Study Math Better Using Psychology: Tips & Guidelines

A number of psychological findings can be used to improve mathematical understanding and mathematical performance. If you are teaching someone math, use these tips to improve math performance. If you are self-studying math, implement these tips alongside your study syllabus.

Let’s talk about math anxiety first. Very rarely is school-level math too difficult for our cognitive abilities like attention, memory, logic, reasoning, etc. Many problems begin with Math anxiety. I’ll describe it using Humbree’s model from 1990^[1]. It’s a simple model that has sound practical uses.

Math triggers fear. Fear triggers avoidance. Avoidance leads to low learning and then failure.

I see 4 common reasons for this fear.

1. The student is conditioned to think it is scary – because others repeat it, teachers punish students for silly mistakes, other students tell each other how confusing or weird it is until they all amplify the thought into “math is scary,” etc.
2. Math is symbolic. And most textbooks make it feel like an unfamiliar, unknown language. People instinctively fear things that are unfamiliar and unknown.
3. Too much importance is placed on acing math. With people constantly warning everyone about math. This makes a student think the cost of failure is too high so they should be perfect and good. But when things get difficult, they dread it and feel math is a mental burden.
4. A student doesn’t want to feel humiliated or dumb. And since math is a sudden new type of learning for many, they are scared of it.

These fears trigger avoidance because the basic instinct is to avoid fear-inducing stimuli. And because a student avoids it, it remains unfamiliar, and the student rarely sees any “success” in math. This breaks confidence. And when they fail during the test because they have avoided learning, the cycle is reinforced.

1. Use the Batman effect

Many people find math boring or tedious, largely because it doesn’t make sense to them. After it gets boring, they stop caring about it or practicing problems. To get children to do more math and motivate, you can ask them to act like “Batman”, a superhero, who needs to solve problems. This changes the child’s mindset^[2] to what they think Batman would do. They will approach math like a superhero strategist has to. In the process, they will distance themselves from math^[3] and experience less intense emotions about math. So it works to reduce math anxiety too. This strategy of distancing yourself and taking on a 3rd person POV^[4] reduces anxiety in adults too. Here’s some more explanation of the Batman effect.

2. Use scaffolding techniques

It’s a fancy word for getting help & support. But, the help, here, is incomplete. This is the part where you are nudged toward an answer with some hints or half-baked solutions. Scaffolding often helps beginners bridge the gap between the problem statement and the solution by showing bits and pieces of what’s in between or how to get to a solution. Help can be considered as external assistance. To maximize learning, gradually let go of external assistance of any kind.

3. Interleave your study sessions

Math needs practice, memory, solving strategies, intuition, and conceptual understanding. All of this can be achieved with a learning technique called interleaving. Take 3 related types of problems A, B, & C. Instead of practicing one type continuously, mix them up. So instead of AAAAAA for 1 hour, BBBBBB for 1 hour, CCCCCC for one hour, do ABC ABC ABC ABC across the day or across your free time. The more related they are, the better this technique works.

4. Sleep & rest enough regularly

To be quick at math and get a feel for numbers, it’s best for you to be relaxed and attentive. Sleep and rest will do that. Sleep will also help solidify your day’s learning. In case you have trouble sleeping, you can use these techniques. And, if you are unable to rest because of anxiety or negative thoughts about math, these will help – One, Two.

5. Don’t stick to one type, learn various problems

Like most types of learning, the more variations of mathematical ideas you learn about, the better you get in each idea. A number of theories predict that exposure to a diverse set of problems and trial and error with a variety of examples improves a specific as well as a general capacity to learn & use a concept. Exposure to related concepts forms a network of information that acts as a web. The more connections there are, the stronger the learning-web is.

6. Vary cognitive representations

Cognitive representations are how you represent a formula or concept. You can speak a formula in words, draw it mentally, write it on paper, etc. The more ways you can represent it, the better it is. Don’t repeat one representation too much the way students learn mathematical tables in many schools (narrating “1 twos are two, 2 twos are 4, 3 twos are 6”). Repeating only one way of narration makes people rely on that narration; without that narration, it’s hard to retrieve the answer. Diversify your experience with concepts.

7. Break down a problem

A classic piece of advice for studying math is to break down a problem into smaller components. Math problems can be divided into smaller problems according to your level of understanding. It’s a skill to identify these smaller problems and simplify the larger problem/concept. Reading up on StackOverflow or other websites can help you. There are many math experts on quora who are good writers. Follow them. Doing this serves two functions – reduce the mental load of a problem & reduce overwhelming problems into, for lack of a fun word, whelming problems.

8. Learn strategies, tips, and tricks

There are ways to go about a problem. Especially mental math. How much is 12% of 50? This problem can be rearranged to what is 50% of 12. That’s easier, right? Here is a simplified version X% of Y is Y% of X. You interchange X & Y to simplify the math. These tricks can easily make a person feel like they have learned something useful and get the confidence that they understood it.

9. Work with symbols & words

Some people work great with symbols, some people work great with objects. If variables throw you off and anxious moments confuse you, try to use the option you are not familiar with. If word problems throw you off, try working with symbols. If symbols throw you off, use objects and people. After all, they are variables so they can take the form of anything you like. Call it apples, people, ants, phones, planets, X, or ^_^. Learn examples of both. That helps with making your learning concrete and flexible.

10. Assign meaning and a context

Humans work great with problems that are personally relevant and relatable. If you can redefine an idea in a way you can relate to, you will build a familiar mathematical context and find the motivation to work it out. Relatability also makes understanding concepts easier. Think math is meaningless or too abstract is usually a problem of not finding sense in it. To find that sense, the context for math needs to be personally relevant. Use math to solve simple everyday problems like – “I have 3 episodes of 42 minutes each to watch and 2 hours. Each episode has 1 credit sequence for 10 seconds and 1 opening sequence and recap for 25 seconds. Do I have enough time to finish all 3 episodes?

11. Have fun and study with a good mood

Math is notorious for being a buzz-kill and carries the cultural weight of intimidation, unfamiliarity, anxiety, and pure dislike. While many, many people don’t like mathematics, trying to find a fun way to learn and develop a good mood while studying can help quite a bit. Research shows that a good mood and enjoyment can improve a number of mental processes that help in thinking and learning – attention, memory, broad and narrow understanding, connecting dots, creativity, etc. So, having fun while learning is one of the best ways to study math.

12. Receive and pay attention to feedback

In general, feedback ranges from judgments to informational content. For example, saying “good job” is feedback, but so is knowing your grade and errors. Feedback goes a lot deeper than just that. There is real-time feedback you receive while solving a problem too – the immediate thoughts and processing of what you are trying to understand. Paying attention to all sorts of feedback is important in grounding your fundamental understanding of a concept. There is some research that shows that all types of feedback, from yourself, automated systems like digital quizzes, teachers, friends, etc. can have different effects on you. Sometimes, feedback at every small step can help you learn a mathematical process better. Sometimes, a vague response like “correct/incorrect” can help in exploring a process.

13. Overcome math anxiety

Math is notorious for the anxiety it causes in many children. Research shows^[5] that math anxiety reduces mathematical problem-solving in children beyond the limits of their cognitive abilities – working memory, processing speed, etc. High math anxiety can further impair working memory, and that can worsen performance. To overcome math anxiety, first there should be familiar ideas discussed mathematically. Second, the narrative that math is difficult and scary should be de-conditioned. Everyone repeats that thought so people inherently start believing it (the illusory truth effect). Third, learns should experience enough success in solving math so their confidence goes up.

Math test anxiety

Test anxiety is the anxiety, nervousness, and lack of confidence that comes during and before an upcoming test. Most standardized exams have a math component, so students are literally afraid of failure and poor performance. That anxiety itself worsens performance. So here are some very effective, low-effort tips to reduce test anxiety:

1. Use a lucky charm or placebo – faith matters during stress, and it works even when you know it’s a lucky charm.
2. Wear a good perfume or smell good – it resets the brain instantly and restores attention.
3. Wear nature-print clothes – nature patterns have a calming effect on the body

I discuss more tips here if you are interested.

These tips are consolidated from the following articles/research findings:

1. https://cognitiontoday.com/the-fundamental-science-of-brain-based-learning-7-subconscious-brain-functions-and-learning-processes/
2. https://cognitiontoday.com/brain-based-learning-theory-strategies-and-concepts/
3. https://cognitiontoday.com/why-fun-improves-learning-mood-senses-neurons-arousal-cognition/
4. https://cognitiontoday.com/the-worst-and-the-best-study-tips-habits-from-psychological-research-how-to/
5. https://cognitiontoday.com/do-not-underestimate-the-effect-of-sleep-on-memory/
6. http://users.math.uoc.gr/~ictm2/Proceedings/pap313.pdf^[6]

I hope you have a better experience studying math and score better grades by using these guidelines.

P.S. Thumbnail Photo by Deepak Gautam ^[7]from Pexels^[8]

Sources