I had a very busy and interesting week recently. I spent a day with Harvard Physics professor Eric Mazur and his design and research team. I then took the train north where I spent the next day visiting math classes at Phillips Exeter Academy where the entire program is problem-based.

Mazur, as many readers know, is the pioneer of using ‘clickers’ in large lecture classes to better engage students, tease out misconceptions, and use class to further in-depth understanding (not just content acquisition). Mazur has over a decade’s worth of solid data that makes crystal-clear the idea that less teaching plus more feedback – even in a 200-person lecture hall – gets better results than typical coverage and is a far better use of (limited) class time.

He and his team have developed a very cool web-based feedback system that is in beta. (Read more about it here.) Students can not only give answers with text and drawings on computers, cellphones or other devices, the software can encourage students to re-group in certain ways if the current seating patterns are leading to wrong answers, or if the teacher wants people who gave different answers to group! You can learn more here.

BTW: Mazur also noted in our conversation that his years of experience on the Physics AP design committee made him less than enthusiastic about AP’s. He has data showing that student who got 5s on the Physics AP do worse than other Harvard Physics students who did not take the AP’s – a sobering thought. [POSTSCRIPT: Dartmouth research leads them to drop AP credit in Psychology.]

However, this was a few years ago – before the complete revamping of APs currently underway, in which I played a role: check out the slide show on the AP revisions in Chemistry and Biology to see what’s up. Here is a sample slide:

The visit to Exeter was equally interesting. They are in year 10 in the math department of being entirely problem-based. There are only problem sets that kids work on; no textbook, no coverage by the teacher. Exeter gets almost all of its students into the elite colleges, as one of the premier prep schools in the country, so there is clearly no excuse, then, for typical HS math teachers to not work this way. After all, isn’t the stated point of math to develop problem solving ability? Then, of course, you should design backward from it. (You can download this year’s problem sets for all 4 years of courses and read their philosophy here.)

What was most impressive was to see students present their work without fear, even when they announced at the start in some cases that they hadn’t solved the problem but would present their start to it. Teachers were very deft about asking probing questions and encouraging student input – much like a good Socratic Seminar in English.

It was also fascinating to see the misconceptions emerge when students are given free rein. five or six 9th graders were quite convinced that 3(x + 15)/3 could be reduced to x + 5 – in violation of the distributive property. It took a few probes by the teacher, and a prod to one student who looked uneasy with the crowd-sourced answer to bring to the fore the misconception. Here are some of the problems I saw presented and discussed:

The essence of the modern revolution in education, begun 60-70 years ago with the implications of Piaget’s and Bruner’s research, is to play out an ugly truth (ugly, that is, for naive teachers): students are not blank slates. They bring firm views and beliefs to the table that must be engaged if in-depth understanding is to occur. Why? Many of those conceptions are mistaken: much of modern disciplinary understanding is counter-intuitive to naïve learners. (You can find a great summary of research on misconceptions in science and math, for example, here and here).

Thus taking the time to probe – whether in a class of 200 or around a table with 12 – is the essential instructional move of the successful teacher. It is not time lost but time gained: we won’t have to keep re-teaching and being frustrated by surprisingly poor results on tests of transfer.