Deepening the mathematical knowledge of secondary mathematics teachers who lack tertiary mathematics qualifications

A professional learning program for unqualified practising secondary mathematics teachers regarding senior secondary mathematics teaching is described in this paper. The VCE (Victorian Certificate of Education) mathematics professional learning program for senior secondary mathematics was designed for practising secondary teachers of mathematics who had no experience of teaching advanced senior secondary mathematics and who had not completed the recommended qualifications. Professional learning episodes, artefacts and reflections of three teachers who participated in the program are analysed to identify the development of these teachers' mathematical and pedagogical content knowledge (PCK). The PCK framework developed by Chick et al. was used to analyse teachers' knowledge, and the cases of teachers' knowledge presented in the paper illustrate the entwining of knowledge of mathematics and knowledge of teaching and learning The findings indicate that a program designed for senior secondary mathematics can enable practising teachers to deepen and broaden their understanding of junior secondary mathematical pedagogy.

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.

Primary and secondary mathematics practice: how different is it?

This paper describes the practices of ninety-nine teachers at the beginning of their involvement in a large-scale project investigating the influence of subject cultures on school and teacher change. Data collected from these teachers, using the IMYMS. Components of effective teaching and Learning mapping procedure, were analysed to investigate similarities and differences in primary and secondary teachers’ perceptions of their practice in mathematics. Results of the analysis show different patterns across a range of components of effective teaching and learning.

A first priority when working with teachers is to help them become aware of and make problematic aspects of their current practice …. Only then would they have reason to attempt to reform their instructional practices when working with us. (Yackel, 1994, p. 386)

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.

Fostering meaningful learning by using word problems in post-secondary mathematics

This research is a case study of action research investigating the effects of using word problems with Chinese Malaysian post-secondary students studying mathematics as an enabling science. A variety of word problems, a discussion method, reflective and peer learning, specific values in mathematics, and relevant socio-cultural and language issues were explored.

Computers for secondary mathematics: who uses them and how?

In the first stage of a three year ARC-funded study in which the effects of using computers for the teaching and learning of mathematics are being explored, a questionnaire has been developed and is being administered to a large number of students in grades 7-10 in a representative sample of co-educational post-primary schools in Victoria. Using open and closed response formats, the information sought includes: background and biographical details; data on computer ownership and use =96 frequency and mode/s =96 for mathematics learning at home and in mathematics classes; and beliefs about mathematics and the use of computers for learning mathematics. In this paper, the focus will be on some of the preliminary findings related to ownership and use of computers for learning mathematics at home and at school. In previous research, factors such as gender, socio-economic background, and ethnicity have been identified as contributors to inequitable mathematics learning outcomes. The questionnaire data will be analysed to examine if these and other factors are related to any inequities identified in student's access to computers and in how they use computers in their learning of mathematics. The results will be presented and pertinent implications discussed.

Computers are taking mathematics into the next century : gender differences in attitudes of secondary mathematics students to the use of computers

Secondary students who participated in a computer enhanced mathematics program expressed positive attitudes about the use of computers. They viewed computers as a source of pleasure, success, relevance and/or power in mathematics. Girls were more likely than boys to qualify their support for the use of computers and more likely to view computers as a source of success in mathematics. Boys were more likely to claim that computers brought pleasure or relevance to mathematics learning.

Supporting "out-of-field" teachers of secondary mathematics

The key aspects of the recommendations made by the Council of Australian Governments in its National Numeracy Report (2008) to help reduce the shortage of teachers of secondary mathematics are discussed. The aims and objectives of the professional learning programs for 'out-of-field' mathematics teachers are highlighted.

Connecting with the horizon : developing teachers' appreciation of mathematical structure

A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers’ mathematical and pedagogical knowledge. The analysis of teachers’ reflections on their learning explored teachers’ understanding of mathematical connections and their appreciation of mathematical structure. The findings indicate that a professional learning program about senior secondary mathematics can enable practicing teachers to deepen and broaden their knowledge for teaching junior secondary mathematics and develop their practice to support their students’ present and future learning of mathematics. Further research is needed about professional learning approaches and tasks that may enable teachers to imbed and develop awareness of structure in their practice.

Teaching out-of-field : factors shaping identities of secondary science and mathematics

It is widely recognised that many teachers work 'out of field', taking subjects outside their specialities. Studies undertaken by the author and by other researchers shed light on how teachers themselves experience and understand out-of-field teaching. The article discusses the issue in relation to junior secondary science and mathematics. Evidence is drawn from the 2009 Teacher Identity In and Across Subjects (TIIAS) study. The article also includes a table summarising the findings of eight major research reports relevant to this issue. The author draws a range of conclusions. Teachers' experience and understanding of out-of-field teaching is determined not only by their subject content knowledge and their pedagogical content knowledge, but also by their context and by the personal resources available to them. Rural teachers often accept the need to teach across a number of subject areas, as part of their professional identity, despite the fact that they often lack easy access to subject specialists. Teachers tend to be more positive about out-of-field teaching when they themselves have had input into which subjects they will teach, and when they have an interest in or informal knowledge of the subject area. Teachers' interest in professional development to support their out-of-field teaching is influenced by whether they see themselves as simply filling in for someone, making the most of an opportunity, or pursuing an interest. Professional learning should ideally be initiated by or negotiated with the teachers, and should be provided at the point of need. School leaderships should maximise teachers' input into subject allocation and provision of professional learning opportunities. Teacher education courses need to prepare pre-service teachers to cope with out-of-field teaching.

Fun or profit : primary students' perceptions of mathematics and science

As the number of students pursuing mathematics and science in higher education decline, it becomes imperative· that we look for the causes of the decline. As part of the Australian Improving Middle Years Mathematics and Science (IMYMS) project, students were asked to rate their perceptions of classroom practice in mathematics and science and their attitudes to these subjects. Results of this survey reveal little difference in perceptions of classroom practice, but significant differences in students' attitudes between mathematics and science. Differences were particularly evident for items relating to the usefulness of mathematics and science (mathematics was more useful) and enjoyment of the subjects (science is more fun). If teachers are aware of such perspectives, it may be possible to change students' attitudes.

Effective student engagement depends on students enjoying their studies in mathematics and science, being confident in their ability and recognising the relevance of these subjects to everyday life, now and in the future.
(Education Training Committee, 2006, p. xvii)

Science and technology are the widely acknowledged foundation of Australia's future development. Underpinning these are the key learning areas of mathematics and science. However, Australia is experiencing a decline in numbers of mathematics and science students in higher education. Moreover, studies over the last two decades have shown a general decline in Australian students' interest and enjoyment of science across the compulsory secondary school years, with a particularly sharp decline across the primary to secondary school transition (e.g. Adams, Doig, & Rosier 1991; Goodrum, Hackling, & Rennie, 200 I) and a decline in the numbers of students studying' advanced mathematical courses in upper secondary school (Thomas, 2000).

Improving teaching and learning in the middle years of schooling (Years 5 to 9) is receiving particular attention because of the coincidence of the disengagement of students with the significance of these years for the preparation of students for their future role in society. Thus the Improving Middle Years Mathematics and Science: The role of subject cultures in school and teacher change (IMYMS) project, which is the source of data for this paper, is investigating the role of mathematics and science' knowledge and subject cultures in mediating change processes in the middle years of schooling.

Mathematics and science are sometimes seen as "love-hate" subjects, rating highest for subjects disliked, but also rating relatively highly among preferred subjects (Hendley & Stables, 1996). Students, even primary aged students, can often shed light on what constitutes good practice (see, for example, 'van den Heuvel-Panhuizen, 2005). Students' attitudes towards mathematics and science and their perceptions of what they regard as positive aspects of classroom practice have been shown to decline from the primary years to junior secondary (Race, 2000). The decline in interest in science in the early years of secondary school is of particular concern, since it is in these years that attitudes to the pursuit of science subjects and careers are formed (Speering & Rennie, 1996). Students' negative attitude towards the relevance of science ,content for their lives was a strong theme in the report by Goodrum, Hackling, & Rennie (2001) on the status and quality of teaching and learning of science.

As part of the IMYMS project, the IMYMS Student Survey was administered to all students in 2004 and 2005. The survey included a 36 item section on students' perceptions of classroom practice and attitudes towards mathematics and science, and a 24 item section on students' learning preferences. Students completed separate, parallel surveys for mathematics and science.

This paper focuses on students' perceptions and attitudes. It explores the differences in 700 Year 5 and 6 students' perceptions of their learning environment and their attitudes to mathematics and science during 2005, the second (and final) year of schools , involvement in the IMYMS project.