Exploring the relationship between K-8 prospective teachers’ algebraic thinking proficiency and the questions they pose during diagnostic algebraic thinking interviews

Kieboom, Leigh A. van den; Magiera, Marta T.; Moyer, John C.

doi:10.1007/s10857-013-9264-1

Cited by 14 publications

(26 citation statements)

References 30 publications

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“…This result is consistent with Van Den Kieboom's et al (2014) result that prospective mathematics teachers with higher algebraic reasoning were able to use appropriate questioning to foster students' algebraic reasoning, whereas prospective mathematics teachers with lower algebraic reasoning were unable to use appropriate questioning to foster students' algebraic reasoning. In this study, prospective middleschool mathematics teachers with poor quantitative reasoning were not able to support their middle-school students' quantitative reasoning in the problem-solving process.…”

Section: Discussionsupporting

confidence: 89%

“…On the other hand, the mathematical content knowledge of the mathematics teacher is a crucial prerequisite in constructing pedagogical content knowledge (van den Kieboom, Magiera, & Moyer, 2014). Baumert et al (2010) emphasize that sufficient content knowledge of mathematics is essential for enhancing pedagogical content knowledge.…”

Section: Introductionmentioning

confidence: 99%

“…Baumert et al (2010) emphasize that sufficient content knowledge of mathematics is essential for enhancing pedagogical content knowledge. For this reason, insufficient mathematical content knowledge is correlated with the lack of pedagogical content knowledge (Van den Kieboom et al, 2014). In other respects, several studies (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Despite there are a few studies regarding teachers' and prospective teachers' questioning ability in the literature (e.g. Moyer & Milewicz, 2002), there is scarcely any study on the relationship between prospective teachers' mathematical content knowledge and questioning ability (van den Kieboom et al, 2014). For example, van den Kieboom et al (2014) explore the relationship between prospective teachers' algebraic thinking proficiency and questioning ability.…”

Section: Introductionmentioning

confidence: 99%

“…Moyer & Milewicz, 2002), there is scarcely any study on the relationship between prospective teachers' mathematical content knowledge and questioning ability (van den Kieboom et al, 2014). For example, van den Kieboom et al (2014) explore the relationship between prospective teachers' algebraic thinking proficiency and questioning ability. Furthermore, no study has been encountered regarding prospective middle-school mathematics teachers' mathematical-content knowledge in terms of quantitative reasoning and their support for middle-school students' quantitative reasoning.…”

Section: Introductionmentioning

confidence: 99%

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Prospective Middle-School Mathematics Teachers’ Quantitative Reasoning and Their Support for Students’ Quantitative Reasoning

Kabael¹,

Akın²

2018

International Journal of Research in Education and Science

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The aim of this research is to examine prospective mathematics teachers' quantitative reasoning, their support for students' quantitative reasoning and the relationship between them, if any. The teaching experiment was used as the research method in this qualitatively designed study. The data of the study were collected through a series of exploratory teaching interviews and debriefing interviews with nine focus group participants, and clinical interviews that the participants conducted with middle-school students. The results indicated that the participants with strong quantitative reasoning use problem-solving approaches that focused on the quantity, whereas the participants with poor quantitative reasoning use problem-solving approaches that focused on performing calculations, using formulas and procedures devoid of quantitative meaning in solving of the problem. During the questioning process, the participants with strong quantitative reasoning led their students to identify and interpret the quantities, determine relationships among the quantities, represent all the quantities and their interrelationships, whereas the participants with poor quantitative reasoning led their students to perform calculations, make algebraic manipulations and focus on numbers by ignoring the quantities in the problem. These results suggest that prospective mathematics teachers' quantitative reasoning is strongly associated with their support for students' quantitative reasoning in the problem-solving process.

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Section: Discussionsupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Prospective Middle-School Mathematics Teachers’ Quantitative Reasoning and Their Support for Students’ Quantitative Reasoning

Kabael¹,

Akın²

2018

International Journal of Research in Education and Science

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Diagnosing 6th Graders’ Understanding of Decimal Fractions: Fostering Mathematics Pre-Service Teachers’ Diagnostic Competences with Simulated One-on-One Interviews

Marczynski

Kaltefleiter

Siebeck

et al. 2022

Learning to Diagnose With Simulations

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One-on-one diagnostic interviews with school students have been proposed as learning opportunities to acquire diagnostic competences. Moreover, role-play-based simulations have proved promising to foster interactive competences similar to diagnosis during early phases of teacher and medical education. Thus, we developed a role-play-based simulation of diagnostic interviews on the topic of decimal fractions for mathematics pre-service teachers. During the role-play, participants either take on the role of a sixth grader, a teacher interviewing a sixth grader, or an observer watching the interview. Based on cognitive labs addressing criteria such as authenticity and immersion in the teacher’s diagnostic task in the role-play, we analyze the feasibility of the chosen simulation approach to measure and foster mathematics pre-service teachers’ diagnostic competences.

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Cognitive and Motivational Person Characteristics as Predictors of Diagnostic Performance: Combined Effects on Pre-Service Teachers’ Diagnostic Task Selection and Accuracy

Kron¹,

Sommerhoff

Achtner³

et al. 2022

J Math Didakt

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The acquisition of diagnostic competences is an essential goal of teacher education. Thus, evidence on how learning environments facilitate pre-service teachers’ acquisition of corresponding competences is important. In teacher education, approximations of practice (such as simulations) are discussed as being learning environments that can support learners in activating acquired knowledge in authentic situations. Simulated diagnostic interviews are recommended to foster teachers’ diagnostic competences.The conceptualization of diagnostic competences highlights the importance of cognitive and motivational characteristics. Motivational learning theories predict that the activation of acquired knowledge in learning situations may be influenced by motivational characteristics such as individual interest. Although teachers’ diagnostic competences constitute an increasing research focus, how cognitive and motivational characteristics interact when shaping the diagnostic process and accuracy in authentic learning situations remains an open question.To address this question, we report on data from 126 simulated diagnostic one-on-one interviews conducted by 63 pre-service secondary school mathematics teachers (students simulated by research assistants), studying the combined effects of interest and professional knowledge on the diagnostic process and accuracy. In addition to the main effect of content knowledge, interaction effects indicate that participants’ interest plays the role of a “door-opener” for the activation of knowledge during simulation-based learning. Thus, the results highlight the importance of both, cognitive and motivational characteristics. This implies that simulation-based learning environments should be designed to arouse participants’ interest to support their learning or to support less interested learners in activating relevant knowledge.

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Exploring the relationship between K-8 prospective teachers’ algebraic thinking proficiency and the questions they pose during diagnostic algebraic thinking interviews

Cited by 14 publications

References 30 publications

Prospective Middle-School Mathematics Teachers’ Quantitative Reasoning and Their Support for Students’ Quantitative Reasoning

Prospective Middle-School Mathematics Teachers’ Quantitative Reasoning and Their Support for Students’ Quantitative Reasoning

Diagnosing 6th Graders’ Understanding of Decimal Fractions: Fostering Mathematics Pre-Service Teachers’ Diagnostic Competences with Simulated One-on-One Interviews

Cognitive and Motivational Person Characteristics as Predictors of Diagnostic Performance: Combined Effects on Pre-Service Teachers’ Diagnostic Task Selection and Accuracy

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