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| Thinking (Image credit: Wikimedia Commons) |
Learning something can sometimes be either difficult or easy, usually in between the two. Just what makes learning differential equations and learning simple arithmetic the difference between learning "complex" and "simple"?
Well, the direct answer would be that to learn differential equations, you must know arithmetic, you and you must know algebra. You also need to know how to use numbers, logic, and algebra to even attempt to learn calculus. Compared to simple arithmetic, all you need to know is how to count. Learning isn't some miracle happening inside your brain, it's a putting together and adding little things we know or have memorized as true. To learn differential equations, you need to put together what you learn from arithmetic, geometry, and algebra.
For example, to learn to add, a child must first learn to count. A child memorizes the numbers 1 through 10. 2 comes after 1, 3 comes after 2, 4 comes after 3, etc. Now, after memorizing the numbers, he is taught the concept of putting two numbers together called adding. 4 plus 5 is counting 5 from 4. 5 (1), 6 (2), 7 (3), 8 (4), 9 (5). There we go, the answer is 9. A child must count twice and know where to count in order to add two numbers together.
As you might guess, learning multiplication is the same thing. A child just has to add the same number some number of times. 4 times 5 is just 4 added with 4 added with 4 added with 4 added with 4.
Now imagine if a child had to learn multiplication without learning how to add or count. The seemingly simple operation would be exceedingly difficult and complex!
I know not all kids are taught the concepts of addition or multiplication. They just memorize big tables. Then again, when we ourselves multiply 4 and 5, we don't actually add 4 to itself 5 times, we just know it's 20. However, it serves as a good example. Why do so many students think math is so difficult? If you don't understand one concept, you will miss the next concept, and the workload piles up.
It isn't just math, it applies to everything. Science, sports, writing blogs, you name it. Anything to add? Post it in the comment section below.
Here is an interesting chart on another take on learning simple to complex. It divides learning a concept into multiple steps for a fuller understanding.
