Is your child struggling with math?
Lack of conceptual understanding may be at fault
TORONTO — Now that children have settled in to their school year, teachers and parents might be noticing that time spent on math homework doesn’t necessarily add up to a successful outcome.
A Calgary educator suggests that some kids may not be getting the deep conceptual understanding they need.
“One of the things we’re finding is teachers tend to have kind of a rich range of interpretations for concepts, but they’re not always aware of the range of interpretations they have or that they’re using,” said Brent Davis, a professor and chair of mathematics education at the University of Calgary.
For example, he said there are at least 12 distinct interpretations of multiplication offered between Grades 1 and 7, “but only one is made explicit: repeated addition, repeated addition, repeated addition.”
“So kids also need to be made explicitly aware that it could be understood in terms of area making, in terms of hopping along a number line, in terms of stretching a number line, in terms of scaling, and the list goes on,” he explained.
“Teachers are aware of these and use all of them. They just have forgotten that they know them.”
“I’ve actually visited high school classes where they’re talking about multiplication of matrices, or multiplication of vectors, and how do you add a vector to itself? ... Even so, the teacher says ‘multiplication is repeated addition.’ It makes no sense.”
At cocktail parties, parents will tell him they liked math or were good at math until about Grade 6.
That jibes with the fact that the big explosion of interpretations around basic operations happens about Grade 5 or 6, he said.
Ron Lancaster, a professor at the Ontario Institute for Studies in Education in Toronto, said he feels strongly that educators need to present math in a different way to kids who don’t get it.
“To light the fires and get them excited about the subject, I’m all for using puzzles and games. There’s a field called recreational mathematics that involves some beautiful engaging mathematics, you know, that’s really neat and intellectually very strong,” he said.
“Much of his work is very mathematical. That’s something that kids could study and learn about, and then end up learning the mathematics through the back door.”
“It’s a great novel that incorporates a lot of mathematics into the story,” he said.
Lancaster described a visit to Paris earlier this year when he used his camera to make a video of the Louvre as his boat passed by. He said it would be great to show students the video and ask them to figure out how fast the boat was going.
“You can look up the length of the Louvre using Google maps or Google Earth ... so now you know how long the building is and you can look at the video and see how long it took to take the video, and you can calculate the speed.”
An approach like this can turn kids on in mathematics, he said, while dry lectures and worksheets turn them off.
Tracy Solomon, a developmental psychologist at the Hospital for Sick Children in Toronto, said she can’t emphasize enough that the comfort level of parents when it comes to math will have an impact on their children.
It is “such a shame” when adults transmit to kids a fear or loathing of math, she indicated.
She said moms and dads can do a lot to help their little ones become comfortable with numbers starting at an early age.
“For example, you can practise counting tasks with small sets of objects,” Solomon said in an interview.
Beyond counting, they can spend time discussing baseball and hockey statistics or playing games that involve a scoring system. Board games that involve strategy might also exercise the “math muscle.”
“Math is part of your everyday life,” she said, noting that kids can count cupcakes at the bakery and help to figure out costs at the supermarket checkout.
“We all use it and we all have to use it.”
When it comes to learning and homework, children have to be focused and develop self-discipline so they’re not distracted by other things, she noted.
Society in general — and a lot of teachers — have a tendency to label kids as being good at math or not, and there has to be a willingness to reach all children, she said.
Practice is key, and a lot can be done to close the gap between those who enter kindergarten with a familiarity of number, measurement and geometry terms, and those who don’t.
As for hiring a tutor, Davis said it can help if the instructor has a sense of the interpretations they’re using, but there’s nothing worse than a tutor pushing kids through rote application.
“We don’t need people who are good human calculators any more, and frankly, as someone who has instructed mathematics at the post-secondary level, people who come from heavily rote-based tutoring are lost in first-year university,” he said.
“They simply are not prepared to grapple with the conceptual complexity of the concepts that arise.”
The Canadian Press