Dr. Rebecca Klemm @numbersalive shares how to help numbers come alive for all ages. From toddler to teenager to Ph.D., Rebecca informs us about the building blocks that build math success.
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Below is an enhanced transcript, modified for your reading pleasure. All comments in the shaded green box are my own. For guests and hyperlinks to resources, scroll down.
5 Ways to Help Numbers Come Alive
Vicki: So today we are talking with Dr. Rebecca Klemm, the “Numbers Lady” about five ways to help numbers come alive in our math classroom. So Rebecca, what’s our first way to help numbers come alive?
Tip #1: Notice numbers and shapes everywhere with students
Rebecca: First of all, math is everywhere and I like to use the numbers to tell the story of where they are in either shape, quantity, order, or name. So, you just look around the classroom.
And one of the things I love to use, cause you probably have windows or if you don’t something else…just look around and find where the numbers are and let the kids pick them out and maybe make a book of it.
So some of them will find shapes. If they’re looking for five, they’re gonna find a pentagon somewhere. If you’re looking at windows you get to decide what is a window, and that’s a really good place sometimes to do multiplication. Because you see them in pairs and you have the horizontal and vertical.
But use that for a great introduction a lot of time in could be whatever size windows you have and you decide what a window is. Or you look at the colors of the shoes, you look at whatever is around the classroom and relate geometry, order, name, and quantity in all the different ways that we encounter numbers.
Pick up the clock, look at the calendar for seven days of the week, or if they figure it out. And let them make a little list and book of the things they find. They can draw them or you take pictures. And it’s a great homework. I like that kind of homework where you go home and you do the same activity with the people you live with. So you look around your environment, take pictures or draw examples of what you see and bring them back. You see that they’re everywhere in all those varieties.
Math Tip #1: Look for Math in the Classroom
Russian Classroom windows – Wikimedia Commons
Vicki: That is so important because of we want kids to relate math to the real world. Rebecca, what’s our second?
Tip #2: Combine Geometry and Arithmetic
Rebecca: The second is combine geometry with arithmetic. So often, we teach shapes with colors, I’ve seen everywhere on all kinds of posters and books.
And then there’s counting.
No, the counting and geometry should go together, and that’s one of the things that I put together in my Number Linx puzzle. That, in fact, teaches them together.
Using simple language: points instead of “vertices”
So you count the points or sometimes people like to call them vertices. But I’m a Ph.D. mathematician and I like to keep the language simple for learners. But let them count with the shapes that actually relate geometrically to the counting of the size or points.
I use a heart for two because it comes into a point at the top and at the bottom.
Math Tip #2: Combine Math and Geometry
Heart – Wikimedia Commons
I use a teardrop for one point and an oval for zero. So I like to relate geometry with counting rather than separately as it typically is done.
Vicki: And you know so many times kids will take algebra and then they go into geometry and they just feel like it’s two separate things. And really they are connected.
Rebecca: Very much so. And in fact, they were developed together.
Geometry is not proofs
And Geometry by the way, because I taught everything from elementary through Ph.D.
Geometry is not proofs. The Greeks did it as proofs because they didn’t have Algebra yet. Their language was beauty, their language was Geometry, there was no zero at the time. So the history concept is really an important part of what I do in teaching teachers about what math is. It’s rarely part of the curriculum for getting people ready to teach that subject.
Vicki: What’s our third?.
Tip #3: Use Units when you’re counting
Rebecca: Third is, use units when you are counting. Two plus three equals five, well let’s make it two dolls plus three dolls, let’s make it three socks plus four socks, make it something that’s relatable, leave the abstraction for later. And in fact, it brings the idea in also of sorting by color and size and shape.
So if it’s one of your shoes that may be different from one of my shoes.
So you can say, “Oh, this is a tennis shoe versus a different kind of shoe. But make them have units and it becomes real.
Vicki: That is excellent advice. Now, what grade level does abstraction come in?
When students can start understanding abstract numbers
Rebecca: Well, I think you can bring it in as you’re starting to get into second grade, third grade. Once they see the pattern of them. Once students begin to realize, and it depends on how sophisticated the students are. Some of them can at a later date, but if you actually start with units and they’ve had a strong pre-school and it’s all about units that’s fine. They may even need to start with the units for sure when they are in first grade.
But as they evolve after that and they’ve got the concept that you’re only adding when they’re same things. So what is it you’re trying to add, and it goes back to the windows.
What is a window? Before you add the windows, count how many windows there are, you need to decide what a window is. Is it one of the panes or is it the complete entire piece?
Vicki: And keeping it the same and understanding those units can even set us up for Algebra. Because we’re going to have those variables. I love how you’re building these building blocks, I think with the end in mind, aren’t you?
Rebecca: Yes, very much so. Because I am looking at what you’re going to be doing for math lifelong.
And getting you ready for creating new math things because the math we teach is not necessarily the math we’re going to need in the future.
It’s an evolving subject, it’s not static.
And I think that’s one of the things people don’t realize about math. It has evolved over the centuries and it is still evolving.
And one of the fun things I have there is that out of my creating a puzzle for young children goes into adults and now is a new conjecture in Geometry. It’s a new idea, that came out of trying to think about putting Geometry and Arithmetic together. I just wanted to put them together, I didn’t realize as I started making that in fact, it evolved into a new conjecture.
So that is a very interesting lesson for children to do. And to see that there are new ideas in math all the time.
Vicki: So what is our fourth idea?
Tip #4: Put subjects in the learner’s world
Rebecca: Put the subjects in the learners‘ world. If they like to make clothes, I’ve had a middle school Algebra teacher say, ”My children just don’t like the subject“. I said, ”You need to make it related to their world“.
So you say all the girls want to do is sew clothes and decorate their lockers. I said Fabulous! Think about all the math that is in there and the measurement. Everybody measures and everybody does arithmetic and some geometry in their entire life. And he said, but I don’t know anything about that. I said, Don’t worry.
They’ll teach you about what’s interesting to them, then you work with them on where the math is relevant to their interests. It flips it, don’t teach the stuff and then you’ll apply it. I did this when I taught university. What are you interested in as your subject. And let’s figure out what arithmetic, math, calculus, it didn’t matter what part of math it was, that’s relevant for your area of interest.
Vicki: Make it relatable. Okay, what’s our fifth?
Tip #5: Don’t tell learners they can’t do something
Rebecca: And the fifth is don’t tell learners they can’t do something. I have an article that went out this March that is the story of a little boy whose teacher told them you can’t subtract three from two. It’s called from Toy Trucks to Trade because it turns into a teaching lesson. I asked him what do you think it would mean?
And he talked about how he has three trucks and his other friend had two. They get together, they have five trucks, notice the units are their trucks. But he wanted to borrow his three trucks and leave him two – he owes me a truck. And I said, “that’s precisely where it came from.” So it’s a teachable moment, ask them why they have a question, and not tell them it can’t be done. I know we all as teachers have good days and bad days but let them ask and tell you what they think it means. And then you can mentor them from that.
How to be an amazing math teacher
Vicki: So Rebecca as we finish up, could you give us a thirty-secondpep talkk for math teachers about how to be amazing math teachers?
Rebecca: Well, I think the first thing is really – work with the children, learners of all ages. Cause I’ve done university and PhD students also, it’s the same.
I put it stories for young children where the numbers are trying to match up their meaning. They’re wandering the world like children are, like we all are for our whole life, we’re trying to figure out what we’re here for and what we’re up to.
So I have the numbers doing that and making it fun and engaging.
They have to see that it is relevant to their world. And if they see that, they’re off and running very fast. Textbooks and worksheets are too often just abstract.
You do need repetition but if you put units on them and if you count the wheels they you can say are they all the same kind of wheels?
So you get into sorting and counting by putting them together in groups. Then the arithmetic makes sense to the things they are interested in and off they go.
Vicki: Well, we got some great advice from Dr. Rebecca Klemm, the Numbers Lady, about how to make numbers come alive in our classroom. And you know what, it relates to every subject we teach. Because it’s all about helping things relate to a student’s world, so that it means something. And that my friends is remarkable!
Bio as submitted
Dr. Rebecca Klemm, also known as The Numbers Lady, is an accomplished mathematician, statistician, world traveler, and teacher. Since receiving her Ph.D. in Statistics, she has specialized in explaining mathematical concepts via everyday language.
After running her own research firm for many years, she founded NumbersAlive! (http://www.numbersalive.org) to share her love of numbers with kids. Dr. Klemm has received numerous awards for her NumbersAlive!® apps, books, puzzles, and games which make math meaningful for all ages.
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