Reasoning, proof and proving in mathematics education

CSI Hall - Phsyical-Mathematical

Organizing team composition

Submission specifications

Guidelines for publication

Papers and discussion documents

Hans Niels Jahnke (Germany)

Maria Alessandra Mariotti (Italy)

Gabriel Stylianides (USA)

kirsti.hemmi@skolutveckling.se and kirsti@math.su.se

The ICME 11 Topic Study Group on « Reasoning, proof and proving in mathematics education » will serve a dual role:

Present an overview of the current state of art in the topic “Reasoning, proof and proving in mathematics education (RPP),” and expositions of outstanding recent contributions to it, as seen from an international perspective

Sharing of ongoing work and perspectives

The topic will be considered at all levels – elementary, secondary, university, and teacher knowledge. Participants could report on research work, on classroom teaching, or on the design of teaching environments or of teaching units for RPP. They also could report on advances made in the development of theoretical frameworks or approaches.

The work of this TSG will focus on four broad themes.

1) Epistemological / historical aspect

What is the role of RPP in the history of mathematics?

What is the role of RPP in the developmental processes of mathematics as a discipline?

What is the status of RPP in mathematics as an academic subject?

What is the role of experimentation?

To what extent should mathematical proofs in the empirical sciences, such as physics, figure as a theme in mathematics teaching so as to provide an adequate and authentic picture of the role of mathematics in the world?

2) Curriculum and textbook aspect

A description of the status of RPP at school, at different grade levels, and in various countries

International comparison of the above status of RPP among countries

Discussion of the mathematical contexts and developmental progression of RPP in curriculum and textbooks

Students’ and teachers’ views or concepts of RPP

Students’ main difficulties in learning RPP

Describing and interpreting students’ behaviors in RPP tasks

Approaches to the teaching of RPP, at different grade levels, and in various mathematical subject areas

What do teachers need to know for the teaching of RPP?

Design of appropriate teaching interventions to overcome students’ difficulties in coping with RPP tasks

Instructional approaches to RPP that have shown some success

What is the role of dynamic software in the teaching of proof?

TSG 18 « Reasoning, proof and proving in mathematics education » invites the submission of contributions related to the topic of the group, as described by the questions, problems and issues listed above. The organizers of the Topic Study Group welcome proposals from both researchers and practitioners and encourage contributions from all countries, representing all economic contexts and cultural backgrounds. Reflecting this diversity is a major goal of the TSG 18 organizers.

The submitted contributions will be reviewed by the TSG 18 organizing team. The accepted contributions will be published on the TSG18 website (http://tsg.icme11.org/tsg /show/19) prior to the congress and presented in poster format during the congress sessions of the group. In the poster presentation it is expected that the contributors will be available to discuss and share their work with the other group members. In addition, authors of some papers, to be selected by the organizing team of the TSG, will be invited to have a paper presentation to the whole group, as a focus for collective discussions. All contributors will be invited to bring copies of accepted papers, including expanded versions and CDs, to be presented-by-distribution during the TSG sessions.

If the circumstances make it practical and desirable, the organizing team will publish a conference book as on the work of TSG 18. Should this happen, the editors, editorial process, and content will be the subject of discussion among the TSG 18 organizing team.

**Submission specifications**

The first version of a submissions can be a short proposal of 3 pages, clearly indicating the aims and the nature of the work, and giving a synopsis of its content and results. Authors of accepted submissions are then invited to send a longer version (8-10 pages) for publication on the Web site of the congress. This published version should present the aims and the nature of the work, the underlying theoretical frameworks or assumptions, the ways it was carried out or the methods that were used, and provide the results and/or questions that arise from the work.

Initial submissions (3pages) should be sent by December 15, 2007, as an email attachment to both chairs of the Topic Study Group at the following addresses:

Hans Niels Jahnke (Germany)

Information about acceptance of the initial submissions, with recommendations for the final version(8-10 pages), will be available by the end of January.

Final versions of accepted submissions should be sent by March 31, 2008.

**Guidelines for publication**

Final texts should be 8 pages (Times 12, single-spaced lines) and fit into an outline of 16 cm x 25 cm. Each submission must have a title (bold, capital, centered, Times 16), be in .doc or .pdf file and be written in English. Indicate below the title, the name of the author(s), affiliation and country and email address (centered, Times 14). Underline the name of the participating author(s) and include a 200-word abstract (Times 10). Indicate whether the paper is research or practice oriented and mention the main theme of the presentation (if possible chosen from among the themes listed in the call for contributions).

International Newsletter on the Teaching and the Learning of Mathematical Proof.

ICME 11; Topic Study Group 18

Session 1: Epistemology (60 minutes)

Maria G. Bartolini Bussi (long presentation 30 minutes):

Experimental mathematics and the teaching and learning of proof

Maria C. Cañadas & Encarnación Castro & Enrique Castro (short presentation 10 minutes):

An inductive reasoning model in linear and quadratic sequences

Michael Meyer (short presentation 10 minutes):

From discoveries to verifications – theoretical framework and

inferential analyses of classroom interaction

Margarida Rodrigues (short presentation 10 minutes):

Reasoning and proof in classroom (9th grade)

Session 2: The Teaching of Proof (90 minutes)

Hagar Gal & Hee-Chan Lew (long presentation 30 minutes):

Is a rectangle A parallelogram? – towards A bypass of van Hiele level

Hagit Sela (short presentation 10 minutes):

Coping with tasks that lead to mathematical contradictions with peers

Hector Rosario (short presentation 10 minutes):

Puzzles and Proofs: Informal Arguments and the mathematical Mind

Naoyuki Masuda (short presentation 10 minutes):

A study of Jogai Toda’s Deductive Method – including the teaching

Stefan Ufer & Aiso Heinze (long presentation 30 minutes):

The development of geometric proof competency from grade 7 to 9: a

Session 3: Curriculum (60 minutes)

Behiye Ubuz (long presentation 30 minutes):

Proof in Elementary Mathematics: A Turkish Perspective

Ildikó Pelczer & Cristian Voica (short presentation 10 minutes):

Proof in Romanian high school introductory analysis textbooks – a

Sharon L. Senk, Denisse R. Thompson & Gwendolyn Johnson (short presentation 10 minutes):

Reasoning and Proof in High School Textbooks from the U.S.A

Yi-Yin Ko, Eric Knuth & Haw-Yaw Shy (short presentation 10 minutes):

Taiwanese Undergraduates’ Performance Constructing Proofs and

Generating Counterexamples in Differentiation

Session 4: The Teaching of Proof (90 minutes)

Andreas J. & Gabriel J. Stylianides (long presentation 30 minutes):

Supporting student learning in the area of proof

Kazuhiko Nunokawa & Toshiyuki Fukuzawa (short presentation 10 minutes):

Operating on and Understanding of Problem Situations in Proving

Kai-Lin Yang & Li-Wen Wang (short presentation 10 minutes):

Propositions Posed under a Proof without its Proposition

John Selden, Annie Selden & Kerry McKee (short presentation 10 minutes):

Improving Advanced Students’ Proving Abilities

Takeshi Miyakawa & Patricio Herbst (long presentation 30 minutes):

Why some theorems are not proven in geometry class: Conditions and

**Papers and discussion documents**

Bartolini Bussi, M. G., Experimental Mathematics and the Learning of Proof (197.00 KB)

Canadas, M. & Castro, E. & Castro, E., An Inductive Reasoning Model in Linear and Quadratic Sequences (146.00 KB)

Ko, Y. & Knuth, E., Taiwanese Undergraduates' Performance Constructing Proofs and Generating Counteraxamples in Differentiation (36.00 KB)

Pelczer, I. & Voica, C., Proof in Romanian High School Introductory Analysis Textbooks - A Historical Overview (128.00 KB)

Rodrigues, M. Reasoning and Proof in Classroom (9th grade) (131.00 KB)

Senk, L. & Thomson, D. R. & Johnson, G., Reasoning and Proof in Hight School Textbooks from the USA (377.00 KB)

Stylianides, A. J. & Stylianides, G. J., 'Cognitive Conflict' as Mechanism for Supporting Developmental Progressions in Students' Knowledge about Proof (407.00 KB)

Ufer, S. & Heinze, A., Development of Geometric Proof Competency from Grade 7 to 9 A Longitudinal Study (191.00 KB)

Yang, K-L. & Wang, L-W., Propositions Posed under a Proof without its Proposition (130.00 KB)

Rosario, H., Puzzles and Proofs: From Informal to Formal Arguments (102.00 KB)

Camargo Urib, L. & Gutierrez, A., Some Aspects of the Sociocultural Practice of Proving in a University Course with Support of Cabri (119.00 KB)

Nunokawa, K. & Fukuzawa, T., Operating on and Understanding of Problem Situations in Proving (149.00 KB)

Miykawa, T. & Herbst, P., Why Some Theorems are not Proven in Geometry Class: Dispositions and Constraints (97.00 KB)

Sela, H., Coping with Mathematical Contradictions with Peers (75.00 KB)

Meyer, M., From Discoveries to Verifications - Theoretical Framework and Inferential Analyses of Classroom Interaction (259.00 KB)

Gal, H. & Lew, H-C, Is a rectangle a parallellogram? Towards a bypass of van Hiele level 3 decision making (202.00 KB)

Selden, J. & Selden, A. & McKee, K., Improving Advanced Students' Proving Abilities (134.00 KB)