Effect of social background on the development of probabilistic concepts

This research explores how the social backgrounds of a group of students contributed to their intuitive knowledge in probabilistic reasoning, and influenced their processing of the associated mathematics. A group of Year 11 students who came from families for whom the phenomenon of track gambling formed an important part of their cultural background was identified. Another group consisting of students in the same mathematics course (Year 11 Maths in Society) but from families for whom the phenomenon of gambling in any form was totally absent from their social backgrounds was identified. Twenty students were selected from each group. The research employed a qualitative methodology in which a phenomenographic approach was used to investigate the qualitatively different ways in which individuals within the two groups thought about concepts involving probabilistic reasoning, and processed the related mathematical skills and concepts. The cognitive processes involved in the applications of probabilistic and related mathematical concepts in a variety of both gambling and non-gambling situations were studied in order to determine whether this culturally based knowledge could be viewed as a type of ‘ethnomathematics.’ Data were obtained through individual structured interviews which enabled patterns of reasoning to be compared and contrasted. Analyses of these data enabled intuitive mathematical understandings possessed by the gamblers not only to be identified, but also to be linked with their social backgrounds. Also differences between how individuals in the two groups processed probabilistic and associated mathematical knowledge were determined. This research complements and extends existing knowledge and theories related to culturally-based mathematical knowledge. Implications for further research, for classroom teaching, and for curriculum development in the study of probability in senior secondary mathematics classes are discussed.

An 'emergent model' for rate of change

Does speed provide a ‘model for’ rate of change in other contexts? Does JavaMathWorlds (JMW), animated simulation software, assist in the development of the ‘model for’ rate of change? This project investigates the transference of understandings of rate gained in a motion context to a non-motion context. Students were 27 14–15 year old students at an Australian secondary school. The instructional sequence, utilising JMW, provided rich learning experiences of rate of change in the context of a moving elevator. This context connects to students’ prior knowledge. The data taken from pre- and post-tests and student interviews revealed a wide variation in students’ understanding of rate of change. The variation was mapped on a hypothetical learning trajectory and interpreted in the terms of the ‘emergent models’ theory (Gravemeijer, Math Think Learn 1(2):155–177, 1999) and illustrated by specific examples from the data. The results demonstrate that most students were able to use the ‘model of’ rate of change developed in a vertical motion context as a ‘model for’ rate of change in a horizontal motion context. A smaller majority of students were able to use their, often incomplete, ‘model of’ rate of change as a ‘model for’ reasoning about rate of change in a non-motion context.

Knowing schooling, identity and pedagogy visually

This research produced in one region in Ghana examines the production of educational practices, relations of power and student experiences within teaching and non-teaching spaces in junior secondary settings. The strength of the visual approach in interrogating school cultural norms and the problematising of the tangled complexities of knowing about schooling, identity and pedagogy are outlined. An important aspect of the study is the foregrounding of educational practice as a social act occurring in response to historical circumstances and changing social contexts (Brown & Jones, 2001). We see this work as an important step towards democratization of the research relationship and empowerment of students to contribute to the way they are educated. But also we are wary of how representation through visual methods also can 'frame' participants and the researchers. We recognise that one way to uncover how school practices are exemplified in Ghana is to put students in the middle of researching their experiences. In this way, our research moved from constructing students as simply consumers of adult designed and managed products to practices based on democratic participation (Thomson & Gunter, 2007). Throughout the research journey we were guided by the fact that knowledge is not neutral or to be discovered. Culture and communicative processes are essential determinants of reality. In this study the students as researchers, produced photographs that trigger dialectical conversations of students’ perspectives that foreground their experiences at school. This enabled us to digress from dominant positivistic empiricism to a more legitimate ethical practice, and understanding of the intricacies of educational practice, the norms and structures that underpin everyday actions in schools.

Building awareness of mathematical modelling at teacher education: a case study in Indonesia

A growing interest to teach mathematics closely connected to its use in daily life has taken place in Indonesia for over a decade (Sembiring, Hadi, and Dolk 2008). This chapter  reports an exploratory case study of  the building of an awareness of mathematical modelling in teacher education in Indonesia. A modelling task, re-designing a parking lot (Ang 2009), was assigned to groups of pre-service secondary mathematics teachers. All groups undertook the stages of collecting data on a parking lot, identifying limitations in the current design of the parking lot, and proposing a new design based on their observations and analyses. The nature of the mathematical models elicited by pre-service teachers during various stages of completing the modelling task will be examined. Implications of this study suggest the need to encourage pre-service teachers to state the assumptions and real-world considerations and link them to the mathematical model in order to validate their models.

Book review : Teaching secondary school mathematics : research and practice for the 21st century

Book review of Teaching Secondary School Mathematics : Research and Practice for the 21st Century by Merrilyn Goos, Gloria Stillman & Colleen Vale

Teaching secondary school mathematics : research and practice for the 21st century

For the last decade or so, educational policy makers and researchers in many countries have been calling for significant changes to the way mathematics is taught in secondary schools. Australian mathematics curriculum documents now promote learning goals that go beyond mastery of a pre-determined body of knowledge and procedures - the traditional emphasis on facts, skills, formulae - to include mathematical reasoning and problem solving, communication, and real world applications. There is also pressure to move away from over-reliance on teacher-centred practices such as exposition and individual seatwork, towards activities that promote learners' involvement in constructing, applying, and evaluating mathematical ideas. Further impetus for reform comes from research recommending that if learners are to develop mathematically powerful forms of thinking and habits of mind, then classrooms should immerse them in the authentic practices of the discipline by supporting a culture of collaboration and sense-making. Teaching Secondary School Mathematics - incorporates recent developments in research and practice and applications to teaching mathematics in Australian secondary schools. Covering such areas as curriculum, pedagogy and assessment; teaching mathematical content; equity and diversity in the classroom; and professional and community engagement, it is an invaluable resource for all practising and pre-service mathematics teachers.

Numeracy across the curriculum: recognising and responding to the demands and numeracy opportunities inherent in secondary teaching

The 1998 Report of the National Standards and Guidelines for Initial Teacher Education Project, 'Preparing a Profession' illustrates the emphasis being placed in Australia on the development of numeracy skills amongst not only primary but also secondary school pupils. This report demands that graduates of all initial teacher training courses should not only be numerate themselves, but should also understand the contribution of numeracy to education and daily life, and be able to identify and respond to pupils' numeracy learning needs. This report and its implementation in Victoria through the 'Guidelines for the Evaluation of Teacher Education Courses' led to the introduction in 1999 of a compulsory unit 'Numeracy across the curriculum' for all Deakin University students in the final year of their secondary teacher training course. This paper discusses the nature of the current emphasis on numeracy. It also describes the rationale, development and delivery of the first year of the 'Numeracy across the curriculum' unit, provides a brief evaluation from the perspective of staff and students, and discusses what impact such teacher education programs might have on secondary schools' approaches to numeracy.

Easier analysis and better reporting : modelling ordinal data in mathematics education research

This article presents an examination of the use of Rasch modelling in a major research project, 'Improving Middle Years Mathematics and Science' (IMYMS). It is unarguable that it is important to take students' perceptions, or views, into account when planning learning and teaching for them. The IMYMS student perceptions survey is an attempt to make visible these student viewpoints, and report them in a way that is accessible to teachers and researchers involved in the project. The project involves four clusters of schools from urban and regions of Victoria to investigate the role of mathematics and science knowledge and subject cultures in mediating change processes in the middle years of schooling. There are five secondary and twenty-eight primary schools. The project has generated both qualitative and quantitative data, with much of the qualitative data being ordinal in nature. Reporting the results of analyses for a range of audiences necessitates careful, well-designed report formats. Some useful new report formats based on Rasch modeling -the Modified Variable Map, the Ordinal Map, the Threshold Map, and the Annotated Ordinal Map - are illustrated using data from the IMYMS project. The Rasch analysis and the derived reporting formats avoid the pitfalls that exist when working with ordinal data and provide insights into the respondents' views about their experiences in schools unavailable by other approaches.

Microworlds and mathematics - make a microworld melody

This article provides step by step instructions to create recognisable melodies using Microworlds melody program. It describes how the program works to create the notes. Through the writing of a program the user can recreate a familiar melody. The program allows the user to include different instruments and rests in the music, as well as the inclusion of a melody gadget which allows the user to hear notes without the programming.

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.

Productive on-line student support : developing a system for primary mathematics trainee teachers

This paper outlines the development project for the 'Productive on-line student support system', a student "self-help" system, at Deakin University. The aim of this project was to provide Deakin primary teacher education students with a web-based learning tool that allowed them to assess and diagnose their strengths and weaknesses in mathematics, and supports students in their mathematics learning, and in so doing produce mathematically competent graduates. This project was, like similar programs, a development of peer or cross-age tutoring common in primary and secondary schools. A grant under the Deakin University Strategic Teaching and Learning Grant Scheme enabled a staff team from the mathematics education group, to develop a sophisticated and well-designed system that catered for a wide range of student needs, provided useful feedback, and was engaging and easy to use. The under-pinning software for the system was WebCT, available to staff through the Deakin Studies On-line system, to which students are connected also. The 'Productive on-line student support system' enabled students to determine their own mathematical needs, and have these addressed whenever they wished, as often as they wished, and allowed self-monitoring of progress. An outline of the system and examples of the assessment materials will be presented.