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Unifying Complexity in Mathematics Teaching-Learning Development: A Theory-Practice Dialectic

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Transforming Mathematics Instruction

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

This chapter addresses theory in relation to mathematics teaching and learning development, drawing on a research study to exemplify theoretical perspectives. In particular it addresses difficulties and issues which arise in a developmental process, from both theoretical and practice-based points of view. The areas of theory are those of inquiry, community and critical alignment, which address developmental processes in mathematics learning and teaching; documentational genesis and instrumentation theory, which address the development of knowledge in teaching; and finally the use of a framework from activity theory, which addresses issues and tensions that emerge from observation and analysis in the research. The illustrative research study addresses perceptions of learning and its outcomes between a teaching team and a cohort of engineering students learning mathematics in a university system. Overall the chapter seeks to address complexity in the developmental process and important synergies between theory, practice and research.

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Notes

  1. 1.

    Relevant here is a special issue of the journal ZDM (ZDM, Vol. 4, Issue 5) which focuses on the didactical triangle of teacher, student and mathematics and important relations between mathematics teaching and learning.

  2. 2.

    Space here has not allowed a dual focus on the development of teaching at both school and university levels. Developmental research at school level focusing on inquiry approaches to developing teaching, used by teachers and didacticians, with activity theory analyses can be found in Jaworski and Goodchild (2006) and Jaworski (2008a).

  3. 3.

    HE STEM has been a major government-sponsored programme in higher education focusing on the subjects science, technology, engineering and mathematics. Funding has been available for projects promoting teaching and learning development within this programme.

  4. 4.

    A level GCE (Advanced Level General Certificate of Education) is a national examination (at 16+) with high stakes outcomes for higher-level study. Many UK universities require the highest grade in A level to qualify for university study in mathematics.

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Acknowledgement

I would like to acknowledge the contributions of Janette Matthews, Carol Robinson and Tony Croft, without whom the examples from research would not have been possible. I also thank two anonymous reviewers for their insights which helped me address important issues in an earlier draft.

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Authors and Affiliations

  1. Mathematics Education Centre, Loughborough University, Loughborough, LE11 3TU, UK

    Barbara Jaworski

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  1. Barbara Jaworski
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Correspondence to Barbara Jaworski .

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Editors and Affiliations

  1. Department of Teaching, Learning and Culture, Texas A&M University, College Station, Texas, USA

    Yeping Li

  2. School of Education, University of Michigan, Ann Arbor, Michigan, USA

    Edward A. Silver

  3. Dept. of Mathematics, East China Normal University, Putuo, China

    Shiqi Li

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Jaworski, B. (2014). Unifying Complexity in Mathematics Teaching-Learning Development: A Theory-Practice Dialectic. In: Li, Y., Silver, E., Li, S. (eds) Transforming Mathematics Instruction. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-04993-9_24

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