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Secondary Mathematics Pre-Service Teachers’ Opinions About The Difficulties With “Proof Without Words”
Many researchers have stressed the importance of visualization and proof in the learning of mathematics and have remarked that research in mathematics education has still a lot to develop about this topic. Visual proofs or proof without words are proofs where the deductive steps are based on figures, diagrams or graphs. This study was conducted to determine secondary mathematics preservice teachers’ opinions about the difficulties with “proof without words”. Case study method was used in this study. Participants of the study consist of 57 secondary mathematics pre-service teachers who were fifth-year students in a state university located in the Central Anatolia. The study was conducted in 2013-2014 education and teaching year in the lesson that “Investigation Projects in Field Education”. Research data was obtained through the open-ended question that directed to pre-service teachers at the end of the period. The open-ended question is exerted to expose the secondary mathematics pre-service teachers’ opinions about the difficulties that they experience in this process. Data were collected in writing. In the analysis of the data, the answers of pre-service teachers were thematically classified in regard to the similarities and differences among their responses. The results of the study indicated that pre-service teachers they had problems inability to understand the given shapes, lack of explanation, failure to develop relationships between proof without words and algebratic proof, lack of knowledge of the field, lack of resources. Therefore, it is said to be proof without words can be challenging and can develop student’s inductive reasoning, spatial reasoning, mental rotation and spatial visualization abilities. Some suggestions were based on the results obtained in this study.

Proof, proof without words, visualisation, visual proof, mathematic education, pre-service teachers

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