There are six things (at least!) about mathematics education which do not work:

- pacing for coverage of curriculum rather than focusing on effective student learning,
- fear that if students take more than five seconds to solve a problem, they will give up,
- teachers spending more time talking than students get to spend thinking,
- teachers working in isolation to plan lessons, units, and understand their students,
- students being forced to work in isolation from their peers as potential resources,
- and an obsession with procedural fluency over conceptual understanding.

The objective of my current work is (collaboratively with the rest of the members of my team at New Visions) to develop tools for teachers that will help address as many of these issues as we can. These tools will be used collaboratively with teachers to look at student work and try to address the question, "What were these students probably thinking?" and "How can I help this student further their understanding of mathematics?"

Well-said. Concise and totally on-target.

Here’s one more which I would place as #2 Look at student work to understand what students have learned and what they are confused about, and make instructional decisions accordingly—even if it messes up the pacing calendar.

Let me rephrase that as a problem so it fits in better with the other 6:

Assessing student learning summatively based on right or wrong answers without unpacking what students were thinking, what they understood, what they were confused about. (missing the myriad opportunities to use student work formatively to inform instruction and lead to better summative results).

Absolutely, that is a problem, and not just in mathematics. The same issue exists in many other content areas as well.

I just noticed that all but #6 are not exclusively problems in mathematics education. Hrmm.

1. I pace at the beginning of the year to get an idea of how to make sure I cover what is needed for my level of math. However, as the year goes along I do not focus on the end date of a topic, but rather making sure students have an understanding before moving onto the next topic. I would agree with you, but I feel that a pacing guide (that can adjust) is needed.

2. I love sitting and just looking at a student who is sitting there waiting for me to tell them the answer. Watching them struggle, but then figuring it out is great. I can out-wait the student waiting on me to give the answer.

3. I caught myself talking too much last year. I am working on changing that this year after reading “Make Just One Change: Teach Students to Ask Their Own Questions ‘By Dan Rothstein and Luz Santana. Students need to explore in math and not just be given the rules.

4. I feel that working with others who are teaching the subject to come up with lessons and units is important. However, I do not have the same students nor teach in the same style as others, so some isolation is needed to make sure that I am reaching my students as they need. I do agree that 100% isolation is not good and can lead to being a stale teacher.

5. My room is NEVER quiet. You have a question? You know your friend can help? Get over there and talk over the work.

6. Everyone figures things out differently. I love having students share how they solve problems.

David, I’m glad that you posted this. I think we need to share this out there with more math teachers. Somewhere along the way teachers having gotten into the rules and ways of mathematics. True mathematicians do not follow step by step rules.