Research **Repository**

See what's under the surface

Formative assessment lessons for concept development and problem solving(2018)

Conference Proceeding

Swan, M., & Foster, C. (2018). Formative assessment lessons for concept development and problem solvingFormative assessment is the process by which teachers and students gather evidence of learning and then use this to adapt the way they teach and learn in the classroom. In this paper we describe a design research project in which we integrated format... Read More

How do you describe mathematics tasks?(2018)

Journal Article

Foster, C., & Inglis, M. (2018). How do you describe mathematics tasks?. Mathematics Teaching -Derby-, 260, ISSN 0025-5785Colin Foster and Matthew Inglis ask what it means to describe a task as ‘rich’.

Defining a rhombus(2018)

Journal Article

Foster, C., Hodgen, J., & Küchemann, D. (in press). Defining a rhombus. Mathematics Teaching -Derby-, 260, ISSN 0025-5785Colin Foster, Jeremy Hodgen and Dietmar Kuchemann exlore how the use of examples and counter-examples can support students developing understandings of definitions.

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 0013-1954Achieving 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

Book review. Validity in educational and psychological assessment, by Paul E. Newton & Stuart D. Shaw.(2017)

Journal Article

Foster, C. (2017). Book review. Validity in educational and psychological assessment, by Paul E. Newton & Stuart D. Shaw. Research in Mathematics Education, 19(2), doi:10.1080/14794802.2017.1318086. ISSN 1479-4802

Questions pupils ask(2017)

Book

Foster, C. (2017). Questions pupils ask. Mathematical AssociationIf two minuses make a plus, why don’t two pluses make a minus? Is there a formula for factorial? And why isn’t pi a whole number? In this collection of over 40 articles from the journals Mathematics in School and Symmetry Plus, Colin Foster takes Que... 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 0013-1954Curricular 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

Two-dice horse race(2016)

Journal Article

Foster, C., & Martin, D. (2016). Two-dice horse race. Teaching Statistics, 38(3), doi:10.1111/test.12108. ISSN 0141-982XIn this article we analyse the “two-dice horse race” task often used in lower secondary school, in which two ordinary dice are thrown repeatedly and each time the sum of the scores determines which horse (numbered 1 to 12) moves forwards one space. T... 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 0013-1954Confidence 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 0020-739XIn 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 1386-4416This 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

The Convergent–Divergent Model: an opportunity for teacher–learner development through principled task design(2015)

Journal Article

design. ISSN 1759-1325The tasks that mathematics teachers are invited to use in their classrooms have profound effects not just on the learners who do them but also on the teachers themselves. This paper introduces the Convergent–Divergent Model (CDM) for the design of ma... Read More

Expression polygons(2015)

Journal Article

Foster, C. (2015). Expression polygons. Journal of Mathematics Teacher Education, 109(1), ISSN 1386-4416A problem-solving task can generate extensive opportunities for developing mathematical fluency in solving linear equations.

Re-conceptualising conceptual understanding in mathematics(2015)

Conference Proceeding

Kent, G., & Foster, C. (2015). Re-conceptualising conceptual understanding in mathematicsIn this theoretical paper we explore interrelationships between conceptual and procedural understanding of mathematics in the context of individuals and groups. We question the enterprise of attempting to assess learners’ mathematical understanding b... 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 0020-739XThis 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 studyAt 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 1492-6156The 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

About Nottingham Repository

© 2018 Worktribe

This application uses the following open-source libraries:

Apache License Version 2.0 (http://www.apache.org/licenses/)

Apache License Version 2.0 (http://www.apache.org/licenses/)

SIL OFL 1.1 (http://scripts.sil.org/OFL)

MIT License (http://opensource.org/licenses/mit-license.html)

CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)