This is a series about “developing the question” in math class.
Curmudgeon has taught math and science for thirty years and runs the Math Arguments 180 blog, an indispensable source of interesting prompts and questions.
In nine classes out of ten, you’ll find a teacher ask her students to calculate the area of those shapes. Maybe Curmudgeon would ask his/her students to calculate their area also. That’s a fine question. But Curmudgeon does an excellent job developing the question of calculating area by first asking:
- What is an easy question we could ask about the shape? A medium difficulty question? A hard question?
- What is the best way to find the area of the shape?
- What combinations of addition or subtraction of figures could you use to find the area?
Each question develops the next question. Earlier questions are informal and amorphous. Later questions are formal and well-defined. They all develop the main question of calculating area. They all make it easier for students to answer the main question of calculating area and they make that main question more interesting also.
This technique runs back to my workshop participant’s advice that “you can always add but you can’t subtract.” Once you tell your students your question, you can’t ask “What questions do you have?” Once you tell students what information matters, you can’t ask them “What information matters here?” Once you tell them to calculate area, it becomes very difficult to ask them, “What shapes combined to make this shape?”
Tomorrow: Why Graphing Stories does a pretty lousy job of developing the question.
Preparation: If the main question is “sketch this real world relationship,” what are ways we could develop that question?