טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentMalek Aliza
Subject"Transparent P-Proofs" as a Didactic Tool in Mathematics
DepartmentDepartment of Education in Science and Technology
Supervisor Professor Emeritus Nitsa Movshovitz-Hada


Abstract

A “transparent pseudo-proof" (p-proof) is a proof of a particular case of the claim that is "[...] small enough to serve as a concrete example, yet large enough to be considered a non-specific representative of the general case [...] One can see the general proof through it because nothing specific to the case enters the proof.” (Movshovitz-Hadar, 1988).

In line with existing learning theories, the present study explored the hypothesis that exposure to p-proofs would facilitate students' reading, understanding, composing, and writing of mathematical proofs, in a better way than exposure to formal mathematical proofs commonly used in college or university teaching of linear algebra.

The study was conducted through work with 10 first year students at Technion - Israel Institute of Technology. It was found that xposure to a transparent p-proof of a mathematical claim lead to better understanding of the written formal proof and to better ability to compose and write a formal proof for a given claim. Furthermore, it was found that students are more capable of proving a different claim with a similar proof to the proof of a claim for which they studied a p-proof. Exposure to a formal proof of the same mathematical claim did not yield similar results.

Conclusion: Transparent p-proofs function as a mediator between the abstraction ability of the learner and the abstraction level needed to read and understand, compose and write a formal mathematical proof. In addition, useful lessons for math instructors were learned about composing and writing transparent p-proofs.