Algebra, Shmalgebra

What and how to teach math to children and young people is one of those topics the rumbles around in my thinking from time to time. Here are two recent articles on the now-common belief that everyone should "know" algebra in order to graduate from high school or be able to move into college courses.

First, progressive education profession Paul Thomas, who questions the premise of having a set body of knowledge generally. A key quote:

The question of whether all children should take algebra is irrelevant as long as we continue to use early algebra readiness to label and sort children, as long as we continue to confuse brain development with smart.

After a lot of thoughtful discussion, Thomas ends with this shocking footnote:

The average age for developing the abstract reasoning ability needed to understand algebra and grammar is 20. Consider how that impacts the labeling and sorting we do to children and young adults throughout schooling.

Second, a letter from CUNY professor of math and computer science Jonathan Cornick, from the Washington Post's Answer Sheet blog. Cornick doesn't pull back his viewfinder quite as far as Thomas, but he still questions the premises of "algebra for all," based on research into how people use math as adults.

What math do people use in their wide-ranging jobs and life experiences? According to Cornick,

...almost everything fell into these categories:

• Percentages – Almost everyone said this.
• Proportions – this encompasses unit conversion skills related to supplies, materials, costs, nutrition, health, etc.
• Descriptive Statistics – finding averages, describing distributions as well as being able to understand and interpret data and charts from business, politics, media, etc.
• Geometry and trigonometry.
• Inferential statistics.

And in general, the common theme was in using arithmetic and logical reasoning skills in context rather than abstractly. Certainly, some skills from a standard algebra curriculum are needed for the above. I would say:

• Arithmetic, including order of operations – with a calculator!
• Simplifying linear expressions.
• Solving linear equations.
• Solving proportions, including percentage problems.
• Geometry including area and volume.
• Radicals including Pythagorean theorem.

However, I don’t believe operations on nonlinear polynomials, factoring and solving quadratic equations, simplifying complicated exponent expressions, and solving radical and rational equations are vital in order to master the aforementioned skills people use.

Cornick's conclusion is that college students shouldn't be prevented from proceeding with their educations just because they can't find their way out of remedial algebra. The American Mathematical Association of Two-Year Colleges agrees with him that there should be other options for students outside STEM fields.