Effect of Preservice Teachers’ Knowledge of Using Concrete Models Developed in a Mathematics Methods Course on Their Questioning during Teaching: A Case of Whole Numbers

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2021-07-07

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Abstract

Teacher questioning in mathematics teaching is assumed central for students to review content knowledge, relate prior knowledge with current and future knowledge, clarify and facilitate their mathematics thinking, and assess student mathematics learning. Teacher questioning varies in cognitive levels and types and plays different roles in shaping student learning. Teachers’ appropriate conceptual understanding of the mathematics content that they teach and how to represent such an understanding concretely to their students presumably influences their questioning. Whole numbers are fundamental and focal for elementary mathematics, and thus become a useful context for examining how preservice teachers’ knowledge of using concrete models, and how they asked questions of the different cognitive levels and types, and how their knowledge of using concrete models may influence their questioning of different cognitive levels and types. This study examined whether preservice teacher’s knowledge of using concrete models influenced their questioning when teaching whole number concepts. The focus, design, and analysis of the study were framed by the conception of questioning developed based on Bloom’s taxonomy of knowledge and the knowledge of using concrete models for representing abstract mathematics ideas. This dissertation drew upon the pre- and post-test data of preservice teacher’s knowledge of using concrete models for representing whole numbers in their methods course module and the videotaped teaching in their practicum associated with the methods course. A dependent sample t test was conducted to examine the change of the preservice teacher knowledge of using concrete models before and after learning how to use concrete models for teaching whole numbers in the mathematics method course module. The levels and types of teacher questioning were described. ANOVA analyses were conducted to compare the differences in the number of questions between the three levels and between the three types of questions at each of the three levels. Regression analyses were conducted to examine the extent to which their knowledge of using concrete models developed in the methods course module influences teacher questioning.
The study showed that preservice teachers made significant progress in their knowledge of using concrete models for teaching whole numbers after the mathematics course module of whole numbers. It also showed that most preservice teachers asked questions at all three levels, and preservice teachers asked questions of 4 – 8 types with an average of 5 types. Few preservice teachers asked questions of symbol type at the factual level, questions of synthesis type at the conceptual level, and questions of assessment type at the proving level. Preservice teachers asked more questions at the conceptual level than at the providing level. The number of questions at the factual level is not significantly different from the number of questions at the conceptual level and the procedural level, respectively. At the factual level, preservice teachers asked few questions of symbol type. They asked significantly more questions of academic word type and procedural step type. At the conceptual level, preservice teachers asked few questions of synthesis type. They asked significantly more questions of comprehension type and application type. At the proving level, preservice teachers asked few questions of assessment type. They asked more questions of analysis type and clarifying type. Preservice teachers’ knowledge of using concrete models contributed significantly to the comprehension questions. The effect size varies with the question types, with a large effect size for the comprehension type questions, the medium effect size for the assessment type questions, and a small to minimal effect size for the other types of questions. The findings of the dissertation suggest that while it is significant to use concrete models to train preservice teachers in the mathematics methods course, it is also important to include other interventions to deepen preservice teacher mathematics content knowledge and broaden other kinds of knowledge, such as the knowledge of questioning levels and types, in the mathematics methods course.


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Keywords

Concrete Models, Questions, Cognitive Levels and Types, Preservice Teachers

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