How to Know If Your Maths Competition Preparation Is Actually Working

Preparing for a maths competition can sometimes feel like a numbers game. You solve 20 questions, then 30, then 50 more. Your notebook gets thicker, but you may still wonder:

Am I actually getting better?

The number of questions you complete is not always the best measure of progress. Good competition preparation should gradually improve several things at the same time: your understanding of mathematical concepts, your ability to approach unfamiliar problems, your accuracy, your decision-making, and your confidence under time pressure.

Here are some practical ways students can measure their progress.

1. Your First Goal Should Not Be a Higher Score

A competition score is useful, but it doesn't tell the whole story.

Imagine that you score 60% on one practice test and 62% on another. That looks like only a small improvement.

But what if, during the second test, you:

• Solved more difficult questions independently
• Made fewer calculation errors
• Finished with more time remaining
• Recognized unfamiliar patterns more quickly
• Needed fewer hints

Those are meaningful improvements even if the overall score changed only slightly.

Instead of tracking only your score, track several indicators of progress.

2. Measure Accuracy by Topic

After completing a practice set, record your performance by topic.

For example:

Topic	Questions	Correct	Accuracy
Arithmetic	10	9	90%
Algebra	10	7	70%
Geometry	10	5	50%
Logical reasoning	10	8	80%

This immediately gives you more information than a single overall score.

If geometry remains your weakest area, you can spend additional time there instead of repeatedly practicing topics you already understand.

3. Track Why You Got a Question Wrong

A wrong answer can happen for many different reasons.

Try placing mistakes into categories:

Concept error — You didn't know how to use the mathematical idea.

Reading error — You misunderstood what the question was asking.

Calculation error — Your approach was correct but the arithmetic went wrong.

Strategy error — You chose an approach that did not work.

Time error — You understood the problem but spent too long on it.

Careless error — You knew what to do but made an avoidable mistake.

This simple classification can reveal weaknesses that a score cannot.

For example, if most of your mistakes are calculation errors, you may not need to learn more advanced mathematics. You may need to slow down and check your work more carefully.

4. Check How Much Help You Need

Another useful measure is independence.

When practicing, classify each problem as:

A — Solved independently

B — Solved after a small hint

C — Understood after seeing the solution

D — Still don't understand

Over time, you want more problems to move from C or D toward A.

This is particularly useful for difficult competition problems. Understanding a solution after someone explains it is valuable, but being able to discover the method yourself is a different skill.

5. Compare Your Time, Not Just Your Score

Competition mathematics often involves making decisions about time.

Suppose you solve a problem correctly in 12 minutes today and correctly in 8 minutes several weeks later.

That is progress.

But don't try to make every problem faster immediately. When learning a new concept, understanding should come first. Once the method becomes familiar, speed can be developed through timed practice.

A good preparation routine therefore includes both:

Untimed learning → timed application

6. Don't Take a Full Mock Test Every Day

Taking complete practice tests repeatedly may seem productive, but it isn't always the best use of practice time.

A full test can tell you where you stand.

It doesn't necessarily teach you how to improve.

A better cycle can be:

Practice test → Analyze mistakes → Study weak area → Practice targeted questions → Take another test

This makes each test useful as a diagnostic tool rather than simply another score.

Several established competition resources use structured practice rather than relying only on repeated full tests. MATHCOUNTS, for example, combines warm-ups, strategy-focused problems, related practice, and optional extensions in its practice plans.

7. Learn to Recognize Unfamiliar Problems

One of the clearest signs of improvement is what happens when you encounter a question you've never seen before.

At the beginning of your preparation, you might immediately think:

"I don't know how to solve this."

Later, you may start thinking:

"I haven't seen this exact problem, but perhaps I can draw a diagram."

Or:

"Maybe there is a pattern here."

Or:

"Could I work backward from the answer?"

That change in thinking is extremely important.

Competition preparation isn't simply about collecting solution methods. It is about developing a larger set of ways to explore a problem.

8. Keep a Problem-Solving Journal

A small notebook or digital document can become one of your most useful preparation tools.

For each interesting problem, record:

• The problem type
• Your first approach
• Where you became stuck
• The successful idea
• Another possible approach
• What you learned

You don't need to record every easy question.

Focus on problems that taught you something new.

After several weeks, you'll have your own collection of mathematical ideas and mistakes to review.

9. Use a “Could I Solve It Again?” Test

Sometimes a student reads a solution and feels that they understand it.

A few days later, they cannot reproduce the method.

To avoid this, return to important problems after some time.

Hide the solution and try again.

If you can solve it independently, the idea is becoming part of your mathematical toolkit.

If you cannot, review the solution again and try a similar problem.

This is more valuable than simply rereading solutions.

10. Make Practice Gradually More Difficult

Your practice should not remain at one difficulty level.

A useful progression is:

Level 1 — Concept practice

Questions designed to make sure you understand the basics.

Level 2 — Standard application

Problems requiring you to choose and apply an appropriate method.

Level 3 — Unfamiliar problems

Questions where the method isn't immediately obvious.

Level 4 — Challenging problems

Problems requiring several ideas or a creative approach.

Level 5 — Timed mixed practice

A realistic combination of different topics and difficulties.

If you are struggling at Level 2, jumping immediately to Level 5 may create frustration rather than improvement.

11. Use Daily Practice to Maintain Momentum

Preparation doesn't have to mean spending hours solving problems every day.

A short daily challenge can keep mathematical thinking active.

For example:

Monday: One number problem

Tuesday: One geometry problem

Wednesday: One algebra problem

Thursday: One logical reasoning problem

Friday: One mixed problem

Weekend: Review the week's difficult questions

A Question of the Day format can be particularly useful because it creates a consistent habit while exposing students to different types of mathematical thinking.

The International Maths Challenge offers a Question of the Day alongside its competition-related resources, which can be incorporated into a broader practice routine.

12. Ask Yourself Better Questions

After every practice session, don't just ask:

"How many did I get right?"

Also ask:

• Which question surprised me?
• Which mistake did I repeat?
• Which topic needs more attention?
• Which problem-solving technique did I learn?
• Did I spend too long on any question?
• Did I give up too quickly?
• Could I explain my solution to another student?
• Which problem should I try again later?

These questions turn practice into reflection.

13. Parents Can Track Progress Without Creating Pressure

Parents can help students monitor preparation, but the goal should be improvement rather than constant comparison.

Instead of asking only:

"What score did you get?"

Try asking:

"What did you learn from today's problems?"

or:

"Which question was the most interesting?"

or:

"What was difficult this week?"

This encourages students to think about their learning process.

A child doesn't need to win every practice test to be making progress.

14. A Simple Monthly Progress Check

At the end of each month, review four areas:

Knowledge

Which mathematical concepts have improved?

Problem solving

Are unfamiliar problems becoming easier to approach?

Accuracy

Are repeated mistakes becoming less common?

Timing

Can you manage your time more comfortably?

Give each area a simple rating such as:

Needs work → Developing → Comfortable → Strong

Then choose one or two areas for the following month.

This keeps preparation focused.

What Real Progress Looks Like

Successful preparation does not always look like dramatically higher scores.

Sometimes progress looks like:

• Spending less time staring at a difficult question
• Trying multiple approaches instead of giving up
• Making fewer repeated mistakes
• Explaining solutions more clearly
• Recognizing useful patterns
• Knowing when to move on
• Becoming comfortable with unfamiliar questions
• Needing fewer hints
• Reviewing mistakes honestly

These are signs that your mathematical problem-solving ability is developing.

Final Thoughts

The best maths competition preparation is not simply the preparation that produces the largest number of completed questions.

It is preparation that helps you understand how you think when solving a problem.

Use practice tests to diagnose weaknesses. Use targeted questions to improve them. Keep track of mistakes. Mix untimed learning with timed practice. Revisit difficult problems. Most importantly, pay attention to whether you are becoming more independent when facing unfamiliar mathematics.

Resources from established mathematics organizations also emphasize regular problem solving and structured practice as important parts of competition preparation.

For students preparing for an international maths competition, resources such as the International Maths Challenge can be included as one part of a wider preparation routine, particularly when combined with school mathematics, targeted topic practice, and regular problem-solving exercises.

The real goal is not simply to become better at taking a test.

It is to become better at thinking mathematically.