Mike Thomas

Research in progress

  • Mathematics Curriculum Change Longitudinal Investigation (Technology Section), 1993-

    The purpose of this study is to monitor mathematics curriculum in New Zealand in order that the mechanisms and effects of curriculum changes can be evaluated, and proposed changes may be better formulated. This study is in its base-line stage. The aim of my part of the collaborative study (with other members of the mathematics education unit) is to capture a "snapshot" of the way in which technology (calculators and computers) is being used in mathematics education in New Zealand schools and the reasons underlying the use. This has to be done in such a way that the procedure can be replicated in 5, 10, 20 years time. This involves ensuring that the "snapshot" is representative of all NZ schools, and that the procedure is robust enough to be duplicated in the future (i.e. the process is to be independent of conditions existing in the present).

  • Algebraic Thinking Processes of Secondary Students, 1993-

  • Problem-Solving by Secondary Algebra Students 1994-

    These projects are investigations of students' understanding of algebra concepts and problem-solving ability and the effect of the computer paradigm on these. The purpose of the research is:

  • to compare the thinking processes of school students with those of 'expert' mathematicians
  • to identify and confirm areas of divergence including the preference for processes.
  • to identify all those areas where the students' preference for procedural methods leads to error or misconceptions.
  • to develop a teaching programme, using materials including custom written computer programs, to attempt to improve students' conceptual understanding of algebra, with particular reference to equations, so that they do not need to use the process preference, will be better able to solve equations, and be less likely to commit errors in algebra.
  • to identify factors influencing students' problem-solving abilities in algebra and to classify these into a hierarchy

  • Student Visualisation in Mathematics 1994 -

    This study is looking at the use of visualisation in mathematics among secondary school pupils who are having difficulty with mathematics. It seeks to show that mathematics recovery may be promoted by enhancing visualisation skills. In this study I am assisted by a masters student. This is a joint project with Ass. Prof. Ivan Beale of the Psychology department.

  • Procedures and Concepts in the Calculus 1995 -

    This study is looking at ways in which computers may be used to enhance students' conceptual understanding of integration. It aims to identify procepts in the calculus and to enable students to learn by combining the benefits of spreadsheets, symbolic manipulators and purpose-written software. The understanding of sixth and seventh form and university students is being investigated in the research.

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    Last updated 16 February 1996

    Send suggestions and queries to e-mail link m.thomas@math.auckland.ac.nz.