Student Teachers’ Proof Schemes on Proof Tasks Involving Inequality: Deductive or Inductive?

Abstract

Exploring student teachers’ proof ability is crucial as it is important for improving the quality of their learning process and help their future students learn how to construct a proof. Hence, this study aims at exploring at the proof schemes of student teachers in the beginning of their studies. Data were collected from 130 proofs resulted by 65 Indonesian student teachers on two proof tasks involving algebraic inequality. To analyse, the proofs were classified into the refined proof schemes level proposed by Lee (2016) ranging from inductive, which only provides irrelevant inferences, to deductive proofs, which consider addressing formal representation. Findings present several examples of each of Lee’s level on the student teachers’ proofs spanning from irrelevant inferences, novice use of examples or logical reasoning, strategic use examples for reasoning, deductive inferences with major and minor logical coherence, and deductive proof with informal and formal representation. Besides, it was also found that more than half of the students’ proofs coded as inductive schemes, which does not meet the requirement for doing the proof for the proof tasks examined in this study. This study suggests teacher educators in teacher colleges to reform the curriculum regarding proof learning which can accommodate the improvement of student teachers’ proving ability from inductive to deductive proof as well from informal to formal proof.