Log 2

Teaching Secondary and Middle School Mathematics Chapter 1

General notes on chapter 1:

This chapter focused on treating mathematics as a process as opposed to a set of contents or techniques to be learned.

The chapter opened with an interesting discussion of the Third International Mathematics and Science Study (TIMSS), where it compared performance of American students to the higher performance of students in Japan and Korea.  The book then discusses mathematical reform movements, starting with the less than successful "new math" movement of the 60s, the rather regressive "back to basics" movement of the 70s, and finally the process oriented reform spearheaded by the NCTM in the 80s.

The remainder of the book is devoted to the topic of "doing" mathematics, and what that means in terms of to following categories:

1. Problem Solving
2. Reasoning and Proof
3. Communication
4. Connections
5. Representation

As a whole, this chapter did a fairly convincing job of presenting good math teaching as being more than just teaching students a list of techniques presented chapter by chapter.

Question 1 - Why did I become a math teacher and how might this reason influence my beliefs about education?

There were a couple of reasons why I became a math teacher:

1. After 20 years of being a software engineer, I was "burnt out" on working in a cubicle and staring at a screen all day, and I wanted to do something that would be more interactive and more involving.
2. I was looking for a second career that would support my desire to travel and to write.

After a couple of semesters of student teaching I have discovered that I also enjoy teaching kids quite a bit, which is something I was unsure of when I started since I didn't have a lot of direct experience with them.

Since I am an engineer and I have experience using math in the field, I tend to view math as a practical tool for getting things done.  However, as a programmer I see a very large correlation between mathematical problem solving and software problem solving, and I believe if a student can really understand how to use math they can fairly easily learn to be programmers.

Question 5 - What does it mean to "place problem solving at the focal point" of the classroom?  How is this different from what is commonly done now?

To place problem solving at the focal point of the classroom would be to emphasize general mathematical thinking and reasoning over learning particular mathematical algorithms.

In my small amount of student teaching experience, it seems to me that very little emphasis is placed on problem solving in California schools.  Rather, it seems there is so much content to be covered that all the emphasis is on learning prepackaged techniques and methods and there is no time left over for talking about how math works and how to use it in a general sense.  To me this seems like an injustice to the students.