I’ve been following Dan Meyer’s process with his 3 acts for quite a while. I greatly appreciate the public nature in which he develops ideas and there is a reason he has so many followers: his ideas are worth paying attention to. As a teacher educator I started thinking about Dan’s three acts with two purposes: 1) What makes 3 Acts an effective strategy, and 2) How might I help my preservice teachers create their own 3 act-like approach to teaching.
What makes 3 Acts effective?
Dan has already written about many ideas as to why 3 Acts works, so pardon any redundancies. I think 3 Acts fits particularly well with what I call Developmental Learning Theory. Specifically, the initial video helps make the problem more concrete and therefore more understandable to the students. Dan often notes that textbooks make the problem abstract far too early. Learners struggle with abstraction and too much abstraction can easily take students beyond their zone of proximal development which leads to reduced motivation. However, developing the problem into the abstract realm is important as the abstract approach/knowledge is what is transferable to diverse contexts. While concrete strategies (such as timing the end of the fan cycle) might work for a specific context, using that context to develop abstract mathematical thinking will be more useful beyond that one problem.
My understanding is that Dan does not intend to use the first act to simply provide context for more traditional instruction during act two. Instead, this is time for students to make predictions and maybe even create strategies to solve the problem. Act two, to me, is the one teachers struggle with the most. In many ways, act two cannot be planned for as the teacher must react to student thinking – thinking that isn’t obvious until the moment. At some point, students will need to be introduced to formal mathematical algorithms. While we might want students to derive formulas, we cannot expect them to do so as novice mathematicians. However, when teachers introduce the more formal algorithm is important. Formulas are some of the most abstract representation of mathematics so formulas should only be introduced after students have wrestled with more concrete representations and maybe even have some intuitive conceptual understanding of the concept. After students have this conceptual understanding, they will be more likely to understand the formula and recognize its utility.
I mentioned transfer earlier. I do not expect students to spontaneously apply new mathematical knowledge to diverse contexts. While we might do that as teachers, students likely lack the interest and knowledge needed to see math wherever they look. However, we can encourage this transfer by explicitly asking students to apply their thinking to new situations. This is where act three of Dan’s approach takes over. These application/extensions take students back to the concrete. That is, they are asked to apply their abstract knowledge to a new concrete situation.
How might teachers create their own 3 Act-like approach?
Dan has recently set up a new site where teachers can submit their act one for “peer review”. I am a big fan of this site and see it as a great way for teachers to try out ideas and get ideas/resources. While this is a great resource I can share with my preservice teachers, I want to go deeper as to what might be a conceptual framework teachers might use to help create videos or even go beyond the three act framework to design effective learning experiences. That is, the three act framework won’t apply to every situation (both within and beyond the math classroom), so what ideas do preservice teachers need to know so that they might be able to do what Dan has done in the creation of 3 Acts? While having more teachers copy the three-act approach would definitely be an improvement in education, I don’t want my preservice teachers to simply copy an approach. Instead, I want my preservice teachers to have a robust knowledge set with which they can evaluate ideas like the 3 Acts and maybe even create their own strategies.
When I first started thinking more deeply about the 3 Acts approach, I realized how much the approach has in common with the Learning Cycle. The first act correlates to the explore phase, the second act to concept development and act three to the application phase. While there are certainly some nuanced differences, I think the learning cycle might be a more far-reaching framework than the three act. That is, Dan’s three acts are a great enactment of the learning cycle, but other approaches might fit within the learning cycle as well. For example, Dan focuses on act one leading to a specific question. However, the learning cycle exploration phase could simply be a data collection event on which students might later reflect. Both specific strategies seem to fit under the broader framework of the learning cycle. Yet, even the learning cycle might be too narrow for the “knowledge set” I want preservice teachers to have so that they might create their own 3 Act-like approach to instruction.
I have some ideas as to what ought to be included in this “knowledge set”, but I think I want to hear from others first. While strategies such as the 3 act or the learning cycle are extremely useful, what do you think preservice teachers need to know in order to evaluate and even create such strategies of their own? I’d love to see a list going in the comments and hope that list expands my own thinking on the topic!