 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum                      Defining Communication  The Communication Standard | Using Effective Questioning | Using Precise Language | Additional Methods | Goals | Your Journal    Teacher's questions can help students think through a problem and communicate coherently so that they truly come to understand their reasoning and problem solving.

Let's look back at the Triangle to Rectangle problem, introduced earlier in this session. We'll use it to focus on this key element of the communication standard, effective questioning. The student said: I folded the top down and cut along the fold. Then I turned the cut piece and moved it to make a rectangle.  Here are a series of questions you might ask the student. Select "Show Answer" for

each of the questions below to see possible answers that the student might give, and decide whether these questions have been effective.

 Teacher: Where did you fold? Show Answer
 Sample Answer: Student: I folded the top vertex down to the vertex of the right angle. Teacher: Why did you choose that fold? Show Answer
 Sample Answer: Student: I chose that fold because it made a perpendicular to the leg with the fold. Sample Answer: Student: The fold line is perpendicular to one leg, so it is parallel to the other leg. Teacher: What do you know about the lengths of the sides that you put together? Show Answer
 Sample Answer: Student: The fold line cuts one leg into two equal pieces. Since it is parallel to the base leg, it also cuts the hypotenuse into two equal pieces. Since the two pieces of the hypotenuse are equal, I can put them together. Teacher: What do you know about the angles that you put together? Show Answer
 Sample Answer: Student: The two angles along the fold line of the hypotenuse add to 180° because they make a straight line. When I rotate the top triangle, I am putting together the same two angles, so they will still make a straight line. The two non-right angles of the original triangle must add to 90° because it is a right triangle. When I rotate the top triangle, the two non-right angles of the original triangle meet at the bottom corner of my figure. They still add to 90� so they make a right angle. Sample Answer: Student: A rectangle is a parallelogram with four equal angles. Teacher: Do you know enough about your figure to be sure that it is a rectangle? Show Answer
 Sample Answer: Student: Yes, it is a rectangle. I know it has four right angles. The top and bottom are parallel lines, and the left and right are equal length. I could show that the top and bottom are equal length too, because the top triangle made by the fold is similar to the original, so the sides are all half the length of the original. If I put together two sides that are half the length of the original, I get the original length.

Effective questioning matters for several reasons. Through your questions, you can help students grow in their ability to describe their own thinking process in a step-by-step manner. This can improve understanding, and such step-wise work is key to many aspects of mathematics. Secondly, student answers provide insights into your students' ideas: what concepts they get, what is misunderstood, and what still eludes them. Finally, you are modeling the kinds of questions that you would like students to begin posing for themselves. Students need to think of useful questions on their own. These may be ones they ask themselves as they solve problems, or those they ask their teacher or classmate. Questions are vital to learning.  Using precise language       Teaching Math Home | Grades 9-12 | Communication | Site Map | © |        