Technology-enhanced mathematics learning: a perspective from cognitive load theory

Cognitive load theory is an instructional theory used to guide the design of effective instruction. The cognitive architecture that underpins cognitive load theory can be described by five principles, essential components that form the basis of many well-tested and well-known cognitive load effects. One of these documented effects, the worked example effect, indicates that showing novices worked solutions rather than asking them to generate solutions could facilitate learning by reducing levels of cognitive load. This paper will demonstrate how the worked example effect can be used in designing interactive podcasts to improve mathematics skills

Cognitive load theory, spacing effect, and working memory resources depletion: implications for instructional design

In classroom, student learning is affected by multiple factors that influence information processing. Working memory with its limited capacity and duration plays a key role in learner ability to process information and, therefore, is critical for student performance. Cognitive load theory, based on human cognitive architecture, focuses on the instructional implications of relations between working memory and learner knowledge base in long-term memory. The ultimate goal of this theory is to generate effective instructional methods that allow managing students' working memory load to optimize their learning, indicating the relations between the form of instructional design and the function of instructional design. This chapter considers recent additions to the theory based on working memory resources depletion that occurs after exerting significant cognitive effort and reverses after a rest period. The discussed implications for instructional design include optimal sequencing of learning and assessment tasks using spaced and massed practice tasks, immediate and delayed tests

Mathematics problem solving skill acquisition: Learning by problem posing or by problem solving

Problem posing is an instructional method where students are asked to create problems based on the given information, then solve them. While in an instructional method of problem solving, students learn by solving given problems. The aim of this study was to test: (1) the differences of efficacy between learning by problem posing and the problem solving method of individual and small group instruction strategies; (2) the interaction effect of learning methods and grouping strategies.With regard to the independent variables, problem solving skill or cognitive load, a quasi experiment with post-test-onlynon-equivalent control group design was used. Year 7 contextual mathematics problems were tested in this experiment, and one hundreds students, who had sufficient prior knowledge, participated. A 2 by 2 anova was employed for data analysis. The results showed that: (1) problem posing method was significantly more effective than problem-solving method; (2) there was no significant difference in efficacy between individualized instruction and small group instruction strategies; (3) the interaction between learning methods and grouping strategies, where it is more likely that learning problem posing was better than problem solving for individual instruction

Effects of worked examples on step performance in solving complex problems

The instructional effect of worked examples has been investigated in many research studies. However, most of them evaluated the overall performance of the participants in solving post-intervention problems, rather than individual step performance in multi-step problems. The two experiments reported in this article investigated the relations between using worked examples and individual step performance in solving isomorphic problems. In Experiment 1, the effect of worked examples was found for overall performance for novice learners, whereas this effect was gradually reduced from Step 1 (the most difficult one) at which the effect was the strongest, to Step 3 (the easiest one) at which the effect was the weakest or even disappeared. In Experiment 2, relatively more knowledgeable participants learned the same sets of materials, and no effect of worked examples was found for either overall performance or individual step performance. Learner levels of expertise and levels of element interactivity were used to explain the results

The worked example effect, the generation effect, and element interactivity

The worked example effect indicates that examples providing full guidance on how to solve a problem result in better test performance than a problem-solving condition with no guidance. The generation effect occurs when learners generating responses demonstrate better test performance than learners in a presentation condition that provides an answer. This contradiction may be resolved by the suggestion that the worked example effect occurs for complex, high-element interactivity materials that impose a heavy working memory load whereas the generation effect is applicable for low-element interactivity materials. Two experiments tested this hypothesis in the area of geometry instruction using students with different levels of prior knowledge in geometry. The results of Experiment 1 indicated a worked example effect obtained for materials high in element interactivity and a generation effect for materials low in element interactivity. As levels of expertise increased in Experiment 2, thus reducing effective complexity, this interaction was replaced by a generation effect for all materials. These results suggest that when students need to learn low-element interactivity material, learning will be enhanced if they generate rather than study responses but if students need to learn high-element interactivity material, study may be preferable to generating responses

When instructional guidance is needed

© Australian Psychological Society Ltd 2016. Studying worked examples providing problem solutions to learners usually leads to better test performance than solving the equivalent problems without guidance, demonstrating the worked-example effect. The generation effect occurs when learners who generate answers without guidance learn better than those who read answers that provide guidance. The contradiction between these results can be hypothesised to be due to differences in the element interactivity of the learning tasks. Primary school students in Year 6 participated in the experiment, which investigated the hypothesis by using geometry materials. A disordinal interaction was obtained between levels of guidance and levels of element interactivity. Higher levels of guidance facilitated learning using high element interactivity information, while lower levels of guidance facilitated learning for low element interactivity information. Cognitive load theory was used to explain these contrasting results. From an educational perspective, it was suggested that when determining levels of guidance, a consideration of element interactivity is essential

Examining the influence of expertise on the effectiveness of diagramming and summarising when studying scientific materials

A 2 (learning strategies: diagram vs. summary) × 2 (levels of expertise: low vs. high) experiment was conducted to compare the effectiveness of using diagrams to writing summaries for students given biological information to learn and who possessed different levels of expertise in that topic area. A main effect of learning strategy used on number of idea units encoded (in diagrams or summaries) was found: drawing diagrams was superior to writing summaries. However, no interaction effect between learning strategies and expertise was found. An examination of students’ subjective ratings of cognitive load revealed that those with low expertise reported higher levels of cognitive load when constructing diagrams. These findings suggest that using diagrams is effective for identifying and encoding important information when learning, but that it would be helpful to provide guidance about diagram use particularly to students who are novices in the topic area to reduce cognitive load

The expertise reversal effect is a variant of the more general element interactivity effect

© 2016, Springer Science+Business Media New York. Within the framework of cognitive load theory, the element interactivity and the expertise reversal effects usually are not treated as closely related effects. We argue that the two effects may be intertwined with the expertise reversal effect constituting a particular example of the element interactivity effect. Specifically, the element interactivity effect relies on changes in element interactivity due to changes in the type of material being learned, while the expertise reversal effect also relies on changes in relative levels of element interactivity but in this case, due to changes in relative levels of expertise. If so, both effects rely on equivalent changes in element interactivity with the changes induced by different factors. Empirical evidence is used to support this contention

Relations between the worked example and generation effects on immediate and delayed tests

© 2016 Elsevier Ltd The contradiction between the worked example effect that occurs when learners presented with more instructional guidance learn more than learners presented with less guidance and the generation effect that occurs when the reverse result is obtained can be resolved by the suggestion that the worked example effect is obtained using materials high in element interactivity, whereas simpler, low element interactivity materials result in the generation effect. A 2 (guidance: low vs. high) × 2 (element interactivity: low vs. high) × 2 (expertise: low vs. high) experiment investigated this hypothesis with high school trigonometry learners. On an immediate test, high guidance reflecting a worked example effect was found for novices, but a generation effect was obtained for more knowledgeable learners. In contrast, on a delayed test, a three-way interaction between guidance, element interactivity and expertise was found. This interaction was caused by a worked example effect for material high in element interactivity and a generation effect for material low in element interactivity for novices while for more knowledgeable learners, a generation effect was obtained for both low and high element interactivity materials. These results suggest firstly, that both the worked example and generation effects may be more likely on delayed than immediate tests and secondly, that the worked example effect relies on high element interactivity material while the generation effect relies on low element interactivity material

Undesirable difficulty effects in the learning of high-element interactivity materials

© 2018 Chen, Castro-Alonso, Paas and Sweller. According to the concept of desirable difficulties, introducing difficulties in learning may sacrifice short-term performance in order to benefit long-term retention of learning. We describe three types of desirable difficulty effects: testing, generation, and varied conditions of practice. The empirical literature indicates that desirable difficulty effects are not always obtained and we suggest that cognitive load theory may be used to explain many of these contradictory results. Many failures to obtain desirable difficulty effects may occur under conditions where working memory is already stressed due to the use of high element interactivity information. Under such conditions, the introduction of additional difficulties may be undesirable rather than desirable. Empirical evidence from diverse experiments is used to support this hypothesis