Skip to main content

Mathematical knowledge for teaching

Don Víctor Gómez Garza Auditorium (FACPYA), C101, C102 and C103

TSG 27 focuses on the problem of teachers’ knowledge of mathematics– what mathematics primary and secondary teachers know and use, as well as what they need to know and know how to use. This TSG investigates how such questions can be studied, and the different answers that scholars have developed. In addition, from the perspective of practice, the TSG will also explore a few different approaches to helping teachers learn the mathematics they need, how well these have worked, and the challenges of figuring out whether a particular approach “works.”

Concern about teacher content knowledge has increased over the last 30 years. Some concerns emanate from perceived lacks; others from the increasing knowledge demands on teachers resulting from reforms in school curricula or teacher policies. Across countries the pressing issues vary. In common, however, are questions about what teachers should know, what they do know, what are valid and reliable indicators of such knowledge, whether and how such knowledge can be measured or assessed, as well as where, when and how this knowledge is best acquired and strengthened.

TSG 27 at ICME11 provides us with time and space for focused examination on the research that has and is being done in different settings, as well as on related innovations in teacher education programs. TSG 27 affords us the opportunity for interrogating varied perspectives and diverse outcomes that are evident across studies, and for sharing experiences of practical developments informed by this work.


Organizing team composition


Focus Questions

The Sessions

Outcomes for this Topic Study Group

Call for Papers and Expressions of Interest

Accepted papers

List of Authors and Paper Titles

Papers and discussion documents

Team chairs:

Jillian Adler (South Africa/ UK)

Deborah Lowenberg Ball (USA)

Team members:

Li Jianhua (China)

Yasuhiro Sekiguchi (Japan)

Heinz Steinbring (Germany)


TSG27 complements and is focused differently from the work of Topic Study Groups 28 and 29. These groups are more generally concerned with pre- and in-service teacher education. We are concerned with teacher content knowledge and its relationship to teaching skill. This implies that mathematical knowledge for teachers and mathematical knowledge for professional mathematicians have similarities and also important differences. What are these differences? These differences are not restricted to different amounts and different areas of mathematical knowledge. The differences have to be understood on the basis of different epistemological views on the nature of mathematical knowledge in different contexts and on the function for which the mathematical knowledge is used. The call for papers below is indicative of this focus. We are not concerned with teacher beliefs, the relationship between beliefs and practice, nor with teacher education practice and approaches that do not focus on knowledge of mathematics and its use in teaching. These aspects of mathematics teacher education, although important, are in the background for this Topic Study Group, whereas they are likely to be more in focus on TSG28 and 29.

Focus Questions

TSG 27’s work is framed by the following focus questions:

Q1. What are (and have been) different perspectives about mathematical knowledge for teaching? What are the bases––theoretical or empirical––for these perspectives? Where are areas of overlap and agreement? Where and what are major differences? Do these represent substantially conflicting views, or do they simply reflect giving attention to different aspects of the question?

Q2. What are (and have been) different methods of studying mathematical knowledge for teaching ––what teachers know and use, or what they need to know and know how to use? What are key common and distinct aspects of the methods used to answer these questions?

Q3. What are (and have been) different empirical research fields or contexts e.g. in primary or secondary classrooms, with or without digital technologies, with or without teachers as co-researchers, in mathematics or maths method classes for teachers? How have these shaped the research questions pursued?

Q4. How could research results gained by different research methodologies (quantitative, qualitative, interpretative research methods) support teachers developing their mathematical knowledge and their professional view on the nature of mathematics in teaching?

Q5. What are some distinct approaches to helping teachers develop the mathematical knowledge they need to know and know how to use? What kinds of evidence are there about how these function and with what effects?

The Sessions


Day 1, MONDAY 7 July 1 hour: Framing the work of the group

Major issues in the terrain of maths knowledge for teaching -Jill Adler,

Deborah Ball An epistemological orientation to the problem of MKT

…Heinz Steinbring

Day 2: WEDNESDAY 9 July 90 mins.

Work in smaller groups on a selection of themes informed by the

submitted papers.

We ask that all participants read the papers prior to the Congress. Some

of the papers speak to more than one of the themes. We think these are

interesting themes that can both inform the discussion, and give scope

for those who have contributed papers to talk about their work within a

larger theme.

Provisional themes * Are MKT and its components most effectively

described and grasped by topic? Big ideas? Mathematical use? (Yasuhiro

Sekiguchi and Mercy Kazima) * Are categories or distinctions within MKT

useful and for what? (Li Jianhua, Dany Huillet) * Is MKT teachable and

in what forms? (Craig Pournara, Raven McCrory). * Is MKT measurable? If

so, what kinds of measures are in use and in what contexts, for what

purposes? How do such measures interact with environments of high stakes

assessments. (Mark HooverThames, Stefan Krauss)

Day 3. FRIDAY 11 JULY, 1 Hour.

Synthesis: What do we seem to agree on, what not, and why?

Brent Davis and Tim Rowland

Day 4 SATURDAY 12 July 90 Mins: Ways forward for this line of work;

critical next steps

Outcomes for this Topic Study Group

1. Greater shared understanding of breadth of question, ranging and developing methodologies (approaches and methods and how they shape the work) as well as emerging knowledge/understanding

2. Exemplars of practice

3. Post–ICME report/publication

Call for Papers and Expressions of Interest

Thirty papers have been received and accepted. See details below. We welcome other participants to the sessions at the Congress.

Accepted papers

The papers listed alphabetically below have all been accepted for discussion in the Topic Study Group TSG27.

(Please note the paper by Thames et al. is not in alphabetical order. It has just been received and uploaded on to the site. The paper can be found at the end of the list. Message posted-20 Jun 08.)

(Please note that the papers by Heid and Senk et al. are not in alphabetical order. They have just been received and uploaded on to the site. The papers can be found at the end of the list. Message posted-30 Jun 08.)

(Please note that the paper by Kristjansdottir is not in alphabetical order. It has just been received and uploaded on to the site. The paper can be found at the end of the list. Message posted-05 Jul 08.)

List of Authors and Paper Titles

Authors Paper Title

Susan Addington, David Dennis & Madeleine Jetter Measurement and Multiplicative Thinking in Prospective Elementary Teachers

Solange Amorim Amato Avoiding the Teaching of Mathematics

Sarah Bansilal Can reform pedagogies be facilitated by teachers who themselves do not have a sound concept image of the crucial mathematics?

Kim Beswick Middle School Mathematics Teachers’ Knowledge for Teaching

Tim Burgress Statistical Knowledge for Teaching: Exploring it in the Classroom

Charalambos Y & Charalambous Mathematical Knowledge for Teaching and Teaching Practices: A Virtual-Design Approach to Study a Complex Relationship

Brent Davis “Concept Study”: Open vs. Closed Understandings of Mathematical Ideas

Juan D. Godino, Mauro Rivas & Walter F. Castro Epistemic and Cognitive Analysis of an Arithmetic- Algebraic Problem Solution

Pedro Gomez & Maria Jose Gonzalez Mathematics Knowledge for Teaching Within a Functional Perspective of Preservice Teacher Training

Raisa Guberman & Dvora Gorev Learning Mathematics for Teaching: Sources of Subject-Matter Knowledge

Lenni Haapasalo & Jozef Hvorecky Perspectives on Mathematical Knowledge for Teaching

Danielle Huillet Mathematics For Teaching: An Anthropological Approach

Mercy Kazima Investigating Mathematics for Teaching through Probability in Practice

Stefan Krauss, Michael Neubrand, Werner Blum & Jürgen Baumert The Professional Knowledge of German Secondary Mathematics Teachers: Investigations in the Context of the COACTIV Project

Anna Kristjansdottir Developing of teachers’ professional knowledge of mathematics. Historical, present and future perspectives

Alexandra Lawson & Wendy Stienstra Pre-service Students’ Partial Understandings of Elementary Mathematics Concepts and Procedures

Katie Makar Knowledge for Teaching Mathematics Through Inquiry

Raven McCrory Resource Use by Instructors of Mathematics Classes for Future Elementary Teachers: Results of a Survey

Shweta Naik The Measures for Understanding Teachers’ Mathematical Knowledge for Teaching Fractions- How do they really work?

Aihui Peng Inquiry into Students’ Mathematical Thinking Through Error Analysis as a Means to Teacher Development

Craig Pournara Developing Mathematical Knowledge for Teaching in a Pre-service Secondary Teacher Education Programme in South Africa

Tim Rowland The Knowledge Quartet: A Theory of Mathematical Knowledge in Teaching

Allan Tarp CATS, Count&Add in Time&Space – a Natural Way to Become a Mathematics Teacher

Kazuko Ito West Japanese High School Mathematics Teacher Competence in Real World Problem Solving

Zhonghe Wu & Shuhua An Using the Model-Strategy-Application Approach to Developing Pre-service Teachers’ Knowledge and Assessing Their Progress in Math Methods Courses

Mark Hoover Thames, Laurie Sleep, Hyman Bass, and Deborah Loewenberg Ball Mathematical Knowledge for Teaching (K-8):Empirical, Theoretical, and Practical Foundations

M. Kathleen Heid Mathematical Knowledge for Secondary School Mathematics Teaching

Sharon L. Senk, Ray Peck, Kiril Bankov, Maria Teresa Tatto Conceptualizing and Measuring Mathematical Knowledge for Teaching: Issues from TEDS-M, an IEA Cross-National Study1

Papers and discussion documents

Addington_ICME11_TSG27_prop (90.00 KB)

Amato_ICME11_TSG27_fullpaper (91.00 KB)

Bansilal_ICME11_TSG27_fullpaper (105.00 KB)

Beswick_ICME11_TSG27_fullpaper (222.00 KB)

Burgess_ICME11_TSG27_prop (173.00 KB)

Charalambous_ICME11_TSG_27_prop (44.00 KB)

Davis_ICME11_TSG27_prop (103.00 KB)

Godino_ICME11_TSG27_fullpaper (188.00 KB)

Gomez_ICME11_TSG27_prop (104.00 KB)

Guberman_ICME11_TSG27_fullPaper (67.00 KB)

HaapasaloHvor_ICME11_TSG27_prop (275.00 KB)

Huillet_ICME11_TSG27_fullpaper (99.00 KB)

Kazima___ICME11__TSG27_prop (54.00 KB)

Krauss_ICME11_TSG27_fullpaper (131.00 KB)

Lawson_ICME11_TSG27_fullpaper (243.00 KB)

McCrory_ICMI_TSG27_prop (63.00 KB)

NAIK_ICME_TSG27 (127.00 KB)

Peng_ICME11_TSG27_fullpaper (177.00 KB)

POURNARA_ICME11_TSG27_fullpaper (58.00 KB)

Rowland_ICME11_TSG27_fullpaper (60.00 KB)

Tarp_ICME11_TSG27_fullpaper (167.00 KB)

West_ICME11_TSG27_fullpaper (100.00 KB)

Wu_ICME11_TSG27_prop (224.00 KB)

Thames_ICME11_TSG27_fullpaper (152.00 KB)

Heid_ICME11_TSG27_fullpaper (149.00 KB)

Senk__ICME11_TSG27_fullpaper (220.00 KB)

Kristjansdottir_ICME11_TSG27_fullpaper (181.00 KB)

Makar_ICME11_TSG27_Prop_1_ (123.00 KB)