## Math in the Middle Institute Partnership

#### Date of this Version

7-2007

#### Abstract

One of the most common mistakes in school mathematics is to list a few terms of a sequence and ask “What term comes next?” For example, a teacher may write: 1 2 4 … and ask what term comes next? The best answer is “almost anything could be the next term.” But people often find that answer unsatisfying. It helps, instead, to give an example. Perhaps, one might respond by saying: “The next number might be 8, but then again, it might be 7.” This answer might, of course, result in an angry teacher, so you need to be prepared with the further comment: “My choice of 8 is based on the sequence: 1, 2, 4, 8, 16, …, 2n, , where n is a number chosen from the sequence of whole numbers, 0, 1, 2, 3, 4, …, n, …. But then the choice could be 7, if we are thinking of the sequence: 1, 2, 4, 7, 11, …, 1 2 2 2 n + n +One of the most common mistakes in school mathematics is to list a few terms of a sequence and ask “What term comes next?” For example, a teacher may write: 1 2 4 … and ask what term comes next? The best answer is “almost anything could be the next term.” But people often find that answer unsatisfying. It helps, instead, to give an example. Perhaps, one might respond by saying: “The next number might be 8, but then again, it might be 7.” This answer might, of course, result in an angry teacher, so you need to be prepared with the further comment: “My choice of 8 is based on the sequence: 1, 2, 4, 8, 16, …, 2n, , where n is a number chosen from the sequence of whole numbers, 0, 1, 2, 3, 4, …, n, …. But then the choice could be 7, if we are thinking of the sequence: 1, 2, 4, 7, 11, …, 1 2 2 2 n + n + , …, where n is chosen from the whole numbers, 0, 1, 2, 3, …, n, ….” , …, where n is chosen from the whole numbers, 0, 1, 2, 3, …, n, ….”

## Comments

In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics in the Department of Mathematics. Jim Lewis, Advisor July 2007