Academic journal article Australian Mathematics Teacher

Managing Cognitive Load in the Mathematics Classroom

Academic journal article Australian Mathematics Teacher

Managing Cognitive Load in the Mathematics Classroom

Article excerpt

Context

Contemporary debates on effective pedagogies for K-12 mathematics have called for shifts in the way teachers and teacher educators conceptualise mathematics as a subject and how it should be taught. This is reflected by changes in the curriculum including the inclusion of a strand called Working Mathematically within K-12 mathematics curriculum documents not only in New South Wales but also across Australia (New South Wales Board of Studies, 2002). This strand brings focus to mental processes that underpin students' ability to acquire mathematical principles, concepts, and conventions, and the use of this knowledge in the solution of problems.

The focus on cognitive processes that support mathematical learning and problem solving is a welcome change. However, there is a paucity of information about the nature of links that need to be made between process and mathematics content, and how students might be assisted to construct the links.

In this paper, we outline results of research about cognitive load that is associated with mental processes, the management of this load so that students can be better supported in the construction of connected mathematical information, and the interpretation of that information in making sense of worked examples. We attempt to show that worked examples can be effective in promoting useful and powerful mathematics schemas.

Cognitive processes that underlie mathematics problem solving

An understanding of the cognitive processes that drive mathematics learning and knowledge organisation is critical for the design of effective approaches to mathematics teaching. Figure 1 shows a model of human memory structures and the processing of information. This model is based on components of working memory advanced by Baddeley and Hitch (2000). The model identifies two key attributes about how students deal with mathematical information.

Firstly, it shows connections between the processing of incoming mathematical information, reorganisation and the subsequent retrieval of that information for later use. Secondly, the model draws attention to the types of cognitive load that students could experience as they attempt to make sense of incoming mathematical information.

[FIGURE 1 OMITTED]

There are three types of memory: sensory memory, working memory (WM), and long term memory (LTM). In the following sections we look at both working and long term memory in some detail as these are more directly related to loads that can be exerted on the processing of incoming information.

Working memory (WM)

Working memory can be approximated to the idea of consciousness. If we are consciously aware of information then we are utilising working memory. A multitude of models of working memory has been proposed over the decades. Despite differences, all models tend to share two common basic characteristics about working memory: limitations in processing capacity and duration.

During a learning episode, new information from the environment is processed through WM. However, there are limitations to both the storage capacity of WM and the duration of time new information can be held and processed in WM. Although learners can process around seven separate items of information at any one time (Miller, 1956) this number significantly declines if items need to be compared or contrasted in some way (Kalyuga, 2006). For example, many young students starting at Stage 1 or 2 multiplication would have difficulty performing 87 x 28 as a mental operation as the task overloads the capacity of WM. This is so because the solution could involve two levels of processing. For example, students will usually have to compute 80 x 28 and 7 x 28 mentally, following which they have to add the resulting values. Both these computations, in turn, demand the use of further mental strategies.

Long-term memory (LTM)

In contrast to working memory, LTM is characterised by its limitless capacity for the storage of organised information. …

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