Concept Maps Provide a Window onto Preservice Elementary Teachers’ Knowledge in the Teaching and Learning of Mathematics - Research Findings and Analysis

Oct 15, 2026

This collaborative concept-mapping study examined how second-year mathematics methods preservice teachers understand mathematics learning and pedagogical content knowledge. Twenty-eight preservice student teachers produced concept maps that were analyzed by counting concepts and links across knowledge, teaching, and learning, and by examining link types between two conceptual domains. Results indicate limited knowledge about how students learn mathematics, while concept maps revealed areas where understanding of mathematics and its pedagogy connections was unsophisticated.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages25

Reading Time1 h 3 min

AccessFree to download

Abstract

Présis

Background and Rationale

Literature Review

Concept Maps Provide a Window onto Preservice Elementary Teachers’Knowledge in the Teaching and Learning of Mathematics Tanya Chichekian McGill University Bruce M. Shore McGill University Acknowledgements We are grateful to Melissa Duffy for her invaluable help in the data collection, and to Professor Annie Savard for allowing the data to be collected during her class time. Abstract This collaborative concept-mapping exercise was conducted in a second-year mathematics methods course. Teachers’visual representations oftheir mathematical content and pedagogical knowledge provided insight into their understanding of how students learn mathematics. We collected 28 preservice student teachers’ concept maps and analyzed them by counting the number of concepts and links within and across knowledge, teaching, and learning. We also examined the nature of the links between two domains of concepts. Preservice teachers revealed limited knowledge about how students learn Canadian Journal of Education / Revue canadienne de l’éducation 36:3 (2013)©2013 Canadian Society for the Study of Education/ Société canadienne pour l’étude de l’éducation [www.cje-rce.ca](www.cje-rce.ca) mathematics. Concept maps successfully identified areas in which preservice teachers held an unsophisticated understanding of mathematics and its connection to pedagogy. Précis Cet exercice collaboratifde schématisation conceptuelle a été conçu pendant la deuxièmeannée d’un programme de formation des maîtres dans un cours de didactique en mathématiques. Les représentations visuelles du contenu mathématique des cours des enseignants, ainsi que la connaissance pédagogique ont permis de comprendre comment les étudiants apprennent les mathématiques. Nous avons recueilli les schématisations conceptuelles de 28 huit étudiants et les avons analysées en comptant le nombre de concepts et les liens avec leurs connaissances en mathématiques et en pédagogie, ainsi que l’apprentissage des mathématiques. Nous avons également étudié la nature de ces liens entre deux domaines conceptuels. Les futurs enseignants avaient une compréhension limitée de l’apprentissage des mathématiques par les étudiants. La schématisation conceptuelle a pu repérer les régions au sein desquelles les futurs enseignants disposaient d’une mauvaise compréhension des mathématiques et de ses liens avec la pédagogie. Canadian Journal of Education / Revue canadienne de l’éducation 36:3 (2013) [www.cje-rce.ca](www.cje-rce.ca) Achieving excellence in teaching elementary-school mathematics requires overcoming many barriers. Curricular standards documents (e.g., AAMT, 2006; NCTM, 1989, 2000) have addressed some of these challenges among preservice and in-service teachers by identifying the need for (a) enhanced conceptual understanding in mathematics and (b) improved ability to plan meaningful learning sequences for students. Both needs address fundamentals of teachers’ subject matter and pedagogical knowledge and their interaction as pedagogical content knowledge (Shulman, 1986, 1988) . Valid means of assessment are necessary to monitor the influence of these forms of knowledge, especially in areas concerning conceptual understanding and instructional planning (Miller et al., 2009) . One way of measuring these knowledge structures is to use concept maps (Briscoe & LaMaster, 1991). At the university level, this form of assessment highlights preservice teachers’knowledge representations of pedagogical content knowledge in a meaningful fashion (Austin & Shore, 1995) . Preservice teachers’ conceptualizations of teaching and learning mathematics have been studied extensively; however, the interplay between content knowledge and pedagogical knowledge (Shulman, 1987), although an important and growing element in educational research, has not yet been explored with concept maps. Assuming that knowledge in mathematics is represented in a hierarchical fashion, organized around central concepts, thi

FAQs

What was the purpose of the concept-mapping exercise?

The study aimed to capture preservice elementary teachers’ structural knowledge representations about teaching and learning mathematics, using concept maps as an assessment tool.

How were the concept maps analyzed?

Researchers counted the number of concepts and links within and across the domains of knowledge, teaching, and learning, and examined the nature of links between two conceptual domains.

What did the study find about preservice teachers’ knowledge?

Preservice teachers showed limited understanding of how students learn mathematics, and concept maps identified areas where their grasp of mathematics and its connection to pedagogy was unsophisticated.

Oct 15, 2026

Uploaded by Well Done