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Welcome fellow Recovering Traditionalists to Episode 127. Today we are taking a look at Thinking versus Mimicking with Pam Harris and Dr. Doug Clements.
For this week’s episode I want to share with you sneak peeks of two Virtual Math Summit sessions that got me contemplating the purpose of math class.
When I was in school, math was all about mimicking the teacher. I am a good rule follower so doing math by mimicking was easy for me.
But is mimicking the teacher really our goal?
Remember I’m sharing just a snippet from a couple summit sessions.The summit is completely free for educators to attend and the sessions will be released on February 26th and 27th but you have 10 days to watch them.
If you want longer access to watch the sessions, and more interaction with some of the presenters, you can do one of the paid levels of the summit. We have a VIP level that is $19.95 and gives you 30 days to watch this year’s sessions plus you get to attend the live Implementation sessions we are doing with some of the speakers throughout the month of March.
The other option is to become a member of the Build Math Minds PD site for $39/month. This gives you access to this year’s summit sessions for as long as you are a member and you can attend the live Implementation sessions just like the VIP. But as a member you get access to all the past 5 years of Virtual Math Summits, plus the hundreds of other PD training sessions we have on the site.
Okay our first sneak peek is from one of Pam Harris’ sessions. She is doing two sessions this year and this is from her full-length session Stop Teaching Algorithms, Start Teaching Real Math:
Pam: “Now we just developed in this one problem string, one of the major 4 addition relationships that I think students need to own. I think students need to own 4 major addition relationships, or strategies, to be able to sort of ‘own’ addition. We just kind of built one of them. We’re not probably done with it, we’d need to do more work to make that more robust, to really strengthen those neural connections in your head, but then when you own those connections you just use those connections. You’re not pulling from rote memory and then mimicking someone else’s thinking. You’re not following steps. You’re using what you own, what you know. Bam! You are Mathematizing. I think we can do that with students as well.
To be clear, y’all, when I was teaching, I didn’t know this was a thing. I thought math was literally:
The teacher tells you what to do.
You memorize the steps.
If you mimic the steps, you get credit.
Right? Remember your teachers who said ‘Show me your work?’ I would submit teachers didn’t actually mean ‘show me YOUR work’, they meant ‘Show me MY work. Mimick me and I’ll give you partial credit. I’ll look and I’ll see what you did and then I can like get like oh here’s where you…’
And now it’s not that I don’t want to see students’ thinking. Notice that as I was representing thinking, we were seeing a lot of thinking happening. The thinking was made visible. I needed to understand what’s happening in kids’ brains, absolutely. But what I don’t need is for them to mimic me. When I say ‘show me your work,’ I actually want to see YOUR work. I want to know what’s happening in YOUR head. Because for all these problems that we just did, we could’ve actually used a different strategy. Many of you probably did. I want to help students own the 4 major strategies for addition because then they can solve any problem that’s reasonable to solve without a calculator, but not just by mimicking someone else’s thinking, but by using what they own. But more importantly, then I can build from there. What do I mean by that? Hang in, let’s keep talking about that in the rest of the presentation. How do we build from there? ‘Pam, my kids are getting answers to addition problems, they don’t need all this. Just one way! They have a hard time with more than one way. I’m just gonna give them one way to do it!’ Hmm, what might be the pitfall of that perspective of teaching kids to think and reason?”
My dad has told me a story about his math teacher in Jr. High that marked his entire homework incorrect even though he had all the answers correct. He marked them as ‘wrong’ because my dad didn’t do it the way that he had taught them how to solve those problems. This is a prime example of wanting kids to mimic instead of think. My dad had his own way of thinking about those problems but because he didn’t show his teacher’s way, he got them all wrong. We want kids to be able to think through problems in their own way. If you want to learn more about how to help kids develop their own thinking strategies in a way that doesn’t confuse them, come watch Pam Harris’ session at the summit, I always enjoy learning from her.
Some other people I have learned a lot from are Doug Clements and Julie Sarama. Doug has a session at this year’s summit about The Surprising Importance of Early Math that a piece of it also got me thinking about kids mimicking teachers.
Doug: “Another warning from research in Australia is ‘don’t ignore it.’ What do you mean ‘don’t ignore?’ Well kids got worse in subitizing in kindergarten. And when the researchers observed the classrooms, they found out why. Let’s pretend kids are playing a board game. They roll a die, they get 5. And the kid just says ‘5!’ If the teacher’s nearby, the teacher would say ‘you don’t know that, count them.’ Do you see what was happening? It was pulling the rug out from under the children’s subitizing. So we don’t want to ignore it, we want kids to know subitizing is a great way to quantify sets. To label sets with a number.
Subitizing is a great way. So is counting. You could use either one. And indeed you can use them together, like we talked about before.”
So even from the start of school, we see teachers who want kids to mimic “their way”. I know I was guilty of this at times with my own kids when they were little. They would tell me how many in a set by subitizing but then I’d make them count the amount to make sure. I’m not saying that’s wrong, and as Dr. Clements said, kids need both counting and subitizing. We spend a lot of time in the early grades teaching kids to count, but sometimes they don’t need to count…they should be subitizing but we have them mimic us by counting out items that don’t need to be counted.
There is a time and place for modeling and showing kids something, but it shouldn’t be all the time. I just want to encourage you to remember that students come in with a lot of their own knowledge. Watch and let them show you what they know and how they are thinking about math ideas before you jump in and tell them what they should do.
I’m not perfect at this by any means. It’s very difficult to get away from that style of teaching. That’s why I call myself a Recovering Traditionalist. I’m still learning and growing. That’s why I love the Virtual Math Summit. It gives me lots of people to learn from each year.
I hope this helped build your math mind, so you can build the math minds of your students.
This episode is brought to you by the Build Math Minds professional development site. It’s an online site full of PD videos designed specifically for elementary teachers to help you build your math mind so you can build the math minds of your students. If you are interested in getting in-depth Math PD at Your Fingertips, become a member of Build Math Minds. Just go to buildmathminds.com/bmm and depending upon when you are listening to this, enrollment might be open or you can join the waitlist and get notified when it opens again.