Today we are moving into the next stage of counting. Last week was emergent, this week is perceptual counters.
Hello and welcome to Making Number Sense Make Sense, a podcast for elementary teachers, specifically early elementary teachers, looking to really make an impact in the number sense of their students.
Emergent counters that we talked about last week are ones who are still working on one-to-one correspondence, learning the number sequence, learning to write their numbers, usually to around five, hopefully beyond.
So now we are into perceptual counters. Perceptual counters need to bring to life or really perceive the things that they're counting.
At this stage they're still learning to make numbers and think about numbers in a more abstract way. At this point they're still very concrete.
A perceptual counter still needs to bring something to life. So if I say count this collection and there's ten objects there, they'll be able to count them but they'll need to touch them, they'll need to perceive them, they'll need to make it real.
Or if I clap ten times they'll be able to count it but they'll really need to keep track of the one, two, three. They need to touch it, tap it, see it, or hear it to be able to count it.
Kids who are perceptual counters will be able to count small objects with one-to-one correspondence. They'll be able to count arrangements of ten, usually write numbers to ten and represent a collection of what's counted.
So if I say how many things are here, there are ten, they could draw a matching set or create a matching set of ten items counting correctly.
They might be able to tell you the number that comes before and after, so what number comes before nine or after twelve, but they might need kind of a running start.
So if I ask what's the number that comes before nine, instead of thinking nine, eight, they'll have to start from one and go one, two, three, four, five, six, seven, eight, nine, and then be like eight. Eight is the number that I'm looking for.
If you ask them to show you eight fingers and they're not really sure about what eight fingers will look like, they might raise up their fingers or you might see them tapping their chin or tapping their face with all of their fingers or a desk or table to make the number eight that you were looking for.
And they are working on still counting to twenty. You're looking out for kids who can count a small collection of fifteen or fewer and tell you how many.
And if you have a large collection of like fifty items and you say, can you get me seven of these fifty things, they could count out seven and give you that many.
So what should you be working on and what can you do to help students in this stage of counting move to the next one?
So at this point, they understand the concept of one to one correspondence, like one number name goes with one object, but they might still have trouble with the later teen number sequences.
So you're going to be wanting to work on number sequences and counting one to one correspondence cardinality for larger quantities up to about twenty.
And you're going to want to be working on subitizing and subitizing. I have an episode about that that I will link for you.
But subitizing is the ability to quickly recognize a small group of objects without counting them.
So if you roll a die and you get the number six, you would just know what the six looks like instead of having to count the three like one, two, three, four, five, six.
You'll just know how many it is. Six.
I don't remember much personally about learning to count, but I do remember that when we were using dice, it took me a long time, like me as a little kid, took me a long time to trust myself to know how many were on each side of a die.
I remember Noah's like, I know that's five, but I'm just going to count to double check.
Like, I got really stuck in that and it took me a while to be able to move past that.
So if you see a student who you're like, I think they really do know it, but they're still counting it, it might just take them a little bit of time to gain that confidence.
And something that helped me was my parents used to play like dice games with me when we were playing it.
You kind of got out of your head about your counting and you just kind of went with it. You're like, I want the game to keep going.
I'm just going to roll with it and hope that I get the right answer.
And when I say that, I don't mean guessing. I mean like having the confidence to be like, I know what this number is.
I know that that's a five. I'm just going to say five.
So for your students who might be a little bit more shy or more tentative, it might take them a little bit longer,
but they really just benefit from that extra practice to gain the confidence to be able to say their numbers and use them in larger purposes, use them for problem solving.
So if it looks like they might be a little nervous, just give them time and games that they can play to help them.
Another thing that they might be able to subitize would be numbers on a 10 frame.
If they're familiar with 10 frames and you've been working on that or number patterns.
So if I said to a kid, can you put up six fingers?
They might be able to put up six without counting one, two, three, four, five, six. They might be able to just show you what six is.
So they're working on understanding how many each number is without counting it for smaller quantities.
So there are two types of subitizing, perceptual and conceptual.
So we can really only subitize around five things easily.
So recognizing five things easily without counting that you're not very familiar with.
But in conceptual subitizing, you start to see smaller numbers inside of the bigger numbers.
So if I had a 10 frame and I had seven on it, kids who are more familiar with it will just know that seven.
But if they're still working on subitizing on a 10 frame, they might see five on the top of the 10 frame and two on the bottom and know five and two is seven.
There are some things that you can do with students at this stage to really help them get ready to move to the next stage of counting, which is figurative counting.
Working on spatial recognition would be a lot of great number sense routines like quick images with dice or quick images with 10 frames, quick images with finger patterns.
All of those kinds of things would be helpful to get students used to subitizing and kind of get used to seeing that as more of a routine than just in isolation.
The kinds of games and centers you want to choose are games and centers that incorporate a lot of these different tools like dice, rec and recs, 10 frames.
But in a way that's kind of engaging and fun.
So maybe in one game they'll have to roll a dice and make a tower or roll a dice and create a pattern.
They might have to pick a card and make a matching set.
They might need to use some kind of spinner to get the number that they're supposed to build on their 10 frame or on their rec and rec.
And there's a lot of ways to make it the same kind of station or center more engaging.
So maybe you change up the manipulatives that they get to use.
Maybe they get to work with a partner, maybe their partner roles and then they build and then you can work in some social skills.
So those types of games are ones that will be really helpful with this stage of counting to get them really familiar and comfortable with the numbers in the range of 0 to 20.
So they'll be able to move on and use what they have learned in the next stage of counting.
The other great thing about games like this dice game, spinner games, number cards is that they're very easy to differentiate.
So there is never a time where everybody in your class is exactly in the same place.
So you might still have some emergent counters, you might have some perceptual counters, and maybe your group of emergent counters would use a smaller number range and build to it.
Or maybe they're working with a partner who might be a little bit stronger and their partner can help them with their numbers to move on to the next level.
So there's lots of choices for differentiation and opportunities for kids to help each other and learn from each other.
So you're really going to want to work on those teen numbers at this stage, which can be really tricky.
And rec and recs are a great way to work with teen numbers.
Rec and recs are bead racks that have two bars and there's 10 of them on the top and 10 of them on the bottom.
Five of them are red, five of them are white on both sides.
So it's still working with five, 10, and 20, which are all friendly anchor numbers. But at the same time, it's just a little bit different than what would be on a 10 frame.
So by using rec and recs and also 10 frames, it helps them build connections between those numbers and seeing them in a different way.
So it can stop being so concrete and they can start to generalize what those numbers look like and what they are in relation to each other.
And I mentioned 10 frames a lot, 10 frames, 20 frames are another great way to work on this type of this number range because it's set up as 10 and extras,
which is like 10s and 1s, which you start to get into decomposing numbers, understanding the beginnings of our number system because our number system is based on 10s.
So really being familiar and flexible with those number combinations really helps kids move on to the next stage of counting.
I do want to say that at this point, you don't want to rush into addition and subtraction because it can start to get really complicated.
You're getting into symbols again or writing number sentences, things like that.
A lot of times people rush to do addition and subtraction or you'll see students doing worksheets or families wanting to be supportive and having their kids do worksheets like addition and subtraction worksheets.
While those can be, you know, practice for students, what you're really wanting to build in them is the ability to work with those numbers in their head in a way that makes sense instead of just going through the motions.
In a number story, number frame, you can work on addition and subtraction, but not necessarily have the number sentences, just understanding how numbers relate to each other if you're joining them or separating them.
Because there's so much happening, it's really easy for kids to just lose sight of all that they're learning and all that they're accomplishing.
So I would really encourage you to keep some kind of record that you're showing to them.
It could be visual goal setting. It could just be letting them know or and giving them something concrete to work towards can really help them continue their own motivation to be intrinsically motivated to keep learning and keep growing.
It's a little quick recap. Perceptual counters are still very much needing to bring their counting to life. They need to touch it. They need to hear it. They need to feel it in order to make it real to them.
And what you're working on at this point is helping them move from that very concrete way of thinking about numbers to a more conceptual way, not rushing it.
But that's your goal. The goal is to have them understand these numbers so well that they can start to manipulate them in their head mentally or have them make sense in relation to one another.
And you can do that with quick images, with centers using Rec and Rec, centers using Dice. I'll have examples of all of these, like I said, listed and keeping track of their goals.
The goal of this stage is to build on what they have learned as emergent counters, as perceptual counters, and start to move them toward being able to use these numbers for problem solving and help them become flexible with the way that they think about numbers and how numbers relate to each other.
Again, I'm going to reiterate, don't rush this. Just kind of let it happen. They need a lot of practice to really make their understanding of number solid and give them a solid foundation for moving forward.
A lot of times when people rush through their gone shaky foundation, we don't want that. We want it to be solid. We want them to really understand what these numbers mean so that as they work with larger numbers, they can still understand how numbers should work in relation to each other.
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