# Preservice and novice teachers’ knowledge on preformal proofs: Triangle postulate as an example

## Keywords:

mathematical knowledge for teaching, preservice teachers, preformal proofs, teachers' knowledge for proof and proving, triangle postulate## Abstract

By considering the example of proving the triangle postulate, this study aimed to explore Hong Kong preservice and novice teachers’ knowledge competencies and their beliefs about preformal and formal proofs. The findings revealed that such teachers are not proficient in using preformal proofs and do not realize that preformal proofs are a useful tool for connecting abstract geometrical concepts with concrete meanings. We conclude by providing strategies for teachers to use preformal proofs effectively in their teaching of geometric propositions.

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