The Interplay between Teacher Questioning and Student Reasoning: Utilizing Probing Questions to Provide the Opportunity for Argumentation, Justification, and Reasoning

DescriptionThe first, in a series of five analytics, describes teacher questioning, and students’ responses and points out the reasoning of the students so that researchers, teachers, and teacher educators can study patterns of teacher questioning techniques and responses from their 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 can serve to elicit in students a greater conceptual understanding of the mathematical problems at hand. Responses of students to teacher questions can offer to teachers a glimpse into the mathematical thinking of the 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 about the ideas at hand, and particular 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. One outcome is that students may come to imitate similar ways of questioning when interacting with peers and also 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. Such probing by teachers may also result in students’ posing these questions to themselves, which in turn could help clarify the solutions in their minds before presenting their ideas to others. It also helps to establish the norms and expectations of the classroom community.

The events in this series of analytics are culled 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). The primary setting of the longitudinal study was in the working-class community of Kenilworth, New Jersey, where a focus group of students was followed as they worked on open-ended strands of mathematical tasks over a period of twelve years. However, a smaller, three and one half year cross-sectional study was also conducted as a part of this larger study, and was situated in Colts Neck, a suburban/rural community in New Jersey, in the urban district of New Brunswick, and in the working-class district of Kenilworth.

These analytics will showcase sessions conducted in the six grade Kenilworth class, in the fourth grade Colts Neck class, as well as sessions from the Informal Math Learning after-school program conducted in Plainfield, New Jersey with seventh graders. They highlight episodes that occurred during sessions conducted in urban, working class, and suburban settings, across a 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 making connections 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 first analytic of the series looks primarily at probing questions posed by researchers that were associated with argumentation and discourse as well as justification and reasoning that becomes increasingly more sophisticated. Probing questions are questions that elicit student answers past their initial replies. Often the researchers asked a probing sequence of questions (Franke et al., 2009) or a string of probing questions. These questions were often used to enable students to see the error in their statement or to help them enhance their explanations. They often consisted of a series of more than two related questions about something specific that a student said and included multiple teacher questions and multiple student responses. Probing questions include elucidating probes that were used to clarify a student response. The teacher used these questions to query a student about what he or she meant and to allow the student to elaborate on what was said. It also includes redirecting questions that required students to consider analyzing the initial question further and think about the implications of the response and how it would relate to other solutions or statements. Questions were also included in the classification of probing if they were used to encourage critical thinking or augment analytical cognizance. This type of probing question was used when the teacher attempted to increase the students’ critical awareness about what their response had been and what their underlying assumptions may have been in making a particular statement or offering a particular answer and thereby make them cognitively aware of the reasons behind their thinking. Probing questions were also used to ask the students whether they had completely answered the question at hand.

In this analytic, Researcher Maher uses probing questions during a whole class discussion at the Colts Neck public school that provide the opportunity for argumentation, reasoning and justification (Yankelewitz & Winter, 2017). Researcher Martino uses probing questions when working one-on-one with Alan, a student at Colts Neck and the subsequent reasoning and justification are described. Alan applies recursive reasoning to build multiple models depicting the comparison between two-fifths and one-half and predicts the form of larger models (Yankelewitz and Salb, 2017). Although mainly probing questions were used 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.

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.

Yankelewitz, D. & Salb, B. (2017). Recursive reasoning. In C.A. Maher and D. Yankelewitz (Eds.), Children’s Reasoning While Building Fraction Ideas. Sense Publishers.

Yankelewitz, D. & Winter E. (2017). A problem with no solution. In C.A. Maher and D. Yankelewitz (Eds.), Children’s Reasoning While Building Fraction Ideas. Sense Publishers.
Created on2016-02-29T22:06:52-0400
Published on2017-09-25T13:41:25-0400
Persistent URL