Algebraic Problem Solving

Driscoll, Page 6

After reading the Five Categories of Teacher’s Questions from Developing Algebraic Habits of Mind, the first place I though of where I could use most of the categories, is in teaching Scatter Plots and Best-fit Lines.

In creating best-fit lines, one of the activities that we do is have students collect data by finding the diameter and circumference of various circular objects. Students work in small groups to gather the data. Any time you have students working in groups you will need to ask managing types of questions. As you move from group to group, it becomes necessary to ask students who is doing the recording, who is doing the measuring, etc. to make sure that all students are actively engaged in the activity.

Clarifying questions are constantly used. As students record the data, and plot the data it never fails that one or two groups will measure incorrectly. As students attempt to create the line of best-fit, you need to ask students questions to find out why they decided to place the line where they placed the line.

You will also need to ask orienting questions as students begin to find the line of best-fit. You need to ask them “How do we draw a line of best-fit?” Once students have drawn the line of best-fit and begin to write the equation, you may need to ask questions such as what do we need to write a line?

Asking students to explain how they arrived at their line of best-fit requires students to think about what they did mathematically. Questions such as “How did you know where to draw your line of best-fit?” will require students to reflect on their answer. Asking students why their line of best-fit and the line of best-fit of another group are similar when you measured different items will require students to reflect of the relationship between circumference and diameter. This type of question would also represent the Questions for Building Rules to Represent Functions. (If I do the same thing with different items, will the results still hold true?)

Finally we can ask students which elicit algebraic thinking. How can we use what we have done? Can we use the line of best-fit that we created to predict the circumference of an item if we have the diameter? We can also ask students to transfer this knowledge to other situations. Could we collect data about the temperature over time and create a line of best-fit? Could the line of best-fit be used to predict the temperature on a given date? Why or why not?