Researcher Powell Introduces Functions in an Informal Math Learning Environment: The Interplay Between Teacher Questioning and Student Reasoning
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TitleResearcher Powell Introduces Functions in an Informal Math Learning Environment: The Interplay Between Teacher Questioning and Student Reasoning
Date Created2016-03-08T22:32:59-0400
Other Date2017-09-25T13:55:10-0400 (modified)
Other Date2017-09-25T16:27:03-0400 (published)
DescriptionThis analytic is the third in a series of analytics that describes teacher questioning and student responses and reasoning so that researchers, teachers and teacher educators can study patterns of teacher questioning techniques and responses from students.
Research reveals the importance of effective teacher questioning and highlights the role that such questioning plays in the development of students’ mathematical reasoning (Klinzing, Klinzing-Eurich & Tisher, 1985; Martino & Maher, 1999). Questioning can serve as a springboard for further discussion, elaboration of incomplete thought, and a greater conceptual understanding of the mathematical problems at hand. Questioning can give teachers a glimpse into the mathematical thinking of their students that may not be apparent otherwise. Not only may it help the teacher estimate students’ understanding of the concept being discussed, but it may also provide the teacher with a better understanding of the students’ thought processes, judgments, concerns, or hesitations when coming up with solutions to open-ended mathematical problems. Modeling of good questions may also have a positive effect on the students. The students may learn to use those forms of questions both when interacting with peers and when working on their own. By asking students for explanations of their work or for further clarification, or by asking students how they would convince their peers of their solutions, teachers may stimulate students to initiate such discussions on their own or prompt them to formulate cogent justifications and reasoning. Probing questions are associated with the production of clarifications of ideas by students. This can be especially helpful to students as they think carefully about ideas before presenting them to others.
The events in this series of analytics are selected from the sessions conducted as part of the longitudinal/cross sectional research study of the development of students’ mathematical thinking and reasoning conducted at Rutgers University that spanned over twenty-five years (Maher, 2010). They highlight events that occurred during sessions conducted in urban, working class, and suburban settings, across a large range of age levels, by a variety of researchers, and amongst a number of content domains. They showcase discourse that occurred during classroom settings as well as informal learning environments.
This series shows how different types of questioning illustrated in the videos were associated with the production of students’ arguments, forms of reasoning, and connections that they made to structurally equivalent problem tasks. During these representative sessions conducted by Researchers Carolyn Maher, Amy Martino, Robert Davis, and Arthur Powell, several varied forms of questioning are noted. The questioning techniques employed by researchers were associated with ways the students formulated their solutions, extended their reasoning, made connections, or otherwise enhanced or refined their solutions. These questions and discourse moves often invited students to build proof-like justifications. Specifically, probing questions, eliciting questions, and questions that encouraged student engagement seemed to be especially effective in providing opportunity for students to express higher-order thinking and reasoning. A complete discussion of the classification of teacher questioning during these and other sessions as well as a description of the association between researcher question and student argumentation, justification, and reasoning can be found in the “Interplay between teacher questioning and student reasoning” (Gerstein, 2017).
This analytic looks primarily at questions posed by the researcher that were associated with student engagement and the presentation of students’ ideas. Some questions were associated with student argumentation and discourse. Questions associated with student engagement show students attentive and on task. They can be observed, listening attentively to their peers. They offered an opportunity to ascertain whether students were engaged and that teacher and student input was clear to all. The questions reveal the confirmation (or not) of agreement, understanding. Sometimes we see a deliberate intent to redirect questions toward another student.
Student ideas were made public when questioning was associated with encouragement of students to formulate their own ideas and strategies. This resulted in making ideas public and explicit; explanations were then visible to other students. Eliciting questions were associated with students’ voicing their ideas and solutions, explaining their thinking and sharing their thoughts or solutions with others.
In this analytic, Researcher Powell uses eliciting questions as well as questions to encourage engagement during a whole class discussion on functions during an Informal Math Learning session in Plainfield, NJ (Baldev, 2009). Although mainly eliciting questions and questions to encourage engagement are observed during the sessions highlighted in this analytic, other forms of questions were posed as well by the researchers and noted in this analytic.
These analytics are designed to provide valuable insight into the dynamics of teacher questioning and student reasoning.
Baldev, Prashant V. (2009) Urban, seventh-grade students building early algebra ideas in an informal after-school program. (Unpublished doctoral dissertation). Rutgers University, New Jersey.
Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380-392.
Gerstein, M. (2017). The interplay between teacher questioning and student reasoning. (Unpublished doctoral dissertation). Rutgers University, New Jersey.
Klinzing, G., Klinzing-Eurich, G., & Tisher, R. P. (1985). Higher cognitive behaviors in classroom discourse: Congruency between teachers’ questions and pupils’ responses. The Australian Journal of Education, 29(1), 63-75.
Maher, C. A. (2010). The Longitudinal Study. In C. A. Maher, A. B. Powell, & E. B. Uptegrove (Eds.), Combinatorics and Reasoning (pp. 3–14). Springer. doi:10.1007/978-0-387-98132-1.
Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. The Journal of Mathematical Behavior, 18(1), 53-78.
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