According to Tad Watanabe, the teacher’s questioning provides a model of the questions that we hope students will internalize–and will learn to ask on their own. The table below explores some basic types and purposes of teacher questioning during each phase of a problem solving lesson. A poster from (below) practicing teachers may refresh your thinking about the teacher moves that help students express their thinking and understand each other’s thinking.
|Lesson Phase||Examples of Questions Students Learn to Ask Themselves|
|Posing and understanding the problem (brief)||
|Independent problem-solving (10 – 20 min). Teacher circulates to record student methods on seating chart and question students.||
|Lesson Phase||Questions teachers ask|
|Presentation of student’s solution approaches and class discussion (orchestrated by teacher’s neriage “kneading” or “polishing”) (15-30min)Students try to understand classmate’s ideas, and to connect and compare them to each other and their own ideas.||
|Summary/Consolidation of knowledge (brief)||
Three video examples help us think through teacher questioning strategies to elicit, support, and advance student thinking. The video is from the series of three lessons “Can You Find the Area?” taught by Dr. Akihiko Takahashi. The is available for reference.
In the first lesson, Dr. Takahashi begins by asking students to make a 4 X 5 rectangle on a geoboard and to copy the shape onto paper (dotted to look like a geoboard). Before watching this video segment, briefly discuss in your group:
What important misunderstanding(s) might this task reveal, and how might you handle the misunderstanding(s)?
Students may be accustomed to listening carefully to the teacher, but not to fellow students. So it may take some careful development of students’ presentation skills and listening habits to build lessons in which students use each other’s thinking as an important resource for development of mathematical ideas.
Watch Video Segment 1 (0:57-3:57) and note down the questions and moves used by Dr. Takahashi to help students:
- Present their solutions in a way that is visible and audible
- Explain their thinking
- Understand and value classmates’ thinking
- Compare ways of thinking
Discuss what you noticed and keep a record of any strategies your team wants to remember for your own teaching through problem-solving.
In the next video segment, Dr. Takahashi poses the problem of finding the area of an L-shaped figure (left). Students work on the problem independently, and then Dr. T. orchestrates a discussion in which selected students share and explain their solutions to classmates. Watch Video Segment 2 (8:14-17:06) and note down:
- The questions and moves by the teacher designed to help students present, explain, attend to and understand each other’s thinking
- The features of materials design and blackboard use that help students grasp each other’s solution methods
- The features that help students connect visual and verbal representations with mathematical expressions
Consider anything new you noticed about the above points, and record any teacher moves or teacher questions you want to remember for your own teaching through problem-solving.
The next video segment (which immediately follows the prior segment of the lesson) shows the final portion of the lesson, in which students look back on what they learned that day and summarize key mathematical points. The neriage, in which students compare solution methods and draw out key mathematical points, has begun in the previous segment and is revisited and summarized in this segment. Before watching the segment, discuss with your team:
- What mathematical ideas has Dr. Takahashi emphasized in the discussion of the solutions so far?
- What do you expect him to emphasize in the summary of the lesson?
- What questions do you expect Dr. T. to ask?
Watch Video Segment 3 (17:06-20:52) and make note of
- The mathematical ideas emphasized
- Teacher questioning and moves to elicit the mathematical ideas
Consider (or discuss with your team) any take-aways about teacher questioning during the neriage and final summary of a lesson, and record in your lesson plan template any teacher questioning strategies and teacher moves you want to try in your research lesson (or in your classroom).