Abstract
<p style="text-align:justify">Mathematics is well known as a subject area where there can be problems in terms of understanding as well as retaining positive attitudes. In a large study involving 813 school students (ages approximately 10-12) drawn from two different school systems in Pakistan, the effect of limited working memory capacity on performance in mathematics was explored along with a survey of areas of difficulty and student attitudes. This involved looking at student perceptions of their experiences, the nature of the difficulties they have with mathematics and possible reasons for these difficulties. The overall aim is to explore the extent of the effect of working memory and to gain insights so that practical ways forward to enhance mathematics education can be identified. It was found that limited working memory capacity has a very strong influence on performance, confirming other studies. Indeed, if the cognitive load exceeds the capacity of working memory, understanding becomes a casualty, with consequent attitude deterioration. Students need to be able to see that mathematics has a purpose in being able to be applied to real-life situations. However, attempts to develop applications may often generate further working memory overload. Curricula devised by those outside the classroom can sometimes be inappropriate while topics causing the greatest problems at these ages and include areas of geometry, statistics and the applications of mathematics.</p>
Highlights
Mathematics is well known as a subject area where there can be problems in terms of understanding as well as retaining positive attitudes
Students need to be able to see that mathematics has a purpose in being able to be applied to real-life situations
Mathematics curricula are rarely determined by practising teachers but are planned and designed by those who themselves are mathematicians and who are committed to mathematics
Summary
There are many studies which have identified areas of difficulty in the learning of mathematics at various levels (eg. Kouba et al, 1997; Lo & Watanabem, 1997; Lucangeli et al, 1998; Moss and Case, 1999; Tirosh, 2000; Watson and Moritz, 2000; Friel et al, 2001; Cramer et al, 2002; Kato et al, 2002; Harries & Suggate, 2006; Harries & Barmby, 2007). Mathematics curricula are rarely determined by practising teachers but are planned and designed by those who themselves are mathematicians and who are committed to mathematics Such curricula are designed around the logic of mathematics and the needs of those who will use or depend on mathematics later in life. Teachers do not decide national certification and yet teachers may be criticised if their students are not successful enough This can lead to a dependence on the memorisation of procedures, understanding being a casualty. Ausubel (1968) talks of meaningful learning where what is understood is 'internalised' This is critical but the limitations of working memory may make such understanding and internalisation very difficult. The key has to be in establishing confidence and competence in the processes and symbolisms at one point in time and, later, adding on the understanding In this way, the limitations imposed by working memory may be reduced. With the procedures more or less automated, enough working memory space is available to think about their meaning and application
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