Discussion group 17:
The changing nature and roles of mathematics textbooks: form, use, access
Martínez Carranza 2 Auditorium - Civil Eng.

To what extents do mathematics textbooks shape the actual teaching and learning of mathematics, for better or worse? What is the balance between textbook impact and that of other forces, e.g. curricula and assessment, which influence mathematics teaching? What are the interests and forces that drive the publication and adoption of textbooks in different countries? Who are the authors of mathematics textbooks in different countries, and what are their backgrounds?

  • Berinderjeet Kaur (Singapore)
  • Kristina Reiss (Germany)
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Team members:
  • Birgit Pepin (United Kingdom)
  • Steven Rasmussen (USA)
  • Elisa Bonilla (Mexico)
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Aims and focus and discussion plan:

The aim of this discussion group is to steer discussion around the nature and role of textbooks. From the nine papers accepted for discussion it is apparent that the key issues that will guide the deliberations during the sessions are:

  • • The role of textbooks
  • • How do authors represent mathematical knowledge
  • • Teachers’ use of textbooks
  • • Evaluation of textbooks and mathematical tasks in textbooks
  • • Developing quality textbooks

Planned structure for the three sessions:

In keeping with the spirit of discussion groups at ICME, there will be no formal presentations. Rather, time is intended for focused discussion and every participant’s contribution will be welcomed. We hope all those coming to the discussion will share generously their knowledge and experience.

First Session (Plenary – 2 hrs)

During this session we will focus our discussion on:

  • • The role of textbooks
  • • How do authors represent mathematical knowledge

For the discussion to be fruitful, we hope all participants will read papers 4, 8 and 9 before the session.

Second Session (Sub-groups – 2 hrs)

During this session we will form two groups. The first group will discuss:

  • • Teachers’ use of textbooks

Please read papers 2, 3 and 7 if you plan to contribute to this group.

The second group will discuss:

  • • Evaluation of textbooks and mathematical tasks in textbooks
  • • Developing quality textbooks

Please read papers 1, 5 and 6 if you plan to contribute to this group.

Each group will nominate a reporter and a recorder. The recorder will make notes of the proceedings of the group discussion while the reporter will share the proceedings with all members of the discussion group during the third and final session.

Third Session (Plenary – 1 hr)

During this session the reporters from the two sub-groups will present the proceedings of their respective groups. Each reporter will have 20 minutes to do so. The rest of the time will be used for a general discussion on related matters.

A brief of the papers follows:

Paper 1 – A methodology for evaluating middle-years mathematics textbooks by Mal Shield and Shelley Dole (Australia)

This paper describes a methodology developed by the authors for evaluating mathematics textbooks.

Paper 2 – Chinese teachers’ construction of their roles in developing curriculum by Li Jun (China)

This paper is about Chinese teachers who construct their own methods of engaging their students in learning mathematics despite the educational reforms and new methodologies presented via “new” textbooks.

Paper 3 – Pedagogical intent and practice by Ann Heirdsfield, Shelley Dole & Elizabeth Warren (Australia)

This paper is about a realistic situation in which the pedagogical intent of textbooks does not match the classroom practice of teachers using the textbooks.

Paper 4 – A multi-dimensional approach to understanding in mathematics textbooks developed by UCSMP by Denisse Thompson & Sharon Senk (United States)

This paper is about two features of textbooks written by the University of Chicago – SPUR perspective and CARE perspective

Paper 5 – ICE-EM mathematics schools project – development and first steps by Janine McIntosh (Australia)

This paper is about the process of developing textbooks by a national agency so as to improve the teaching and learning of mathematics in Australian schools.

Paper 6 – Mathematical Tasks in textbooks – Developing an analytical tool based on ‘connectivity’ by Bergit Pepin (United Kingdom)

This paper is about a framework against which mathematical tasks in textbooks may be benchmarked when analyzing textbooks.

Paper 7 – Too close, too far: mathematical knowledge and the knowledge of the textbook in geometry 6th and 7th EGB Year by Ibarra Lidia (Argentina)

This paper is about the manner in which textbook materials are used by teachers to help pupils construct their knowledge in geometry. Pupils appear not to have a copy of the textbook. They depend on whatever the teacher decides to Xerox and give them for work. There appears to be a lack of coherence in the construction of knowledge by the pupils resulting from (i) the way in which concepts are explained in the texts, (ii) the lack of the complete text, and (iii) poor knowledge of teachers and their inability to guide the pupils in learning concepts.

Paper 8 – Using situations in a more mathematical way by Guozhong Ding (China)

This paper is about how a change in the intended curriculum manifested by textbooks has brought about a change in pupils attitudes towards the learning of mathematics, but the mathematics classes have become less mathematical. Are too many real life factors diluting the mathematical taste and fascination for the subject? The author has some suggestions as to how real situations may be represented in deeper mathematical ways.

Paper 9 – The reforms and characteristics of Korean elementary mathematics textbooks by Bae Jong Soo, Sihn Hang Gyun, Park Do-yong & Park Mangoo (Korea)

This paper is about how educational reform has impacted Korean elementary mathematics textbooks for the better – learning of mathematics in the context of daily life.

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Questions we might additionally discuss:

Other questions central to the discussion that we might want to discuss include:

  • • What do textbooks look like?
  • • Do textbooks reflect educational standards of specific national or international contexts?
  • • How do the authors represent mathematical knowledge?
  • • How does the interplay between educational values, conceptual understanding, and procedural fluency unfold in mathematics textbooks?
  • • What are the pedagogical intentions (implicit, or explicit) of textbooks?
  • • Does the incipient movement for wiki-based textbooks hold promise for better mathematics programs?
  • • What are the challenges in using new technologies to design and develop coherent educational materials?
  • • What impact do commercial publishers (good, bad, and neutral) have on the nature of mathematics learning in schools?
  • • To what extent does research inform the contents of textbooks?
  • • How are students, or teachers, expected to use the textbook?
  • • Is it a student or teacher book?
  • • Who has access to (which) textbooks in classrooms/schools?
  • • What does that mean in terms of learning opportunities for pupils?
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We have accepted nine papers. You can download them below. We wish to thank the authors for their work and valuable contributions to starting our discussion.

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