Episode 4 – Early Math skills
Welcome to the second episode in the Distance Learning Opportunity Series!
This second episode is diving into Math. Last time we briefly talked about how to know if your child really is falling behind. I hear this over and over again, that parents are worried their kids are falling behind. They are worried that their kids aren’t learning as much this school year and last spring as they would have if it had been a normal school year. And this may be true for some kids, and for others it isn’t true.
I think it is empowering for parents to understand just what their child should know at any given point during their educational career. So today, we are focusing on math, early math skills. I will primarily be talking about kids that are in Kindergarten through second grade; however, if you are listening and thinking this doesn’t apply to you because you don’t have a child in those grades, and you are going to stop listening – I think that is a mistake. Because in my years of experience teaching math; these core concepts that I am going to be diving into are missing in even fifth and sixth graders. I have worked with some kids that don’t know these skills because it is skipped over, or maybe not highlighted in curriculums as much as it should be. But this stuff is important baseline, foundational math understanding that really needs to be there to make future math topics and skills easier for kids to comprehend and learn. That is what we see a lot and that is why I am starting with math. I am starting with math because kids get really frustrated really easily with math and that is probably because of our pre-disposed narratives around math. A lot of us have heard from our parents, teachers, or even other adults close to us as a child saying things like,
“You know what? It is okay that you aren’t good at math! I wasn’t good at math either, so don’t worry about it. Math is hard.”messages we get as children
These types of narratives happen so much around math. I am trying really hard to shift that, because math doesn’t have to be hard. Especially these concepts that we are going to be talking about within the episode today. Some people think I am ridiculous, but I love math. And I am excited about math, excited about teaching math. It is important for kids not to be afraid of math. This can change their entire trajectory through their schooling career. Just think about when you were in high school and you were walking to your math class. You weren’t excited. More likely than not you were dreading it because it was Math, and no one likes math class. Right?
I think that can shift and change because math can be incredible. We can see and understand the world around us in such wonderful and concrete ways. So if we can shift our own thinking and encourage our children to love math, then that is what will happen.
I can speak from experience. (It is harder to shift the thinking and narrative around math with older students. They have already been hearing these negative narratives and it will take more time to change their thinking). I have taught kindergarten for many years and my stance has always been one of excitement. I would try and schedule math first in the day and really emphasize how much I love math. How much I love teaching math. And how these different concepts are just so cool. Look what our brains can do! Look how we can explain our world using numbers. And I really make it fun. I have to tell you, when I started doing that, and I would assess my kids (I would do a self-assessment) where I would ask the kids what their favorite subject was and I would get a lot of answers like: gym, music, recess, lunch. But then I would say, “OK, what is your favorite class in the classroom? Is it math, reading, phonics, groups?” And a lot of the time, maybe 90% or more of my kids would say Math.
Math can be fun. We can make it fun as teachers, it isn’t that difficult to do – we just need to take the time to learn how to do it. Right? And I mean, that is the same with anything.
I just have so many stories with kids and math. We could be here forever, so instead let’s move into comments from parents and educators.
Today’s topic! Early Numeracy Skills – and how to know if your child is behind.
I am very excited to dive into today’s topic of early numeracy skills. These skills should be learned, solidified, mastered in preschool, kindergarten, first, and second grade. However, older kids who are struggling in math should go through this checklist as well. Their struggles may be because they haven’t mastered the skills we are about to talk about. And they really need to.
So for all of you who are worried that your child is behind, or a teacher worried that your class is behind, maybe your third, fourth, or fifth graders are just not understanding the current math. I highly suggest you go back to these early numeracy skills to make sure they are there. And if not – provide opportunities for those kids to practice. They may need explicit instruction. But a lot of kids already have that introduction, they just haven’t mastered the skill yet. And that can cause frustration and difficulty in learning math, so practice practice practice these early skills!
The National Council of Teachers of Mathematics has a progression that I did research on and put into a checklist that I have used for many years in teaching intervention and teaching math. It really helped guide my instruction and I use this progression all the way through fifth grade, even though – like I have said before – the teaching of these concepts stop at second grade. But the mastery needs to continue to be there.
This math progression talks primarily about counting, so that is the first thing in my checklist. I have students count out loud as far as they can. I write down the number they say correctly before they make an error.
For example: in kindergarten we want them to be able to count to 31 without error. In first grade, we want them to count to 120. And in second grade we want them to be able to count fluently within 1000. Now I am not saying you should just sit there and make a student count from 1 to 1000. That would be incredibly time consuming and not really appropriate. So, what I have done is stop them at 50 if they haven’t made any errors. Because we are going to talk more about counting in higher numbers later in the progression checklist. But again, kindergarten is only 31. The reason it is to 31 is because in kindergarten we are learning about calendar. We are learning about the days of the week and those types of things. They are really important and part of the kindergarten curriculum, so it just makes sense that they should be able to count to 31.
Of course that doesn’t mean they can’t count higher, they certainly can, but the standard is to 31. So typically I stop if they can get to 31 because I know they are on grade level. First and above I stop at 50.
Next on the progression I want to make sure they actually understand counting. So the next level is being able to count correctly when counting objects. Do they have 1:1 correspondence? If I were to put some counting bears in front of them, do they have one to one correspondence? Do they point to one object at a time when the are counting a set?
If not, this is a really good indicator that you really have to start at the beginning and they are still pretty low on the math progression. They need a lot of concrete experience with counting and probably counting first just to 5 or 10. Counting objects and manipulating those objects. So I could give them hot wheels cars and ask, “show me how many hot wheels cars do you have?” I am making sure they move the object and touch the object as they are saying the number one and moving the car. And then touching the next car and saying two as they move the car. A lot of the time we see kids counting too fast and either skipping an object or they are counting the same object more than once because they aren’t really paying attention to what they are touching. And this is an indication that they don’t yet have an understanding of counting.
OK, so then my favorite on the progression is subitizing. Subitizing is the third step on our progression. What in the world is subitizing? Well subitizing is when you look at a set of objects or set of dots and you know how many there are without actually counting every single one. So the best example I can give that would reach the most amount of people listening would be when you look at a domino. And you see those 5 dots. The two on the left, the two on the right, and the one in the middle. You know that it’s five without counting each dot. That is subitizing.
The National Council of Teachers of Mathematics says we should be able to subitize numbers 0-20 in certain situations: dominos, or tens fames, or dice. So in kindergarten I focus first on numbers 0 through 5. There are a lot of really awesome YouTube video’s for subitizing 0-5 and 0-10. For kindergarten I typically start with fingers. So if I hold up 3 fingers can you tell me it is three without counting each finger? Then you get more and more complicated or complex. Maybe you don’t hold up the three fingers right next to each other, instead hold up one finger on one hand and two fingers on the other hand. They should still be able to tell you that it is three without counting each finger.
Then it gets more and more complicated. We move on from fingers to other visual representations like using a tens frame. If you are not familiar with what a tens frame is I will add a picture of it to my transcript.
It is exactly what it sounds like. A frame with 10 squares. 5 on the top and 5 on the bottom. If I filled in four of those squares with red circles they should be able to tell me that the number is four without counting every single dot.
After mastering subitizing numbers 0-5 we move to numbers 0-10 and then to 0-20 once that is mastered. I always make sure to introduce subitizing 0-20 by the end of kindergarten. But it should be a mastered skill by the end of second grade.
OK, next on my list again is counting. It’s being able to count to 100 skip counting by ones and tens. So can they count from 1 to 100. If earlier in the assessment (on my checklist) they were able to count to 50 then I would maybe ask them, “OK let’s start at 50 and let’s count to 100”. I then ask them to skip count by tens. Skip counting is really important. It is a foundational skill for multiplication, addition – all of these higher level math skills. Without these foundational skills it’s going to be much more challenging when moving on to more complex math.
After counting by ones and tens to one-hundred we look at the ability to count on, starting at any given number. If I were to give them a number could they continue counting to whenever I tell him to stop. For kindergarten (beginning early in the year) I should be able to say, “all right start at four and count to 10”. They should be able to go 4,5,6,7,8,9,10.
What I do see and why this is important is kids that don’t understand counting on you’ll know it because they won’t start at four as in my example. Or you can see them mouthing 1234 and saying out loud 56789. They can’t just start at four they have to go back to the beginning and that’s important for so many reasons. Then you know by the end of the year I want to be able to give them any number 0-31 and have them continue to count.
In first grade I am looking at being able to count within 120. So if I cam them the number 23 they continue to count on from 23. Then I give them the number 94 and I did choose 94 very intentionally because that’s when it switches from two digits to three digits. I want to know that they can make that transition when they’re counting from 2 to 3 digits correctly. Then I don’t stop them until they count to 120, because I want to know they can count correctly from 100-120.
In second grade we are looking to see that students can count within 0-1000. I give them two different numbers to start at and then I stop them at a certain number. One number I give them is 768 and then I have them count for a while. If they’re doing really well I stop them earlier but if they’re kind of stumbling I want to see how far they can get (but I stop them for sure at 850). The second number I give them is 970. It doesn’t have to be 970 but it should be something below 1000. it’s the same as why I chose 94 for the first graders because I wanna make sure they make the transition from three digits to four digits effortlessly.
Next on my list is writing the numeral for the set. I have sets of objects. Typically I use counting bears or Legos or little dinosaurs. I want to make sure that they can write the number correctly. This is also one of the ways for me to make sure they do have that one to one correspondence we talked about earlier. I was very intentional with the numbers I chose.
- 12 – to make sure they understand place value
- 25 – kids often mix-up the writing of 2 and 5, so I want to make sure they are able to write these two numbers correctly
- 7 – the number 7 is often written backwards
- 14 – fourteen is a number that is often missed when counting before students have a true understanding of counting and 1:1 correspondence. So this is a really good indication of whether or not the student understands counting.
The final item on the list is skip counting within 1000. In kindergarten we want them to be able to skip count by 10’s to 100. In First grade they should be able to skip count by 5’s to 100. In Second Grade they should be able to count by 100’s to 1000.