Math is a subject that very quickly requires abstract thinking. We turn a number of objects (like three beads) into the number 3 and teach our kids that they mean the same quantity. Then we teach our kids that we can add and subtract, multiply and divide these numbers and do all sorts of things with them. Often we just teach them the numbers and what to do with them, but leave the concrete out. This, unfortunately has a detrimental effect with kids. Kids need something they can hold in their hands. They need the concrete. They need a whole lot of it. They do develop the abstract notions in time, but not as fast as our schools expect them to. So some fall behind. Because they do not understand the abstract beginner level stuff, they do not develop an understanding of the advanced level stuff and finally they just have so much gaps in their learning that it eventually stops all together.
So, with that rant over, I wanted to introduce the concept of multiplication with my five year old. We already do this in our everyday lives. She needs to multiply (or add) to get enough dinner plates on the table or xylitol-tablets after dinner (two per person) to each. They help prevent cavities, but back to topic. So she is ready to understand the idea of multiplication. I wanted to make it concrete, so she can use the concrete tools as long as she needs them until she understands the concept and can do the multiplication by herself without it.
For this we used cups and diamond-beads I happened to have around. You can use an egg carton, yoghurt-cups, glasses, plates, or what ever you have around the house and are willing to use for this. For the beads you can use coins, wooden beads, hamabeads, play dough, or make beads out of magic dough (the recipe can be found here where we made atoms out of it). It doesn’t really matter what you use as long as it is something that doesn’t break and is ok to lose a cup or bead.
First I asked what number between 2-4 she wanted to multiply. She said four. So we counted four in each cup. Then we started to count them. I wrote the multiplication out on a blackboard. After the first group of four, we had 1×4=4. After the second, we had 2×4=8 and so forth. We counted up until we had 6×4=24, before it became boring to her.
Then I changed tactics. I told her that we can count all kinds of things with this. I said that now, we need 6 xylitols after each meal, because 3 people eat them and one takes 2 at a time. While talking, I put two beads in 3 cups and counted that we have 6 altogether. Then I asked her, how much we need after each meal after the baby starts to eat them as well and added 2 more beads in yet another cup. She quickly counted that then we need 8 xylitols after each meal. Then I said that we can count pretty big numbers as well. I asked how many kids were in her playgroup today and wondered how many xylitols they need after each meal. She replied 9 kids, so I put enough beads in enough cups to have 2 beads in 9 cups and counted that they need 18 xylitols altogether. Then we counted the adults as well and how many they need then. I left this idea then because she was ready to move onto new things. But we will return to this as many times as is needed for her to understand multiplication.
This interaction is not something you need to repeat. Instead I suggest using what ever practical problem you can think of in your everyday life, so that the skill is something that actually solves a problem instead of being a unnecessary trick. Then return to this with new problems as situations arise so 1) it seems necessary for their brains to retain – a message the brain gets with repetition, 2) that it is something that actually solves everyday problems, because that is what math is basically about. It is about solving problems all around us. Multiplication is another skill in the child’s skill set so that they can solve the problems they need to.
Copyright text and images: Satu Korhonen. You are free to try these experiments out, use them in your teaching. But instead of copying the text or images, link back to this page.