Using everyday experiences in teaching secondary mathematics in Malawi : possibilities and constraints for change

Proponents of socially and culturally oriented mathematics education have argued that teaching approaches which value and connect with the learner's prior knowledge and everyday experience are more likely to promote active, meaningful, relevant and liberatory learning than approaches which rely on transmission and abstract presentation of mathematical content. In Malawi, proposals to reform the outdated secondary mathematics curriculum have been made with the aim of aligning mathematics instruction with the social and political changes in the current Malawian society. Using a case study approach, this study investigated the extent to which everyday experiences could be used as a vehicle for changing the learning and teaching of secondary mathematics in Malawi. The study was collaborative, taking place over a period of five months in severely overcrowded and poorly resourced classes in two schools. It involved three mathematics teachers in a cycle of planning and teaching mathematics lessons based on the use of everyday experiences, and observation of and reflection on these lessons, in order to document the effects of using everyday experiences on student learning and teachers' teaching practices. The data was collected through student questionnaires; classroom observations and fieldnotes; interviews and reflective meetings with teachers; and informal meetings with key education officials in Malawi. Mathematics examination results from students involved in this study and a corresponding group from the previous year were collected. A reflective and critical approach was adopted in the interpretation and discussion of the data. Teachers' participation in this study resulted in heightened awareness of their teaching roles and the value of linking school mathematics with everyday experience. The study also shows that students found mathematics interesting and important to learn despite their lack of success in it. In addition, the study documented a number of constraints to change in mathematics instruction such as teachers' focus on mathematics content and examination requirements, and students' resistance to inquiry learning. It also recorded possibilities and barriers to collaboration both between teachers and researchers, and teachers themselves. The findings of this study are timely since they could serve to inform the reform of the Malawian secondary mathematics curriculum currently being undertaken, which began without a critical examination of the classroom conditions necessary to accommodate a socio-politically relevant mathematics education.

Windows on practice : investigating equity in technology based mathematics classrooms

The strengths and weaknesses of using ethnographic research to investigate equity in a study of a grade 9 class that used a dynamic geometry program with laptop computers will be presented. It will be argued that research approaches that involve “windows on practice” provide understanding of not only who is advantaged and disadvantaged in technology-mediated classrooms but how this occurs. The way that other paradigms such as reflexive methods may enhance qualitative research will be proposed. Studies that involve “windows on equitable practice” will provide mathematics educators with models for advancing equity in mathematics learning when teaching with technology.

Distinguishing between mathematics classrooms in Australia, China, Japan, Korea and the USA through the lens of the distribution of responsibility for knowledge generation : public oral interactivity and mathematical orality

The research reported in this paper examined spoken mathematics in particular well-taught classrooms in Australia, China (both Shanghai and Hong Kong), Japan, Korea and the USA from the perspective of the distribution of responsibility for knowledge generation in order to identify similarities and differences in classroom practice and the implicit pedagogical principles that underlie those practices. The methodology of the Learner’s Perspective Study (LPS) documented the voicing of mathematical ideas in public discussion and in teacher-student conversations and the relative priority accorded by different teachers to student oral contributions to classroom activity. Significant differences were identified among the classrooms studied, challenging simplistic characterisations of ‘the Asian classroom’ as enacting a single pedagogy, and suggesting that, irrespective of cultural similarities, local pedagogies reflect very different assumptions about learning and instruction. We have employed spoken mathematical terms as a form of surrogate variable, possibly indicative of the location of the agency for knowledge generation in the various classrooms studied (but also of interest in itself). The analysis distinguished one classroom from another on the basis of “public oral interactivity” (the number of utterances in whole class and teacher-student interactions in each lesson) and “mathematical orality” (the frequency of occurrence of key mathematical terms in each lesson). Classrooms characterized by high public oral interactivity were not necessarily sites of high mathematical orality. In particular, the results suggest that one characteristic that might be identified with a national norm of practice could be the level of mathematical orality: relatively high mathematical orality characterising the mathematics classes in Shanghai with some consistency, while lessons in Seoul and Hong Kong consistently involved much less frequent spoken mathematical terms. The relative contributions of teacher and students to this spoken mathematics provided an indication of how the responsibility for knowledge generation was shared between teacher and student in those classrooms. Specific analysis of the patterns of interaction by which key mathematical terms were introduced or solicited revealed significant differences. It is suggested that the empirical investigation of mathematical orality and its likely connection to the distribution of the responsibility for knowledge generation are central to the development of any theory of mathematics instruction.

The teaching contest as a professional development activity to promote classroom instruction excellence in China

Teaching contests might be alien to many readers outside of China mainland, but as one of professional development activities, it is well known by most of Chinese school teachers. This chapter, based on the data collected by mail surveys to the contest organizers, evaluation panel members, contest winners, and ordinary participating teachers, and detailed notes taken from various meetings of the evaluation committee, as well as a lesson video of one of the three contest winners, we aimed to the 2011 national high school teachers' teaching contests carefully, to examine the aims and processes of teaching contests, their possible merits or weaknesses for teachers’ professional development, and features of exemplary lessons demonstrated during the national teaching contest. It was found that the aim of the teaching contest was totally not the competition per se., to promote curriculum development and teachers' professional development, to provide a big platform for those teachers who pursue excellence in teaching to display, discuss, explore, and share with others about mathematics instruction were real intentions of the organizers.

Using spreadsheets in chemical education to avoid symbolic mathematics.

Traditionally, quantum theory has traditionally relied heavily on the use of  mathematics. However, there is a significant cohort of students who are  weak in mathematics, for example, students who are majoring in   biochemistry, biological sciences, etc. This paper reports on the use of  spreadsheets to generate approximate numerical solutions and visual  (graphical) descriptions as a method of avoiding or minimizing symbolic  manipulations, mathematical derivations and numerical computation. A  specific example from quantum theory is provided. Some aspects of  educational pedagogy of spreadsheet usage are discussed.

Trends and factors concerning gender and mathematics in Australasia

For many years now gender differences in average mathematics achievement in Australia and New Zealand have not been significant in large-scale domestic and international studies. However there is some recent evidence, from Australia at least, that gender differences in achievement favouring males may be re-emerging and, despite some positive affective findings and trends with respect to affect and participation leading up to the turn of the century, a pattern of lower interest and declining participation in mathematics among girls is evident. In this paper, trends in gender equity with respect to participation, achievement and affect reported in the literature over the past decade will be presented and analysed. Of particular interest are the factors that may have influenced these trends. Findings from recent research will be discussed. However it would seem that the attempts made by researchers to explain these trends are either limited in their capacity to establish an explanation or imply a deficit view of girls. An alternate position on gender equity and explanation of these trends will be presented in this paper with the purpose of making a contribution to the debate on curriculum and pedagogy in mathematics education.

Mathematics teacher education and technology

Various applications of electronic technology have contributed to the field of mathematics teacher education, but the array of tools now' available to teacher educators in developed countries can be somewhat daunting. In this chapter, the authors present an overview of some of these tools and the ways that they are being used. In addition, they address issues surrounding the development and applications of digital technology in teacher education programs in a number of countries. In particular, they present recent applications of videotapes, multimedia resources, internet-based communities, and tutorial conferencing facilities in pre-service and in-service education of mathematics teachers. As professionals who have used technology in teacher education, the authors blend their own insights into this review of technological tools and relevant issues.

Pop art: making mathematics popular

Leicha Bragg shares an effective activity for integrating visual arts, technology and mathematics. Such an approach has the potential to enhance students' visual reasoning and spatial ability by using multiple perspectives of learning. 

Case studies in learning disability: implications for instruction

A significant number of children with learning disabilities may hold negative attributions about themselves which not only impact on their willingness to learn but put themselves at risk of developing depression. A multi-disciplinary assessment team found evidence for the existence of at least two distinct patterns of learning disability. It was concluded that interventions must focus not only on content areas but on the individual attributions the child holds about his or her ability and potential.

Teachers and computers for secondary mathematics

In the first stage of a three-year study in which the effects of using computers for the teaching and learning of mathematics are being explored, a questionnaire was developed and administered to teachers of students in grades 7–10 in a representative sample of co-educational post-primary schools in Victoria, Australia. Using open and closed response formats, the information sought included data on the teachers' professional backgrounds, computer ownership and use, and their beliefs and practices in using computers for the teaching of mathematics. In this article, findings related to ownership, professional development, perceptions of technological skills, beliefs about the efficacy of computer use in mathematics, and data on how teachers are using computers for teaching secondary mathematics are presented and discussed.

Can an online tutorial pass the test for library instruction? An evaluation and comparison of library skills instruction methods for first year students at Deakin University

An online, interactive tutorial, Smart Searcher, was introduced at Deakin University as part of the Iibrary's information skills program in late 2000. As liaison librarians responsible for library skills training we wanted to compare and evaluate this mode of instruction with our normal face-to-face delivery of library instruction. This study found that students with face-to-face instruction did, in fact, gain higher posttest mean scores than students completing the online tutorial. Also, students attending these library sessions felt more confident about their library skills than those in the online tutorial only session.

Psychometric data on the mathematics self-efficacy scale

Descriptive measurement reliability and validity data are reported on scores from the Mathematics Self-Efficacy Scale (MSES) in two contexts—class and test—for a sample of 302 Australian high school students. Summated scores on the MSES correlated r = .74, and together these items yielded one component that explained 49% of the variance. MSES scores demonstrated internal reliability for both class and test (Cronbach alphas = .86 and .90). Statistically significant correlations between MSES scores, past mathematics grades, and Marsh’s Self-Description Questionnaire III (Math) were used to indicate the convergent validity of scores for the MSES. Discriminant validity of the MSES scores was suggested by the lack of significant correlations between the MSES measures and students’ desired English grades. Statistically significant correlations between MSES scores and students’ desired mathematics grades indicated concurrent validity of the MSES measures. A statistically significant difference between class and test scores supported Bandura’s prescription for context specificity in efficacy research.

Exploration of Year 10 students' conceptual change during instruction

This article reports on a classroom-based case study of a group of six Year 10 students, within a class of 23 students. The study implemented constructivist-informed teaching and learning approaches within a classroom setting in the topic of optics and documented any changes in the conceptual understanding students had about seven central concepts of geometrical optics over a teaching sequence lasting nine weeks.