Various research methods have been used (both quantitative and qualitative), including:

1.  Case studies developed through frequent interactions among students and researchers and teachers and researchers;

2.  Research questionnaire (Proof Beliefs Questionnaire);

3.  Performance assessment instrument (Proof Construction Assessment);

4.  Clinical interviews.

The research questionnaire and performance assessment instruments were developed to document student ability to construct proofs and characterize student beliefs about what constitutes a proof. Observing student-teacher interaction in the classroom environment and the construction of case studies will help us to link characterizations of students' evolving proof-construction abilities to aspects of the classroom microculture including social norms, sociomathematical norms, classroom mathematical practices, and teacher pedagogical choices. This evidence will be supported by the results of the performance assessment instruments and clinical interviews.

Instruments:

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Proof Beliefs Questionnaire

Open-Ended Proof Beliefs Questionnaire

Proof Construction Assessment