Like your videos. The relatively narrow focus on one class of things is a good way to refresh old knowledge. (old = high school in late 60's). I raise a note of caution which could, perhaps, be part of some future presentation: This issue comes with "proportion" used as a fraction: I begin with your example of 1:20, 1 teacher to 20 students. I've seen more than one person do a faceplant when working with a proportion later on while playing with introductory level statistics. They think of 1:20 as 1/20, as one-twentieth, as 1 in 20, as 1 of 20. Nope. The first form was correct. The second form--the fraction form--is correct when taken IN CONTEXT. The last three are common misinterpretations. There are 21 people there. Similarly, I have seen people improperly create a proportion: I have 27 people in my class and 5 of those persons have blonde hair. Thus, the proportion is 5:27. Wrong. The proportion is 5:22. In context, 5/22 also works. However, it is also true that 5/27, or five twenty-sevenths, or 5 in 27, or 5 of 27 have blonde hair. Somehow 5/22 and 5/27 are both correct. The symbology of the fraction bar can be even more confusing than the semantics. The roots of the confusion are laid early on in teaching fractions. Classically, a segmented pie is used to introduce fractions. There, the elements--the individual wedges--are part of a common whole--that juicy round pie. The fraction 1/8 is one-eighth or 1 of 8 or 1 in 8. Proportion notation comes later with that tricky word, "to." The early "inclusionary" numerator seems to subliminally override the later "exclusionary" numerator in some persons' thinking. Awhile back I watched your video on the multiple uses of two upright lines: |-3| (absolute value, vector, determinant). In object oriented computer programming language terms, that symbol set ( | | )is "overloaded." It is not wrong, it is just context sensitive. The same is true of the symbol "/". It is overloaded and must always be carefully kept in context or else the misapplied term gives you incorrect results. I prefer to stay with the colon (:) symbol when reporting proportion.
Like your videos. The relatively narrow focus on one class of things is a good way to refresh old knowledge. (old = high school in late 60's).
I raise a note of caution which could, perhaps, be part of some future presentation:
This issue comes with "proportion" used as a fraction: I begin with your example of 1:20, 1 teacher to 20 students. I've seen more than one person do a faceplant when working with a proportion later on while playing with introductory level statistics. They think of 1:20 as 1/20, as one-twentieth, as 1 in 20, as 1 of 20. Nope. The first form was correct. The second form--the fraction form--is correct when taken IN CONTEXT. The last three are common misinterpretations. There are 21 people there.
Similarly, I have seen people improperly create a proportion: I have 27 people in my class and 5 of those persons have blonde hair. Thus, the proportion is 5:27. Wrong. The proportion is 5:22. In context, 5/22 also works. However, it is also true that 5/27, or five twenty-sevenths, or 5 in 27, or 5 of 27 have blonde hair. Somehow 5/22 and 5/27 are both correct. The symbology of the fraction bar can be even more confusing than the semantics.
The roots of the confusion are laid early on in teaching fractions. Classically, a segmented pie is used to introduce fractions. There, the elements--the individual wedges--are part of a common whole--that juicy round pie. The fraction 1/8 is one-eighth or 1 of 8 or 1 in 8. Proportion notation comes later with that tricky word, "to." The early "inclusionary" numerator seems to subliminally override the later "exclusionary" numerator in some persons' thinking.
Awhile back I watched your video on the multiple uses of two upright lines: |-3| (absolute value, vector, determinant). In object oriented computer programming language terms, that symbol set ( | | )is "overloaded." It is not wrong, it is just context sensitive. The same is true of the symbol "/". It is overloaded and must always be carefully kept in context or else the misapplied term gives you incorrect results. I prefer to stay with the colon (:) symbol when reporting proportion.
Good teaching method👍
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Testimony I studied all of this none of it was on the test College Math and God stepped in I said I will be a pillar to others and let them know