We do not need a national examination to know the state of our mathematics teaching. We only need to go to the classroom. By the following signs you can tell if something is not right.

1. When the test includes items like

In , what is the value of a, b, and c?

2. When you hear heated arguments about whether or not AB should have a bar above it when talking about its length.

3. When the classroom routine is teacher lectures, teacher hands worksheets, teacher collects worksheets.

4. When the lesson always starts with a drill of skills, for example, on working with integers, fractions, etc.

5. When the students solve a problem using the teacher’s method only.

6. When the teaching starts with the definition of the concept to be learned.

7. When in the task: *If , what is *, the students solved for the value of x first to find the value of .

8. When the teaching style is the same for learning the definition of cosine and proving the addition formulas.

9. When problem solving tasks are given only as application tasks and always at the end of the lesson, unit or chapter.

10. When the teacher explains the theorem first and then uses dynamic geometry software to show that the theorem works!

The first 3 and #8 were inspired by AL Cuoco’s paper titled Mathematics for Teaching. No, I did not name the blog after it. I had my blog named Mathematics for Teaching before I discovered this article or knew that there is a graduate course in Harvard called Mathematics for Teaching.

After retiring from the classroom I developed flash cards for Math Basics and for Algebra Basics. Using flash cards had worked for many students in my classes that needed the focus, immediate reinforcement, and unlimited perfect practice that flash cards provide. I am now marketing the cards but would love to have the cards used in a research study to test their effectiveness. Please go to the website: millsmath.com.