Acknowledgement: The graphic at the right of the heading is an ambigram by Scott Kim.

Welcome to “What I Learned About Why My Students Didn’t Learn More”. My name is Don Byrd. This blog is addressed mostly to secondary-school math teachers, though I hope some of it will be of interest to other STEM teachers and to parents. Who am I, and why should you read what I write?

**Background: Where I’m Coming From**

I spent many years working in industry as a technologist, designing and writing software (especially music, graphics, geographic information systems, and information retrieval), soundware (for music synthesizers), and user interfaces. I returned to academia in the mid-1990’s, mostly as a researcher but also doing some teaching. But funding for research and college teaching opportunities for me faded away around the start of the Great Recession. Then I found out about the Woodrow Wilson National Fellowship Foundation and its fellowships to professionals in the STEM disciplines to retrain as teachers. I’d always loved mathematics but had never concentrated on it; besides, I’d become very concerned about the average American’s lack of understanding of math. So, in 2010, I applied for and received a Woodrow Wilson fellowship. I did a lot of student teaching and got my secondary math teacher’s license, but then had trouble getting a regular teaching job. After teaching college calculus for a semester, I spent a couple of months full-time in a high-school classroom as a maternity-leave replacement.

**Frontground: Where I (Think I’m) Going**

I found being a classroom teacher very rewarding in some ways, but also very stressful — so stressful, in fact, that I decided against continuing as a classroom teacher. Since then, I’ve been trying to contribute to math education by tutoring, working on math-education software, and writing this blog.

**What’s Wrong with U.S. Math Education?**

In my opinion:

Basic Problem 1: TOO MUCH ABSTRACTION. The way we teach math is far too abstract to make much sense to many students. Paul Lockhart’s A Mathematician’s Lament is an eloquent and searing indictment of this aspect of “the system”.

Basic Problem 2: NOT ENOUGH MOTIVATION TO SUPPORT ENGAGEMENT. By the time they reach middle school, few American students have much interest in learn math. Things are, if anything, even worse for students starting high school. To a great extent, this is a result of BP1.

To go into more detail, we:

– neglect helping students discovering things for themselves => BP1 and 2

– emphasize rigor and formalisms much too early => BP1

– rely on symbolic descriptions far too much => BP1

– don’t try to promote intrinsic motivation => BP2

– try to do external motivation by appealing to phony future needs => BP2

– forget there’s more to teaching than just instruction

– attempt both to make things more concrete and to get students engaged with “word problems” that are completely artificial and boring, neither “authentic” problems nor even toy problems that are fun. (Peter Taylor’s book *Calculus: The Analysis of Functions* has tons of examples of fun toy problems.)

– assess teaching and learning mostly with rigid evaluation of answers to boring, non-authentic questions that prove very little

I think it’s possible to do much better, and one of the main things I hope to accomplish with this blog is to give some indications of how. This is hardly an original idea: see numerous blogs (e.g., those by Dan Meyer, Christopher Danielson, and Michael Goldenberg), Web pages (Bret Victor’s, etc.), and books (among others, Paul Lockhart’s). But — with my unusual background — I think I have a viewpoint of my own! Please take a look.

Click the Edit link to make changes to this page or add another page.

I’d be interested in your reaction to the following two papers —

On the impact of background knowledge in math on science instruction:

“Automaticity in Computation and Student Success in Introductory Physical Science Courses“ at http://arxiv.org/abs/1608.05006

and

“Cognitive Science and the Common Core Mathematics Standards” at http://www.ChemReview.Net/CCMS.pdf .

— EA (rick) nelson

Very interesting, Rick, and good work! As a 6th grade (student) teacher, I found many students counting on their fingers: sad but not surprising. I was more surprised as a high-school teacher to find a fair number of my algebra 2 students — in fact, algebra 2 honors — having trouble factoring, say, 36x^2 – 4 because they didn’t realize 36 is a perfect square. And yes, working memory is very limited.