Math and physics tutoring by Dr. Dave
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Why is Math So Hard?

The real title should be: Why does math sometimes seem hard to learn?

Researchers think it has to do with the abstract nature of most concepts in mathematics. In other words, it can be difficult to make a genuine connection to a new idea in math, like "what is a logarithm." On the other hand, it's easy to understand something like like "ice on the sidewalk is slippery" or "that thing in your hand is a shoehorn."

Other abstract concepts not related to math are much easier to grasp: they are often related to emotions and therefore different because we have personal experience with them at every age. The good news is that anyone can master difficult new concepts and become good at math by following a few simple approaches to studying and learning.

This is where practice comes in. Practice is extremely important to lock in those abstract ideas, which have no physical or emotional anchor. The more abstract something is, the more important it is to practice because repetition builds and strengthens the neural pathways that are required for understanding and remembering.

After intense practice, take a break and do something different, like play a musical instrument or exercise. This allows your brain to process new concepts and strategies in the background.

Effective practice builds new neural structures - or chunks - and is like building a brick foundation: you have to stop every once in a while to let the cement dry, so that you will have the most organized and solid structure possible. Cramming is the opposite of this: it's disorganized and usually results in a messy looking and shaky wall or foundation.

So how can we remember new ideas later when the quiz or test comes along? We're not able to store more than about four things in our working memory (short-term), so we must convert everything to long-term memory. The most effective way to accomplish this is to do repeated studying a few times over several days with breaks in between, rather than cramming it all at once. Again, it is very important to repeat new types of problems and take breaks to let that cement dry and build youself the neatest and strongest foundation possible.

Exercise and sleep are both crucial to the learning process and should be a respected and regular part of your study plans.