Making mathematics together by modeling shared experiences

IntroductionThis article illustrates a pedagogical approach to integrating models and modeling in Geometry with mathematics teacher-learners (MTLs). It analyzes the work of MTLs in a course titled “Computers, Teaching, and Mathematical Visualization” (or “MathViz”), which is designed to engage MTLs...

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Main Author: Corey Brady
Format: Article
Language:English
Published: Frontiers Media S.A. 2023-07-01
Series:Frontiers in Education
Subjects:
Online Access:https://www.frontiersin.org/articles/10.3389/feduc.2023.1165228/full
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author Corey Brady
author_facet Corey Brady
author_sort Corey Brady
collection DOAJ
description IntroductionThis article illustrates a pedagogical approach to integrating models and modeling in Geometry with mathematics teacher-learners (MTLs). It analyzes the work of MTLs in a course titled “Computers, Teaching, and Mathematical Visualization” (or “MathViz”), which is designed to engage MTLs in making mathematics together. They use a range of both physical and virtual models of 2-manifolds to formulate and investigate geometric conjectures of their own.ObjectivesThe article articulates the theoretical basis and design rationale of MathViz; it analyzes illustrative examples of the discourse produced in collaborative investigations; and it describes the impact of this approach in the students’ own voices.MethodsMathViz has been iteratively refined and researched over the past 6 years. This study focuses on one iteration, aiming to capture the phenomenological experience of the MTLs as they structured and pursued their own mathematical investigations. Video data from two class sessions of the Fall 2021 iteration of the course are analyzed to illustrate the discourse of collaborating students and the nature of their shared inquiry. Excerpts from this class’s Learning Journals are then analyzed to capture themes across students’ experience of the course and their perspectives on its impact.ResultsAnalysis of students’ discourse (while investigating cones) shows how they used models and gesture to make sense of geometric phenomena; forged connections with investigations they had conducted throughout the course on different surfaces; and articulated and proved mathematical conjectures of their own. Analysis of students’ Learning Journals illustrates how experiences in MathViz contributed to their conceptualization of making mathematics together, using a variety of models and technologies, and developing a set of practices that that they could introduce with their future students.DiscussionAn argument is made that this approach to collective mathematical investigation is not only viable and valuable for MTLs, but is also relevant to philosophical reflections about the nature of mathematical knowledge-creation.
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spelling doaj.art-c9214b3cbe07473d980b57a737c72e4c2023-07-28T18:13:34ZengFrontiers Media S.A.Frontiers in Education2504-284X2023-07-01810.3389/feduc.2023.11652281165228Making mathematics together by modeling shared experiencesCorey BradyIntroductionThis article illustrates a pedagogical approach to integrating models and modeling in Geometry with mathematics teacher-learners (MTLs). It analyzes the work of MTLs in a course titled “Computers, Teaching, and Mathematical Visualization” (or “MathViz”), which is designed to engage MTLs in making mathematics together. They use a range of both physical and virtual models of 2-manifolds to formulate and investigate geometric conjectures of their own.ObjectivesThe article articulates the theoretical basis and design rationale of MathViz; it analyzes illustrative examples of the discourse produced in collaborative investigations; and it describes the impact of this approach in the students’ own voices.MethodsMathViz has been iteratively refined and researched over the past 6 years. This study focuses on one iteration, aiming to capture the phenomenological experience of the MTLs as they structured and pursued their own mathematical investigations. Video data from two class sessions of the Fall 2021 iteration of the course are analyzed to illustrate the discourse of collaborating students and the nature of their shared inquiry. Excerpts from this class’s Learning Journals are then analyzed to capture themes across students’ experience of the course and their perspectives on its impact.ResultsAnalysis of students’ discourse (while investigating cones) shows how they used models and gesture to make sense of geometric phenomena; forged connections with investigations they had conducted throughout the course on different surfaces; and articulated and proved mathematical conjectures of their own. Analysis of students’ Learning Journals illustrates how experiences in MathViz contributed to their conceptualization of making mathematics together, using a variety of models and technologies, and developing a set of practices that that they could introduce with their future students.DiscussionAn argument is made that this approach to collective mathematical investigation is not only viable and valuable for MTLs, but is also relevant to philosophical reflections about the nature of mathematical knowledge-creation.https://www.frontiersin.org/articles/10.3389/feduc.2023.1165228/fullmathematical creativitymodels and modelinggeometryteacher preparationmathematizing
spellingShingle Corey Brady
Making mathematics together by modeling shared experiences
Frontiers in Education
mathematical creativity
models and modeling
geometry
teacher preparation
mathematizing
title Making mathematics together by modeling shared experiences
title_full Making mathematics together by modeling shared experiences
title_fullStr Making mathematics together by modeling shared experiences
title_full_unstemmed Making mathematics together by modeling shared experiences
title_short Making mathematics together by modeling shared experiences
title_sort making mathematics together by modeling shared experiences
topic mathematical creativity
models and modeling
geometry
teacher preparation
mathematizing
url https://www.frontiersin.org/articles/10.3389/feduc.2023.1165228/full
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