| Summary: | 碩士 === 國立新竹教育大學 === 數理教育研究所 === 105 === This study aimed to explore how teachers support students development proof under the mathematical reasoning norms. This study observed the teaching strategies used by mathematics teachers in primary schools. Making use of the three components: a set of accepted statements, modes of argumentation, and modes of argument representation, as presented by Stylianides (2007), to analysis how teachers using teaching strategies in developing each component to enable students to produce mathematical proof.
The results showed that:
(1) To support students in developing a set of accepted statements, teachers has to develop students' habit of thinking and explaining the causes, train students to question unproven mathematical narratives, and reinforce the vertical linkages of knowledge in teaching.
(2) In the development of exhaustive method, it is necessary to clearly define the scope of the proof of the beginning and end; the development of modus pones of deductive reasoning, teachers need to affirmed that students have enough mathematical knowledge and disassembled the complexity process into several steps. To help students create statements and using counterexample to refute the wrong statements could support students to develop inductive reasoning.
(3) To help students improve the modes of argument representation, teachers can correspond graphics and symbols and use numerical examples, make students generate digital and algebraic symbols .
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