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.

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.

Keeping all students on the learning path

A powerful notion to guide thinking about whole-class mathematics teaching is Vygotsky’s zone of proximal development (ZPD). Our research with primary and secondary teachers over the last six years has identified roles of teachers in relation to the ZPD, and ways of overcoming some typical barriers to students’ movement through their zones. Methods have included focus groups of experts, video analysis of classroom interactions, classroom observation, and analysis of lesson plans and teachers’ reflections teaching processes their outcomes. The research has involved the gradual development, trailing, evaluation, and adjustment of a six-component model for planning and teaching mathematics. The focus of this paper is on the use of one of its components, “differentiated learning trajectories”.

Living improvement : a case study of a secondary school in England

Schools in England are being urged to personalize the curriculum and make school experiences more responsive to all students. We report on an evaluation project which investigated innovation in teaching and learning in a successful secondary school in the north of England. Data were gathered from a sample of teaching staff, a questionnaire to all students, lesson and meeting observations, and meetings with the governing body and parents: the student-guided evaluation canvassed recent and planned changes to the structure and experience of teaching and learning. This article illuminates how one school is breaking the ‘traditional schooling rules’ that limit improvement and how in doing so it is developing new insights about the nature and process of improvement. We show how staff and students have been engaged in the change process, and focus in particular on analysing the interplay between improvement as a plan, a practice and a lived experience.

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.

Potential of technology and a familiar context to enhance students' concept of rate of change

Students' concept image of rate of change may be incomplete or erroneous. This paper reports a pilot study, with secondary school students, which explores the potential of technology (JavaMathWorlds), depicting a familiar context of motion, to develop students' existing schema of informal understandings of rate of change to more formal mathematical representations. Students developed numerous 'models of' rate of change in a motion context which then transferred to serve as a 'model for' rate of change in other contexts.

Gifted are lifted higher : an exploration of the development of higher order thinking skills of gifted students playing strategy games

Strategy games can provide an opportunity to develop higher order thinking skills in students gifted in mathematics. Extending and engaging gifted students is a demanding task. This paper reports on a twelve-week project undertaken with a group of nine gifted lower secondary school students. These students played and analysed five traditional strategy games. Following this experience, they were asked to create a challenging strategy game of their own. This paper discusses the rationale for the use of traditional strategy games, outlines the methodology employed, explains the selection of specific games and describes the observed improvement in students' higher order thinking skills.

Creating digital divas-scaffolding perception change through secondary school and university alliances

Over the last 20 years much has been done to encourage female students to choose computing courses and computing careers. Some instances of positive effects have been reported, yet the proportional disparity in gender in this discipline continues to grow. This paper reports on a program called 'Digital Divas'. Digital Divas aims to scaffold positive perceptions around computing in the early years of secondary school by involving female students in upbeat computing experiences over a semester. It introduces university undergraduates to the secondary classroom to provide informal role models and mentors, as well as interactions with young computing professionals. This classroom environment enables computer applications to be more strongly linked with future careers. The commitment to a semester length unit was influential in changing perceptions about girls and computing, and the program was supported by the wider school community. We posit that this type of curriculum intervention is needed and has the potential to build technical human capital in female students.

Multiliteracies : resources for meaning-making in the secondary english classroom

This chapter draws on practitioner research with classes in a surburban secondary college in Melbourne, Australia to examine some of the complex interactions between school literacy practices and the literacy practices students engage in within school and outside of school. In particular, it focuses on student texts as instances of successful experiences of using multiliteracies for reading, writing and speaking in English classrooms.

English education for international students in local schools : practices of inclusion and discourses of exclusion

This paper is concerned with the ways secondary teachers in Victoria, Australia, speak about inclusive education for international students. Preliminary analysis of recent research shows teachers understand that English language teaching is crucial and are committed to its good practice. Nevertheless, further analysis suggests teacher approaches to education are contested, support a deficit view of teaching practice, and simplify notions of language and culture to their discrete and systemic characteristics vis-a-vis their embodied and ontological aspects. Even as teachers work to include all of their students, their efforts are mediated by discourses that negotiate the nexus between identity and difference, language and culture, and English language education. Together these discourses work to inscribe international students differently within the community, redefine the education provided to them, and constrain their access to contemporary and globalized life-worlds.

Popular culture : a resource for writing in secondary English classrooms

This chapter explores how a secondary English teacher working with students aged 14-15 enabled them to use their popular culture practices as a resource for writing. The chapter provides examples of conventional classroom situations in which this teacher created a space for students to bring their own semiotic resources to bear on the curriculum. It argues the need for English teachers to become sensitized to the complex literacy practices in which their students engage outside school and to the ways these practices are bound up with their social relationships and sense of identity. The discussion challenges conventional understandings of ‘reading’, ‘writing’, ‘speaking’, and ‘listening’ as components of the English curriculum, arguing that a more contemporary understanding of literacy must take into account the multi-modal practices in which students engage in beyond school.

Doing research with teachers, parents and students : the ethics and politics of collaborative research

Truly collaborative research partnerships between universities and schools are seldom commonplace (Potter, 2001). Many schools – particularly those in disadvantaged communities – have long histories of being involved in research yet few see themselves with real investment in, ownership of and/or benefiting from the experience. In this chapter we discuss research conceived with more mutually beneficial researcher-researched relations, cognisant of the ‘importance of respecting and ultimately giving more than we take to the communities we research’ (Schultz, 2001, p. 1). The research involved teachers’, parents’ and students’ engagement with schooling in a secondary school in regional Australia. Rather than conducting the research on others, we attempted to craft our project with them. Michelle Fine (1994) argues that a decision to work with those we once might have written about or for, necessarily changes our work, making it both more ethical and more explicitly connected to struggles for social justice. This chapter draws on the voices of the teachers, parents and students we worked with and alongside during the research to explore the ethics and politics of such an approach.

'I'm your new teacher' : the impact of teacher mobility on educational opportunities for marginalised students

This article provides an alternative perspective on what it means to 'do school' in a disadvantaged community, particularly in the way that disadvantage is reproduced for marginalised students. It explores the mobility of teachers (temporarily) working in a small secondary school located in an economically depressed regional community in Australia, characterised by high levels of unemployment, high welfare dependency and a significant indigenous population. Like many disadvantaged schools, the school has difficulty attracting and retaining high ability teachers, instead relying on a high turnover of often-reluctant staff who are sent to (or feel compelled to) fill positions unable to be resourced through teacher choice procedures. Drawing on parent, student, and teacher interviews, we ask: how does teacher mobility in this context influence the educational opportunities of students who are 'on the margins' of school success and of the socio-economic structure? Specifically, we explore the ways that teacher mobility can reproduce disadvantage by limiting students' access to the dominant cultural capital. We argue that educational policies and politics that reward teacher mobility for moving out of these communities, work to disadvantage students. What is needed is a transformation in policies governing staff placements to establish alternatives that redefine the reward system for teachers in ways that permit these students to succeed.

Under what conditions? Including students with learning disabilities within Australian classrooms

In Australian schools, "inclusion" is a term that is used to challenge a previously narrow focus on students with disabilities and their integration within and distribution amongst "mainstream" schools and classrooms. Nevertheless, this article argues that, as a concept, "inclusion" requires further broadening and deepening, particularly in arenas of practice, if it is to serve the interests of all students. Informed by notions of recognitive justice, the paper advocates rethinking inclusion to accommodate student differences in more socially just ways - emphasising students' contributions rather than their disabilities - and what this means for the organisation of classrooms and schools. Within the article, research data are focused primarily on students with learning disabilities and draw on twenty semi-structured interviews conducted with parents and teachers across six Australian state primary and secondary schools. Three sets of conditions are proposed as necessary for inclusive classroom and school processes: specifically, those that promote self-identity and respect, self expression and development and selfdetermination and decision-making.

The mathematical and science skills of students who are deaf or hard of hearing educated in inclusive settings

This study examined the science and mathematics achievements of 16 Year 9 students with hearing loss in an inclusive high-school setting in Western Australia. Results from the Monitoring Standards in Education (MSE) compulsory state tests were compared with state and class averages for students with normal hearing. Data were collected from three cohorts of Year 9 students across a 3-year period (2005‐2007). Results from mathematics MSE9 and the MSE9 science assessments showed that the majority of students with hearing loss performed below the state average (88%). Findings in this study suggest that students with hearing loss demonstrated more mathematical strength in the areas of space and measurement, which use visuo-spatial skills. Results for students with hearing loss in the five sections of the science assessment suggest more consistency across the different areas tested in the MSE. Comparisons with the MSE9 English paper for the 2005 cohort of students with hearing loss suggest a strong relationship between reading and writing skills and performance on mathematics and science assessment. In particular, questions with high language content created difficulty. On the science assessment, questions requiring a written explanation appeared to be particularly challenging. These findings have implications for teaching and learning in these crucial areas for students with hearing loss in inclusive secondary school settings. Greater attention to the interpretation of the language of mathematics and to writing about science concepts may help to improve outcomes for students with hearing loss on statewide assessments