Design of learning objects for concept learning in algebra : effects of multimedia learning principles and an instructional approach

Abstract

A number of studies have shown that students do routine mathematical tasks that they have learned in school very well, but are not so good at solving problems they have never encountered. A conceptual model, a type of learning object that combines a representation of key and/or related concepts of a subject, is an appropriate learning tool to switch students from passive to active learners. However, the effectiveness of developing conceptual understanding in the learner depends on conceptual model design, and there are often gaps between tools designed by researchers and teachers. The literature suggests the use of multimedia learning principles in the design of instructional material. However, recommendations on the application of multimedia learning principles are scarce. Further, these principles may not be sufficient in designing conceptual models for concept learning in mathematics, especially when requiring high order thinking skills. The present study addresses this by extending upon existing theoretical work on two conceptual model design approaches of – those using multimedia learning design principles and instructional approaches. To validate the applicability of these two approaches, this study adopted an experimental design with semi-structured interviews that investigated the effects of an instructional approach, and included two teaching techniques – (a) variation theory, and (b) representations of subject matter – in the context of designing conceptual models for secondary school algebra concept learning. The experimental model was designed and developed in a redesign development cycle. The model was tested and trialed in the classroom with 68 students involved, then redesigned according to their responses and comments. After two models were developed for the experimental and control groups, two groups comprising a total of 70 secondary school senior form students participated in the experiment. The results of pre and post testing showed that the experimental group significantly outperformed the control group in algebra learning achievement as demonstrated in conceptual and procedural knowledge performance. The results also showed that only the experimental design with the addition of the instructional approach resulted in the students developing high order mathematical thinking skills of conceptual knowledge and improved procedural knowledge. Further analysis revealed that prior knowledge predicted the performance level in conceptual knowledge associated with low order thinking skills; the model design predicted the performance level in conceptual knowledge associated with high order thinking skills; and there was no interaction of prior knowledge and model design. Analysis of interview data revealed that if multimedia learning principles were applied, concept learning was simplified when the information was presented by the instructional approach. The results implicate that use of the instructional approach can reduce extraneous processing by requiring less recall process, and can foster generative processing by encouraging comparing learning contents and building relationships among audio and visual representations. Using the instructional approach and multimedia learning in the design of the conceptual model can reduce the risk of cognitive overload and engaging cognitive processing. Finally, limitations of this study and recommendations for future research were suggested.