In pre-school Jimmy loved counting his plastic dinosaurs and cars. So his parents were perplexed when he struggled with math in elementary school. They wanted to know what happened. They later discovered that Jimmy was struggling with the abstractness of symbols.
A number is a symbol representing a quantity. Symbols are part of the written language of math and arithmetic. Symbols reduce the amount of space it takes to write a complex idea. Consider the difference of writing 12 ÷ 4, versus “using the quantity of ************, create **** equal groups.” What would happen when people wanted to represent large quantities? Without symbols, math books would be 3,000 pages long and accounting would be a nightmare. Symbols are necessary, but they also complicate learning math.
Symbols Provide Partial Information
Imagine a toddler seeing a picture of dog. If he studies the picture he will get a shallow understanding of what a dog looks like. The toddler may even recognize the symbol enough to say “dog.” But a toddler with a real dog will have a much richer learning experience. He will learn about how dogs look, feel, smell, behave, move, sound, interact and more. He will have a much stronger memory and deeper understanding of what is a dog. The toddler who plays with a real dog and then sees a picture or a symbol of a dog will use his memory of the actual dog to fill in the gaps of information from the picture. He may say “soft fur” or “lick” even though the picture does not indicate those attributes. A toddler who has never played with a real dog does not have that rich memory to draw upon when looking at the picture of a dog. He only knows what he sees.
Arithmetic Symbols
Unlike the picture of a dog, the Arabic math symbols we use are not pictorial. A 6 doesn’t look like the quantity it represents. Children learning to read and write numbers and operation signs have to rely 100 percent on memory to fill in the missing attributes of the quantity and action.
Imagine a toddler who can count to three, but hasn’t learned to recognize numerals, looking at the following math sentence.
2 + 1 = 3
He would have no idea what that sentence means.
If he saw this picture he might say “Three doggies, two dogs stand. One dog lay down.” Basically describing 2 + 1 = 3. Learning the math concepts is often much easier than relating it to the symbols with which it is associated.
How Does Learning Symbols Affect Math Education in Elementary School?
A lot of time must be given for children to explore math in a concrete way. They need to experience mathematical relationships concretely all the way through 5th or 6th grade. They need to be able to touch objects, move them, see how different quantities look and change when different actions, like multiplying, are done to the concrete objects. Children who are given time and opportunity in this way will develop strong foundational skills. For children with the math learning disability dyscalculia tangible experience is critical. For the rest of the population it helps them use mathematical reasoning instead of, or in addition to, relying on algorithms. Tangible experience is especially helpful with place value and fractions, two of the most abstract concepts in early math education.
How Can Students Get Concrete Experience?
Arithmetic lends itself to concrete experience. Even kindergartners can experience concepts like large numbers and fractions with the right materials. Using “manipulatives” or hands-on materials, children who don’t know the algorithm for regrouping can solve 103-46= 57. It’s a laborious process, but possible. Many types of manipulatives exist to help children explore the relationships between numbers. Some of our favorite manipulatives at Mathnasium of Littleton include: base-10 blocks, unifix cubes, the Judy clock, dice, dominos, popsicle sticks and coffee stir sticks and fraction tiles.
Do Kids Get Enough Concrete Experience?
Most kids do not get enough time with manipulatives at school to fully make the transition to using abstract symbols with confidence. Unfortunately, teachers do not have the luxury to cover concepts in depth, due to the curriculum pacing set by the district. This results in significant learning gaps that will affect their confidence and abilities through college level math. Well-meaning parents of elementary children may resort to teaching “rules” and shortcuts. While these rules and shortcuts may help in the short-term it can actually be a problem down the road.
How can Mathnasium Help
At Mathnasium of Littleton we work with concrete materials and abstract symbols and give students as much time and experience as they need to learn a concept. We don’t teach tricks and tips until a child has mastered the concept. Most kids breathe a sigh of relief when they get the help they need.
This article was written by and owned by Cuttlefish Copywriting, www.cuttlefishcopywriting.com . It is copyright protected. Mathnasium of Littleton has permission to use it. Other Mathnasium locations should contact Heather at [email protected] before using it.
