# Introductory Challenge

## Introduction

Jessica was in the sixth grade, in Mr. O’Neill’s math class.  It was November. Jessica was unhappy.

The main point of the class seemed to be computing the answers for questions like 876 times 697.  Or 54,321 divided by 26. It was torture! She hated it!

The most annoying part was that Mr. O’Neill did not approve of calculators. That would be cheating, he said. He wanted his students to be really good at calculation.  It was very important for doing well in math in high school.  Later in the year, he said, they might use calculators. But for now calculators were banned.

Math class was the worst part of Jessica’s day. It was becoming a pattern.

Jessica and three other students, though, had a particular problem. They hadn’t learned the times tables. It seemed hopeless. Each week so far, Mr. O’Neill had given timed quizzes for multiplication facts. By November 10, everyone else in class had learned the times tables; only Jessica and three others continued to fail the timed quizzes. Jessica would actually be able to pass the tests if she had about 30 seconds more. No matter how hard she tried, though, a group of facts just wouldn’t come into her head fast enough. It was maddening:

7 x 8      7 x 9

6 x 9      6 x 7

8 x 7      8 x 8

They looked confusingly the same! Her mother even worked with her at home, using a stack of flash cards. She was discouraged, depressed, and angry.

And Mr. O’Neill kept reducing the grades of students who did not pass.  It was simple: if they wanted better grades, all they had to do was get through the timed tests. Everyone could do it eventually, said Mr. O’Neill. So Jessica was in trouble with her Mom, again, for her grades in math.

Would she ever pass?

Actually, she never did!  After Jessica’s mother talked with Mr. O’Neill, he waved her on. She did not have to take any more tests.

## Challenge Questions

• Do you know any adults who have trouble giving the answers to the multiplication “facts” in the list above?  How do they explain their situation?
• Can you think of any way to compute 8 x 8 accurately in your head (pretend you can’t remember!)? How about 6 x 7?
• How often and in what circumstances do you use a calculator at home? At work?
• How often and in what circumstances do you think numerically at home? At work?