7 tricks to get better at Maths

For beginners to advanced

As a teacher, my work often consists in deconstructing biases, stereotypes and helping students gain confidence. This short story aims to share some tricks to help students change perspective on mathematics and science, from primary to high school, and beyond.

Trick #1 — Start asking questions

Science isn’t about solving problems, it’s about asking questions.

Remember when you were a kid and asked the question why? Why is the ocean blue?

Adults would answer because… and you would ask why again Why is the sky blue?

That’s maybe when the conversation would end.

Here’s a quote I love from Richard Feynman, which summarizes the idea:

I would rather have questions that can’t be answered than answers that can’t be questioned.

I’ve been using the 4 questions below since mid school to pass exams, carry out research and projects:

• What do we want?
• What do we have?
• What do we know?
• What can we conclude?

These questions aren’t the solution to a problem (if any!) but a way to it. A simple solution would look like

• J’observe que… (what we have)
• Or, on sait que… (what we know)
• Donc… (what we conclude)

Start asking questions and be curious.

Trick #2 — Start drawing, somewhere

A picture is worth 1000 words.

If you don’t know how to start, drawing a picture will spark your creativity and trigger your intuition.

Try to reformulate, summarize the question. For example if you have a problem with three random points A, B, C, start drawing three points randomly.

You could just list the known information to start. What distances and durations are given?

Craft a solution from your drawing or your notes. Write it down when you have a plan (a plan is enough, you don’t need to have the full solution at this point).

A drawing is the easiest way to communicate a problem or a solution.

Having a starting point can help you avoid the blank page syndrome:

• I don’t know how to start
• I don’t know what to solve
• I give up

Use your environment, your creativity, your own words, your symbols to reformulate problems and understand them.

Failure isn’t about doing mistakes. You don’t fail when you try to understand a problem.

Don’t ask yourself what’s the answer, that’s the problem. Start drawing.

Trick #3 — Know your strengths

How do you remember a phone number? Is it written or recorded somewhere in your head or is it on the tip of your fingers? Is your memory visual, auditive, tactile or all three?

Know your strengths and focus on them before working on your weaknesses.

Finding the right combination of visual, auditive and tactile memory could help you learn way more effectively. Depending on what works best for you, you might want to:

• Color and highlight your courses, for example green to learn definitions, red or blue for properties and purple or black for proofs. 🎨
• Use rhymes and memo, for example I remember that a question that starts with “Montrer que pour tout x …” can be solved starting with “Soit x…”. It’s wired in my brain like a rhyme. 🎶
• Read your course or exercices out loud to stimulate and activate different parts of your brain together. This will strengthen your long term memory. ✨
• Use or introduce notations that connect your problem to what you learned and know, for example mu and sigma in statistics or p for a probability.

Try as much as possible to be regular. Avoid working 12 hours the day before an exam. It’s important to rest.

Working less but more often, for example 30 to 45 minutes, twice a week, will save you time. It doesn’t require long efforts but regular exercising, just like gym.

Trick #4 — Trust your intuition

Dan Ariely’s book Predictibly Irrational presents some experiments and concrete examples of irrational behaviors. My favorite one is the free cookie experiment. The rational theory predicts people would take all the cookies for free, when in reality people just have one or two.

The world in which we live isn’t rational. I don’t consider myself to be rational, rather intuitive. I use my imagination to ask questions and experiment. That’s why I chose to study physics and chemistry as an undergraduate.

You don’t need to be rational to be good at maths. There are other types of intelligences — intuition, spatial, kinesthesic, empathy…

Language, music, art have an important role in understanding mathematics. The golden ratio (nombre d’or in French) has inspired thinkers of all disciplines - biologists, artists, musicians, historians, architects, psychologists… - like no other number in the history of mathematics.

Trick #5 — Teach to learn

You don’t need to be an expert to teach. Start with your family, your friends, classmates, people your age, younger or older. Consider specific chapters, for example Pythagore or Thales in geometry.

You could also start with yourself. For example, hide some words, definitions or properties in your course and learn how to fill the gaps.

Teaching is the best way to master a subject. Helping others reformulate, understand through examples, will help you learn more advanced topics. Team work and collaborations are needed in real life. We all have something to teach to and learn from others, we just don’t realize it sometimes.

Trick #6 — Proofread yourself

Mathematics is a language on its own, with its own set of characters, alphabet, grammar so it’s normal to ask yourself if your work is readable?

The same way a story has a narrative, does your work have a story line? Did you lose any information from a line to another one? For example, are your signs consistent, coherent? Can you read the story the other way round, from the conclusion back to your starting point?

Some students often lose points because of these mistakes. It has nothing to do with being logic or not. Proofreading helps them increase their grades, from 60% to 90% (18/20).

The trick I use to make it a good habit is to ask them to correct themselves as if it wasn’t their answers and try to spot errors.

Trick #7 — Beware of experts

Physicists, chemists, economists, mathematicians, computer scientists use differents words for the same concepts. As an example, in a linear model y=ax+b, mathematicians will refer to “a” as “taux d’accroissement”, while chemists will call it “coefficient de proportionnalité”. Both physicists and computer scientists have a concept called entropy, related to disorder and information theory, but they use different symbols for it, S or H.

It can get confusing.

Experts tend to use jargon and make errors with high confidence. The rational theory of economy doesn’t match reality, neither do many theories.

Assumptions are proven wrong.

Be pragmatic.

Take the opportunity of school to learn to learn.

Conclusion

As Richard Feynman said

Science is the belief in the ignorance of experts

You can learn mathematics at any age.

Below is a summary of the 7 tricks to get better at Maths. Let me know which one works best for you? 😊

1. Start asking question
2. Start drawing, somewhere
3. Know your strengths
4. Trust your intuition
5. Teach to learn
6. Proofread yourself
7. Beware of experts