Quote:
Originally Posted by Lil' Lavery
But what I meant by "discrete skill" was that algebra as a tool isn't particularly useful to a large portion of the population (though ManicMechanic makes a strong counterpoint to this). You don't need algebra to balance your checkbook or figure out your monthly finances. Most people are probably never going to balance an equation outside of an academic setting.
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Most people DON'T use algebra, but most people COULD, and if they did, it would make their lives better. I teach lower-level math (prealgebra through statistics), and I tell my students, "Not every formula or technique in this course will be used by everyone, but every formula could be used by someone, and you never know when the person who needs that formula could be you." I've always been able to think of a plausible useful real-life scenario for every formula I teach.
For example, one of the nastiest formulas from statistics is for the standard deviation of the difference of difference of means for 2 populations -- a 6-layered complex fraction. When would you ever use that? Well, I came across an article stating that some cholesterol drugs may be far less effective in women than in men, and that it wasn't certain whether more tests were needed for the women (but not the men). Two populations: men and women. Difference of means: cholesterol level before and after medication. Difference of difference of means: men's improvement is different from women's improvement. How to evaluate whether more studies needed to verify hypothesis: evaluate standard deviation.
One of my neatest classroom experiences was a student who, after hearing multiple tie-ins to formulas said, "I bet you could never find an application for the problem 1/(1+(1/(1+(1/1+1)))), our homework problem." As I thought about it, this formula is tied to the Fibonnaci sequence, whose real-life application has to do with the fractions that ensue: 1/2, 2/3, 3/5, 5/8. As you traverse these fractional increments around a circle and draw rays to the edge of the circle, this mimics a bird's eye view of a corn plant that shoots out leaves at these fractional increments, for maximum sun exposure. I suggested that this pattern could be used to optimize water coverage for certain patterns in the design of a sprinkler system. The student came the next day with a box of apricots -- his family is in the farming business -- they grow corn and design sprinkler systems, and this was something they could use.
It's our job as "math literates" to see these connections and help the people around us to use these connections to improve their lives.