Students' difficulties, conceptions and attitudes towards learning algebra : an intervention study to improve teaching and learning

The skills necessary to identify and analyse errors and misconceptions made by students are needed by teachers of all levels especially at the lower secondary school level in Malaysia. If students are to be successful in tackling mathematical problems later in their schooling, the one prerequisite is the mastery of basic concepts in algebra. Despite the best efforts of the teachers, students still develop algebra misconceptions. Is it possible to reduce or eliminate these misconceptions? The research involved a survey of 14 year-old students in Form 2 (Grade 8) in the Penampang district of Sabah, East Malaysia. The focus of this study lies in students’ difficulties, conceptions and attitudes towards learning algebra in the framework of conceptual change. A possible way to help students overcome their learning difficulties and misconceptions is by implementing diagnostic teaching involving conflict to foster conceptual change. The study involved evaluating the efficacy of a conceptual change instructional programme involving cognitive conflict in (1) facilitating Form 2 students’ understanding of algebra concepts, and (2) assessing changes in students’ attitudes towards learning mathematics, in a mixed quantitativequalitative research design.A 24-item Algebra Diagnostic Test and a 20-item Test of Mathematics-Related Attitudes (TOMRA) questionnaire were administered as a pretest and a posttest to 39 students in each of a heterogeneous high-achieving class and a below-average achieving class. In addition 9 students were purposefully selected to participate in the interview.The results of the study indicated that students’ difficulties and misconceptions from both classes fell into five broad areas: (1) basic understanding of letters and their place in mathematics, (2) manipulation of these letters or variables, (3) use of rules of manipulation to solve equations, (4) use of knowledge of algebraic structure and syntax to form equations, and (5) generalisation of rule for repetitive patterns or sequences of shapes.The results also showed that there was significant improvement in students’ achievement in mathematics. Further, students’ attitude towards inquiry of mathematics lessons showed significant positive improvement. Enjoyment remained high even though enjoyment of mathematics lesson showed no change. Also, changes in students’ understanding (from unintelligible to intelligible, intelligible to plausible, plausible to fruitful) illustrated the extent of changes in their conceptions.Different pedagogies can affect how conceptual change and challenge of misconceptions occurs. Therefore, knowledge of the origin of different types of misconceptions can be useful in selecting more effective pedagogical techniques for challenging particular misconceptions. Also, for teachers to create an effective learning experience they should be aware of and acknowledge students’ prior knowledge acquired from academic settings and from everyday previous personal experiences. Since all learning involves transfer from prior knowledge and previous experiences, an awareness and understanding of a student’s initial conceptual framework and/or topic can be used to formulate more effective teaching strategies. If this idea is taken a step further, it could be said that, because misconceptions comprise part of a conceptual framework, then understanding origins of misconceptions would further facilitate development of effective teaching strategies.Further research is needed to help teachers to understand how students experience conflict, how students feel when they experience conflict, and how these experiences are related to their final responses because cognitive conflict has both constructive and destructive potential. Thus, by being able to interpret, recognise and manage cognitive conflict, a teacher can then successfully interpret his/her students’ cognitive conflict and be able to make conceptual change more likely or help students to have meaningful learning experiences in secondary school algebra

Intimate strangers: perspectives on female converts to Islam in Britain

This article explores the relationships between female converts to Islam in Britain and their close friends and family. It pays attention to the perspectives of converts but focuses on the reactions of their intimates to the conversion. We argue that converts become ‘intimate strangers’ through conversion—estranged on the level of understanding and belief but intimate on the emotional plane. This strangeness is symbolised by the Orientalist stereotypes associated with the converts. At the same time, friends and family shun engagement with the conversion itself, thus keeping alive the stereotypes and precluding understanding. In refusing to engage with matters of belief even within the intimate space of the family, secularism’s orthodox private/public divide gets busted where religiosity, instead, becomes an issue between the (individual) private and the (family) public. Lacking reciprocity and with no access to the inner depths of the people they are closest to, the liberal rhetoric of friends and family about personal choice and equal acceptance of all paths amounts to bigotry and turns out to be painful for both the converts and their intimates.Arts and Humanities Research Council, Prince Alwaleed Bin Talal Centre of Islamic Studie

‘Being there’ the experience of shadowing a British Muslim Hospital chaplain

This article critically evaluates ‘shadowing’ as a qualitative research method. Sometimes described as the relatively straightforward opportunity to observe and record the actions and behaviours of a single individual during the course of their everyday working activities (McDonald, 2005), this article demonstrates that shadowing is often a highly disruptive and to some extent performative undertaking, both for the researched and for the researcher. Yet, it is precisely the disruptive potential of shadowing that makes it a valuable data collection method, offering the opportunity to gain significant insights that would be largely unobtainable via any other method. Following a brief discussion of shadowing as a research tool and an introduction to the ‘Muslim Chaplaincy Project’, the remainder of the article describes the experience of shadowing an individual Muslim hospital chaplain in detail. What becomes apparent is that shadowing has the potential to blur into other qualitative data collection methods (e.g. interviewing), especially when those we are shadowing have developed roles that engage them in various discursive communities, and a range of cooperative networks. Shadowing such individuals complicates our understanding of how this method operates in practice

Is the British weather anti-Islamic? Prayer times, the ulama and application of the shari’a

In the absence of clear-cut guidance from the primary sources of the shari‘a, how do Muslim scholars derive a workable religious praxis in changing circumstances and which authorities do they invoke in the process? This article explores possible answers to these questions by conducting a detailed analysis of a debate between two groups of Deobandi scholars in Britain over establishing the correct time for the commencement of morning (Fajr) and the onset of fasting for Ramadan. I argue that besides the primary sources, these Deobandi scholars invoke alternate forms of extra-scriptural authority such as the weight of precedence deriving from the akabir (elders) of the Deobandi tradition, as also their reliance on modern scientific knowledge. The article highlights the complex interplay of factors which determines the way that Muslims in Britain negotiate the practice of their religion in new socio-cultural milieu and the way they attempt to incorporate these changes within the parameters of an established religious discourse