Lesson Study

Challenges in Mathematics Education

Maitree Inprasitha, Masami Isoda, Patsy Wang-Iverson, Ban-Har Yeap

• Publisher: WSPC
• Year: 2015
• eBook ISBN: 9789814641081
• Topic: Mathematics
• Subtopic: Teaching Mathematics
• Index: Mathematics

Classroom Innovations through Lesson Study is an APEC EDNET (Asia-Pacific Economic Cooperation Education Network) project that aims to improve the quality of education in the area of mathematics. This book includes challenges of lesson study implementation from members of the APEC economies.

Lesson study is one of the best ways to improve the quality of teaching. It is a model approach for improvement of teacher education across the globe. This book focuses on mathematics education, teacher education, and curriculum implementation and reforms.

Contents:

• The Role of Lesson Study in Overcoming Challenges in Mathematics Education:
  • Mathematics Education for the Knowledge-Based Society (Alan J Bishop)
  • Mathematical Thinking for Classroom Decision Making (Kaye Stacey)
  • Setting Lesson Study within a Long-Term Framework of Learning (David Tall)
  • Lesson Study: An Essential Process for Improving Mathematics Teaching and Learning (Akihiko Takahashi)
  • Comparative Study of Mathematics Classrooms — What can be Learned from the TIMSS 1999 Video Study? (Frederick K S Leung)
  • The Science of Lesson Study in the Problem Solving Approach (Masami Isoda)
  • Preparing Ground for the Introduction of Lesson Study in Thailand (Maitree Inprasitha)
• Perspectives on Lesson Study and Professional Development:
  • History of Lesson Study to Develop Good Practices in Japan (Shizumi Shimizu & Kimiho Chino)
  • What have We Learned about Lesson Study Outside Japan? (Catherine Lewis)
  • Enhancing Mathematics Teachers' Professional Development through Lesson Study ~ A Case Study in Singapore ~ (Ban-Har Yeap, Peggy Foo & Poh Suan Soh)
  • Using Lesson Study to Develop an Approach to Problem Solving: Adding and Subtracting Fractions (Kazuyoshi Okubo & Hiroko Tsuji)
  • Prospective Teacher Education in Mathematics through Lesson Study (Maitree Inprasitha)
  • In-service Teacher Education in Mathematics through Lesson Study (Soledad A Ulep)
• Lesson Study for Illustrating Innovative Approaches in the Classroom:
  • Transforming Education through Lesson Study: Thailand's Decade-Long Journey (Maitree Inprasitha)
  • Mathematics Teachers Professional Development through Lesson Study in Indonesia (Marsigit)
  • Lesson Study in Chile (Grecia Gálvez)
  • Initiating Lesson Study to Promote Good Practices: A Malaysian Experience (Chap Sam Lim & Chin Mon Chiew)
  • Using Lesson Study as a Means to Innovation for Teaching and Learning Mathematics in Vietnam: Research Lesson on the Property of the Three Medians in a Triangle (Tran Vui)
  • Lesson Study in Singapore: A Case of Division with Remainder in a Third Grade Mathematics Classroom (Yanping Fang & Christine Kim Eng Lee)
  • Enabling Teachers to Introduce Innovations in the Classroom through Lesson Study (Soledad A Ulep)
  • What is a Good Lesson in Japan? An Analysis (Takeshi Miyakawa)
  • Using Lesson Study to Connect Procedural Knowledge with Mathematical Thinking (Patsy Wang-Iverson & Marian Palumbo)

Readership: Mathematics educators of teacher training colleges, mathematics teachers, prospective teachers (elementary and secondary school) and undergraduate students in mathematics.
Key Features:

• Presents the world reform movement by top researchers
• Includes the challenges of lesson study and videos of model lessons in the world (lesson videos will be available on the website: http://www.criced.tsukuba.ac.jp/math/apec)
• Includes the Japanese teaching methods called “problem-solving approaches”

Section 1

The Role of Lesson Study in Overcoming Challenges in Mathematics Education

Alan Bishop opens the section by providing the readers with the idea of using ‘Lesson Study’ as a means for developing both the theory and practice of mathematics teacher education under the title “Mathematics Education for Knowledge-based Society.” Kaye Stacey shows some analogies of mathematical thinking with schooling, way of learning mathematics, and teaching mathematics. She offers illustrations of how strong mathematical thinking can provide teachers with many possible decisions and actions. Lessons are considered along with students’ mathematical understanding via interesting pragmatic examples shown in the paper. In addition, the paper concludes with the teaching of mathematics, drawing on general pedagogy as well as mathematical pedagogical content knowledge to contribute to the solution. David Tall makes some remarkable statements about mathematics classrooms related with Lesson Study in which it serves as the platform for long-term development of individual children. The long-term development depends not only on the experiences of the lesson, but in the prior experiences of the children, and how those prior experiences have been integrated into the children’s current knowledge described by the good practices of mathematics classrooms using Lesson Study in Japan according to the Developmental Framework through Embodiment and Symbolism of the three mental worlds. Akihiko Takahashi provides a vivid idea of how Lesson Study can be used as a process for improving mathematics teaching and learning. He reminds us that we need to distinguish between two types of professional development programs; one is to learn new ideas and knowledge, the other is to practice how to incorporate new ideas and procedures in various situations. He then suggests Lesson Study as an ideal phase of the two Professional Developments. TIMSS has had a great impact on many countries. The TIMSS 1999 Video Study has become a potential tool in this APEC project; it has become accessible to more people through the recent availability of all 53 public release videos online (www.timssvideo.com). Frederick K.S. Leung provides the analysis of TIMSS Video Study data for Hong Kong, SAR to see whether there are classroom practices that can be used to explain East Asian students’ high achievement in mathematics. He also provides an idea on how conflicting results coming from qualitative and quantitative analyses point to the complexity in interpreting video data on classroom practices and of achievement data in international studies. This also provides us with insight into how cultural aspects come into play in interpreting data. Masami Isoda then discusses the meaning of Lesson Study in the Japanese historical context combined with how theories of mathematics education as a science of teaching have been built by using the subject-based lesson study and school-based lesson study. Obviously, these theories are not meant to prove a scientific proposition but rather to develop classrooms in schools implementing the problem solving approach. Teachers develop their own theory of teaching and improve their practice in Lesson Study cycle. In the last chapter, Maitree Inprasitha describes how to implement Lesson Study to be sustainable in Thailand in which it is integrated with the Open Approach in teachers’ professional development. There are some social and cultural aspects influencing the Thai educational system to which the reformers have to be sensitive when they attempt to introduce some innovations. In addition, he shows some empirical data of what has been changing in both teachers and students in Thai school systems that would yield deeper comprehension for those who will use this innovation in their context, especially the schoolteachers who take major roles in the classroom.

SECTION 1.1

MATHEMATICS EDUCATION FOR THE KNOWLEDGE-BASED SOCIETY

Alan J. Bishop

1. WHAT AM I OFFERING IN THIS CHAPTER?

This chapter will offer the following five contexts for you, which I will briefly clarify now:

•A frame for discussion?

We are focussed on teacher education in mathematics and particularly on the use of ‘lesson study’ as a means for developing both the theory and the practice of mathematics teacher education. But it is necessary to keep this topic framed.

•A context for considering generalisations?

Mathematicians and mathematics educators love generalising – it is valued as one of the basic means for developing mathematical ideas. The challenge for us however is that where mathematics seeks to develop ever more abstract ideas, teacher education must always strike a balance between abstract theory and concrete practice.

Both student teachers and experienced teachers will reject any ideas for teacher education that does not strike what they feel is the right balance between the two objectives.

•Some hidden assumptions made explicit?

In my research on values in mathematics education, it is clear that most values teaching and learning take place implicitly in the mathematics classroom. This is also likely to be the case in the context of this project, which is even more problematic since we come from very different cultural and social contexts. It is vital that in our discussions we keep aware of the hidden assumptions and values which are not necessarily shared by all.

•A personal view on the values involved in this project?

Having mentioned values above, it is necessary for me also to clarify my values and assumptions within this topic. No researcher is value-free!

•An opening up of some of the issues involved?

Although my topic is not especially about lesson study, nevertheless I feel it is necessary for me at least to expose my ideas about some of the issues involved in this development.

2. DEFINITION OF KNOWLEDGE-BASED SOCIETY

My topic is certainly an interesting one, full of issues of definition, values, goals and predictions. But in 2003 there took place the World Science Forum in Budapest, Hungary, and the theme for that conference was Knowledge and Society.¹ The forum provided a useful definition of a Knowledge-based society, and here are the main points:

•A knowledge-based society is an innovative and life-long learning society.

•It possesses a community of scholars, researchers, technicians, and firms engaged in research and in production of high-technology goods and service provision.

•It forms a national innovation-production system, which is integrated into international networks of knowledge production, diffusion, utilization, and protection.

•Its communication and information technological tools make vast amounts of human knowledge easily accessible.

•Knowledge is used to empower and enrich people culturally and materially, and to build a sustainable society.

•National and international networks of learning communities.

•Information Communications Technology (ICT) goods and service provision.

In some ways this is a formidable list, containing both descriptive and prescriptive ideas. Every country would have something to aspire to from this list and all of us attending this conference here today would have reservations about whether our countries are achieving any of these goal descriptions. But it is good to have such a challenging list to begin our deliberations here.

3. HOW TO CONSIDER EDUCATION IN THIS NEW CONTEXT?

In particular it is a challenge to consider education within this new context. But is a knowledge-based society really a new idea? We should ask ourselves what is different now. Society has always used and taught knowledge, but originally it was the family context which provided the education, from whom the knowledge came and with the elders being the ‘teachers’. Gradually as education became more formalised, the schools developed from the families. Also the content of what was taught became more organised, and became based on the knowledge supplied from the ‘academy’. Finally the teachers became officially recognised, needing official qualifications and eventually being specifically trained.

Now as the knowledge society is developing, we find that the new knowledge comes from ‘outside’ the accepted sources: from the Web, from the media, from peer-group networks and also from wide international sources. But many questions also arise for us in education: Whose knowledge is it? Who is producing it? Whose personal knowledge is being exploited, and whose personal knowledge is being ignored? Basically the question now facing us is: What is the source of the authority of any new knowledge?

4. KINDS OF EDUCATION => KINDS OF MATHEMATICS EDUCATION

Coombs (1985) gave a very helpful analysis in his book ‘The world crisis in education.’ He based his analysis on three kinds of education: formal, non-formal and informal. According to Coombs, there are crucial distinctions to be made between these, and I feel that we too need to be aware of these within our special field. Thus I offer you three kinds of mathematics education, based on Coombs’ work, whose distinctions I think are crucial in considering our roles in a knowledge-based society.

Formal mathematics education is the formal system most of us are part of, and it consists basically of the state system which exists in most countries. It is largely the only kind which gets recognised in research in our field, and operates up to student ages of around 16 or 18 years. It is:

•Structured

•Compulsory

•A coordinated system, which is

•Staffed by recognised teachers.

Non-Formal mathematics education is the kind of non-compulsory and optional education offered by courses such as for adult education, or vocational education and training. For formal school-age students, it could be after school classes, cram-school classes etc. Generally it is:

•Structured

•Non-compulsory/optional

•With a specific focus

•Coordinated to a certain extent, and

•Some teachers are recognised, some not.

Informal ma...

Table of contents

• Cover Page
• Title Page
• Copyright
• Contents
• Foreword
• Section 1: The Role of Lesson Study in Overcoming Challenges in Mathematics Education
• Section 2: Perspectives on Lesson Study and Professional Development
• Section 3: Lesson Study for Illustrating Innovative Approaches in the Classroom
• Contributors