Comparing different types of instructional videos in a flipped proof-based classroom

BackgroundProofs are a key component in undergraduate mathematics, but understanding presented proofs and constructing proofs is a challenge for many students. Flipped undergraduate mathematics classrooms often employ instructional videos, yet little is known about their potential to help students u...

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Main Authors: Laura Wirth, Katharina Kirsten, Christian Serpé, Gilbert Greefrath
Format: Article
Language:English
Published: Frontiers Media S.A. 2024-11-01
Series:Frontiers in Education
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Online Access:https://www.frontiersin.org/articles/10.3389/feduc.2024.1438355/full
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author Laura Wirth
Katharina Kirsten
Christian Serpé
Gilbert Greefrath
author_facet Laura Wirth
Katharina Kirsten
Christian Serpé
Gilbert Greefrath
author_sort Laura Wirth
collection DOAJ
description BackgroundProofs are a key component in undergraduate mathematics, but understanding presented proofs and constructing proofs is a challenge for many students. Flipped undergraduate mathematics classrooms often employ instructional videos, yet little is known about their potential to help students understand and construct proofs.ObjectiveThis study investigates the potential of video-based proof presentations on student learning. We compared a video that presented the proof construction process (proof video); a video that heuristically presented the proof construction process, which modeled key decisions and named the phases of proof construction and activities (heuristic proof video); and a video that offered prompts during the proof construction process, where self-explanation prompts guided students through these phases and activities (prompted proof video).MethodsA between-subjects design was employed, involving 177 mathematics (teacher) students in a first-semester proof-based linear algebra course. Data were collected on students’ comprehension of the presented proof, their knowledge for proof construction, and their evaluative perceptions. Statistical analyses were performed using ANOVA (proof comprehension) and MANOVA (evaluative perceptions) to compare the groups. Qualitative content analysis was employed to identify different facets of knowledge for proof construction and the groups were contrasted using χ2-tests.ResultsWe found that independent of the video they watched, students achieved a rather local comprehension of the presented proof. The heuristic proof video showed potential for offering meta-knowledge of how to approach proof construction and knowledge on process-related activities that support individual phases of proof construction but required more time. Yet, while students perceived all videos positively, they liked the heuristic proof video best.ConclusionThe results provide insights into the design of instructional videos, suggesting that, in the early stages of learning about proofs, a heuristic proof video may help address the challenges students face.
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spelling doaj-art-a1cd99ef144a41e39dafed0b9efe1edc2024-11-27T06:33:07ZengFrontiers Media S.A.Frontiers in Education2504-284X2024-11-01910.3389/feduc.2024.14383551438355Comparing different types of instructional videos in a flipped proof-based classroomLaura Wirth0Katharina Kirsten1Christian Serpé2Gilbert Greefrath3Institute of Mathematics Education and Computer Science Education, University of Münster, Münster, GermanyInstitute of Mathematics Education and Computer Science Education, University of Münster, Münster, GermanyMathematical Institute, University of Münster, Münster, GermanyInstitute of Mathematics Education and Computer Science Education, University of Münster, Münster, GermanyBackgroundProofs are a key component in undergraduate mathematics, but understanding presented proofs and constructing proofs is a challenge for many students. Flipped undergraduate mathematics classrooms often employ instructional videos, yet little is known about their potential to help students understand and construct proofs.ObjectiveThis study investigates the potential of video-based proof presentations on student learning. We compared a video that presented the proof construction process (proof video); a video that heuristically presented the proof construction process, which modeled key decisions and named the phases of proof construction and activities (heuristic proof video); and a video that offered prompts during the proof construction process, where self-explanation prompts guided students through these phases and activities (prompted proof video).MethodsA between-subjects design was employed, involving 177 mathematics (teacher) students in a first-semester proof-based linear algebra course. Data were collected on students’ comprehension of the presented proof, their knowledge for proof construction, and their evaluative perceptions. Statistical analyses were performed using ANOVA (proof comprehension) and MANOVA (evaluative perceptions) to compare the groups. Qualitative content analysis was employed to identify different facets of knowledge for proof construction and the groups were contrasted using χ2-tests.ResultsWe found that independent of the video they watched, students achieved a rather local comprehension of the presented proof. The heuristic proof video showed potential for offering meta-knowledge of how to approach proof construction and knowledge on process-related activities that support individual phases of proof construction but required more time. Yet, while students perceived all videos positively, they liked the heuristic proof video best.ConclusionThe results provide insights into the design of instructional videos, suggesting that, in the early stages of learning about proofs, a heuristic proof video may help address the challenges students face.https://www.frontiersin.org/articles/10.3389/feduc.2024.1438355/fullinstructional videosproof videosheuristic examplesproof comprehensionproof constructionlinear algebra
spellingShingle Laura Wirth
Katharina Kirsten
Christian Serpé
Gilbert Greefrath
Comparing different types of instructional videos in a flipped proof-based classroom
Frontiers in Education
instructional videos
proof videos
heuristic examples
proof comprehension
proof construction
linear algebra
title Comparing different types of instructional videos in a flipped proof-based classroom
title_full Comparing different types of instructional videos in a flipped proof-based classroom
title_fullStr Comparing different types of instructional videos in a flipped proof-based classroom
title_full_unstemmed Comparing different types of instructional videos in a flipped proof-based classroom
title_short Comparing different types of instructional videos in a flipped proof-based classroom
title_sort comparing different types of instructional videos in a flipped proof based classroom
topic instructional videos
proof videos
heuristic examples
proof comprehension
proof construction
linear algebra
url https://www.frontiersin.org/articles/10.3389/feduc.2024.1438355/full
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