I've heard a lot about this three part math lesson and even attempted to implement in into my classroom, but always felt like I was missing a piece of the puzzle. On our Feb. 3 Professional Development day, I had the opportunity to attend several workshops hosted by my union local, including one for math. Through that workshop, I gained a much clearer picture of how to conduct a three part problem solving math lesson and make it effective. Today, I implemented the model once more and found it to be highly successful, so I thought I would use my lesson as an example to explain this model of teaching.

Part 1 - Activating prior knowledge
I've been working on addition with my grade ones. I have taught them several strategies for solving addition problems, as well as how to explain their answers to a word problem using pictures, numbers, and words. Today, I wanted to focus on the strategies they have already learned so that they can feel confident choosing a variety of strategies and using several in their answer. So, to begin the lesson, we reviewed what adding means and then made a list of all of the strategies we could think of. Some of these strategies included manipulatives, number lines, ten frames, and tallies. I also reminded them that we need to include a number sentence (i.e. 2 + 3 = 5), and write our answer in words (i.e. "Sally had 5 toys altogether").

Part 2 - Working collaboratively
After our review lesson, I split the class up into groups of three. These groups were pre-determined according to their strengths. I tried to keep students who were around the same skill level together. There are two reasons for this: if I put a very low student with a very high student, the high student will take over; keeping students around the same level together means I will have examples of varying degrees of understanding to discuss in step 3. I posted a word problem for everyone to work on (and we read it as a class), gave each group a large piece of paper, and asked each group to appoint a recorder to write down all the ideas of the group. Once they were working away in their groups, I wandered around, asking open-ended questions to stimulate their thinking, and occasionally intervening in disputes. As they were finishing, I had the early finishers check our chart to make sure they had everything and also encouraged them to add additional strategies. I also made note of what strategies each group used and which components they were missing. As we reconvened on the carpet, I chose four groups to share based on how in-depth their answers were.

Part 3 - "Bansho"
"Bansho" means Japanese blackboard. This idea was imported from Japan and was the missing piece I struggled with the first few times I tried three part lessons. This is how it works...
I had my first group come up and share their answer. I chose the group that had the weakest answer to go first. They only had their names on the page and had spent most of the time bickering so they didn't really have an answer or strategy at all. However, I didn't discuss that fact, only allowed them to present their ideas. After that, I posted in on the left side of the whiteboard. Then I had the second group do the same; this group had an answer, but had made some mistakes and were missing some components. Again, they presented and I posted it to the right of the first answer. The third and fourth groups did the same, with their answers increasing in depth and thoroughness. Once all the answers were posted, we went back to the first and looked at each critically. My questions to the class were "What does this answer have that we need?" and "What is this answer missing?"  I wrote on the board under each question the things they included successfully and the things that were missed. One of the students from the second group even explained were they made their mistake. I focused on the number of strategies they used and the components (strategy, number sentence, answer in words) that were included, rather than on whether or not the answer was correct. At the end, they could clearly see what made for a successful and thorough answer and which level each answer would earn on an assessment.

As a follow-up tomorrow, I will have them work independently on a word problem to apply what we learned today in a new context. This will give me an even clearer picture of who is getting it, and who needs extra help. From there, I can make some small groups that require extra assistance to work with me or my EA, when she is available. I'm hoping I'll be able to conduct my summative assessment next week and move on to subtraction, which should be much quicker and easier, now that they are used to problem solving.

As a side note, this took my full double period for math. At the workshop, I learned that you do not have to complete the whole lesson in one day. You may do Part 1 and start Part 2, then come back to it another day to finish Part 2 and do Part 3. The important thing is to give them enough time to thoroughly think about and record their ideas, and not rush through the steps. If need be, you can always do a quick review before getting back into it, or stop them during Part 2 if you notice that they need extra guidance. You also can't use this model for every single math lesson; sometimes, you still need to do some direct teaching, which was certainly true with my class. I had to formally teach most of the strategies that we are now using. It is all about scaffolding; meeting them where they are, giving them the knowledge and skills they need to get to the next level, and allowing them opportunities to apply the skills and knowledge in various contexts.


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