Working Group: International Perspective on Proof and Proving – PME 43

July 07-12, 2019 Pretoria, South Africa
David Reid, Keith Jones and Ruhama Even.

The aim of the group was to foster research on proof and proving from an international perspective, by organising networks of researchers interested in collaborating on comparative research focussed on proof and proving.

Among the participants in the PME WG there was interest in continuing to work on several sub-topics:

• Pre-Primary and Primary Argumentation and Proof
• Secondary Level Argumentation and Proof
• University Level Proof Teaching and Learning
• Proof in the Primary & Secondary School Curriculum
• How are Argumentation and Proof conceptualised internationally?
• Interrelationships between Visualisation and Proving

The short term plan is for interested researchers to conduct research projects on each of these topics in the next year, and to report back (either in person, or in writing) to the PME WG at PME 44. The long term plan is to present the outcomes of these projects in a research forum at PME 45 and/or in an edited book.

Readers of the Newsletter are welcome (encouraged) to join in the research projects. All levels of participation are needed, from being fully involved in planning and conducting the research, to providing information about your country. If you are interested in participating, please contact the coordinators listed below.

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Thesis: Assessing ITP Students' Validating Ability: Framing, Developing and Validating a Pilot Assessment

Joshua B. Fagan (2019)

In this paper I discuss the process of creating a closed-form multiple-choice assessment of students’ ability to validate mathematical proofs at the introduction to proof (ITP) level. This process involved:

1. creating and validating a cohesive framework of common validity issues (CVI) in proof writing as a basis for assessment creation through a mathematician survey (N = 228) and two focus groups (N = 4 & N = 7);
2. creating and piloting an open version of the assessment as a means to create distractors for the closed assessment;
3. creating, piloting (N = 187) and analyzing the results from the closed form assessment; and
4. conducting interviews with student participants after the pilot to determine the characteristics of the process that students took during the pilot.

The results of the processes offer an assessment that, with some refinement, can authentically measure students’ ability to validate mathematical arguments from a number of perspectives in the ITP setting.

To know more…