Research Repository

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Developing mathematical fluency: comparing exercises and rich tasks (2017)
Journal Article
Foster, C. (in press). Developing mathematical fluency: comparing exercises and rich tasks. Educational Studies in Mathematics, doi:10.1007/s10649-017-9788-x. ISSN 0013-1954

Achieving fluency in important mathematical procedures is fundamental to students’ mathematical development. The usual way to develop procedural fluency is to practise repetitive exercises, but is this the only effective way?This paper reports three... Read More

Teachers’ appraisals of adjectives relating to mathematics tasks (2017)
Journal Article
Foster, C., & Inglis, M. (2017). Teachers’ appraisals of adjectives relating to mathematics tasks. Educational Studies in Mathematics, 95(3), doi:10.1007/s10649-017-9750-y. ISSN 0013-1954

Curricular implementations are unlikely to deliver the anticipated benefits for mathematics learners if written guidance to teachers is interpreted and enacted differently from the ways that policymakers and curriculum designers intend. One way in wh... Read More

Confidence and competence with mathematical procedures (2016)
Journal Article
Foster, C. (2016). Confidence and competence with mathematical procedures. Educational Studies in Mathematics, 91(2), doi:10.1007/s10649-015-9660-9. ISSN 0013-1954

Confidence assessment (CA), in which students state alongside each of their answers a confidence level expressing how certain they are, has been employed successfully within higher education. However, it has not been widely explored with school pupil... Read More

The definition of the scalar product: an analysis and critique of a classroom episode (2015)
Journal Article
Foster, C., & de Villiers, M. (in press). The definition of the scalar product: an analysis and critique of a classroom episode. International Journal of Mathematical Education in Science and Technology, 47(5), doi:10.1080/0020739X.2015.1117148. ISSN 0020-739X

In this paper we present, analyse and critique an episode from a secondary school lesson involving an introduction to the definition of the scalar product. Although the teacher attempted to be explicit about the difference between a definition and a... Read More

Professional learning through the collaborative design of problem-solving lessons (2015)
Journal Article
Wake, G., Swan, M., & Foster, C. (2015). Professional learning through the collaborative design of problem-solving lessons. Journal of Mathematics Teacher Education, doi:10.1007/s10857-015-9332-9. ISSN 1386-4416

This paper analyses lesson study as a mode of professional learning, focused on the development of mathematical problem solving processes, using the lens of Cultural-Historical Activity Theory. In particular we draw attention to two activity systems,... Read More

Closed but provocative questions: curves enclosing unit area (2014)
Journal Article
Foster, C. (2014). Closed but provocative questions: curves enclosing unit area. International Journal of Mathematical Education in Science and Technology, 46(5), doi:10.1080/0020739X.2014.992989. ISSN 0020-739X

This article describes a task leading to work on curve sketching, simultaneous equations and integration to find the area enclosed between two curves. An initial closed question is used to confront students with a provocative answer, which they then... Read More

Understanding issues in mathematical problem solving and modeling: lessons from lesson study (2014)
Conference Proceeding
Wake, G., Foster, C., & Swan, M. (2014). Understanding issues in mathematical problem solving and modeling: lessons from lesson study

At the heart of our concern, and research, has been to understand how, in classroom learning, students might develop capabilities towards mathematical literacy (Steen, 2001). We have sought to gain insight into how to teach students to be able to app... Read More

Confidence trick: the interpretation of confidence intervals (2014)
Journal Article
Foster, C. (2014). Confidence trick: the interpretation of confidence intervals. Canadian Journal of Science, Mathematics and Technology Education, 4(1), doi:10.1080/14926156.2014.874615. ISSN 1492-6156

The frequent misinterpretation of the nature of confidence intervals by students has been well documented. This article examines the problem as an aspect of the learning of mathematical definitions and considers the tension between parroting mathemat... Read More