Fattening foods - perceptions and misconceptions: a qualitative and quantitative exploration

Describes adults' perceptions and beliefs about foods that are considered "fattening". Use of qualitative and quantitative methods to determine the prevalence of the perceptions among adults; Range of factors that are considered when judging foods as "fattening"; Limitations in the public's understandings of "fattening foods" which are inconsistent with dietary recommendations.

Mathematical games with the alphabet

John Gough once again makes the ordinary fascinating as he piques our curiosity about the origins of the alphabet and turns the various mathematical properties of letters into bases for games.

Algebra skills and traps and diagnostic teaching for the future

Explores on some research about teaching and learning algebra and related classroom issues. Diagnostic instruments that may be used by senior secondary teachers in teaching algebra to senior classes; Strategies for remediating algebraic difficulties and misconceptions; Impact of technology on the algebra curriculum; Usefulness of copying algebraic expressions while using Computer Algebra Systems or mathematics processing software in a calculus class.

Mathematical modelling of the refractive index reconstruction through global optimization

We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental da.ta..

Developing formal mathematical assessment for 4-to-8-year-olds

The assessment of children in their years before school and their first years of school has been, traditionally, informal. Further, assessment of children's mathematical skills at this level has been infrequent compared to social, emotional and physical assessments. However, there are contexts where reliable, valid, standardised data from assessment in mathematics are required. This paper outlines the development of two assessment tools for mathematics that were originally developed for such contexts. Item Response Theory (IRT) analyses enabled the construction of assessment forms that address the range of abilities of 4- to 8-year-old children, and provided the scales used for constructing formative and summative reports of achievement. A description of the development of the assessment tools and the IRT analysis that provides the reporting formats are presented together with some research uses of the tools.

On the EA-style integrated processing of self-contained mathematical texts

A sound and complete first-order goal-oriented sequent-type calculus is developed with ``large-block'' inference rules. In particular, the calculus contains formal analogues of such natural proof-search techniques as handling definitions and applying auxiliary propositions.

Evidence Algorithm and Processing Formalized Mathematical Texts

The goal of a research programme Evidence Algorithm is a development of an open system of automated proving that is able to accumulate mathematical knowledge and to prove theorems in a context of a self-contained mathematical text. By now, the first version of such a system called a System for Automated Deduction, SAD, is implemented in software. The system SAD possesses the following main features: mathematical texts are formalized using a specific formal language that is close to a natural language of mathematical publications; a proof search is based on special sequent-type calculi formalizing natural reasoning style, such as application of definitions and auxiliary propositions. These calculi also admit a separation of equality handling from deduction that gives an opportunity to integrate logical reasoning with symbolic calculation.

Hops, steps and jumps : mathematical progress in the early years

While curriculum frameworks ale major influences on learning, teachers know that children progress at different rates. Sometimes this is evident within a particular topic. and at other times more obvious across different topics. In this paper. we present the hops, steps, and jumps of numeracy learning of some 3000 Australian children. All were assessed using I Can Do Maths, and their achievements mapped to provide a detailed picture of how children hop, step and jump on their numeracy journey. This mapping provides teachers with infonnation about key hurdles to numeracy learning for Australian children.

Mathematical and pedagogical understanding as situated cognition

One mathematics lesson was planned by two Grade 2 teachers together. TheirSeparate teaching of it was videotaped. and each teacher was interviewed before and after her lesson. The "same" lesson resulted in different sets of worthwhile learning outcomes. In this research report. the notion of situated cognition is used as a tool for analysis of how this divergence seemed to happen. It is agued that the teachers' development and uses of mathematical concepts were mediated by the social situations.

An aspect of mathematical understanding: the notion of 'connected knowing'

Much advice about teaching for understanding implies that teacher should help children to develop connections between aspects of their experience, knowledge, and skills. This paper outlines points from the literature about different types of connections and describes relevant points from four case study teachers said and did.

Mathematical knowledge of some entrants to a pre-service education course

Standards for teaching emphasise the need for teachers to have deep content knowledge. To assess the mathematical knowledge of students enrolling in its B.Ed. program, the University of New England has introduced a mathematics diagnostic test. This work is the first stage of an ongoing research project into the numeracy needs of students entering the B.Ed. program. The test is a pen-andpaper test that replaces previous on-line, multiple-choice tests. This paper reports on the test results, discusses some common errors made by students and outlines the future direction of the research.