It has finally dawned on me why teaching Pyret felt both foreign and familiar. We are teaching the same material, but in a different order. At this point, we would have drawn some pictures using Pyret already. I absolutely understand why we skipped the playing with Pyret portion of the introduction. We simply don’t have a lot of face to face classroom time.
In addition to the change of order of the material, the Physics team has added function notation to the mathematical representation. Initially, it seemed silly and extraneous, but as we were reviewing the material, I see why.
For a problem like how many chocolate chips will I need if each brownie needs 6 chips? We know to set it up, it’d be like
1 brownie = 6 chips; 2 brownies = 12 chips…
If we put it through our function machine the rule would be
Input: number of brownies
Output: number of total chocolate chips needed
Rule: number of brownies * 6
Equation: C = 6 * b
Up to this point, students are very familiar with what we’re trying to do. It’s now writing it as a function notation where the wires get crossed.
C(b) = 6 * b
The sentence would be: the total number of chocolate chips (as a function of brownies) is six times the number of brownies. The idea that this equation can also be a rule for a real-life word problem went over some heads. It might be time that function notation be taught as part of writing equations. I think the students were getting stuck since parentheses always meant multiply. (And again—advocating for why PEMDAS is wrong). Having the students write out and SAY the sentence hopefully gets them into opening up their thinking that y can also be written has f(x).
I was sick when the 1-Argument Functions were taught. I was VERY proud of the students as they were able to whiteboard the problem for 2-Argument Functions. The students who had the confidence to just jump into a new and different problem loved to wonder how they can show two inputs in their function notation. Eventually, a group thought to do it by putting both variables with a comma to separate—like a list. Either we’re starting computer programming thinking in earlier grades, or it’s becoming more natural for the students to see their world in this way.
The added layer now is explaining each part of the Design Recipe. I wonder if I had equated it to a cookbook recipe if there would be some translation—hence a smoother transition. Or would that confuse them more?
Learning with Ms. Medrano 