Topic Study Group 34:
Research and development in task design and analysis
B306 and B305 Rooms

Background

In our initial plans and reading for the TSG, we discerned a wide range of task types, and several different categorisations:

- problems

- extended tasks

- real tasks

- group tasks

- technology-rich tasks

- realistic tasks

- practising tasks

- tasks which create uncertainty

- tasks which provoke cognitive conflict

- question sequences which scaffold conceptual understanding

- exercising tasks

- non-routine tasks

- structured variation tasks

- application tasks

Clearly as a community we think about tasks not merely as ‘things to be done’ but as crucial in framing subsequent mathematical activity. Identifying relations between task structure, tool use, and mathematical activity can inform the design and analysis of tasks, and also gives insight into the nature of engagement and learning which takes place while tasks are being carried out. It is our hope that vague descriptions like ‘problems’ or distinctions such as ‘open/closed questions’ will give way to thinking instead about what mathematical activity and thinking a task can prompt a learner to do, given an appropriate pedagogical context.

We have a particular interest in tasks which enable learners to make shifts in understanding which are central to secondary mathematics. For example, we are interested in shifts from additive to multiplicative (and exponential) thinking. We are also interested in how learning mathematics at secondary level involves combining earlier conceptual understandings. For example, approaches to trigonometry need to include consideration of the meaning of angle, and maybe theorems about triangles, but need not focus on types and measures of angle which have been learnt earlier. We would welcome attenders at the TSG who are prepared to engage in thinking of this kind.

The aim of the TSG sessions at icme-11 is to develop a coherent, emerging story that reflects the ´state-of-the-art´ in this domain.

Organisation

This TSG consist of invited contributions from a range of international researchers who have worked substantially and consistently in the field. The theme is task design and its underlying design principles and theoretical approaches, as well as task analysis. The field is so vast that we decided to focus only on secondary education (student age 11 years and older).

There are four sessions, and in each session two papers are presented. The presentations will focus on design and contain:

- a theoretical framework that guides task design and/or analysis

- some explicit task design principles

- an example of a task that the audience can work on and/or discuss for a short period during the presentation.

The presenters will work in pairs and include a comparison of their two approaches. Through these comparisons we hope to learn more about the affordances and limitations of the principles and the way they are put into practice.

The reactors will have worked on the task before the conference and will offer critical reflective reports focusing on analysis, containing:

- An elaboration of the examples of tasks (using technology if appropriate)

- Comments on the design principles.

Web-based proceedings will be available before the start of the conference and a contribution to this is expected from both presenters and reactors.

In this way we hope to make the TSG into an active study group in which we can all make progress in our thinking about the design and analysis of tasks.

Contributions

We have decided to invite contributions to ensure that the diversity of task-types is fully represented. Some of the contributors focus on tool use and technology, some focus on the nature of learning, some focus on how tasks reflect the nature of mathematics. We have not chosen presenters who have a ‘delivery’ view of the curriculum; none of the papers assume that tasks somehow cause learning in a direct fashion.

  • Anne Watson (United Kingdom)
    anne.watson@edstud.ox.ac.uk
  • Paul Drijvers (The Netherlands)
    p.drijvers@fi.uu.nl
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Team members:
  • Hanako Senuma (Japan)
    hanako@nier.go.jp
  • Paul Goldenberg (USA)
    pgoldenberg@edc.org
  • Isabelle Bloch (France)
    isabelle.bloch@univ-pau.fr and isabelle.bloch@aquitaine.iufm.fr
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TSG34 Program

ICME-11 TSG 34 Research and development in task design and analysis
Programme

Session 1 (60 mins)

- speaker 1 (30 min): Malcolm Swan (University of Nottingham):
The design of multiple representation tasks to foster conceptual development.

- speaker 2 (30 min): Orit Zaslavsky (Technion – Haifa):
Attention to similarities and differences: a fundamental principle for task design and implementation in mathematics education.

Session 2 (90 mins)

- speaker 1 (30 min): Janet Ainley (University of Leicester):
Task design based on Purpose and Utility.

- speaker 2 (30 min): Jean Schmittau (State University of New York):
Task design: a cultural-historical perspective.

- reactor (15 minutes): Anne Watson

- discussion (15 minutes): Paul Drijvers to chair

Session 3 (60 mins)

- speaker 1 (30 min): Michal Tabach & Alex Friedlander (Weizmann Institute): Designer concerns versus student work: the case of improving grades.

- speaker 2 (30 min): Viviane Durand-Guerrier (University of Lyon):
What we learn from logical analysis of mathematical tasks in a semantic perspective?

Session 4 (90 mins)

- speaker 1 (30 min): Arthur Lee & Allen Leung (University of Hong Kong):
Variational tasks in dynamic geometry environment.

- speaker 2 (30 min): Aad Goddijn (Freudenthal Institute):
Polygons, triangles and capes: designing a one day team task for senior high school.

- reactor (15 minutes): Paul Goldenberg

- discussion (15 minutes): Anne Watson to chair

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