Chunking Strategy for Math: 9 Steps for Skill Mastery

What does chunking mean? Use sports as an example.

Have you ever tried to learn a new sport? I noticed that others were acting with more accuracy, skill, coordination, and speed compared to when you try to copy them.  Maybe they can kick a soccer ball further than you can kick it, or they hit a tennis ball with better form.  When you ask them how they do these things, they pause and struggle to explain.  It’s not that they don’t know, of course, it’s just that these moves have become second nature to them, so it’s difficult for them to break it down for a beginner.  This phenomenon occurs because the move has been chunked in their minds.

Here’s a great question: what is chunking?

If we’re talking about sports, chunking refers to breaking down complex movements or skills into smaller, manageable parts.  Athletes use chunking to learn and improve on their technique by focusing on specific aspects of performance.  Take for example this forward sculling movement that this girl is doing here. Most likely she was taught to look forward, put her arms out for balance, keep her weight slightly forward to push out, then use her adductor muscles to bring her feet back in.  For a beginner, that’s a lot to remember all at once, but when she chunks this forward sculling, she will be able to integrate all these steps into one fluid movement.  Then in the future, she would be able to use what she learned in forward sculling as one step in a more complicated chunk.  This is how you build up skating skills.

I like using the illustration of sports to introduce the concept of chunking.  I think that many people have the experience of trying to learn a new sport, and having to juggle various instructions in their minds, while simultaneously carrying them out with their body.  And in sports, it’s easy to tell the difference between someone who has chunked a skill and someone who has not.

I’m not a sports coach, though. I’m an online math tutor, and today I’m going to be talking about chunking as it applies to learning math.  How can chunking help us learn math?  Why do we need to do it? And how do we do it?

 

What does chunking mean in academic terms?

Chunking is breaking down information into smaller, manageable pieces to enhance memory retention and processing efficiency.  Imagine you are creating a password that needs to be 27 characters long. I could use a password generator to make one like this: bdkuekjpllovnkslefsepwitrnl.  Something like this would be very difficult to memorize because there is no meaning behind it, but I could choose a different password of the same length like this: wehaveweighttrainingclasses.  And this would be a lot easier to remember because it is just one phrase. This phrase is one chunk.

Examples of a skill to chunk in math include solving a trig equation, using proportional reasoning to solve problems, converting between fractions and decimals, graphing quadratic functions, and deriving and integrating functions.  If you have these skills chunked, it means that you can do it in one fluid movement. And you don’t need to open up a YouTube video to see what they did, and then try to apply their solution to your problem.

How does chunking work?

When you learn something new, you’re engaging your working memory.  Working memory temporarily holds and allows you to manipulate separate chunks in your head.  For example, if you’re following a recipe like this, each separate item is one chunk.  Once you complete the step, you no longer need to hold this piece of information in your head.  The accepted limit of human working memory is four items.  I know this holds true for me. If I have a recipe like this, I can remember exactly these four items, and then I need to look at the recipe again.  So you see, working memory cannot juggle very much new information at once.

That’s why it’s very important to transfer knowledge and skills from your working memory to your long-term memory, so that you can free up more space in your working memory.  When you’re learning something new in math, it is very important that you have already chunked the prerequisite skills.  

 

How to chunk: example of solving ax=b equations

To be able to learn the skill, you must already know the following.

  • “ax” written together means “a times x”
  • multiplication and division undo each other
  • division facts
  • division involving decimals, fractions, integers

On top of that, we’re going to add the skill of using a systematic algebraic procedure to solve the problem.  You would need to learn the following:

  • solving an equation means finding the value of x that makes the equation true
  • use an inverse operation to “undo” what’s been done to x
  • division is shown as a denominator in a fraction

If you already had the prerequisite knowledge, it is not that much more to add, but if you struggle with things like division facts, then these questions become a lot harder.  You will experience cognitive overload.  Cognitive overload refers to a situation where a person’s cognitive resources are overwhelmed by the amount or complexity of information that they’re trying to process.  It occurs when the brain is presented with more information than it can handle in its working memory.  Have you ever experienced this while studying?  The remedy would not be to keep working on one-step equations, but to review division facts in isolation.

 

9 steps to creating a powerful chunk

    1. Focus with intention. What you want to chunk. No distractions. Use the Pomodoro technique.

 

    1. Try to understand the basic idea that you are trying to chunk.  You should have different worked examples given to you by your teacher or textbook.  When you first go through the problem, your only job is to understand the steps that were taken to solve the problem. Why was each step necessary?

 

    1. Try to work through a key problem by yourself on paper.  Don’t look at the solution unless you absolutely have to. Make sure you understand each step. Don’t skip steps, or do the problem in your head.

 

All the while you do this, you need to gain context. When do you use this chunk? When do you not use it?  The reason why we need to do this is that when you write a test on solving linear equations, you’re going to have several different types to solve. You need to know when to use which procedure.

    1. Do similar problems the same way and check your answers.

 

    1. Take a break.  Give your diffused mode some time to internalize the problem.

 

    1. Before you sleep, review the problems that you found difficult.

 

    1. Do a repetition of key problems as soon as you can.

 

    1. Add a new type of problem using steps 1 to 7.

 

  1. Mentally review the types of problems that you learned while walking, sitting on the bus, or waiting for a class to start. If you can go through problems while you’re not in your regular working environment, you can do these problems anywhere, like in an examination room.

 

As we discussed in a previous video, solidifying a chunked library takes time.  Sleeping in between studying sessions is integral to putting things that you learned into your long-term memory.  That is why you don’t want to learn all the different skills at once.  When you review the material, make sure to test yourself to retrieve knowledge.  Talk to yourself or a friend about how you would solve a certain type of problem. When you would use this procedure and when you would not.  Redo questions or do new questions on the same concept and check your answers.  Whatever you do, do not just reread over your notes or look over the examples that were done in class.  This only proves that your teacher knew how to do the questions, but it doesn’t mean that you know how to do them.  I’ve unfortunately heard from students who tell me that they studied by rereading their notes. It is not to my surprise that they did not do very well in the test.

So this is my advice on what you should actually be doing during your Pomodoro study sessions.  If this information helped you, check out my other videos on studying smart.

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