# Introductory Challenge

## Setup

In Unit 3, we read briefly about Sam and Jessica’s common 9th grade algebra experience with Mrs. Jones—common, in the sense that they were in the same class. As you may remember, their actual experiences differed quite a bit, both in terms of their relationship with the teacher and their relationship with the material. There was another way in which their algebra experiences differed: their relationship with the algebra textbook.

Jessica saw the book as an instrument of torture, a way for Mrs. Jones to exert her authority over the class. But Jessica was determined to pass the class and defy Mrs. Jones along the way. Unlike several of her classmates who skipped the book altogether, Jessica read everything that was assigned. It was boring and tedious for the most part. She felt the same way she had felt on her family’s vacation to Montreal when she was surrounded by a language she scarcely understood. When reading her math book, she at least had a vague understanding of what each individual word meant. But by the second chapter, she gave up trying to make sense of any overall messages.

Sam’s relationship with the textbook was quite different. He also read everything that was assigned, but in a different way than Jessica did. Jessica read her math book straight through without stopping, just as she would read any other book. Sam never sat down to read his math book without a pencil and paper nearby so that he could work out problems along the way. He often read the same sentence three or four times to make sure he understood it, especially if it seemed important. He tried to work through the examples before looking at the solutions. Sometimes he even made up his own problems and solved them, just to see if he really did have the hang of the concept he was learning about. When all was said and done, it took Sam four or five times longer than it did Jessica to read the same section. However, by the time Sam got to the homework exercises at the end of each section, he could usually solve most of them much more quickly and accurately than Jessica could.

## Challenge Questions

(to be answered by yourself or in a group)

1. How do you read math textbooks? (If you haven’t read portions of a math textbook recently, think back to the last time you took a math class.)
2. Sam’s approach might more aptly be described as “interacting with the textbook” rather than just “reading” it. How do you think this interactive approach might help someone learn math?
3. Many students don’t spend time reading their math books because they think it’s too complicated, they don’t understand it, or they don’t have time. When working with students who have these reactions, how might you encourage them to interact with their textbook?