In this article the development of two teachers as they make the transition from pre-service teachers to experienced teachers is examined. While these teachers participated in the same mathematics methods course and similar collaborative environments in their practicum experiences, their mathematics classroom instructional practices revealed stark…

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

The purpose of this article is to describe a middle school mathematics teacher's model of his students' responses to algebraic tasks involving equivalent expressions and the distributive property. The teacher engaged in two model-eliciting activities designed for teachers by creating a library of his students' work and an accompanying "Ways of…

Teacher quality has become a national policy concern in the US, especially in mathematics. This study provides insights into the conceptualisation of high quality mathematics teaching from the perspective of approximately 750 students in grades nine through twelve. Results from Rasch analysis yield information about the quality of the "Mathematics…

This paper reports the use of several quantitative analytic methods, including Rasch analysis, to re-examine teacher responses to questionnaire items probing opinions related to the compulsory numeracy tests conducted in Years 3, 5, and 7 in Queensland, Australia. Nisbet and Grimbeek (2004) previously reported an interpretable and statistically…

This study uses Partial Credit Rasch analysis to study a complex data set of student responses to survey items relating to chance and data. The items were administered in the classroom and collected from 1993 to 2003 in the Australian state of Tasmania. Data were collected from a total of 5514 individual students across Grades 3 to 11 over the…

This paper presents an examination of the use of Rasch modelling in a major research project, "Improving Middle Years Mathematics and Science" (IMYMS). 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…

The basic theory of Rasch measurement applies to situations where a person has a certain level of a trait being investigated, and this level of ability is what determines (to within a measurement error) how well the person does on each item in a test. This paper responds to frequent suggestions from colleagues that the use of Rasch measurement…

This research examined students' responses to mathematics problem-solving tasks and applied a general multidimensional IRT model at the response category level. In doing so, cognitive processes were identified and modelled through item response modelling to extract more information than would be provided using conventional practices in scoring…

This study reports on the algebraic generalisation strategies used by two fifth grade students along with the factors that appeared to influence these strategies. These students were examined over 18 instructional sessions using a teaching experiment methodology. The results highlighted the complex factors that appeared to influence student…

Computer-based technologies are now commonplace in classrooms, and the integration of these media into the teaching and learning of mathematics is supported by government policy in most developed countries. However, many questions about the impact of computer-based technologies on classroom mathematics learning remain unanswered, and debates about…

This study examined the development of a mathematics teacher's proficiency in managing whole-class discussion in the context of an inquiry-based classroom. We analysed three lessons taught with the same class by a teacher-researcher. The first and second lessons were 10 months apart, the second and third lessons were 6 months apart. For each of…

This paper reports the results of two interventions involving the integrated study of mathematics and technology practice to girls in Years 6 and 7. The focus of the study was to look at factors that contributed to girls' disengagement with mathematics study and seek pedagogical solutions for this. The key mathematics concepts embedded in the two…

This paper is concerned with the use of spreadsheets within mathematical investigational tasks. Considering the learning of both children and pre-service teaching students, it examines how mathematical phenomena can be seen as a function of the pedagogical media through which they are encountered. In particular, it shows how pedagogical apparatus…

As part of the Victorian Early Numeracy Research Project, over 1400 Victorian children in the first (Preparatory) year of school were assessed in mathematics by their classroom teachers. Using a task-based, one-to-one interview, administered during the first and last month of the school year, a picture emerged of the mathematical knowledge and…