How Addition and Subtraction of Fractions Could Have Been Developed

[@jwoodswce]

I recall learning everything backwards in school. First they taught the mechanical process, then they wanted the student to do "word" problems about reality. The teacher focused on given formulas and following the mechanical technique while ignoring the importance of the reality based word problems as if those were not important.

[@Inductica]

Yeah, we need an inductive math curriculum.

[@juanmanuelmunozhernandez7032]

I agree. The system is designed for the convenience of the mediocre, hard as it sounds. The mediocre teacher who doesn't want to do the hard part of his job, which is figuring out the best way to help students integrate the knowledge. And the mediocre student who would rather follow instructions than explore ideas actively.

[@Inductica]

@@juanmanuelmunozhernandez7032 that’s a good way to put it. I remember that when I was in first grade, I would come up with all kinds of personal methods of doing arithmetic in my head. My teachers would tell me that I had to show my work, which of course is a good idea, since thinking on paper is a valuable skill, but they wouldn’t give any reasons, so I thought it was just one more way they were trying to get me to prevent me from thinking.

[@markcromer4069]

@@juanmanuelmunozhernandez7032 Calling everyone mediocre is incredibly condescending. It also shows zero empathy and zero understanding. As an elementary school teacher I have an hour and a half each day, usually interrupted, to teach thirty kids of varying abilities the math lesson. Sometimes these kids are hungry, sometimes they're sleepy, sometimes they're stressed because their parents are fighting or their best friend isn't their best friend anymore, etc... Take all of that and then realize that I have a pacing guide. If Suzie doesn't understand how to add fractions, we have to move on without her. There's no other possibility. I am not allowed to take 4 days to teach Aydin, Aiden, and Ayden to think critically about how this applies to calculating the perimeter of a shape with sides of a fractional length. They need to grasp the method, apply it to get the correct answer, and move on. That does not make them, or me, mediocre. Jerk.

[@juanmanuelmunozhernandez7032]

This example is particularly interesting, again from the inductive perspective: it illustrates how trivially simple an idea can get when looked at from an inductive perspective, versus how obscure and mystical it looks when taught mechanically. Relatively speaking, I expect fraction multiplication and division to be less simple inductively.

[@Inductica]

@@juanmanuelmunozhernandez7032 I’m working on a way to make it almost as simple right now!

[@BuckPowers]

I was blocked on arithmetic for fractions for quite a while in school. I was in a Montessori-like public school. Once I managed to unblock myself, I was able to do pretty well in math. I really could have used this approach, then.

[@Inductica]

@@BuckPowers interesting; what specifically blocked you? What ended up getting you past it?