By Troy Therrien on 10th October 2017

Image from iStock

*It’s halfway through the school year when I am asked to start with a new student, Elly. Her parents tell me she has been failing maths and she needs some help to prepare for an upcoming test. I spend one session with Elly and we start trying to right the ship, but I realise she is very far behind in her understanding of the course materials. I am unsurprised when the following week Elly reports that she has failed her test again. I tell her that it’s okay; she may fail her next quiz as well, but that eventually, we will fix the gaps in her knowledge and she will be able to master the course material in time. Unfortunately, her parents give up and cancel Elly’s tutoring sessions. I can only assume she failed that course – and as a result, Elly is unable to pursue the career path she really wants.*

Mathematics is a foundational subject. Every year, the new syllabus builds upon the knowledge gained in the previous courses. As gaps begin to develop in a student’s understanding, each module becomes successively more difficult to grasp. Typically, once a student starts to fall behind, their grades will continue to suffer if they don’t put in extra effort. It’s a vicious cycle.

But if a student receives help at the first sign of trouble – or even before – it is much easier for the student to keep her marks up and grasp the concepts. This ensures she is able to tackle new concepts and prevents the downward spiral I described earlier.

In Elly’s case, the gaps in her knowledge that I identified stretched back years. At that point, I couldn’t help her with the current course material until we had backed up and worked on filling in the gaps in her foundation.

This takes a lot of time, and it’s very difficult to show the student and the parent the value of working on material that doesn’t seem to be related to the topics they are currently struggling with. But this is often the only way forward, as simpler concepts must be mastered before they can tackle more advanced concepts.

For example, Elly was trying to factor polynomial expressions, such as 7x^{2 }+ 10x - 8. To do this, you need to find two factors of the product of 7 and 8 (7 x 8) that will add or subtract to give you 10. I soon found that Elly was struggling with her basic multiplication figures and couldn’t tell me that 7 x 8 was 56 without a calculator, never mind that 14 x 4 is also 56 and that 14 - 4 = 10. This meant I had to start with basic multiplication and work up from there.

There are tutors who just “teach to the test”. While it’s possible to memorise and drill a student so that they can pass a multiple choice quiz, this doesn’t result in greater understanding of the material, and the student will only run into the same issues again in the future.

Good tutors will take the time to make sure a student truly understands the subject, and if the student doesn’t, a good tutor will take the time to get to the root of the problem.

But even the best tutor isn’t a miracle worker. The further behind the student is, the longer it is going to take to turn failing grades around. Parents have to realise that results will not be immediate, but if the student is willing to put in the time and effort, eventually the results will be forthcoming.

*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.*