Stop Using Base 10 Blocks to 'Teach' the Algorithms!
The book study over at Math Coach’s Corner on the book Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking
Let’s revisit Base 10 Blocks, most textbooks use them to show kids how to do the algorithm. But the algorithm is only one way that you can use them. Let’s say we are subtracting 51-29. If I start modeling that problem with Base 10 blocks, the U.S. traditional algorithm is the last way I would use them to solve the problem. Here are some ways kids could potentially use Base 10 Blocks to solve the problem if we would let them decide how they wanted to solve the problem (Just an FYI, these images were all created using the Number Pieces app by The Math Learning Center and cropped using the Skitch app):
Are there other ways that you have seen kids use Base 10 Blocks to solve a subtraction problem? Or are you seeing kids only using them to model the traditional algorithm?
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., et al. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
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GREAT blog post! I love the research citation. 🙂
Thanks, Donna. Hiebert’s book was one of the first that got me started on my journey to teach math differently.
Totally diggin’ this post Christina!
Many teachers show students how to use manipulatives which kills flexibility in thinking.
I think it would be really cool to have students model their Number Talk Strategies with base-ten blocks before and after the 10-15 mini lesson. What I continue to notice is a disconnect between the student-invented strategies built during Number Talks and the traditional day-to-day math work session.
You’re post pulls the veil back on bad teaching practice because using base ten blocks to teach the standard algorithm denies students the opportunity to engage in many of the SMPs…and that cripples many students!!!
I’m definitely sharing this!
Thanks, Graham. I was reading the chapter in the book when I came across a tweet about a study that suggests the use of manipulatives with struggling 1st graders is ineffective and that we need to just focus on the basics. It got me thinking that maybe it’s because what we are doing with the manipulatives is ineffective???? Here’s the link to the article about the study: http://bit.ly/1nRGa6U
Teach old school and new…….whatever each individual kid grasps the concept of the best. Teaching is individual to that particular child or person…….or at least it should be.
You are right, each kid approaches a problem differently and we need to be able to let them instead of teaching one way that is supposed to fit all the kids.
The “old school” way is still taught… just later (before they finish elementary school). It is important not to teach the traditional algorithm too early because without having developed the necessary number sense to understand it, the traditional algorithm is a meaningless procedure that can limit your ability to understand and apply it to more complex mathematical situations…
Algebra and Calculus make a lot more sense when you have true number sense!
It seems to me that this right here is the heart of the matter:
I have been noticing in conversations I have with adults recently (both those in my courses, and those—pity them—who I encounter outside of school contexts) that the strategy you didn’t think of yourself often seems like the rare one. And the rare one is rare because it is either “difficult” or requires tremendous insight. In this case, the gasp represents the perceived difficulty of keeping track of which cubes are bags and which are cookies.
The important shift is from looking for a single strategy and making sure kids execute it flawlessly, to curiosity about how kids will think something through.You model that really well here. Thanks for it.
Thanks, Christopher. I’ve talked a lot about this in the PD I do, but never put it down formally. So this was good for me to do and then have it to use with the teachers. I think you are right about most adults not liking the ones they don’t understand.
This is fantastic!
Great post! I oftentimes see a fear of using manipulatives at the high school level because the teachers themselves don’t feel comfortable with them. Could this be that the teachers there is only one “correct” way to use the manipulative and if they haven’t been formally trained then they should avoid it. Rather, teachers themselves should spend time “playing” with the manipulatives as a student might. This too will help them see the different ways that students might use them.
I’m not sure, I’ve always thought the use of manipulatives diminished as kids go up in grade because teachers feel like manipulatives are only for young kids. But maybe I am wrong. I know when I taught middle school (back when I was a traditionalist), I felt that way…the smart kids didn’t need manipulatives and I only brought them out if I had to for the kids who weren’t getting it. Again, that was back then and now I see the power of using manipulatives with all grade levels and with all kids, but letting the kids play and figure out how they want to use them.
Love this post! Any chance you can share the video you referenced?
No, unfortunately, I can’t. The project I worked on bought the videos as part of a PD package from the CGI group for use in our PD. We don’t own the rights to the videos, we could only use them for our class, so I can’t post the video on here in a public forum.
Love your quote: “kids could potentially use Base 10 Blocks to solve the problem if we would let them decide how they wanted to solve the problem.” It is important that math become a creative process and the manipulative facilitates the discovery process. I love Digi-Blocks (www.digiblock.com) just for that reason. The model prevents trading mistakes so students don’t get tripped up by counting error.