International Portal of Teacher Education

Source: Action in Teacher Education, v. 32 no. 3 (Fall 2010) p. 79-89.
(Reviewed by the Portal Team)

In this article, the author was interested to learn more about how 1st-year mathematics teachers use questioning strategies as a method for improving student engagement in whole-class discussions.

The author observed two new mathematics teacher whom he mentored in the university.
The two teachers, who the author calls them Steve and Bethany, taught mathematics in public schools that had significant cultural and ethnic diversity.

The two teachers had different educational and academic backgrounds in the teaching and study of mathematics.
Steve's undergraduate training was in science, but he took mathematics classes.
Bethany received her undergraduate training in mathematics, with her highest level of mathematics being an advanced calculus course.

Over the course of 4 months, the author observed Steve and Bethany teach six lessons each, three during the first 2 months and three in the last 2 months.
After the first set of three observations, the author sat down with each teacher to talk about how he or she was using questions to engage students in mathematical discussions.
By the end of the term, the teachers included more students in discussions, asked more questions that probed for understanding, and reduced the amount of time spent delivering Instruction.

Comparison of two teachers
The author compares the teachers' observational data in two ways.
First, the teachers will be compared individually between their mid- and end-of-term reviews, looking at how they changed their questioning practices to include more students in mathematical discourse.
Second, an analysis is made between the two teachers focusing on their efforts to improve mathematical discourse.

During each of their midterm observations, Steve and Bethany were presenting lessons that exceeded 50% of the total class period . Therefore, the teachers spent less time on engaging students in mathematics discussions. Furthermore, the teachers asked the students only few number of questions that required the students to think in more complex ways and with even fewer opportunities for students to confer with one another.
After each midterm conversation, both teachers increase the amount of time that students were discussing mathematics. By the end of the semester, however, Steve's percentage of change for each category was greater than that of Bethany. Steve was spending dramatically less time presenting his lessons but asking nearly the same number of follow-up questions and probing questions, as well as increasing student participation by selecting nearly the same number of students to answer questions. But of special importance, he was generally asking more questions that probed for understanding.

The Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000) emphasizes the need for teachers and students to communicate mathematics in the language of mathematics -- to ask questions, to make connections.
Hence, teachers of mathematics should strive toward increasing student engagement through open discussions of mathematics, and it is their role to facilitate this discourse if it does not naturally occur.

However, new teachers often need frequent support, guidance, and meaningful feedback to help them become better teachers (Rice, 2002; Wasley, 1999). This support requires regular, supportive, and collaborative interactions, including detailed observations of their practice.
As for improving whole-class discourse in mathematics, new teachers need to understand and be aware of the types of questions they ask, how often they are asked, and to whom they are addressed.

References
National Council of Teachers of Mathematics. (2000). Principles and standards for school
mathematics. Reston, VA: Author.
Rice, K. (2002). Surviving your first year in the classroom. Middle Ground, 10(1), 43-45.
Wasley, P. (1999). Teaching worth celebrating. Educational Leadership, 56(8), 8-13.