Each of the TED-Ed videos is meticulously animated and represents, I am sure, many many (many) hours of effort. Knowing this made the TED-Ed take on logarithms rather painful to watch:
Oof. Let me attempt to sort my thoughts:
1. The hook baffled me.
A hook should, optimally, be incorporated into the topic being learned. This hook was simply a preview of a future part of the video, and didn’t carry much interest on its own. The “red eyes” made me think it was referring to the eye-bleedingly long numbers being presented.
While my own logarithm video isn’t perfect (also not entirely comparable since it’s about the addition property in particular) I do at least manage a hook that’s useful in the explanation of the topic.
2. “…small numbers and in some cases extremely large numbers leading us to the concept of logarithms.”
Logarithms come out of the inverse concept of an exponential. The numbers don’t have to be large or small. (If you want to get historical, they were often used as a method to multiply quickly by turning the operation into addition.) While a logarithmic scale can be used to handle large or small numbers, I don’t see how that leads to the statement in the video.
3. “the exponent p is said to be the logarithm of the number n”
Math videos often are on the glacially slow side, but this part was presented so fast parts of my brain melted.
Look: Logarithms represent, in essence, the first new mathematical operation students have had to reckon with since grade school. They cause intuitions to fail. I have seen students who have never had problems with mathematics before have them for the first time with logarithms.
It’s worthwhile, then, to spend a little more than five seconds on your definition.
The definition is confusing, anyway; a logarithm is a function. It applies from one number to another number in a specific way. It is not simply an extract from an exponential equation. While the video mentions that (sort of) it waffles on the implications of introducing a new mathematical operation.
4. “…log base 10 is used so frequently in the sciences that it has the honor of having its own button.”
First off, no: the sciences often use base e (given how much continuous growth and decay happens in real life). Base 10 logarithms do still get used for logarithmic scales, but the statement as given in the video is just confusing.
Also, that’s a TI graphing calculator? Which one of has a logarithm button but not a natural logarithm button? Even the TI-81 has one.
5. “If the calculator will figure out logarithms for you, why study them?”
The answer the video gives … is so you can figure out a logarithm base 2.
That’s a terribly weak answer, given a.) yes there are many applications of logarithms where understanding the mathematics is both good and necessary, and the video even goes into one application immediately after making this statement b.) the answer doesn’t really answer the question (since it doesn’t explain where the computer science-related equation came from) c.) with the current operating system, Texas Instruments calculators are perfectly capable of putting in alternate bases without a change of base formula (The video incidentally doesn’t mention the change of base formula even though one of the questions in the post assessment asks what it is.) and d.) The statement presumes the use of a calculator in the first place (computer-based systems are also perfectly capable of doing logarithms with alternate bases).
6. The video then wants to show how useful logarithms are by giving a formula from science.
Based on the post-test, I’m guessing this part is here merely to show how logarithms are used in “real life”.
In the master catalog of Ways to Convince Students Why Something is Useful, “look, a formula that shows up in science!” ranks somewhere between “because math is good for you” and “so you can get into a good college”.
Is it really that bad? Am I just being grouchy here?