The Science and Art of Teaching Math
by Kathleen Cotter Clayton
Teaching math to your children is both a science and an art. It is a science because much research has been done into how children learn. It is an art because each child is different, requiring the parent to tweak the lesson to help each individual.
Research has shown that 40% of what a student learns depends upon their teacher, so let’s start with the parent’s beliefs and attitudes.
If the parent shows math anxiety, the child will probably absorb some of that fear and dread. If the parent views math simply as a bunch of facts and rules to be memorized, the child’s math education will be built on a shaky foundation. If the parent believes the myth of “a math person,” the child may decide they do not qualify and stop trying.
On the other hand, fortunate is the child whose parent:
- is convinced of the importance of math for daily living, future careers, and understanding of our world.
- views math problems like solving a puzzle, trying different methods, and looking for several solutions.
- realizes there is more than one way to do calculations, some more efficiently than others.
- knows not everything needs to be written down.
- abstains from flash cards and timed tests, and instead approaches facts using number sense and games.
- knows mastery is achieved through thinking, not blindly following an example or practicing some rule over and over.
- uses math to help their student develop self-confidence and independent thinking.
- understands that some frustration is a normal part of learning and encourages the child to persist.
- does not constantly dispense rewards, verbal or otherwise, causing the child to rely on the parent for assurance instead of their own thinking for every step of the way.
- is aware that a child develops concentration by being allowed to concentrate and so protects him from unnecessary interruptions.
- radiates joy and helps the child develop a love of mathematics.
Teach the basics.
While it is true that one goal of education is the ability to learn independently, the basics of any discipline must be learned first. Skiing down an expert run before mastering control of the skis would lead to disaster. Competing in a triathlon before learning to swim would lead to a waterlogged failure. In the same way, giving a young child a math workbook without any instructions and expecting them to master elementary math is wishful thinking. They are merely learning how to fill in the blanks. There is no one to answer questions and no way to assess understanding. There is no one to listen to and encourage the child’s alternate way of thinking. There is no one to cultivate a desire for deep understanding.
It is easy to think that the way we learned math, often by rote and without much comprehension, is adequate. On the contrary, we now know that a deep understanding of concepts removes anxiety, lessens the burden of memorizing, makes advanced math easier to grasp, and makes math more enjoyable.
Teach sufficient math.
It is so easy to think that the math we learned as children is sufficient for our children and grandchildren. The fact is today’s children need different math. They need to learn topics in geometry, equations, probability, statistics, fractals, and combinatorics, to name a few.
Some of the reasons we read to our children are to foster a love of reading, to enlarge their worlds, and to expand their vocabularies. Similar reasons apply to the realm of math. Use precise vocabulary especially to the younger child: when appropriate, say ellipse, not oval and rhombus, not diamond. Refrain from implying that squares aren’t rectangles (they are), that you can’t take 7 from 5 (you can: the answer is –2), that the product after multiplying is always greater than either factor (not so: 2 × 0 = 0, which is not greater than 2).
Don’t just memorize; play!
If math is viewed as numerous rules and procedures to be memorized, having lots of homework might make sense because anything memorized without understanding needs frequent review to remain in memory. On the other hand, games are a fantastic way to apply and practice math facts. These games need to provide the children with immediate feedback from their peers or from the game itself, increasing their proficiency while enjoying practicing math.
Don’t think of math as exclusively a paper and pencil activity. On the contrary, what we write on paper is a shortcut for expressing a concept often found in some form in the real world.
Find beauty in math.
One interesting fact recently discovered by researchers is that when mathematicians discover beauty in math, their brains light up in the same regions as that of artists when they find beauty in art. I hope you and your children have much success in learning and discovering mathematics.
Kathleen Cotter Clayton is the daughter of Dr. Joan A. Cotter, author and developer of the RightStart™ Mathematics program. Kathleen is involved with curriculum development and has written or co-authored 18 manuals. She travels, teaches online middle-school classes, and speaks across the US and Canada, sharing the mission to help everyone understand, apply, and enjoy mathematics.
