The importance of building a foundation

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‘What I Wish Parents Knew’ is a series on issues parents should know, from a private tutor’s perspective.

I’ve been tutoring Andrew for some time now. He’s a student with average ability in maths but he doesn’t want to put in the time to master concepts. Instead, he looks for mechanical ways to solve the problems related to the current unit he’s on. For example, when he was learning fractions, all he did was follow the steps without bothering to understand why, using simple shortcuts that allowed him to pass his tests (but only by the skin of his teeth). Unfortunately, Andrew doesn’t seem to retain the shortcuts after the test is over. Despite my strongest encouragement, neither Andrew nor his parents seem to value learning the fundamentals, and instead are just focused on passing the test.

Now, Andrew is in grade 10 and the rubber has hit the road. Problems now involve new concepts that blend and make use of all the previous concepts. For example, to multiply and evaluate numbers with fractional exponents, Andrew now needs to refamiliarise himself with the rules for exponential multiplication, remember how to add fractions and finally, remember how to unpack the resulting fraction. This is just too many mechanical steps to learn and re-learn, so the wheels begin to fall off. Andrew is barely getting by with his homework and won’t be able to pass this year if he doesn’t shore up his understanding of basic concepts.

Sadly, Andrew is not the only student I’ve tutored that suffers from this problem. It’s not entirely his fault – for students who don’t like maths, spending more time to dig deep and understand a topic is not particularly appealing. It’s doubly hard to convince the student (and the parents) that putting in this time is worth their while, especially when they can use shortcuts or “cheats” to pass a simple test.

The thing is, mastering mathematics is a cumulative effort. The concepts you learn one year are used again the following year. They grow more complex, and failing to understand the basics will severely hinder your ability to learn more difficult topics. Fully understanding a concept means being able to apply the concept where appropriate, and recall it even at a much later date. It means being able to adapt that understanding and relate it to different, unusual problems, which will ultimately allow you to blend different concepts together to tackle more complex problems.

For students such as Andrew, this “studying for the test” method works until it doesn’t. When problems become more complex (usually around secondary school or high school), test scores plummet.

You can avoid falling into this trap by watching out for maths scores that are consistently middling. If a student really understands the maths concepts taught in school, their scores should be high. A test result that is only in the 60 per cent to 75 per cent range indicates that while the concept is understood at a basic level, the student is not getting the tougher questions correct, or is making silly errors because they don’t fully understand the topic.

The good news is that this problem is easy to solve. High school maths topics are challenging but anyone with an average intelligence can master them if they are willing to put in the time. That effort simply needs to start in the earlier grades so the students can move on to higher grades with a solid foundation to build upon.


Troy Therrien is a tutor who believes that learning can be, and should be, for everyone. Find out more about him and his tutoring business at

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