When I learned the fundamental theorem of Calculus first, I used the inductive reasoning. We looked at two graphs and made a general statement:. After a few minutes, we did some examples, and while doing examples on the board, I forgot what I just generalized. So, on the next day, when we had lots of free time to do homework, I thought of the two graphs as an example. And they reminded me of the fundamental theorem. I used inductive reasoning again.
But, while doing homework, I found a pattern and I got used to using it. So, this time, it is a deductive reasoning. I think learning inductively first and solving questions deductively is the best! When I have to do homework or something very quickly, I would do it deductively, because it takes less time and requires less thinking.
But, my small concern is I might forget how the fundamental theorem worked if I use only deductive reasoning. I think reviewing inductive reasoning by making and solving my own examples will be helpful! If I do the inductive reasoning a few times for a few days, I wouldn't forget the concept.
The fundamental theorem is important especially when we look for the area under the curve on [x^2, x^3]. <- those are variables; we couldn't find the area algebraically. Because the area under the curve implies the rate of change, it has some kind of significant roles. But, I don't know when we need the fundamental theorem yet. When we go to next chapter, we might learn the application of the fundamental theorem, and at that point, I could answer why it is important!!
But, while doing homework, I found a pattern and I got used to using it. So, this time, it is a deductive reasoning. I think learning inductively first and solving questions deductively is the best! When I have to do homework or something very quickly, I would do it deductively, because it takes less time and requires less thinking.
But, my small concern is I might forget how the fundamental theorem worked if I use only deductive reasoning. I think reviewing inductive reasoning by making and solving my own examples will be helpful! If I do the inductive reasoning a few times for a few days, I wouldn't forget the concept.
The fundamental theorem is important especially when we look for the area under the curve on [x^2, x^3]. <- those are variables; we couldn't find the area algebraically. Because the area under the curve implies the rate of change, it has some kind of significant roles. But, I don't know when we need the fundamental theorem yet. When we go to next chapter, we might learn the application of the fundamental theorem, and at that point, I could answer why it is important!!