Mathematics is unusually unforgiving about order. In most subjects a student can miss a chunk and still cope with what comes next. In maths, the next thing is built directly on the last thing, so a gap does not stay a gap. It compounds.
This is why a student can go from comfortable in Grade 9 to struggling in Grade 11 without anything obvious happening in between.
What compounding actually looks like
Take a common one. In Grade 7 or 8 a student never becomes fully fluent with negative numbers – they can do them, slowly, with a number line in their head. It is not flagged, because the questions at that level are short enough to survive the slowness.
In Grade 9 they meet algebra. Now every expansion involves negatives, and the slowness costs time and accuracy. Still survivable. In Grade 10 they meet factoring, which is negatives plus pattern recognition under time pressure. Marks start slipping. In Pre-Calculus 11 they meet quadratics, rational expressions and radicals, all of which assume factoring is automatic.
By now the student says they are bad at quadratics. They are not. They are three years behind on negatives, and quadratics is simply the first topic that made that impossible to hide.
Why the current unit is the wrong place to start
The instinct – your child is failing quadratics, so get help with quadratics – is understandable and usually wrong. It is possible to drill a student through a quadratics unit test. It does not help, because rational expressions arrive next month and the same underlying gap will surface again in a new costume.
The alternative feels slower and is not. Spend two sessions finding what is actually missing, close it properly, and the current unit often becomes manageable without ever being taught directly.
The gaps that cause the most damage
Four come up repeatedly, and they are worth checking for by name:
- Fractions. Not the arithmetic – the concept that a fraction is a division, and that algebraic fractions obey the same rules as numerical ones.
- Negative numbers. Particularly negatives inside brackets, and subtracting a negative.
- Rearranging equations. Whether the student is following a memorised sequence of moves or actually understands that both sides stay balanced.
- Factoring. The single highest-leverage skill in Pre-Calculus 11. If it is not automatic, everything takes twice as long.
How to find the gap without a formal assessment
You can do a rough version of this at home. Take a question the student is currently stuck on and ask them to talk you through it, out loud, from the first line. Do not correct anything. Just listen for where the fluency stops – where they slow down, guess, or say “I think you do this bit.” That hesitation point is almost always upstream of the topic they are supposedly struggling with.
Closing it properly
Closing a gap is not re-teaching a lesson. It is building fluency, which means short, frequent, mixed practice over a few weeks rather than one long session. Ten minutes of factoring a day for three weeks does more than a three-hour catch-up on a Saturday.
It also means mixing it back in. Once the gap is closed in isolation, the student needs to meet it inside the harder current work, or the two never connect.
The best time to do this
Summer, or any break, is the ideal window because there is no new material arriving on top. A student going into Pre-Calculus 11 who spends a few weeks in July on factoring and fractions starts September in a completely different position from one who does not.
Failing that, the second-best time is now. Our math tutoring in Surrey starts every new student with a diagnostic rather than a syllabus. Call 604-725-6845 or book a $50 trial class.
Closing a gap like this is most of what we do. See how OOTB works as a math tutor in Surrey, in person or online.
