I would like to know why elementary teachers insist on teaching students the inequality signs using that stupid alligator eating the fish analogy. It drives me crazy. I was working with a college student on piecewise functions and she had to stop, hold up her hand and make eating motions.
Honestly, I never learned it that way and when a student explained it to me, it made no sense what so ever.
It works if the inequality is written in a standard way such as x<4 but it doesn't work quite as well if you write it as 4 > x.
I honestly don't know the best way to teach this concept or the best way to present it to high school students. What I can say is I work on having students connect directly to the signs without using the alligator.
I try to teach inequalities in one variable by relating it to a number line so they have a visual. For instance x < 4 tells me I am looking for a value smaller than 4. If you look at the sign, it is like the head of an arrow and points towards the numbers which meet the criteria. If its 4 > x, I teach students that this states that 4 is going to be larger than any value for x and the sign is telling you that 4 is always bigger than the value you choose.
I think this is more important than using alligators because it helps students relate to the directions rather than trying to remember the eating part. This tells me they have not developed a real understanding of inequalities and their relationship to numbers.
Fortunately, they drop the alligator when we start graphing systems of linear inequalities but they still have trouble with the concept it is an area which can be the answer. On a line, its a series of numbers they deal with. Its like traveling on a road, you just follow it and go in a certain direction but when they graduate to linear inequalities, they suddenly are dealing with a boundary acting like a type of fence marking the end of a region.
So they have to learn to think in terms of areas and where does this region lie. I sometimes equate it with a fenced ranch. This is easier for them to relate to. I'd love suggestions from others on how they teach this topic. I'd also love to hear your feelings regarding the alligator story.