Those of you who read my blog know that I am a fan of Dan Meyer’s 3-Act approach to problem solving. This past summer, I traveled from Vermont to Palo Alto to attend a workshop that Dan was co-teaching at Stanford University, Technology Applications in Math and Science Classrooms.
During the 4-day workshop, I watched Dan’s “teacher moves” as he led us through several 3-Act problems. I came away from the experience even more convinced that using the approach of presenting a problem via a short video or still image, followed by a well-prepared approach to leading the students through the process, was a way to develop students acquisition of the CCSSM Standards for Mathematical Practice (SMP). After the class worked through the “Penny Pyramid” problem, I told Dan that the moves he had used in his questioning and facilitation had touched upon all 8 of the SMPs. He politely disagreed, so I went back to my hotel room and filled in a table that showed all 8 SMPs, his teacher moves, and our student evidence of practicing the SMP. I have since shared Penny Pyramid aligned to SMP with several audiences and have created the blank SMP Lesson Alignment Template using the format that can be used for teacher planning or for lesson observations.
In addition to Dan’s TED talks, presentations at conferences, and his prolific contributions to the math blogosphere, he is a doctoral student at Stanford University. He recently published his Qualifying Paper, entitled Informed or Not: The Distorted Treatment of Applied Mathematics in Math Curricula and Its Effect on Students and a video of the presentation of his paper on his blog dy/dan. Although I had many things in my own work to catch up on, I decided to take a peek at the 11 minute video, which then drew me into reading his 26 page paper.
Even though my own work got put on the back burner, I’m glad that I was drawn in. Both the video and the paper informed my own practice. Below is an open letter to Dan thanking him for sharing his qualifying paper and for providing me with more reasons to continue to recommend the 3-Act approach to math problem solving.
Your qualifying paper made explicit to me a lot of the ideas surrounding your 3-Act approach to problem solving, which I have been sharing with teachers in my work. You chose a succinct word, “distortion”, to describe how math problems in print textbooks can bastardize attempts at real world applied problems. One of the issues is the static nature of print that does not allow students to experience a “problem” other than through language. The slow but (one can only hope) sure shift to digital textbooks should help to alleviate that issue.
Far more disturbing to me is the fact that the distortion is actually reinforced by some (not all) teachers and their “Yeah, but…this all sounds well and good, but what about…” (fill in the blank with “getting through the content that we have to cover” or “those students who just don’t care” or “how can we expect students to be able to solve a problem if they can’t even multiply”, …etc). As I was reading your paper, early on I found something that the “yeah-buts” would jump on. It took longer, on average, for the experimental groups to arrive at their answer. So, some may ask, “Why would we want to take yet more of our precious instructional time to try a new approach to problem solving?”, ignoring the fact that the experimental groups were given less information to start with.
I am giving the “yeah-buts” a bit of a hard time here. Actually, anyone who chooses to be a math teacher for a living has to genuinely care about the students and their learning. No one would put themselves through the ups and downs of teaching if they didn’t care. It’s the downs and the lack of time to collaborate with others and learn new approaches that nudge them towards the curmudgeon stage. Your take that using the traditional problem solving approach is more a case of “preserving a system that keeps students confident and productive” sheds a more positive light on the decision making that goes into choosing the more direct route of giving them all the information they need and asking a specific question. You then follow, however, with “whether or not that confidence is misplaced and whether or not the students could be even more productive.” The latter statement is the one that I hang my hat on, and what keeps me intrigued about the 3-Act approach.
Besides “distortion”, the other phrase that crystalized a new conceptual idea for me in your paper was “silent partner”. This is a great phrase to describe what can also be called “spoon feeding” or “scaffolding”. The limitations of the medium of print textbooks help to generate the need to create pseudo-real world problems in what Boaler calls pseudocontexts. I was intrigued that the two “more mathematically gifted” students in your study depended on the silent partner to be there for them and were uncomfortable when it was absent. They had figured out the key to success in math class, not necessarily the key to mathematical thinking.
The idea found in Thevenot’s study that simply moving the question in a problem from the end to the beginning was very interesting. That is such an easy fix! The fact that the study showed that it had the most positive effect on lower-achieving students is promising.
In conclusion, thank you for sharing your qualifying paper and it’s accompanying video. It heartens me that there is now some research directly related to the 3-Act approach that I can share with teachers. Also, I thank you for providing me with some new vocabulary with which to discuss math problems, primarily distortion and silent partner. Lastly, you have also provided me with a quick fix for the print problems that are currently in our textbooks…move the question to the top!