What does it mean to be "literate" in math? Literate, as opposed to being and expert, means having the minimum amount of working knowledge for everyday purposes. In trying to define literacy, I want to focus on those math skills that creep up in everyday life enough to be an inconvenience if you do not know them. To be literate in math, not only should you know the mechanics of these skills enough to do them without looking them up or using a calculator, but you should also be able to know in what situations these skills may be appropriate. The true "math literate" is not someone who has lots of math knowledge, it is someone who correctly applies the skills they do have to given situations.
That being said, here is my list of minimum math skills every adult should possess. The list is not a final one by any means. I would be open to suggestions, and I will update this list when I get good ones. E-mail suggestions to me at paul@mathmistakes.com .
Arithmetic:
It should be obvious that everyone should know arithmetic. Add, subtract, multiply and divide positive and negative integers, fractions and decimals. They should also know how to simplify fractions, scientific notation, convert between fractions and decimals, and know concepts such as roots, exponents, ratios, percentages, reciprocals, and absolute values.
Measurement:
Another obvious concept. Everyone should know both traditional and metric measures of length, area, volume, weight (or mass), time and temperature, and they should know how to convert between these measures.
Algebra:
Here is where things get controversial. The algebraic skills I believe everyone should know are the following:
You will note the lack of quadratic polynomials, conic sections, etc. It is not that these more advanced skills are useless (I for one would not want to fly in an airplane where the navigator did not understand conic sections, who knows where we would end up going) I am merely saying they are not needed by everybody. When was the last time you used the quadratic formula in an everyday situation?
Geometry:
Probability:
Statistics:
Logic:
This list represents the math concepts we run into all the time. For example, just yesterday I was doing some photo editing, combining two photos together, and the color schemes did not match. The tool in the software available to fix this problem was not working right. The solution came down to a rational equation problem the ratio of red green and blue colors did not match from picture to picture. A few calculations later, and the problem was solved.
A person who is literate in math should have no problems with any of the above concepts, and could easily come up with situations where each one could be used. Moreover, given a situation, they should be able to determine which concepts could be used. To do this requires not just a familiarity with math, but a full understanding. Creating a test of math literacy would have to focus on testing this understanding, not just a bunch of math problems to solve.
I know what most readers will be saying: "I understand that you are simply trying to list the bare minimum amount of math people should know, but it is simply not enough. People should study Algebra and Calculus, Differential Equations, and advanced Geometry, because it is needed in high tech fields, and engineering fields, and medical professions, etc. If you are proposing these as minimum requirements for grade school students to graduate, you run the risk of schools teaching to the test and students ignoring advanced mathematics, because it is not a requirement." The truth is that I agree with this sentiment.
My philosophy behind the list is not what we should be schooled in. It has something in common with an old Saturday Night Live sketch where comedian Father Guido Sarducci described a Five Minute University. In five minutes he would teach you everything that you would remember from college five years after graduation. Like Economics class would be the phrase "Supply and Demand", and business class would be "buy low, sell high", etc. The math literacy list above does not represent concepts to cram in to you head, spew them out on a test, then forget them. These are the concepts you should remember years later. They are the foundational concepts for all higher level math. I think I learned more Algebra taking Calculus than I did taking Algebra, because in Calculus we used Algebra over and over until it became second nature.
By the way, what is the Five Minute University version of a Calculus class? I think it would go like this, "If you have an object that is 'curvy', you can find its area and volume using Calculus." Forgetting our unused Calculus skills is not necessarily a bad thing. At the very least, when I run into a problem requiring calculus to solve, I can recognize that, and pull out my old calculus book to look up how to solve it. A person who has never studied Calculus could never recognize what problems are solvable by Calculus. The point is, the math we should study and the math we need to know are two different things.
More to follow as suggestions come in.