Friends! Before I tell you more about this rad type of math that I’m working on I have to tell you what I did today. (pause for dramatic effect) I went running outside today for the first time today since the end of the school year. It’s been super nice out for 2 days in a row; normally DC is about 95% humidity in the summertime because the Founding Fathers decided to drain a swamp to build the nation’s capital. I felt like it was a sign that I should head outside for a run. When I opened my Nike+ app it totally shamed me. It said “it’s been 8 jillion days since your last run”. So embarrassing. But then I did a 5K, and I didn’t die so I’m going to go ahead and label that a success.
But back to this inverted math. I’m pretty into it. What I want to tell you about today is how crafting a task to use with this model is different from a standard or typical word problem. I think one of the easiest areas to see this difference is in addition and subtraction. So, when you teach a unit on adding and subtracting you’re generally spending part of the time teaching students how to solve word problems. A normal word problem might sound something like this: “Mattison has 4 cookies. James has 3 cookies. How many cookies are there altogether?” But when you’re using the inverted model, you’re going to write a task that is either open-ended, or has multiple answers (sometimes both). Going to the original example, a task for this model on the same content might read something like this: “In all, Mattison and James have 7 cookies. How many cookies could each kid have?” What you really want is a task that has multiple points of entry, and that kids could really spend a significant amount of time working to solve. In this example, you could encourage kids to think about how many different ways they could put 2 numbers together to get 7. It’s also likely, in this example, that you would be pushing students to notice how turning numbers around represents a different problem. I find that the easiest way to get started crafting tasks is by working backwards–starting with something more traditional or typical, and then thinking about how I could make it more open-ended or how I could turn it into a problem with multiple solutions. One more piece that’s important in this model is that students are generally using a combination of words, numbers, and pictures to show their work/thinking. There’s also a heavy emphasis on using labels, but I’ll get into that more when I talk about evaluation and sharing.
Another important part of this math model is that students are usually working with a partner, and that they almost always have a variety of tools available to them. Obviously that implies that at the beginning of the year you’re teaching your students how to work with a partner and use tools, but that’s likely to be something you’re teaching at the beginning of the year, regardless of the type of math you plan to use in your classroom. Since you’re also usually giving students a materials choice when using this model, you also have to help them figure out what tools are best for different tasks. But I generally feel like these are things that smart teachers are doing at the beginning of the year, anyway, so I’m not going to waste your time talking about all of that here.
I’ll be back tomorrow or Sunday (it’s supposed to rain on Sunday) to talk about evaluating tasks and how the structure is different when you’re teaching at the end, instead of the beginning of the workshop. Happy Friday!