Last week I received this letter from a student named Morgan R. (I’m withholding his last name), with no return address or contact information, so I thought I’d respond to him here. First, Morgan’s letter:
I’m sorry that this Investigation has caused you such consternation. I assure you that this is not an error in the textbook, and so you should not be concerned about additional errors that may affect your math grade. Since you contacted us, however, I’d like to offer a few suggestions that could positively affect your experience in learning math, and by extension, your grade as well.
First, let’s consider the Investigation you mention. Here are the first couple of steps:
Take a look at Step 1, Morgan, and ask yourself this question: Are “a student takes math” and “a student takes science” mutually exclusive? That is, can a student be in both groups, or does being in one mean that you cannot be in the other? I expect that you are taking both math and science. If not, surely you know someone who is. So, no, these events are not mutually exclusive. Now try filling in the Venn diagram in Step 2 and see what happens. I think you’ll start to understand the point of this Investigation, and the error in your thinking.
If it’s still not quite clear to you, you might try discussing your thinking with your classmates or teacher, or a friend or family member if you’re outside of class. You’ll often find that collaborating with someone else on a problem will help you see aspects of it that you hadn’t thought of before. This is a great technique to use when you reach a roadblock such as this. In this case, I suspect that you would’ve seen your misunderstanding quite quickly if you’d talked about it with someone; and I’m afraid that typing and mailing a letter to a publisher or author (especially without a return address) will not get you feedback that is as timely.
I don’t know what math textbooks you’ve used in the past, but you should know that Discovering Advanced Algebra has a focus on real contexts and making sense of situations. Perhaps your prior experiences in the math classroom have not asked that of you. But now, in your math class—just as when you use math in your life outside of school—you’ll need to think critically about the context. Don’t expect that simply performing some chosen operation on numbers in a “word problem” will produce a correct answer.
I hope that you will find learning 2nd-year algebra with Discovering Advanced Algebra to be an enlightening experience.