3 Mental Models for Learning Math and Science

Since I was a kid I always thought that successful people had something up their sleeves.

A krabby patty formula for success if you will.

But…

As time has passed, I realized that there is no magic formula. However, there are useful things that successful people do that certainly help them get ahead.

One of them is the idea of mental models.

Used by people like:

Elon Musk

Charlie Munger (Rest in peace)

Jeff Bezos

Richard Feynman

Albert Einstein

When solving problems in different contexts.

My goal with this article is to answer the following two questions.

  • Why they are useful?

  • How to use them?

And show you 3 mental models I’ve found useful for learning Math and Science.

Let’s start by defining it.

A mental model is a pattern that shows up over and over again and can be used to explain different phenomena.

It was first coined by the American philosopher Kenneth Craik in his 1943 book, “The Nature of Explanation.” He suggested that the mind constructs small-scale models of reality to anticipate events, understand the environment, and solve problems.

They aren’t meant to be 100 percent accurate at all times they are a useful abstract estimate for many scenarios.

Some mental models that tend to apply across a wide range of contexts are:

Natural Selection

You often find the idea of ‘survival of the fittest’ to be relevant in many different contexts.

  • Business Markets

  • Employment

  • Research

Compounding

Variables that grow onto themselves are frequent. Where it starts slow in the beginning but then snowballs into something much larger.

  • Investments

  • Personal Development and Habits

  • Learning

Systems thinking

There are lots of systems in this world that can be thought of through the lens of inputs and outputs.

  • Business Systems

  • Science

  • Engineering

  • Programming

But why are mental models so useful?

Mental models help us map new knowledge onto old knowledge-which has a tremendous effect on learning.

Consider this.

“How much you’re able to learn depends on what you already know. Research finds that the amount of knowledge retained from a text depends on prior knowledge of the topic. This effect can even outweigh general intelligence in some situations.” — Scott Young

Prior knowledge is the key to making the learning process smoother and faster. The more prior knowledge we have when learning a subject the easier it is to understand and remember what we are learning.

How to use the mental models when learning

Now let’s see how to use them in practice.

But before we do this we need to obtain a brief understanding of what chunking is.

Chunks refer to when we group similar pieces of information under one common label.

For example:

  • Food (This contains things like vegetables, fruits, meat, etc…)

  • Cars (Toyota, Bugatti, Lamborghini, etc…)

  • Sports (Soccer, Baseball, Basketball, etc…)

The idea with mental models is to have a set of them in our tool kit that we can use as labels whenever we find similar patterns to them. As you go through the material you might say to yourself “Oh, this common pattern can be grouped using this mental model as a label”.

The more frequently you use each mental model, the more likely it is that you will remember them when you need them most.

The Mental Models

Now let’s get into the mental models.

1. Structures

A common theme I’ve found in Math, Science, and even Computer-Science is that when you are learning it, they teach you about different ‘structures’

Structure:

- Mathematics: Often refers to the way elements are arranged within a mathematical set or system, such as in algebraic structures (groups, rings, fields) or geometric structures.

- Science: It can pertain to the physical arrangement of atoms in molecules, the organization of cells in an organism, etc…

-Computer science: Commonly denotes the arrangement of data and algorithms in programming (e.g., data structures like arrays, trees, and graphs) and the architecture of software and systems.

2. Processes

- Math: I would say that this mental model isn’t as relevant in the case of math.

- Science: These are especially relevant to chemistry and biology where we have chemical processes and biological processes but also in physics, you find physical processes like different types of decay, thermodynamics processes, etc….

- Computer Science: A series of coded instructions or algorithms that a computer follows to execute tasks.

3. Techniques

Mathematics: Specific methods or strategies used to solve problems or prove theorems. Techniques in math can range from computational algorithms to problem-solving strategies like induction, proof by contradiction, or the use of specific formulas and theorems.

Science: Practical methods or procedures used in conducting experiments, making observations, carrying out research, or also for solving problems in the sciences (like using conservation laws in physics or “gene sequencing” in biology or “titration” in chemistry)

Computer Science This includes programming methodologies, algorithm design, debugging techniques, data modeling approaches, etc…

Next time when you are learning anything science or math-related, try and see if you can spot these patterns and apply them. You’ll learn much more quickly.

Until Next time!