Math is a touchy subject for many adults. For a long time in education, people believed you either “got it” or you didn’t. There was no in-between. You were a math person, or you weren’t.
This led to a lot of misconceptions about math, as well as about our individual abilities to understand and be proficient in math.
Now we know that math is another language, and that this language can be learned by anyone. There are many things we understand about math instruction now that we didn’t know thirty years ago. There are also many things we currently understand about our brains and the ways they work that we didn’t previously know.
The math itself has not changed. The way we understand it and teach it has. Here are the things we know now that may help you as you help young children enter the world of mathematics.
Seen, Not Just Heard
Young children particularly need to be able to use the majority of their senses to understand the world around them.
If you’ve ever seen a baby put it’s mouth on everything, you know that this is one way they learn about the world.
The concept is strange to adults (and it would be really weird for an adult to do) because we have a lot of concrete knowledge given to us by our experiences. We don’t have to use our other senses as much. We can hear a word and our brains can picture the idea without having to have a tangible object to understand.
Most babies grow out of the “putting-things-in-their-mouths” phase. Most children will grow out of the sensory seeking ways they collect information about the world around them. However, until then, we must supply them with the tools they need.
As a teacher, I once was giving instructions to a classroom of Kindergarteners in which I told them to color the bark of a tree brown. I expected them to have issues with the word “bark”, so I explained what that meant.
One little boy was still staring into nothing with a perplexed look on his face. I thought he was still struggling with the word “bark”, so I tapped the area of the tree I was talking about. He looked up at me, nodded, and said, “Yes, but what is a “brown” (actually, he said, “Yeth, but what ith a bwown?” and it was adorable.)
We adults forget what it was like to look at lines on paper and not understand that they were letters, words, and sentences. We forget that we didn’t understand what our teachers or parents were asking for when they wanted “nine” blocks.
So the first order of business when teaching a young child about math is to give them something they are familiar with that can help them as they build new experiences and understanding.
We call these “known” things “manipulatives”, meaning “things you can manipulate” or move around.
What’s a “Manipulative”?
Just about anything can be used as a manipulative.
Don’t limit yourself to just your child’s room for manipulatives. Try the kitchen and bathroom! Here are a few of the many things we’ve used for math:
- measuring and baking tools
- cereal pieces
- small round candies
- dry beans
- dry pasta
Nature is also a wonderful place to find manipulatives. My own kids and I did a lot of nature walks and “math-in-the-park” when they were younger. Leaves and nuts that have fallen on the ground, small sticks, flowers, fruits and veggies that need to be harvested anyway… nature is filled with teaching tools perfect for math. Children tend to be very drawn to these nature manipulatives, too.
Whatever you choose, let your child help you gather and collect these items. Have two or three types of manipulatives handy wherever you do math work (ie: the kitchen table, or a desk in your child’s room). When you are starting math for that day, allow your child to choose from the collections.
This gives them a sense of control and ownership that will translate to the material, making the information also “theirs”.
How Long Do Kids Need Manipulatives?
Children should use manipulatives until THEY are ready to stop. Usually, by fourth grade kids feel comfortable enough with mathematical ideas that are abstract (unable to touch – something that is just an idea, not anything physically represented); however, some kids need longer with manipulatives.
Typically, children will use manipulatives until the concept they are working on becomes solid enough in their mind that they can visualize it without the manipulatives. From this point, they can create pictures.
Representing numbers, measurements, and mathematical ideas in pictures they make with their own hand is a very important next step in understanding basic math concepts. The pictures have to be made by the child in order to work when they are transitioning away from manipulatives.
Picture representations do not have to be fancy or detailed. A circle, a “stick” or straight line, or even a dot can work. Sometimes young artists take this way too far and want to draw lovely works of art. I always tell them, “This is a tool, not artwork, so it should be a quick mark, not a masterpiece.”
From this phase where they are creating their own picture representations, students can move to counting or relying on pictures created for them, like graphics on a worksheet.
Many educators don’t realize that they are skipping important developmental phases when they move straight to graphics on worksheets rather than having children either use manipulatives or pictures of their own.
It is vital, though, for young learners to connect to the manipulatives and create ownership. Otherwise, they may never be able to internalize the vocabulary and meaning of math concepts.
For a long while, educators focused on “rote memory” of facts and mathematical information. Many parents remember their own struggles with memorizing addition, subtraction, multiplication, or division “facts”.
About 50 years ago, educators started to realize that this method of memorizing “facts” was not working for many students. While children were doing the “memorizing”, when they were asked to apply the information, they would rely on methods from before, like counting on their fingers (manipulatives you’ll always have!) or drawing the equation in question rather than answering outright.
The short explanation is that memorizing is great, and it is still done today. However, rather than just memorizing meaningless vocabulary, students should work through problems, representing them visually and with manipulatives, until the equations solidify in their minds.
Having a child represent 9 groups of 6 candies enough times to remember that there are 54 all together is far different than just saying “9 x 6 = 54” over and over again.
Make meaning by providing anchors for truly understanding the information, and in time, they will have the information memorized AND be able to use it more proficiently.
Never Underestimate the Power of Games
Board and card games remain one of the most effective ways to teach young children anything. They love to play, and play provides us with the most powerful connection to information – even more powerful than the connection we have with manipulatives.
You can find games that target each math skill your child is working on, but there are many games that you probably already play with your child that are teaching these skills. Recognizing and talking about the fact that they are already doing math is a great way to make a positive connection to those skills.
At ArgoPrep, we know a lot about math education, and we work to engage our students with eye-catching, attention-grabbing graphics. We leave room for kids to literally “make their mark” when working with pictures, and we encourage the frequent use of manipulatives and self-created artwork and tools when kids are learning.