A number of psychological findings can be used to improve mathematical understanding and mathematical performance. Here is a broad summary of the best math study tips, applications of psychological processes, and learning guidelines. Let’s dive right in.
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.
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.
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.
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.
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.
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.
Learn strategies, tips, and tricks:
There are ways to go about a problem. Especially mental math. How much is 12% of 50% of 100? This problem can be rearranged to what is 50% of 12% of 100. That’s easier, right? Here is a simplified version X% of Y is Y% of X. You interchange X & Y to simplify the math.
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.
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.
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.
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.
These tips are consolidated from the following articles/research-findings:
I hope you have a better experience studying math and score better grades by using these guidelines.