Mathematics as a second language : looking for a bridge between mathematical language and the language of thought

Our thoughts are in one language, and mathematical results are expressed in a language foreign to the way we think. Mathematics is a unique foreign language with all the components of a language; it has its own grammar, vocabulary, conventions, synonyms, sentence structure, and paragraph structure. Students need to learn these components to partake in a thorough discussion of how to read, write, speak and think mathematics. Beginning with the students natural language and expanding that language to include symbolism and logic is the key. Providing lessons in concrete, pictorial, written and verbal terms allows the instructor to create a translation bridge between the grammar of the mother language and the grammar of mathematics. This papers presents methods to create the translation bridge for students so that they become articulate members of the mathematics community. The students "mother" language, expanded to include the symbols of mathematics and logic, is the the key to both the learning of mathematics and its effective application to problem situations. The use of appropriate language is the key to making mathematics understandable.

The moral reasoning abilities of Australian and Malaysian accounting students : a comparative analysis

If national culture is a significant determinant of ethical attitudes, it is not unreasonable to expect ethical decision-making to be influenced by one's culture. However, problems arise when the notion of right differs from one culture to another. The question addressed in this paper is whether the moral reasoning abilities of Australian and Malaysian accounting students in their final year of study differ because of their cultural upbringing. This study uses primary data collected from 34 final year accounting students (12 Australian and 22 Malaysian) enrolled in an Australian degree program. The test scores collected at the beginning and end of the academic year indicate that culture and other explanatory variables do not have an affect on students' moral judgment. The findings in this study suggest that culture as an independent variable does not influence the way accounting students analyse and resolve ethical dilemmas.

Mathematical modelling of the crankshaft pin grinding process

Novel mathematical models to predict crankshaft pin grinding forces, out-of-roundness and thermal damage were developed as part of this thesis. The models were validated at a local automotive manufacturer's plant. The outcomes of this research have resulted in reduced scrap and warranty costs, improved manufacturing process quality and reduced lead times.

Developing mathematical understanding

The notion of scaffolding is used to introduce research on differentiated learning trajectories that make use of activities termed 'prompts'. The prompts are used to enable children to develop the necessary mathematical understanding and skills to keep up with the rest of the class.  They focus on aspects of teaching that teachers identified as important aspects of classroom interactivity that contribute to the understanding: the use of physical representation of concepts: actions aimed at building conceptual links; and the use of language based activity.

Developing mathematical concepts in Australian pre-school settings : the background

The SIMERR project Mathematical Thinking of Pre-school Children in Rural and Regional Australia: Research and Practice included a review of relevant research literature with the aim of making this accessible to researchers as well as early childhood teachers and educators. This paper introduces the methods used in the project and provides a brief summary of the literature pertaining to the development of mathematical concepts.

Assessment of mathematical development in early childhood : some views of preschool practitioners in regional and rural Australia

As part of the project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice directors, teachers, and assistants in prior-to-school settings from regional and rural eastern Australia were interviewed to ascertain their beliefs and practices concerning early childhood mathematics. This paper reports the responses to  uestions about their assessment of children’s mathematical activity and development. The practitioners provided examples of both incidental and planned assessment activities, the different forms these took, methods of recording, and how the results were used.

Tasks and pedagogies that facilitate mathematical problem solving

This is a report from one aspect of a project seeking to identify teacher actions that support mathematical problem solving. The project developed a planning and teaching model that describes the type of classroom tasks that can facilitate mathematical problem solving, the sequencing of the tasks, the nature of teaching heterogeneous groups, ways of dfferentiating tasks, and particular pedagogies. We report here one teacher's implementation of the
model using a unit of work that he planned and taught. The report provides important insights into the implementation of the theoretically founded model and the responses of students. We found that the model can be used for planning and teaching and for encouraging problem solving. The model has a positive effect on the learning of most students. Specific teachers actions were identified in order to address the needs of the students we are most
keen to support, those experiencing dfficulties.

How early childhood practitioners view young children's mathematical thinking

Interviews were held with 64 professionals in childcare centres. This paper reports on their responses to 3 questions seeking their perceptions of mathematical thinking in very young children. Generally, the interviewees were found to have a good sense of mathematical concepts relevant to babies and toddlers, and they cited evidence of young children’s mathematical development. It is concluded that this practical knowledge would provide a strong foundation for further professional development.

General practitioners’ decision to refer patients to dietitians : insight into the clinical reasoning process

The aim of this project was to describe general practitioners’ (GPs’) decision-making process for reducing nutrition risk in cardiac patients through referring a patient to a dietitian. The setting was primary care practices in Victoria. The method we employed was mixed methods research: in Study 1, 30 GPs were interviewed. Recorded interviews were transcribed and narratives analysed thematically. Study 2 involved a survey of statewide random sample of GPs. Frequencies and analyses of variance were used to explore the impact of demographic variables on decisions to refer. We found that the referral decision involved four elements: (i) synthesising management information; (ii) forecasting outcomes; (iii) planning management; and (iv) actioning referrals. GPs applied cognitive and collaborative strategies to develop a treatment plan. In Study 2, doctors (248 GPs, 30%) concurred with identified barriers/enabling factors for patients’ referral. There was no association between GPs’ sex, age or hours worked per week and referral factors. We conclude that a GP’s judgment to offer a dietetic referral to an adult patient is a four element reasoning process. Attention to how these elements interact may assist clinical decision making. Apart from the sole use of prescribed medications/surgical procedures for cardiac care, patients offered a dietetic referral were those who were considered able to commit to dietary change and who were willing to attend a dietetic consultation. Improvements in provision of patients’ nutrition intervention information to GPs are needed. Further investigation is justified to determine how to resolve this practice gap.

Using web-based mathematical interactive exercises and exploratory investigations : the possibilities and pitfalls

This case study looks at how a teacher used interactive exercises and exploratory investigations to reinforce concepts that have been learnt in a Year 8 Mathematics class. It highlights the practical problems faced by the teacher in terms of technical issues such as slow download times and logging on problems as well as class management issues. The findings are discussed in the light of the teacher’s mediation with the affordances of the Internet.

A primer on mathematical modelling in economics

The Commission on Graduate Education in Economics had raised several concerns regarding the role of mathematics in graduate training in economics (Krueger, 1991; Colander, 1998, 2005). This paper undertakes a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across mathematical concepts and results that are used by economists. In the process one arrives at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of Arrow's impossibility theorem. Common knowledge of the patterns in mathematical concepts and results could be effective in enhancing communication between students, teachers and researchers specializing in different sub-fields of economics.