Investigating Students’ Proof Reasoning: Analyzing Students’ Oral Proof Explanations and their Written Proofs in High School Geometry

Michael L. Winer; Michael T. Battista

doi:10.29333/iejme/11713

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Michael L. Winer ¹ ^* , Michael T. Battista ²

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¹ Eastern Washington University, USA² The Ohio State University, USA^* Corresponding Author

Abstract

Constructing formal geometry proofs in is an important topic in the mathematics curriculum. But students’ difficulties with proof are well documented. This article focuses on proofs that use triangle congruence postulates in US high school geometry. Examining students’ proof reasoning in one-on-one task-based interviews, we analyzed students’ oral planning/explanations and two-column written proofs. We found that much of the reasoning students conveyed in their oral planning/explanations was not incorporated into their written proofs, resulting in formalization and fatal logical reasoning gaps. We found that the majority of the students utilized sound reasoning in their oral explanations, but struggled to capture that reasoning in their written two-column proofs. We link our findings to learning progression research, further elaborating the van Hiele levels. Our research contributes to understanding the learning and teaching of proof and to the ongoing controversy over the use of two-column proofs in the high school geometry curriculum.

Keywords

geometry proofs
two-column proofs
learning progressions
student cognition
mathematics education

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2022, Volume 17, Issue 2, Article No: em0677

https://doi.org/10.29333/iejme/11713

Publication date: 09 Feb 2022

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

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How to cite this article

APA

Winer, M. L., & Battista, M. T. (2022). Investigating Students’ Proof Reasoning: Analyzing Students’ Oral Proof Explanations and their Written Proofs in High School Geometry. International Electronic Journal of Mathematics Education, 17(2), em0677. https://doi.org/10.29333/iejme/11713

Vancouver

Winer ML, Battista MT. Investigating Students’ Proof Reasoning: Analyzing Students’ Oral Proof Explanations and their Written Proofs in High School Geometry. INT ELECT J MATH ED. 2022;17(2):em0677. https://doi.org/10.29333/iejme/11713

AMA

Winer ML, Battista MT. Investigating Students’ Proof Reasoning: Analyzing Students’ Oral Proof Explanations and their Written Proofs in High School Geometry. INT ELECT J MATH ED. 2022;17(2), em0677. https://doi.org/10.29333/iejme/11713

Chicago

Winer, Michael L., and Michael T. Battista. "Investigating Students’ Proof Reasoning: Analyzing Students’ Oral Proof Explanations and their Written Proofs in High School Geometry". International Electronic Journal of Mathematics Education 2022 17 no. 2 (2022): em0677. https://doi.org/10.29333/iejme/11713

Harvard

Winer, M. L., and Battista, M. T. (2022). Investigating Students’ Proof Reasoning: Analyzing Students’ Oral Proof Explanations and their Written Proofs in High School Geometry. International Electronic Journal of Mathematics Education, 17(2), em0677. https://doi.org/10.29333/iejme/11713

MLA

Winer, Michael L. et al. "Investigating Students’ Proof Reasoning: Analyzing Students’ Oral Proof Explanations and their Written Proofs in High School Geometry". International Electronic Journal of Mathematics Education, vol. 17, no. 2, 2022, em0677. https://doi.org/10.29333/iejme/11713