If you think about it, we have evolved to want to try and use the least energy possible. When you have to hunt or gather for every single bit of food – well, this just makes sense. My experience has been that this is no different when it comes to trying to learn something new. If you give your brain a crutch, it will use it all in the name of saving energy.
In order to understand math, you have to practice the same way you would if you were learning a language or even a musical instrument, right? … and the easiest way to practice for most people is to use the problems in the textbook, right? My argument is that when you combine these with the brain’s urge to be lazy sometimes you can actually undercut the learning process!
All of the problems in the textbook are in order – a big issue! If you know that chapter 4 is all about using a certain formula then you brain won’t try to really read the problems for more than that – it will shift into “let’s apply that formula” mode and it will feel like you are learning a lot while, in reality, you are just getting really good at that one technique. Not only that, you are only getting good at that one technique when you know its the technique to use. A computer can do that!
Most math problems have many ways to do them and the real skill is reading carefully to know which method to use. This is the human / creative element to math! Knowing what section or chapter a problem came from even subconciously can take this element out of it and its the most important element to deeper understanding.
So, how can you get around this and make your brain work harder? You have to mix the problems up! A great way to do this is to make flashcards out of random problems from each section, then mix them up and do your practice problems that way. This is especially good for final exams or standardized tests which are typically not “in order” at all.
Some tips:
- Make sure that you put a page number on the back with an answer so that if you get really stuck you can go back and read the section
- Try to get as much of a variety of problems as possible – the goal is to get your brain used to seeing problems that are totally different to eachother back to back
- Still use your book for the routine stuff! – You still need to practice the skill of simply applying a technique. At first, go ahead and work the basic problems and then use this when you need to start learning to pick methods better.
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