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Abstract
Teaching mathematical concepts is often accompanied by the use of worked examples, and the use of manipulative materials. Worked examples have been shown to be an effective method of instruction with novice learners, as shown by higher test performance and shorter acquisition times. Often worked examples are accompanied by illustrations of manipulative materials, and the physical use of such materials. One such example is the use of Multi-base Arithmetic Blocks (MAB) to teach place value. Whilst the use of worked examples alongside illustrations of MAB in instructional material is common, their efficacy has not been investigated in young students. Using the concepts of cognitive load theory, which investigates how the learner’s limited working memory and vast long-term memory can be used to efficiently design educational material, this research examines the effects of using worked examples alongside MAB to teach place value to young students. Experiment 1 examined whether it was possible to facilitate a more efficient transition from the manipulative material to the abstract concept of place value. Using the abacus and MAB, and two methods of instruction, the results of Experiment 1 showed no significant differences in student performance between the methods of instruction, or the manipulative materials. Using worked examples in Experiment 2, no significant differences in the performance of students using either the abacus or MAB, were found. Experiment 3 reduced the level of the reading comprehension in the instructional material. The control group, with no access to MAB, performed better in the post-test than the group using MAB. Experiment 4 examined whether the use of MAB produced a redundancy effect, by providing identical information in three different formats. No significant differences were found due to the complexity of the instructional material. In Experiment 5, the expertise of students with respect to the experimental materials was decreased. The non-MAB group performed better in the post-test and the delayed test, than the group using MAB. Thus, despite the widespread use of MAB in primary school to teach place value, this research suggests that the blocks may produce a redundancy effect, leading to an increased extraneous load, and negatively affecting learning.