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Using Academic Mathematical Knowledge When Working on Interface Tasks--Analyses of Pre-Service Teachers' Arguments about Rotationally Symmetric Figures

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Title: Using Academic Mathematical Knowledge When Working on Interface Tasks--Analyses of Pre-Service Teachers' Arguments about Rotationally Symmetric Figures
Language: English
Authors: Max Hoffmann (ORCID 0000-0002-6964-7123), Rolf Biehler
Source: ZDM: Mathematics Education. 2024 56(7):1445-1458.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 14
Publication Date: 2024
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Elementary Education
Descriptors: Preservice Teachers, Preservice Teacher Education, Mathematical Concepts, Mathematics Education, Elementary School Mathematics, Developmental Tasks, Geometry, Thinking Skills, Teaching Skills, Teacher Competencies
DOI: 10.1007/s11858-024-01633-4
ISSN: 1863-9690
1863-9704
Abstract: Special tasks for pre-service teachers (PSTs) in university mathematics courses ("interface tasks") are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and skills in a professionally relevant way. In this paper, we analyze answers that PSTs have created to an interface task on symmetry. The PSTs were asked to clarify a student's question from a mathematical perspective and then give a suitable elementarized answer. We situate these two steps theoretically and reconstruct the mathematical reasoning in PSTs' answers. Through qualitative content analysis, we examined how PSTs justify figures' symmetries from a university mathematics perspective and when responding to the fictitious student. The scenario of a student questioning the existence of 100° rotationally symmetrical figures elicited rich and varied responses, proving suitable for an interface task. We compared PSTs' reasoning related to mathematical clarification with the reasoning related to elementarization. In many cases, this revealed a productive use of course content. An interesting result is that there is no uniform picture as to whether the arguments are more detailed in the mathematical clarification or in the elementarization.
Abstractor: As Provided
Entry Date: 2024
Accession Number: EJ1450652
Database: ERIC
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  Data: Special tasks for pre-service teachers (PSTs) in university mathematics courses ("interface tasks") are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and skills in a professionally relevant way. In this paper, we analyze answers that PSTs have created to an interface task on symmetry. The PSTs were asked to clarify a student's question from a mathematical perspective and then give a suitable elementarized answer. We situate these two steps theoretically and reconstruct the mathematical reasoning in PSTs' answers. Through qualitative content analysis, we examined how PSTs justify figures' symmetries from a university mathematics perspective and when responding to the fictitious student. The scenario of a student questioning the existence of 100° rotationally symmetrical figures elicited rich and varied responses, proving suitable for an interface task. We compared PSTs' reasoning related to mathematical clarification with the reasoning related to elementarization. In many cases, this revealed a productive use of course content. An interesting result is that there is no uniform picture as to whether the arguments are more detailed in the mathematical clarification or in the elementarization.
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