Thanks for tracking down this paper. I began teaching in 1962, was fortunate enough to have had Robert B. Davis as my undergraduate advisor (he was also part of the movement that Ed Begel describes), and used early SMSG materials with my eighth grade students in California for several years. I’m still working on sorting out how to best help students learn math.

While Begel seemed weary, he was still looking forward. In his final paragraph, he pointed to a possible direction for progress. He wrote: “It seems likely that evaluation will play a more prominent role during the 70’s than it has in the past. We will need to not only continue the production of more refined measuring instruments, but also to educate school administrators, school boards, and concerned parents to the existence of more useful tests and more penetrating evaluation procedures.” I wonder what he would think now.

In my more difficult and puzzling moments, I remind myself that futility is better than apathy.

Well, one thing hasn’t changed at all – the quality of research into math education is still poor, and not helped by the axe grinding approach of “This method, which is my pet method, is better” as the starting point.
Fascinating article, and I didn’t feel the weariness, only a very down-to-earth practical and honest assessment.
Can you get a better scan?

Thank you for sharing this. I love Begle’s wording of 2nd law. It is my opinion that this might be true for imparting knowledge period – not just math. Although math is highlighted because of the importance of the topic and the mindset that it is okay to not “be good” at math. Educating others is a very complicated process. It is so personal for both the teacher and the student. There is not one approach that works for every student or every teacher. When we find an approach that works for a topic and you think (and are very excited) that you have found THE Answer to teaching your students math, you wake up the next day to find that IT doesn’t work for next topic or situation. We just keep struggling to educate every child to the best of our ability. As Marilyn stated so wonderfully, “futility is better than apathy”. It is our job as educators to keep trying to find what works – our students deserve it.

Teaching Math is HARD work but so worth it when you see in your student’s eyes the light of understanding and/or the spark of love for Math.

The longer I am in education and the longer the challenges continue, I can’t help but think we need to make some systematic changes (specifically in mathematics education).

First, we make a broad and, in my opinion, inaccurate assumption that all children are capable of learning a defined set of information solely because of their age. Many children never gain a mastery of skills before they are introduced to a new set of skills. In all likelihood, the new skills require a mastery of the previous set of skills.

It is no wonder that the above described situation leads to two things; students who don’t feel confident in math and students who don’t like math. The first feeds into the second.

We are stuck in a system that was developed at the dawn of the industrial revolution and we treat our students as though they are part of an assembly line.

We need to think creatively about how we group children for success starting at an early age. This idea conjures up that I advocate “leveling”. This term developed its negative reputation as a result of how ineffectively it was used in classes prior to the heterogeneous classroom grouping. Children were leveled based on very little data. The delivery of math education that I envision is far more complex.

What is vastly different now is that we have solid tools understand the needs of each learner. Let’s use progress monitoring to make sound decisions about what our students know and what they need more time to learn.

My prediction is that if we created a system based on this approach, it would be extremely cost effective. A regular teacher could effectively meet the needs of his/her students. There would far less demand for special education thus saving districts money.

Oh, by “they” I meant the corporate reform movement writ large — Common Core, RttT, etc. It seems clear to me that if you aren’t starting from a solid consensus — like, say, Japan’s curriculum — and steadily iterating on that… well, if you don’t have that, you have a very large problem. Throw in the partisan “math wars” part, and it is pretty much impossible.

My sense is that there are TONS of things that have been found to work, mostly in the category of teaching techniques, but that none of them have been found to be scalable. As a result, almost no strategies pan out in large-scale randomized trials.

My personal example is a discussion technique called Accountable Talk, which I’ve been trying to learn to do for years. I’m not sure it’ll ever work for me. That said, each of these techniques can be mastered, and when they are, you usually get great results. (This is a falsifiable statement, in the sense that recognized experts in these techniques can reliably identify others teachers who are using them faithfully, and those other teachers’ students will generally be found to learn quite well).

Dan,

Nice to see you tracing into your Stanford, and Math Ed, roots. As a high school student, my school was one of the ‘experimental’ trial schools for the SMSG curriculum. Oh, you should have seen (maybe you have) the mimeographed materials we worked from.