How to Study Maths
Maths is not a spectator subject. Watching a teacher solve a problem is like watching someone ride a bicycle: informative, but no substitute for wobbling along yourself.
Maria Montessori built her mathematics materials on a simple idea — begin with the concrete, then climb gently toward the abstract. That staircase, paired with honest practice, is still the most reliable way up.
Move From Concrete to Abstract
Whenever a topic feels foggy, step down a level. Abstract rules make sense once you have handled the idea in a tangible form.
- Use drawings, number lines, or objects to model a new concept before using symbols.
- Work simple numerical examples until the pattern shows itself, then name the rule.
- Ask what a formula is doing, not just how to apply it.
Practise Deliberately, Not Passively
Understanding grows in the attempt. Do problems with the solution covered, and let effort — not comfort — guide your choices.
- Attempt first, check second; the struggle before the answer is where learning happens.
- Mix problem types within a session so you must choose the method, not just repeat it.
- Return to older topics weekly; spaced practice keeps skills from quietly fading.
Make Friends With Your Mistakes
Montessori materials carry a built-in control of error, letting children correct themselves without shame. Give yourself the same courtesy: an error is feedback, delivered precisely where you need it.
- Rework each wrong problem until you can explain the correct path aloud.
- Keep a small notebook of errors and re-attempt them days later.
- Notice patterns: sign slips, misread questions, rushed final steps.
Frequently asked questions
Why do I understand in class but struggle alone?
Watching creates familiarity, not skill. Bridge the gap by re-solving classwork examples from memory the same evening, without looking at the steps.
How many maths problems should I practise daily?
Enough to stretch you, not exhaust you. A focused set attempted honestly, with errors reviewed, beats pages of mechanical repetition.
Is it bad to use my fingers or drawings?
Not at all. Concrete supports are how understanding begins. Use them freely, and let the abstraction arrive when the pattern is truly yours.
What should I do when a problem completely stumps me?
Sit with it briefly, try a simpler version, then study one line of the solution and continue alone. Return to the same problem a few days later.
In depth
Between watching solutions and solving cold there is a well-studied middle path: fading the support step by step. Study one worked example closely, explaining to yourself why each step exists. Then take a similar problem with the last steps missing and complete it. Then one where only the setup is given. Then a blank one. Each stage removes a little scaffolding, so effort rises gradually instead of jumping from comfortable watching to hopeless staring. When a chapter defeats you, you have usually skipped a rung — return to one level more support, not to rereading.
Self-explanation is the quiet engine of that ladder. Students who narrate why a step works — dividing both sides to isolate x, substituting to turn this into a quadratic — learn far more from the same examples than students who merely verify each line looks legal and move on. And a surprising share of lost marks has nothing to do with mathematics at all: the question asked for the perimeter and you supplied the area, or the final answer needed different units. Underline what is actually being asked, and reread the question once more before writing your final line.
- Stuck for a while? Ask which given piece of information you have not yet used — well-set problems rarely include decoration.
- Check answers by substitution or estimation before calling a problem finished; verification is itself a skill exams reward.
- Keep number facts and algebraic manipulation fluent; hesitation there steals the working memory that harder reasoning needs.