“I understood it in class but failed the test”: what’s going on

Following a solution is not the same as producing one

When the teacher works an example at the board, your child's job is to check each line: does this step follow from the one before? That is real understanding, and it is why “I got it in class” is honest. But by the time the first line is on the board, the teacher has already done the hard part:

• recognised what kind of problem it is,
• chosen the method,
• written the first line,
• decided what to do next at every step.

A test asks for all four, alone, with no example on the page and a clock running. Watching ten problems solved builds the skill of recognising a correct solution. It builds very little of the skill of starting one.

The report card is built the same way. In Quebec high school, math is marked on two competencies, solves a situational problem (30% of the mark) and uses mathematical reasoning (70%). Both describe work your child does, not work they watch.

A small example

In class, the teacher takes 15% off a pair of skates priced at $80: 15% of 80 is 12, so the sale price is $68. Every step makes sense, and your child could explain it back.

On the test, the question runs the other way: after a 15% discount, a pair of skates costs $68. What was the price before the discount?

A very common answer is $78.20: 15% of 68 is 10.20, added back on. It copies the class example faithfully, and it is wrong, because the 15% was taken from the original price, the one number the question does not give. The right answer needs a step the class example never showed: the sale price is 85% of the original, so the original is $68÷0.85=80$ dollars, the price the class example started from.

Nothing here is hard. In class your child never had to decide anything, and the test was nothing but decisions. In Secondary 4 and 5 the topics get harder, but the gap is the same one.

Why homework doesn't show it

Homework usually hides the gap, for reasons that have nothing to do with effort:

• It is done on the day of the lesson, with the example a page back in the notebook.
• Every question is on one topic, so the method is never in doubt: it is whatever was taught that day.
• The notes, the textbook and a friend's message are all within reach, and there is no clock.
• Reading over notes before a test feels like studying, because everything on the page looks familiar. Familiar is not the same as being able to produce it.

A test takes all of that away at once: weeks of material, mixed, closed book, timed. So a student can get the homework right, freeze on a test question's first line, and honestly not know why.

Signs this is what's happening

It is worth telling this apart from other causes, because the fix is different. It is the likely explanation if several of these are true:

• Homework is done and mostly right, but test marks are clearly lower.
• When the test comes back, the corrections make sense straight away: “Oh, I knew that.”
• Marks are lost on questions left blank or abandoned after a line, more than on arithmetic slips.
• Word problems cost far more than plain exercises.
• Short quizzes right after a lesson go well; unit tests that mix several lessons do not.
• “Studying” means reading notes or watching someone else solve problems.

If the work is right at home without notes and falls apart only in the exam room, nerves may be the bigger part. If the mistakes are everywhere, homework included, the trouble is probably an earlier topic that was never solid. The routine below tells these apart.

A 20-minute routine to close the gap

Three or four times a week, on the topic being taught right now. You do not need to know the math to run it.

1. Pick three or four questions your child has not seen solved. Exercises from the textbook that were not assigned work well, or a free worksheet from this site, with sets for Secondary 1 to 5. Print it: the PDF holds the questions and room to work, and no answers.
2. Close the notebook and set a timer for 15 minutes. Blank paper, no notes, no phone. Your child writes everything, including the first line, because the first line is the skill being practised.
3. When stuck, write down where, then move on. “Didn't know how to start” and “stuck after the second line” are different problems, and both are worth knowing. No peeking yet.
4. Then check. Use the textbook's answers, or the class notes, or the method written out on the worksheet's page. For each miss, find the first line that went wrong: was it the start (choosing the method) or later (carrying it out)?
5. Two days later, redo the misses from a blank page, without looking at the earlier correction. Redoing them straight after the correction only shows that your child can copy something just seen.
6. Once a week, add one question from an older chapter. Tests mix topics, so practice has to as well.

Your part is not to teach. Two questions are enough: “How did you know to start that way?” and “Can you show me without your notes?”

What doesn't help

• More reading over notes. It makes the material feel more familiar, and that feeling is what misled your child in the first place.
• More videos and worked solutions. Watching is following, and following is already the strong part.
• Looking only at the mark. The marked test shows which questions were left blank and where the work stopped, which tells you far more than the number.

When outside help makes sense

For many students the routine is enough. Look for help from outside when:

• after three or four weeks of it, your child still cannot write the first line of most questions without notes;
• the misses trace back to an earlier year, such as a Secondary 4 student whose real trouble is Secondary 3 algebra;
• the routine has turned into a nightly argument (being stuck in front of someone who is not a parent is often easier);
• a test that matters is close, and there is no time to find the gap by trial and error.

Whoever you choose, look for help where your child does the problems rather than watches them being done, or each session becomes one more worked example. The useful shape is a written check of what is actually solid first, then practice on the exact topic, marked, with each error traced back to what caused it.

Free worksheets to practise with

• Secondary 3 math worksheets
• Secondary 4 math worksheets
• Secondary 5 math worksheets