
limitationNo significant three-way interaction was obtained for cognitive load, which the authors attribute to participants' unfamiliarity with the cognitive-load categories on the self-report questionnaire.— “The failure to obtain a significant threeway interaction by cognitive load indicates that more work is needed to help learners understand the types of cognitive load when responding to the questionnaire.”limitations[0]
limitationThe study is underpowered.— “Another limitation is the power of the study.”limitations[1]
limitationUsing the tri-split method to define high- and low-prior-knowledge groups discarded the middle third and may have weakened statistical power; a larger sample is needed.— “More participants may be needed, especially the current study used the tri-split methods in defining high- and lowprior knowledge learners which could weaken the power of the study.”limitations[2]
limitationThe construct does not order the outcome it is used to explain, and the paper says so in both directions.— “However, high cognitive load does not necessarily end up in low performance and low cognitive load does not mean learners will always perform well in learning.”limitations[3]
limitationThe whole construct is measured by asking learners, on a single ten-item self-report instrument.— “It is a 10-item self-report questionnaire with a Likert scale from 0 (Not at all the case) to 10 (Completely the case). The instrument measures three aspects of cognitive load”limitations[4]
limitationThe design compares immediate effects only, and the authors name retention and transfer as what was not examined.— “The current study explored the immediate effects of worked examples in relation to prior knowledge and task difficulty. Future research may examine the long-term effect by inviting participants back after a period of time to study learners’ knowledge retention and transfer.”limitations[5]
Content tags
content-observations: finding · quantity · variable · definition · key-term — grounded in the full text
findingA significant three-way interaction between prior knowledge, worked example and task difficulty was found on posttest performance, but none was found on any type of cognitive load.— “There was a significant three-way between-subjects effects by posttest (F1, 107 = 4.61, p < .05, ŋ2 = .04) (Figure 2), but no significant three-way interaction for types of cognitive load was detected.”content_tags.findings[0]
findingLow-prior-knowledge learners scored higher with full-worked examples while high-prior-knowledge learners scored higher with completion-worked examples, an expertise reversal pattern.— “It was found that lower-prior knowledge learners performed better with full-worked examples than completion-worked examples whereas higher-prior knowledge learners performed better with completion-worked…content_tags.findings[1]
findingGermane cognitive load was significantly positively correlated with learners' interest in the task.content_tags.findings[2]
findingExtraneous and germane cognitive load were negatively correlated, confirming the predicted trade-off between them.content_tags.findings[3]
findingTask difficulty produced significant differences in intrinsic and extraneous cognitive load but not in germane cognitive load.
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content_tags.findings[4]
findingHigh- and low-prior-knowledge learners differed significantly in intrinsic and germane cognitive load but not at all in extraneous cognitive load.
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content_tags.findings[5]
findingIntrinsic cognitive load correlated positively with anxiety and with perceived challenge, and negatively with perceived probability of success.
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content_tags.findings[6]
findingPrior knowledge and worked-example type interacted significantly on germane cognitive load.
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content_tags.findings[7]
quantityOne hundred and sixty — Number of participants recruited for the study
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content_tags.quantities[0]
quantityF1, 107 = 4.61, p < .05, ŋ2 = .04 — F-statistic, p-value and effect size for the three-way interaction on posttest performance
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content_tags.quantities[1]
quantityr = .264, p < .01 — Correlation between germane cognitive load and interest
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content_tags.quantities[2]
quantityr = -.264, p < .01 — Correlation between extraneous and germane cognitive load
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content_tags.quantities[3]
quantityn = 55, m = 10.564, SD = 1.808 — Size and pretest mean/SD of the high-prior-knowledge group after the split (low group was n = 60, m = 3.458)
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content_tags.quantities[4]
quantityt(1,26) = 1.98, p = .05, 2-tailed — Test statistic for low-prior-knowledge learners doing better on the posttest with full- than completion-worked examples
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content_tags.quantities[5]
quantityCronbach’s Alpha = .89 — Item reliability of the final algebra problem set in the pilot study
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content_tags.quantities[6]
quantity23.25 — Mean age of the participants, with a standard deviation of 6.01
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variableworked example (independent)
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content_tags.variables[0]
variabletask difficulty (easy vs. difficult) (independent)
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content_tags.variables[1]
variabledomain prior knowledge (high vs. low) (independent)
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content_tags.variables[2]
variablecognitive load (dependent)
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content_tags.variables[3]
variableperformance (dependent)
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definitionintrinsic cognitive load
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definitionextraneous cognitive load
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definitiongermane cognitive load
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definitionexpertise reversal effect
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definitiontask difficulty
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definitioncompletion-worked example
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definitiontri-split method
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definitionproduction/solution step method
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Concepts
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conceptcognitive load
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conceptintrinsic cognitive load
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concepts[1]
conceptextraneous cognitive load
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concepts[2]
Statistics — cross-field join keys
field-invariant statistical terms, used in their statistical sense (gated on a number / symbol / test). A p-value or a standard deviation means the SAME thing in physics, biology, psychology and sociology — so these are the strongest cross-field join keys. Grounded verbatim.
ANOVA F as written: 2 x 2 x 2 one-way ANOVA
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correlation r as written: correlation analyses
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t-test t as written: t(1,26) = 1.98, p = .05, 2-tailed
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Cronbach's alpha as written: interrater reliability of Cronbach’s Alpha
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Wilks' Lambda λ
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effect size ŋ2 as written: ŋ2
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statistical-significance α as written: family-wise alpha level of .05
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biserial correlation as written: biserial correlations
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standard deviation SD as written: one-standard deviation above the mean
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