Rounding Up Season 3 | Episode 7 – Number Sense Guest: Dr. James Brickwedde Mike Wallus: Carry the 1, add a 0, cross multiply. All of these are phrases that educators heard when they were growing up. This language is so ingrained we often use it without even thinking. But what's the long-term impact of language like this on our students’ number sense? Today we're talking with Dr. James Brickwedde about the impact of language and the ways educators can use it to cultivate their students’ number sense. Welcome to the podcast, James. I'm excited to be talking with you today. James Brickwedde: Glad to be here. Mike: Well, I want to start with something that you said as we were preparing for this podcast. You described how an educator’s language can play a critical role in helping students think in value rather than digits. And I'm wondering if you can start by explaining what you mean when you say that. James: Well, thinking first of primary students, so kindergarten, second grade, that age bracket; kindergartners, in particular, come to school thinking that numbers are just piles of 1s. They're trying to figure out the standard order. They're trying to figure out cardinality. There are a lot of those initial counting principles that lead to strong number sense that they are trying to integrate neurologically. And so, one of the goals of kindergarten, first grade and above is to build the solid quantity sense—number sense—of how one number is relative to the next number in terms of its size, magnitude, et cetera. And then as you get beyond 10 and you start dealing with the place value components that are inherent behind our multidigit numbers, it's important for teachers to really think carefully of the language that they're using so that, neurologically, students are connecting the value that goes with the quantities that they're after. So, helping the brain to understand that 23 can be thought of not only as that pile of 1s, but I can decompose it into a pile of 20 1s and three 1s and eventually that 20 can be organized into two groups of 10. And so, using manipulatives, tracking your language so that when somebody asks, “How do I write 23?” it's not a 2 and a 3 that you put together, which is what a lot of young children think is happening. But rather, they realize that there's the 20 and the 3. Mike: So, you're making me think about the words in the number sequence that we use to describe quantities. And I wonder about the types of tasks or the language that can help children build a meaningful understanding of whole numbers, like say, 11 or 23. James: The English language is not as kind to our learners ( laughs ) as other languages around the world are when it comes to multidigit numbers. We have in English 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. And when we get beyond 10, we have this unique word called “eleven” and another unique word called “twelve.” And so, they really are words capturing collections of 1s really then capturing any sort of 10s in 1s relationship. There's been a lot of wonderful documentation around the Chinese-based languages. So, that would be Chinese, Japanese, Korean, Vietnamese, Hmong follows the similar language patterns where when they get after 10, it literally translates as ten 1, ten 2. When they get to 20, it's two ten, two ten 1, two ten 2. And so, the place-value language is inherent in the words that they are saying to describe the quantities. The teen numbers, when you get to 13, a lot of young children try to write 13 as three 1 because they're trying to follow the language patterns of other numbers where you start left to right. And so, they're bringing meaning to something, which of course is not the social convention. So, the teens are all screwed up in terms of English. Spanish does begin to do some regularizing when they get to 16 because of the name diez y seis, so ten 6. But prior to that you have, again, sort of more unique names that either don't follow the order of how you write the number or they're unique like 11 and 12 is. Somali is another interesting language in that—and I apologize to anybody who is fluent in that language because I'm hoping I'm going to articulate it correctly—I believe that there, when they get into the teens, it's one and 10, two and 10, is the literal translation. So, while it may not be the ten 1 sort of order, it still is giving that the fact that there's ten-ness there as you go. So, for the classrooms that I have been in and out of both as my own classroom years ago as well as the ones I still go in and out of now, I try to encourage teachers to tap the language assets that are among their students so that they can use them to think about the English numbers, the English language, that can help them wire that brain so that the various representations, the manipulatives, expanded notation cards or dice, the numbers that I write, how I break the numbers apart, say that 23 is equal to 20 plus 3. All of ...
