How to Relearn Math and Science - Examined Existence

How to Relearn Math and Science

Math and Science are off-putting subjects to many in high school and even in college.  But as we grow a bit older, we start to realize its necessity.  Math and Science are all around us—it is what allows us to advance as a civilization. And recently, it has become very useful knowledge to have when applying for jobs. And if you were like me and didn’t care to learn about Math and Science in high school and college, it’s not too late.  You can relearn it. In this post, I will show you the steps I took to relearn Algebra and Geometry.  I used many of the concepts highlighted in Barbara Oakley’s book, “A Mind for Numbers: How to Excel at Math and Science (Even if you Flunked Algebra). Whatever level Math or Science you want to learn or relearn, use these tips to do it.

Tips for Relearning Math and Science

Believe it or not, there is a difference between learning Math and Science the first time and relearning it.  When you are relearning, you are already familiar with some of the concepts and there are also concepts that are vaguely familiar but will become robust knowledge once you get your feet wet again.  Then there are of course concepts that are still completely foreign to you.  So the plan for relearning Math and Science is going to be slightly different than if you were learning it the first time.  So what does this previous background mean?  It means you will not have to read every single word in the textbook and do rote repetitions of problems until you are bored out of your mind.  You aren’t forced to do homework this time.

So with that in mind, here are the tips that will allow you to relearn Math and Science well.

1.  See how much you know.

The first thing you should do is take a test to see how much you know/remember.  A great place to do this is at khanacademy.org. There is no use in starting from scratch if you are already familiar with some concepts.

2. Spaced repetition.

According to the Forgetting Curve, we will only remember about 20 percent of what was learned if we do not review the material within 24 hours. And that is where spaced repetition comes in. Spaced repetition is just about one of the most important things you can do to retain your knowledge. I learned this intuitively in my Brazillian Jiu Jitsu class and would only come to know it as spaced repetition when I read Barbara Oakley’s book “A Mind for Numbers: How to Excel in Math and Science (Even if You Flunked Algebra).” In my jiu jitsu class, instead of taking notes in class or immediately after class, I would wait until the next day to try and recall and write down the notes from the previous day’s class. Doing this recall exercise forced me to dig inside my memory bank and reinforce the learned material.

For Math and Science, repetition is extremely important as some of the concepts cannot be memorized, they must be internalized. When you are studying the material, instead of doing 50 problems from 1 chapter all in one sitting, you should space out the 50 problems over the course of a week or two, giving you a chance to repeatedly try to recall the material. This task of repeatedly trying to recall the material enhances understanding and memorization of the material. Here is an illustration of how and why repeatedly recalling/reviewing the material helps you retain material much better.

theforgettingcurve

As you can see, the learned material is strengthened in the mind after each subsequent review.

3. Move on after you have a firm grasp on a concept

Remember this, repeatedly practicing something after you have a firm grasp on it will give you diminishing returns.  The first 50 problem sets you did for a particular chapter lets you master the material—but the next 50 problems you do in the same chapter will get you minimal benefit.  Time is thus better spent on another concept.  You are busy, you do not have time to waste.

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Once you are sure you have a firm grasp on a subject, move on and come back to it later to review it. Science has shown that doing too many problems of the same kind in immediate succession provides diminishing returns.  Your time is better spent moving on and coming back later to review.

4. Interleave your practice.

Interleaving is when you practice new concepts and mix it in with older concepts. Interleaving is an important topic that Barbara Oakley talked about in her book. Interleaving means practice by doing a mixture of different kinds of problems requiring different strategies. When you do the same problems over and over again, your mind will trick you into thinking that you have mastered that topic; but true mastery of the topic means knowing when to use a method and when to use a different method. As stated above, doing too many problems of the same kind in immediate succession provides diminishing returns. Make it a point to skip around through problems from previous chapters and materials. This can sometimes make you learning more difficult; but in reality, it helps you learn more deeply.

5. Recall instead of reread.

In terms of long-term learning, rereading does little good. Instead, try to recall the main ideas from what you are reading. Here is how you can use recall to deepen your understanding of concepts, instead of rereading:

-After reading 1-2 pages, look away from the book and try to recall the main ideas.
-After reading a chapter, look away and try to recall the main ideas.
-As you are taking a random break or walking, try to recall the main ideas you have learned.
-Instead of rereading, try recalling the learned concepts in spaced intervals, not waiting too long between recalls.

The ability to generate ideas from within is one of the key indicators of good learning.

6. Use different resources.

Do not stick to just one resource when learning. Learn from multiple (but reputable) resources. Having one resource means you are taught only one way of looking at a concept or problem. But if you use different resources, your mind is open to multiple ways of looking at a concept and solving a problem. Sometimes, the one method that you use as your main guide will still leave you with a lot of questions about what you are learning. That is why it is important to take a look at other sources, as they can fill in the holes in those knowledge gaps.

7. Test.  Test.  Test.

Consistently testing yourself is probably the most important thing when learning anything. Testing has been shown to reinforce learning, no matter how well you do on the test. So consistently test yourself. But testing doesn’t have to be a sit down session in a quiet place with 25 problems. You can test yourself by using flash cards with solutions on the back. You can test yourself mentally by asking yourself questions as you are walking. And yes, you can test yourself by sitting down and attempting to do problems without looking up the answers until you are done.

8. Learn the underlying principle of concepts.

Learning how to apply a concept to a problem set is one thing, but learning the underlying principle of the concept is another. Once you understand the underlying principle of the concept, when you understand why it is done that way and why it works, you will begin to truly understand the concept in its most abstract form. Understanding concepts in its most abstract forms allows you to commit it better to memory, know exactly when the method is applied, and allows you to apply it to concepts in everyday life and not just problem sets within the book. When you get to the point of understanding how and why a concept works, that is when you begin to approach true mastery.

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Follow these 8 tips and you will probably get more out of Math and Science than the first time you learned it.

 

About the author

Tri

Netflix enthusiast, horrible speller, jiujitsu hobbyist, weekend drinker, and occasional poker player. Favorite quote is "[o]ut of suffering have emerged the strongest souls; the most massive characters are seared with scars."

1 comment
Z - June 18, 2015

The ideas discussed above are also covered in the excellent book, Make It Stick, by pyschologists Henry Roediger and Mark McDaniel (Washington U, St. Louis). The secret is spaced retrieval practice interleaved with other topics. This will help mitigate the effects of the Ebbinghaus Forgetting Curve that is shown above.

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