Ali, Asma Amanat
Perceptions, difficulties and working memory capacity related to mathematics performance.
MSc(R) thesis, University of Glasgow.
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There is a general view that students of not have a positive attitude towards mathematics. In general, mathematics is considered a ‘difficult’ subject and sometimes there is a lack of enjoyment. Mathematics is often portrayed as being abstract and unrelated to life.
In the light of the key role mathematics has in the curriculum, the aim of this study is to explore the difficulties and self-perceptions of students aged about 10-12 in Pakistan as they undertake their studies in mathematics. The study uses a survey of student perceptions, working with samples of students drawn from both Urdu and English medium schools (N = 813). In addition, working memory capacity of those in grade 5 (age about 10) was measured and information was gained about their performance in mathematics examinations. The data is analysed to consider how their self-perceptions related to their experiences in learning mathematics which varies with age, language background and gender. Any relationships between these self perceptions, mathematics marks and measured working memory capacity are explored as well. The observed outcomes can be used to inform the agenda for action or further study.
It was found that the vast majority (English medium and Urdu medium) appreciate the role and the importance of studies in mathematics although topics like geometry, fractions, topics with life applications, statistics are causing problems. It is almost certain that these topics place demands on working memory which make understanding very difficult.
In the Urdu medium schools, the curriculum in grade 6 is clearly causing major problems while, in both systems, pressures for success based on examination performance have generated a complete industry of private tutors. Many of the gender differences can be interpreted in terms of the social roles in Pakistani society. However, girls do seem more positive and more committed in relation to their studies in mathematics.
The study has revealed two major issues which need careful consideration. One is the whole issue of memorisation and understanding. The goal of meaningful learning must be stressed more if positive attitudes are to be retained. The whole issue of making the mathematics studied become related in some way to the lifestyle of the learner seems very important but this is not easy without overloading working memory. In considering both of these issues, the critical role of assessment has to be addressed: if assessment offers rewards almost entirely for the recall and correct execution of mathematical procedures, then this will be reflected in textbooks and teaching approaches. Along with curriculum design and teaching approaches which are consistent with the known limitations of working memory, assessment is perhaps the single most important issue to be considered.
Very significant correlations were found for grade 5 students when their measured working memory capacity was related to their mathematics examination performance. Indeed, the correlation value for Urdu medium students is the highest such correlation which has been found in any discipline. This suggests major curriculum design problems in the national syllabus for Urdu medium schools as well as assessment problems.
The study has pinpointed many areas of success along with specific areas where there are serious problems. In this way, an agenda for future research and action has been described.
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