Mathematical knowledge for teaching and mathematics didactic knowledge: a comparative study

Scheiner, Thorsten; Buchholtz, Nils; Kaiser, Gabriele

doi:10.1007/s10857-023-09598-z

J Math Teacher Educ

2023

DOI: 10.1007/s10857-023-09598-z

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Mathematical knowledge for teaching and mathematics didactic knowledge: a comparative study

Thorsten Scheiner,

Nils Buchholtz,

Gabriele Kaiser

Abstract: This paper compares and contrasts two approaches that are widely used in the English- and German-speaking discourse on mathematics teacher knowledge: ‘mathematical knowledge for teaching’ and ‘mathematics didactic knowledge’. It is proposed that these constructs are based on distinct theoretical and conceptual positions and origins. Mathematical knowledge for teaching is viewed as a utilitarian-pragmatic approach rooted in English-speaking traditions as it focuses on its use in teaching and represents a practi… Show more

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2024

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Cited by 4 publications

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“…In this context, 'mathematics didactic knowledge' refers to the normative, principles-based knowledge within didactics of mathematics, distinct from 'mathematical knowledge for teaching' which is a practiceoriented knowledge used in actual mathematics teaching tasks (for a comparison, seeScheiner et al, 2023).…”

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Exploring prospective teachers’ stances in making sense of students’ mathematical ideas

Scheiner,

Montes

2024

J Math Teacher Educ

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In this paper, we explore the critical practice of making sense of students’ mathematical ideas. We extend previous research by studying stances prospective teachers adopt, the extent or depth to which they do so, and the types of prospective teachers making sense of students’ mathematical ideas. Analyzing the responses of 123 prospective teachers to students’ different ideas on an ambiguous mathematical task, our study identifies various stances—descriptive, evaluative, comparative, interpretive, inquiry-based, connective, and projective—and explores the complexity of attributing value, meaning, and significance to student ideas. Our findings offer insights into various types of making sense of students’ ideas and suggest that different kinds of attributions are at play for the purposes of observation, assessment, understanding and projection/prediction.

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Exploring prospective teachers’ stances in making sense of students’ mathematical ideas

Scheiner,

Montes

2024

J Math Teacher Educ

Self Cite

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Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures

Hoffmann,

Biehler

2024

ZDM Mathematics Education

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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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Pre-Service Teachers’ Approaches in Solving Mathematics Tasks with ChatGPT

Noster,

Gerber,

Siller

2024

Digit Exp Math Educ

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The use of large language models like ChatGPT is widely discussed for educational purposes. Using this technology requires teachers to have appropriate competences that incorporate knowledge of how to make use of this technology. In this study, we investigate pre-service teachers’ knowledge through the lens of the KTMT model (“Knowledge for Teaching Mathematics with Technology” model), a domain-specific variant of the TPACK-model. One component is represented in mathematical fidelity as knowledge of the mathematical accuracy of the technology, which in case of large language models is of special interest, as it may produce erroneous but plausible-sounding information. Furthermore, prompting techniques are of interest as technological knowledge, which influence mathematical fidelity. For this study, eleven pre-service teachers were asked to solve four different mathematical tasks with the help of ChatGPT. The chatlogs and information provided in an interview after working on the tasks are analyzed using qualitative content analysis. Results show that both correct and incorrect answers were produced for all tasks. The rate of pre-service teachers providing an incorrect answer is high when having been presented with an incorrect answer generated by the large language model. Despite having access to ChatGPT as a tool, many of the participants were not able to provide correct answers to all tasks. Furthermore, the mathematical fidelity was often over- and, in some cases, underrated. The mathematical knowledge seems to have changed while working with ChatGPT. Based on the applied prompting techniques, the pre-service teachers showed a deficiency in technological knowledge.

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Mathematical knowledge for teaching and mathematics didactic knowledge: a comparative study

Cited by 4 publications

References 67 publications

Exploring prospective teachers’ stances in making sense of students’ mathematical ideas

Exploring prospective teachers’ stances in making sense of students’ mathematical ideas

Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures

Pre-Service Teachers’ Approaches in Solving Mathematics Tasks with ChatGPT

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