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‘What I Wish Parents Knew’ is a series on issues parents should know, from a private tutor’s perspective.
Andy is working on factoring the expression x2 - 5x + 6. To do this, he knows he has to find two numbers that, when multiplied together give you 6, and when added together give you 5. He reaches for his calculator and tries testing random numbers to find the solution. He quickly gets frustrated and gives up.
Sadly, this scenario is all too common among students nowadays. Calculators have become an unnecessary crutch among students who have a weaker foundation in maths. They are not needed, except for more complicated computations that cannot be done mentally or by hand, and excessively relying on them to solve simple maths problems actually does more harm than good.
This is something I wish parents would understand better. When I see an older student reach for a calculator to find out what 30 x 50 is, that shows they don’t quite understand the most basic ways in which numbers work together. Consequently, it explains why they struggle to do well in maths as the concepts get increasingly difficult.
What parents need to do is to encourage their children to resist the urge to rely on the calculator.
In Singapore, calculators are only allowed in classrooms at the Primary 5 level. Teachers also emphasise that calculators should only be used for calculations that can’t be done mentally, such as for square root and exponential calculations.
Parents need to support this strategy, rather than undermine it. If your child constantly reaches for a calculator, encourage him to try solving it mentally first, if possible. Use these instances to find out where your child’s weak spots are, and help him shore up his basic mathematical literacy. This means understanding the very elemental properties of numbers and operations. Concepts such as the associative, distributive, identity and inverse properties of multiplication.
To go back to the example, a student should recognise that 30 x 50 is actually (3 x 5) x (10 x 10) – at which point, the solution should be obvious.
If your child figures this out on his own without the help of a calculator, he will have a much better chance of gaining a thorough understanding of these basic mathematical building blocks. Through repetitive use, your child will become familiar with basic maths facts, such as the times table.
This is also a great way to grasp maths facts without resorting to rote memorisation of multiplication tables, which is a tedious and unnecessary way to learn. Instead, encourage your child to work on understanding the properties above. For example, if he knows that 3 x 7 = 21, then figuring out 3 x 8 is easy – after all,
3 x 8
= 3 x (7 + 1)
= (3 x 7) + 3
= 21 + 3
Using the same methods, he can then subtract 3 to find out the answer to 3 x 6. Or add 7 to find out what 4 x 7 is. He will realise that 6 x 7 is just 3 x 7 doubled, or 3 x 14. Do this enough, and you’ll find that your child will easily be able to recall the whole multiplication table.
This familiarity is irreplaceable when your child starts to learn how to manipulate fractions, factor trinomials, or simplify and expand rational expressions. When students like Andy come to me struggling with these concepts, I find that it is almost always because they simply don’t know their times tables, usually because they use a calculator to solve even simple problems.
So, ditch that calculator, as much as possible. You’ll be doing your child a favour in the long run.
Troy Therrien is a maths and science tutor who believes that maths can be, and should be, for everyone. Find out more about him and his tutoring business at www.learncomoxvalley.com.