Dr. Cotter on Helping Teach Math

The best way a grandparent, family member, or friend can help a child with math is valuing math and showing a positive attitude. Sadly, about 50% of Americans are afflicted with a strong distaste for math. Unfortunately, developing math anxiety becomes a severe handicap preventing a child from learning and benefiting from a good mathematics education. Enjoying math with a child by playing math games is much more productive than mindlessly flipping flash cards or trying to decipher some obscure problem on a worksheet.

Along with showing a love of math, we can be an encourager for the child. Helping with a math problem is like working on a jigsaw puzzle. You don’t show the child where every piece goes and you know mistakes are inevitable. Rather, we gently encourage persistence, often by asking questions. And we don’t offer a reward for every correct piece. Internal motivation is much stronger than external motivation.

It’s also helpful to keep in mind some math myths that are being transmitted and hurting the next generation. One myth is that you need a special math brain to be good in math. Nonsense. Virtually anyone with a human brain can learn mathematics. The rest of the world rightly believes good instruction and some hard work are what it takes to master math.

Another myth is that boys are naturally better in math than girls. The only case where that might be true is in spatial relationships; researchers suspect this occurs because boys’ play is more visually oriented than girls’. 

One myth is especially damaging: that children must be able to spout their facts instantaneously. This was important in bygone days when humans did all the calculating. Today electronic calculators and computers do the heavy work. Tragically, millions of people point to this obsession with flash cards and timed tests as the cause of their math trauma. Incidentally, the only person who likes flash cards is the person who doesn’t need them.

Another myth we’d all like to believe is that the math we learned in school is sufficient and necessary for today’s students. The fact is that the field of math, like that of science, is growing exponentially. The total amount of math known is doubling every seven years. One example is fractals, not a branch of mathematics until the 1970s, but now is the basis of some computer modeling, including movies like Jurassic Park. 

On the unnecessary list are finding square roots (which I learned in ninth grade) and division by more than a single digit. They take an inordinate amount of time to learn and do not contribute to deep understanding nor are they needed for advanced math. These are best done with a calculator.

Strange as it may seem, counting is not the basis of arithmetic. We spend several years teaching kids to be good counters and then we tell them to stop counting because it is a bad habit. Instead, teach the name of quantities, that three is 3, not 1, 2, 3. Even small babies can tell the difference between two and three teddy bears. We can recognize instantly the number of objects up to five without counting. Then to recognize six to ten objects without counting, group into five and the 1 to 5 more.

To make sense of advanced math, students need a deep understanding of concepts. This most basic knowledge is called number sense, which is grounded in place value. Number sense allows us to work flexibly with numbers. Incidentally, if your protege says “ten-7” for seventeen, as RightStart Math does for a short time, do not correct them. Saying ten-7 reminds the student that 17 is 10 and 7 ones, not merely 17 ones.

As far as learning the facts is concerned, the task is much simpler with good number sense. It is much easier to remember something meaningful rather than an isolated fact. For example, to find 9 + 4, rather than start at 9 and count on 4 more to reach 13, a better strategy is to take 1 from 4 to change the 9 to a 10. Then 9 + 4 becomes 10 + 3 = 13. Keep in mind a child is considered to know a fact if they can respond in 2 or 3 seconds; it’s okay to take time to think.

Number sense also helps for multiplication facts. The fact 8 × 3 can be thought as twice 4 × 3, that is 12 times 2, which is 24. Or, 9 × 7 can be thought of as 10 × 7 – 7, which is 70 – 7 = 63.

We are hearing more and more today that people have short attention spans. But what is even more critical for children is their ability to concentrate. Concentration occurs when we become completely absorbed in what we are doing and are unaware of anything else. Concentrating while reading means you’re unaware of the act of reading. After concentrating we feel refreshed and satisfied. Sadly, television and screen time often interfere with children developing concentration because of commercial interruptions and frequent topic changing. Concentration is like sleep in that we cannot directly cause it. For either concentration or sleep, we can help by setting up favorable conditions and protecting the child from interruptions. That also means ignoring the clock and not ending an activity when a child is truly concentrating. Concentration span grows through practice, in the same way as a baby learns to sleep through the night. 

Paying attention, on the other hand, is forcing one’s mind to stay on a topic of little interest at the moment. It is very tiring. For children the rule of thumb for paying attention is 1 minute per age in years, so a 5-year-old can pay attention for only 5 minutes. Real learning and understanding take place during concentration. 

An example of an activity children and adults can enjoy together is the simple game of Go to the Dump, found in RightStart’s Math Card Games. The game is played with cards having numbers 1 to 9. The object is to match cards that total ten according to rules similar to Go Fish. So, 1 and 9 is a pair, as is 2 and 8, 3 and 7, 4 and 6, and 5 and 5. The drawback is that children do not want to quit playing.

In conclusion, the best way to help children learn math is to keep it fun. Also, encourage the child to persist through minor frustrations, and to use their number sense, their mathematical common sense. And point out all the many ways math is used in our world. It is all around us.