Stephen John Norton

Exploring Secondary Mathematics Teachers’ Reasons for Not Using Computers in Their Teaching: Five Case Studies

Abstract Despite the availability of hardware and software, the mathematics staff in a technology-rich secondary school rarely used computers in their teaching. This study investigates the reasons for this phenomenon. The results indicate that individual teachers’ resistance was related to their beliefs about mathematics teaching and learning and their existing pedagogies, including their perceptions about examinations, concerns about time constraints, and preference for particular text resources. It was also found that teachers with transmission/absorption images of teaching and learning and teacher-cent-red, content-focused pedagogy had a restricted image of the potential of computers in mathematics teaching and learning. By contrast, one teacher with images of teaching consistent with social constructivist learning theory and a learner-focused pedagogy had a broader image of the potential of computers in mathematics teaching. Further, staff discourse was also found to be important in determining whether computers would be used by students to facilitate their conceptualisation of mathematics. These finings have implications for professional development related to the integrated use of computers in mathematics teaching.

Teachers’ responses to an investigative mathematics syllabus: Their goals and practices

Despite attempts to encourage teachers to adopt investigative teaching behaviours, there is strong evidence of the resilience of teacher-centred school mathematics teaching. This study uses interpretive research methods to explore teachers’ practices and relate these to their goals. Analysis of case studies indicates that syllabus documents have influenced teachers’ choices of teaching strategies. Most teachers had calculation-based goals for less able students and conceptual goals for more able students. Three distinct teaching strategies were identified and described. The relationships between teachers’ goals, beliefs, and practices can guide the construction of teacher programmes that focus on student construction of knowledge.

Students' Attitudes towards Mathematics in Single-Sex and Coeducational Schools.

This paper examines students’ attitudes towards mathematics at the secondary school level. Using five of the Fennema-Sherman scales, the attitudes of boys and girls in Grades 8 to 12 in four schools were compared: a single-sex boys’ and a single-sex girls’ private school, and a state and a private coeducational school. Multivariate analysis of variance was used to guide an exploration of how students’ attitudes varied according to grade, sex and educational setting. There were no differences between students in the two coeducational schools. In general, students’ attitudes were found to be less positive in more senior grades; and overall, boys had more positive attitudes than girls. There were clear differences between boys and girls on the Mathematics as a Male Domain scale, with girls being less stereotyped in their perceptions than boys. Except for this scale, effects related to the sex of the student were small, and effects relating to grade level and school type on all variables were also small. Implications are drawn for future research in this area.

Pedagogies for the Engagement of Girls in the Learning of Proportional Reasoning through Technology Practice.

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 interventions were proportional reasoning and ratio. A design based research methodology was adopted. The study started with the assumption that by integrating mathematics study with technology practice students would see the mathematics as authentic and understandable. The results of the first intervention indicated that a significant proportion of the girls did not develop the hoped for improvement in perceptions about the value of studying mathematics through technology practice, despite an improvement in their understanding of proportion and ratio. These results informed the second intervention in which modified tasks and pedagogy were implemented. The results of the second intervention were similar in terms of cognitive outcomes. However, when students were given explicit scaffolding in “within” and “beyond” the domain of mathematics integration as well as tasks that they considered authentic, student perceptions of mathematics study improved.

Mathematics engagement in an Australian lower secondary school

Abstract The importance of actively engaging in mathematics discourse in order to learn mathematics is well recognized. In this paper, I use Basil Bernstein’s concepts of pedagogic discourse to document and analyse academic learning time of students in Years 8 and 9 at a suburban lower secondary school: in particular, for what proportion of class time students reported being academically engaged, their explanations for this engagement and how they felt about the discourse. It was found that many students had disengaged from mathematical endeavour as a result of the failure of the instructional discourse either to engage students or to serve the purpose of developing discipline-specific content knowledge. The reasons for this relate to the overemphasis on mundane mathematics resulting in some students lacking the cognitive tools to engage with the concepts and having neither the intrinsic nor instrumental motivation to persist with secondary school esoteric mathematics. The implications for mathematics curriculum development are discussed.