Then, the 5 minute edited videos appeared in my feed and I saw it again with this tweet. I've since watched it three times.
His main message was to do less. Less problems. Less words. Less numbers. The results: More; More evidence of student thinking, more student sense making, and more understanding relationships.
Less problems - allow for student thinking to be documented. Allow them to show their work. BONUS! With less problems, they will have more time to share their strategies and discuss the problem. Hmmm.... Now, there's something to have in a classroom environment. 😂
Less words - make sense making the focus. Too often kids pull out the numbers and do some sort calculation with them without meaningful connection to the problem. Without all of the messy words in the problem, students can focus on what the problem is about and making a model to help them connect the mathematics.
Less numbers - so students are not wanting to "plug and chug" <side note: I DESPISE this term, seriously - If I am just plugging and chugging with my math, then there is no meaning to what I am doing> When you take the numbers out, the students see the relationships forming in the problem, they will know what to do with the numbers when they receive that information. BAM.
So, bottom line: Do less to get more out of it. Ok. I'm sold. So lets try it. (and if you haven't watched the video, you really, really should).
My class is working on populations and samples - (CCSS 7SPA1) and taking a random sample to apply to the population. We have not done this and I have not pre- taught any of this. We have talked about samples, populations and biasness; but not specifically how you would take a sample and make a judgement about a population based on the sample.
We started with a single problem (do less problems), with the unnecessary language removed (less words) and no numbers (less numbers).
We had a conversation about the problem and talked about what they would do if they were the manager. Then I asked:
They wanted to know sample size (🙌), how many were in the shipment (👏) and how many were defective (🎉).
After I gave them the information they desired, I also gave them time to work independently, in pairs, or as a trio. I also provided them with a large sheet of paper to document their thinking.
And so it began. Each group got to work (I 💙 my students). Some were more focused on the details of the problem then others, but I loved that each and every individual, pair, or trio was involved and documented their thinking.
After they had enough time to get everything down on paper, we hung their work outside of my classroom in the hallway. I asked the students to walk around and take a look at each other's work. I asked - What do you notice, what do you wonder - as you walk around? When they were finished and had a chance to look at it all, they sat down (right there in the hallway) and we had a chat.
Students noticed which strategies were similar and which were different. They noticed which ones had the same answer and which ones didn't. They wondered what the answer was (because they are so trained to get the answer and move on!) and why two different ways came up with the same answer. It was from this conversation that I was able to launch into mine.
We talked about how two different strategies determined the same answer (and I did not confirm or deny that the answer was correct). We talked about what the 3,500 meant; what multiplying it by 3 resulted in, and what dividing that by 50 meant. We put meaning to each of the numbers. (I ended up labeling this student work)
Here we did the same thing, but talked about the different strategy of dividing first, then multiplying. Again, labeling the numbers involved. What did this calculation model do as far as the manager was concerned?
Then we talked about this strategy (below), which afforded us to uncover some misconceptions. This student worked independently and knew that dividing the fraction 3/50 would get him a percent... so we had a loooongggg discussion about this poster and clarified a few things here..... The student took the lead on the conversation, and actually chose to redo his documentation to correct his error when we were through. 🎊
My favorite (ssshhhhh.... I'm not telling the student) was this one, because he knew that he could set up a ratio. But he didn't quite realize it was a ratio until he did quite a bit of work. He just kept making a pattern until it became too time consuming. 😂. When he spoke, he talked about how he realized, he could double some of the work he had done, and add to it other work he had done to get the numbers he wanted (note how he went from 1,250 to 2,550 - he added the 1,000 'work' to 1,250). Unfortunately, he ran out of time to document all of his thinking on his large paper.... So we also talked about efficiency.
And then there was this group, who knew right away, they could use a ratio. They set it up, found a multiplicative relationship and used it to solve for the defective units in the shipment. This was intentionally the last set I talked about and used it to solidify and anchor the thoughts that had surfaced through our conversations.
Because I let the students struggle through this one and only problem and gave them the information only when they asked, I believe these students had become attached to the problem. I never had to explain (direct instruction) that samples and population have a relationship with ratios - they self discovered that through our conversations.
This was one problem. I allowed students to document their thinking, and used that to spawn our conversation and solidify our lesson understanding. And in my classroom, to me, this proves that you can do less and get more. Thanks Brian.
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