Recently I have been participating with a group called the Eugene Math Group. One of the issues it is addressing is how to enrich the math education of students during their “no school” days necessitated by tight school budgets. The goal is also to enhance the “at home” math education of students whose parents and volunteers are willing to work with children.

Because of my interest in areas such as math maturity, brain science, computers, and math education, I tend to disrupt the groups orderly exploration of developing math content materials that are aligned with and supportive of the new Common Core State Standards  (CCSS) math.

At our most recent meeting, we talked about math habits of mind. We agreed that this is an important aspect of what we want to do—however, after we get a good start on other things. This is a transdisciplinary topic. Within each discipline one can explore habits of mind specific to the discipline. Thus, there is a lot of literature on math habits of mind.

As I browsed the literature, I looked for whether “mind” referred only to a human’s brain, or whether it also included a computer’s brain. This way of thinking is explored in my IAE-pedia entry Two Brains Are Better Than One article at http://iae-pedia.org/Two_Brains_Are_Better_Than_One.

As I read some of the habits of mind literature, I looked for whether the authors were including the idea that computers provide us with an auxiliary brain—a very powerful aid to our minds. Of course, I was not surprised at the little mention of “computational thinking” being an important mind habit. See http://iae-pedia.org/Computational_Thinking.

This, in turn, reminded me of when I was a graduate student in mathematics. In my second year of graduate school I took a Complex Variable course taught by Walter Rudin. He was a highly respected mathematician and author of the book used in the course. One of the students in the class asked him where he was getting all of the hard, challenging problems he assigned as homework. (They were not problems from the book.) He responded that these were research problems from the literature of 20 to 30 years earlier.

Hmm, I said to myself. If I can solve such problems, then all I need to do is find a math discipline that is not so old. It turned out that I took a numerical analysis course at that year, and I learned that computers were becoming both powerful enough and readily available so that all of the “old, traditional” results in numerical analysis could be reanalyzed from the point of view of current capabilities and limitations of computers. So, I became a computer-oriented numerical analyst and I experienced a reasonably amount of success in this phase of my professional career.

The purpose of this story is that I see a similar opportunity in math habits of mind. The “old, traditional” topic of math habits of mind becomes a new frontier as one integrates in computers and computational thinking.

I have mentioned my belief in the idea that two brains are better than one. Actually, I now tend to think in terms of five brains. I have previously written an IAE Blog posting Five Brains Are Better Than One IAE Blog available at  http://i-a-e.org/iae-blog/five-brains-are-better-than-one.html. From a math education point of view these are:

• Human brain.
• Tool and artifact brain. This is the idea that many of the tools of the past were (and, still are) embodied with a type of intelligence coming from the tool inventor/designer. Math has a long history of developing and using tools that aid the brain in learning and doing math.
•  Speech (oral communication).
• Reading and writing brain. This has been key to the continuing accumulation and widespread dissemination of oral and written communication that are key components of math teaching. Think in terms of the “math textbook” and the “traditional chalk and talk approach” approaches to math teaching.
• Computer brain. Computational thinking, artificial intelligence, automation of many procedures, and information storage and retrieval of information have been greatly aided by computers.

 I believe that when we integrate in computational thinking and artificial intelligence, habits of mind becomes a very important component of math education and a good area for math education research.Also, of course, computational thinking is now a common aspect of many different disciplines.