The stereotyping of mathematics: gender and cultural factors

The Who and mathematics instrument is used to measure the extent to which mathematics is considered a male, female or gender-neutral domain. Data from students in grades 7-10 in Australia and Greece were compared to explore the impact of the cultural environment. The data were also examined for within country gender differences and possible differences among males and among females across the two countries. An additional perspective on the influence of prevailing cultural norms - Greek ethnic home background and the broader Australian milieu - was provided by the findings from a small sample of Australian students who attended a school with a strong Greek affiliation and who completed a trial version of the Who and mathematics instrument.

Teacher actions to maximize mathematics learning opportunities in heterogeneous classrooms

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11–12) class.

A primary numeracy : a mapping review and analysis of Australian research in numeracy learning at the primary school level : report

The outcome from this project produces a database of over 185 projects and 726 publications relating to numeracy research to systematically ‘mapped’ Australian research on primary school numeracy over the last decade. The database incorporates research summaries and findings that are easily accessible to teachers and teacher educators, and act as a valuable tool for determining further research directions. The project report examines the available research and organises the discussion of the research findings under a set of themes and sub-themes.

Some summarised examples from the report reveals that:

* Effective teachers of numeracy:
- have high expectations of their students;
- focus on children’s mathematical learning, rather than on providing pleasant classroom experiences;
- provide a challenging curriculum;
- use higher-order questioning;
- make connections both within mathematics and between mathematics in different contexts; and
- use highly interactive teaching involvement with students in class discussion.

* Effective professional development programmes:
- provide teachers with the time and appropriate resources to enable them to reflect on their teaching;
- provide continuing support and encouragement while teachers explore possibilities and trial new strategies in their classrooms;
- involve teachers in school-based and wider networks;
- are of sufficient duration to allow significant changes to habitual beliefs and practices; and
- create opportunities for the exploration of theory-practice relationships.

Middle school melding: liaising primary-to-secondary transition

Discusses the transition from primary to secondary education in relation to mathematics. Discusses how to minimise the disruption and maximise the communication between, and effective outcomes for both levels of schooling, to help the students, while easing the professional demands placed on teachers.

Making a numeracy across the curriculum policy for your school

If your school has already made a Literacy policy, and cleaned up its Literacy practices, what about Numeracy? What is it, and what are you going to do about it? Consider the following steps towards a policy and practice. Define “numeracy” (it is a subset of mathematics, used in particular ways). Identify numeracy needs and assessment activities in nonmathematics KLAs, including ICT and communication. Link mathematics learning outcomes with nonmathematics KLA numeracy needs. Establish school and year-level entry screening, and follow-up. Develop staff PD and teacher-parent discussion.

Engaging students in authentic science through school - community links : learning from the rural experience

There is an increase in school-community linked initiatives in school science. A substantial proportion of these involve rural schools. This article asks the question: In what ways do these initiatives offer possibilities for better engaging rural students with school science? The paper draws on information from a number of school-community linked science initiatives in rural areas, including exemplars from the recent Australian School Innovation in Science, Technology and Mathematics (ASISTM) project, which were obtained primarily through interviews with participants. The initiatives are analysed in terms of an 'innovation framework', concerning the ideas and purposes underlying them, the knowledge and pedagogies used, and the experiences of the participants in the initiative. The paper concludes that these initiatives differ in significant respects from traditional school science, and offer the possibility of productive future directions. The authors discuss the challenges and policy directions that need to be pursued to represent these practices in mainstream curricula.

Designing open-ended problems to challenge preservice teachers' views on mathematics and pedagogy

This study examines preservice elementary teachers' reported experiences of posing open-ended mathematics problems. Responses of 33 students in a mathematics teacher education course were analysed for the strategies participants used, what they learned and the challenges encountered from an opportunity to collect digital images and pose open-ended problems related to those images. Results indicate that preservice teachers reported a shift in the ways they viewed mathematics and how it might be taught. The school curriculum both constrained and provided possibilities for preservice teachers in noticing mathematics beyond the textbook and mathematics classroom. This study adds to our understanding of teaching as a learning practice and the art of posing mathematical problems as a significant aspect of that practice.

Spatial thinking processes employed by primary school students engaged in mathematical problem solving

This thesis describes changes in the spatial thinking of Year 2 and Year 4 students who participated in a six-week long spatio-mathematical program. The main investigation, which contained quantitative and qualitative components, was designed to answer questions which were identified in a comprehensive review of pertinent literatures dealing with (a) young children's development of spatial concepts and skills, (b) how students solve problems and learn in different types of classrooms, and (c) the special roles of visual imagery, equipment, and classroom discourse in spatial problem solving. The quantitative investigation into the effects of a two-dimensional spatial program used a matched-group experimental design. Parallel forms of a specially developed spatio-mathematical group test were administered on three occasions—before, immediately after, and six to eight weeks after the spatial program. The test contained items requiring spatial thinking about two-dimensional space and other items requiring transfer to thinking about three-dimensional space. The results of the experimental group were compared with those of a ‘control’ group who were involved in number problem-solving activities. The investigation took into account gender and year at school. In addition, the effects of different classroom organisations on spatial thinking were investigated~one group worked mainly individually and the other group in small cooperative groups. The study found that improvements in scores on the delayed posttest of two-dimensional spatial thinking by students who were engaged in the spatial learning experiences were statistically significantly greater than those of the control group when pretest scores were used as covariates. Gender was the only variable to show an effect on the three-dimensional delayed posttest. The study also attempted to explain how improvements in, spatial thinking occurred. The qualitative component of the study involved students in different contexts. Students were video-taped as they worked, and much observational and interview data were obtained and analysed to develop categories which were described and inter-related in a model of children's responsiveness to spatial problem-solving experiences. The model and the details of children's thinking were related to literatures on visual imagery, selective attention, representation, and concept construction.

Investigation into the skill levels achieved by mathematics students in the V.C.E. and the H.S.C. mathematics courses

This study examines whether recent changes to the mathematics courses offered in the final year of secondary school (Year 12) in the state of Victoria, Australia have affected the learning outcomes of students in terms of then: skill levels in algebra, calculus and problem solving; and in terms of their preparation for a tertiary mathematics unit. The impact of these changes on the transition from secondary to tertiary mathematics is also considered. A comparison is made between students who attempted a first year mathematics unit at the University of Melbourne (U. of M.) having completed the new V.C.E. (Victorian Certificate of Education) mathematics courses and mathematics courses from the previous H.S.C. (Higher School Certificate) system. The comparison involves the use of tests administered upon entrance to a tertiary mathematics unit at the U. of M., and questionnaires. In 1991, V.C.E, students and H.S.C. students attempted the same mathematics test at the U. of M. and their results were compared. In 1992, the tests were attempted by V.C.E. students only. To compare new V.C.E. students and H.S.C. students, questions on the 1991 test were matched with similar questions on the 1992 tests and a panel of experts determined what the H.S.C. students who attempted the 1991 test would have been expected to average on these matched questions on the 1992 tests had they attempted them. These expected average scores were then compared with the actual scores of the new V.C.E. students. The scores of the groups were scaled when necessary. Questionnaires were administered to 1991 U. of M, mathematics students who were part of the V.C.E. pilot group in 1990, secondary mathematics educators, tertiary mathematics educators, and 1991 V.C.E. (1992 U. of M.) students. The mathematical misconceptions exhibited by new V.C.E. students are discussed and their frequencies stated. The research indicates that the new V.C.E. mathematics courses have provided the V.C.E. mathematics students in this study with significantly lower skill levels and a significantly poorer preparation for a tertiary mathematics unit than those which were previously provided by the H.S.C. mathematics courses.

Implementation of student active learning in primary mathematics in Indonesia

Twenty years after the first pilot projects began to develop Student Active Learning (SAL) in Indonesia, and four years since it was adopted for use in the last provinces, this research investigates the implementation of Student Active Learning in Indonesian primary mathematics classrooms. A study of the relevant literature indicates that teaching based on constructivist principles is unlikely to be implemented well in mathematics classrooms unless there are high quality teachers, readily available manipulative materials, and a supportive learning environment. As Indonesian schools often lack one or more of these aspects, it seemed likely that Student Active Learning principles might not be ‘fully’ implemented in Indonesian primary mathematics classrooms. Thus a smaller scale, parallel study was carried out in Australian schools where there is no policy of Student Active Learning, but where its underlying principles are compatible with the stated views about learning and teaching mathematics. The study employed a qualitative interpretive methodology. Sixteen primary teachers from four urban and four rural Indonesian schools and four teachers from two Victorian schools were observed for four mathematics lessons each. The twenty teachers, as well as fourteen Indonesian headteachers and other education professionals, were interviewed in order to establish links between the background and beliefs of participants, and their implementation of Student Active Learning. Information on perceived constraints on the implementation of SAL was also sought. The results of this study suggest that Student Active learning has been implemented at four levels in Indonesian primary mathematics classrooms, ranging from essentially no implementation to a relatively high level of implementation, with an even higher level of implementation in three of the four Australian classrooms observed. Indonesian teachers, headteachers and supervisors hold a range of views of SAL and also of mathematics learning and teaching. These views largely depended on their in-service training in SAL and, more particularly, on their participation in the PEQIP project Typically, participants’ expressed views of SAL were at the same or higher level as their views of mathematics learning and teaching, with a similar pattern being observed in the relationship between these latter views and their implementation of SAL principles. Three factors were identified as influencing teacher change in terms of implementation of SAL: policy, curricular and organisational, and attitudes. Recommendations arising from this study include the adoption of reflection as an underlying principle in the theory of SAL, the continuation and extension of PEQIP type projects, changes in government policy on curriculum coverage and pre-service teacher training, and more support for teachers at the school and local authority levels.

Continuous professional learning through school based strategic planning

There is ample evidence that in many countries school science is in difficulty, with declining student attitudes and uptake of science. This presentation argues that a key to addressing the problem lies in transforming teachers’ classroom practice, and that pedagogical innovation is best supported within a school context. Evidence for effective change will draw on the School Innovation in Science (SIS) initiative in Victoria, which has developed and evaluated a model to improve science teaching and learning across a school system. The model involves a framework for describing effective teaching and learning, and a strategy that allows schools flexibility to develop their practice to suit local conditions and to maintain ownership of the change process. SIS has proved successful in improving science teaching and learning in primary and secondary schools. Experience from SIS and related projects, from a national Australian science and literacy project, and from system wide science initiatives in Europe, will be used to explore the factors that affect the success and the path of innovation in schools.

Implementing cooperative learning in grade four mathematics classes in Thailand

This study showed that successful implementation of cooperative learning in Thai primary mathematics classrooms requires three components: preparation of teachers, preparation of instructional materials and the preparation of pupils. In addition, cooperative learning was found to have a positive effect on pupils' mathematics achievement and their attitude towards mathematics.

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.