Steven Nisbet

Mathematics‐teachers’ Knowledge Bases: implications for teacher education

Abstract Understanding the knowledge bases of mathematics teachers is an important task in working towards the construction of adequate models for: (i) teacher education and development, and (ii) teacher operations in the classroom. To date, little systematic attention has been focused on this task. The primary aim of this study is to obtain a view from the field of mathematics teacher knowledge with respect to content knowledge in mathematics, content‐specific pedagogical knowledge in mathematics and curriculum knowledge relevant to teaching tasks. This study has used data obtained from a survey of primary teachers and secondary mathematics teachers. Analysis of the results has indicated that less than half of the teachers in the study believed that they were sufficiently prepared in mathematics content, and that almost two‐thirds of the teachers in the sample believed that their level of knowledge in contemporary teaching methodologies in mathematics is not sufficient for their role as school teachers. ...

A new instrument to measure pre-service primary teachers’ attitudes to teaching mathematics

This article outlines the development of an instrument to measure pre-service primary teachers’ attitudes to teaching mathematics. A trial questionnaire was devised using the set of Fennema-Sherman scales on students’ attitudes to the subject mathematics as a model. Analysis of the responses to the questionnaire by 155 student teachers was carried out to develop meaningful attitude scales and to refine the instrument. The end-product is a new instrument which can be used to monitor the attitudes of student teachers. The attitude scales identified in the analysis and built into the final form of the questionnaire are (i) anxiety, (ii) confidence and enjoyment, (iii) desire for recognition and (iv) pressure to conform.

Surveying Primary Teachers about Compulsory Numeracy Testing: Combining Factor Analysis with Rasch Analysis

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 acceptable 6-factor exploratory factor solution. The present paper improved on this outcome by utilising Rasch analysis to identify items with orderly sequences of scores across response categories, and to subject these to fresh exploratory and confirmatory factor analysis. The resulting 3-factor scale proved acceptable in terms of exploratory and confirmatory factor analysis as well as in terms of Rasch item analysis. The paper briefly discusses the implications of these outcomes in relation to the refined instrument’s capacity to gather information about how teachers view the Queensland numeracy reporting system.

Collaboration and Sharing as Crucial Elements of Professional Development

In this chapter, the notions of collaboration and co-operation are explored in the context of a large-scale project of professional development of mathematics teachers in performance-based assessment. The overall project consisted of series of co-operative workshops in which teachers themselves were employed as facilitators to lead groups of their peers. Although the project was not very successful overall, there were a few successful activities, which occurred during the life of the project. One involved the setting up of a collaborative writing group the purpose of which was to produce a set of rich assessment tasks. Reasons for the success of this activity include the high level of collaboration in the group, the sharing of goals by members of the group, and the knowledge and skills of the facilitator. Another successful activity was a series of school-based workshops held over a long period of time in a provincial area, organised by a very competent regional numeracy advisor. The results of the project indicate that many ingredients are necessary for a successful large-scale professional development programme. These ingredients include addressing teachers’ beliefs as well as teachers’ knowledge; conducting a series of activities over a long period; facilitators having knowledge and skills in cooperative professional development as well as in the content area of the programme; building in support structures for facilitators; and providing opportunities for facilitators to experience success in the classroom implementation of the professional development topic. Key ingredients are the opportunities for close collaboration and the sharing of ideas and experiences.

Children's Representation and Organisation of Data

This study investigated how children organised and represented data and also examined relationships between their organisation and representation of data. Two protocols, one involving categorical data and the other involving numerical data, were used to interview 15 students, 3 from each of Grades 1 through 5. Although there were differences between Grade 1 students and the rest, the study suggested that numerical data was significantly harder for children to organise and represent than categorical data. Children beyond Grade 1 could make connections between organising and representing data for categorical data but their connections for numerical data were more tenuous. The process of reorganising numerical data into frequencies was not intuitive for the children in this study but they showed greater readiness in recognising and interpreting data that had already been reorganised as a frequency representation. Given this latter result, a pedagogical approach that asks students to make links between raw data and a frequency representation of it may prepare students to create and construct their own frequency representations.

Primary School Students’ Attitudes To and Beliefs About Probability

This chapter relates to the role of attitudes and beliefs in the teaching and learning of probability in schools. A study was conducted in which two Year 7 teachers in an Australian primary school and the students in their combined class participated in a teaching experiment. The study involved implementing a program of probability games and activities which aligned with both the Probabilistic Reasoning framework of Jones et al. (Stiff and Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12, 1999 Yearbook, National Council of Teachers of Mathematics (NCTM), Reston, 1999b), and the formal Year 7 curriculum. The program was designed to improve attitudes to probability, challenge beliefs about luck, and support the learning of probability concepts. Data were collected from students and teachers with respect to attitudes, beliefs, and understanding before and after the program. It was concluded that an activity approach to the teaching of probability improved students’ attitudes to and beliefs about probability, at least in the short term. Students had a greater appreciation of the relevance of probability in the world around them and their superstitions about luck lessened. There was evidence of positive links between attitudes and understanding. It was noted also that a lack of prerequisite number skills impacted on students’ motivation to remain involved. At the end of the study, teachers were more confident and enthusiastic about teaching probability in the future.