The Academic Community’s Perceptions of the Two-Column Proof

Pair, Jeffrey; Strachota, Susanne; Singh, Rashmi

doi:10.54870/1551-3440.1521

Cited by 2 publications

(2 citation statements)

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“…In the US, the most common context for formal geometry proof is the two-column format (Herbst, 2002;Pair et al, 2021), which was created to make proof accessible to high school students (Herbst, 2002). Even though the two-column proof format continues to be widely used in US high school geometry textbooks and classrooms (Kelley, 2013;Stylianides et al, 2017), the use of such proofs is controversial.…”

Section: Introductionmentioning

confidence: 99%

“…Even though the two-column proof format continues to be widely used in US high school geometry textbooks and classrooms (Kelley, 2013;Stylianides et al, 2017), the use of such proofs is controversial. In a survey of recent mathematics education conference attendees, Pair et al (2021) found that 79% of respondents stated that there is value in two-column proofs and 43.5% said that they were probably or definitely not in favor of eliminating two-column proofs. In contrast, 21% of respondents did not see the value of such proofs, and 35.5% probably or definitely thought that such proofs should be eliminated.…”

Section: Introductionmentioning

confidence: 99%

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

Winer¹,

Battista²

2022

INT ELECT J MATH ED

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%