• Season 2 | Episode 12 – Counting - Guest: Dr. Kim Hartweg

  • Feb 22 2024
  • Duración: 19 m
  • Podcast

Season 2 | Episode 12 – Counting - Guest: Dr. Kim Hartweg Por arte de portada

Season 2 | Episode 12 – Counting - Guest: Dr. Kim Hartweg

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  • Rounding Up Season 2 | Episode 12 – Counting Guest: Dr. Kim Hartweg Mike Wallus: Counting is a process that involves a complex and interconnected set of concepts and skills. This means that for most children, the path to counting proficiency is not a linear process. Today we're talking with Dr. Kim Hartweg from Western Illinois University about the big ideas and skills that are a part of counting, and the ways educators can support their students on this important part of their math journey. Mike: Well, hey, Kim, welcome to the podcast. We're excited to be talking with you about counting. Kim Hartweg: Ah, thanks for having me. I'm excited, too. Mike: So, I'm fascinated by all of the things that we're learning about how young kids count, or at least the way that they attend to quantities. Kim: Yeah, it's exciting what all is taking place, with the research and everything going on with early childhood education, especially in regards to number and number sense. And I think back to an article I read about a 6-month-old baby who's in a crib and there's three pictures in this crib. One of them has two dots on it, another one has one dot, and then a third one has three dots. And a drum sounds, and it goes boom, boom, boom. And the 6-month-old baby turns their head and eyes and they look at the picture with three dots on it. And I just think that's exciting that even at that age they're recognizing that three dots [go] with three drum beats. So, it's just exciting. Mike: So, you're actually taking us to a place that I was hoping we could go to, which is, there are some ideas and some concepts that we associate with counting. And I'm wondering if we could start the podcast by naming and unpacking a few of the really important ones. Kim: OK, sure. I think of the fundamental counting principles, three different areas. And for me, the first one is that counting sequence, or just learning the language and that we count 1, 2, 3, 4, 5. However, in the English language, it's much more difficult [than] in other languages when we get beyond 10 because we have numbers like 11, 12, 13 that we never hear again. Like, you hear 21, 31, 41, but you don't hear 11. Again, it's the only time it's ever mentioned. So, I think it's harder for students to get that counting sequence for those who speak English. Mike: I appreciate you saying that because I remember reading at one point that in certain Asian languages, the number 11, the translation is essentially 10 and 1, as opposed to for English speakers where it really is 11, which doesn't really follow the cadence of the number sequence that kids are learning: 1, 2, 3, 4, and so on. Kim: Exactly. Yes. Mike: It picks up again at 21, but this interim space where the teen numbers show up and we're first talking about a 10 and however many more, it's not a great thing about the English language that suddenly we decided to call those things that don't have that same cadence. Kim: Yeah, after you get past 20, yes. And if you think of kids when they hear the number 16, a lot of times they'll say, “A 1 and a 6 or a 6 and a 1?” Because they hear 16, so you hear the 6 first. But like you said, in other languages, it's 10 six, 10 seven, 10 eight. So, it kind of fits more naturally with the way we talk and the language. Mike: So, there's the language of the counting sequence. Let's talk about a couple of the other things. Kim: OK. One-to-one correspondence is a key idea, and I think of this when I was first starting to teach undergraduate students about early math education. I had kids at the same age, so at a restaurant or wherever we happened to be, I'd get out the sugar packets and I would have them count. And at first when they're maybe 2 years old or so, and they're just learning the language, they may count those sugar packets as 1, 2, 3. There may be two packets. There may be five packets. But everything is 1, 2, 3, whether there's again, five packets or two packets. So, once they get that idea that each time they say a number word that it counts for an actual object and they can match them up, that's that idea of one-to-one correspondence to where they say a number and they either point or move the object so you can tell they're matching those up. Mike: OK, let's talk about cardinality because this is one that I think when I first started teaching kindergarten, I took for granted how big of a leap this one is. Kim: Yeah, that's interesting. So, once they can count out and you have five sugar packets and they count 1, 2, 3, 4, 5, and you ask how many are there, they should be able to say five. That's cardinality of number. If they have to count again, 1, 2, 3, 4, 5, then they don't have cardinality of number, where whatever number they count last is how many is in that set. Mike: Which is kind of amazing actually. We're asking kids to decide that “I've figured out this idea that when I say a number name, I'm talking about an ...
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