Recently, *The New York Times* published an op-ed calling for curricular changes in K-12 math education:

Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a “reform” version in which these topics are interwoven). This has been codified by the Common Core State Standards, recently adopted by more than 40 states. This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life.

For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a “group of transformations” or a “complex number”? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood.

What the authors call for is an applied approach to teaching math:

A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations. The former is how algebra courses currently proceed — introducing the mysterious variable x, which many students struggle to understand. By contrast, a contextual approach, in the style of all working scientists, would introduce formulas using abbreviations for simple quantities — for instance, Einstein’s famous equation E=mc

^{2}, where E stands for energy, m for mass and c for the speed of light.Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers.

I have no idea if this would work. It sounds good, but I would like to see some data (I know similar approaches have been tried before, with mixed results). The other concern is that this approach has been used in Finland:

A plausible hypothesis stems from differences in the content of the two tests. The content of PISA is a better match with Finland’s curriculum than is the TIMSS content. The objective of TIMSS is to assess what students have learned in school. Thus,

the content of the test reflects topics in mathematics that are commonly taught in the world’s school systems. Traditional domains of mathematics–algebra, geometry, operations with numbers–are well represented on TIMSS.The objective of PISA, in contrast, is

not to assess achievement “in relation to the teaching and learning of a body of knowledge.”As noted above, that same objective motivates attaching the term “literacy” to otherwise universally recognized school subjects. Jan de Lange, the head of the mathematics expert group for PISA, explains, “Mathematics curricula have focused on school-based knowledge whereas mathematical literacy involves mathematics as it is used in the real world.” PISA’s Schleicher often draws a distinction between achievement tests (presumably including TIMSS) that “look back at what students were expected to have learned” and PISA, which “looks ahead to how well they can extrapolate from what they have learned and apply their knowledge and skills in novel settings.”

The emphasis on learner-centered, collaborative instruction and a future oriented, relevant curriculum that focuses on creativity and problem solving has made PISA. Several education researchers from Finland have attributed their nation’s strong showing to the compatibility of recent reforms with the content of PISA.theinternational test for reformers promoting constructivist learning and 21st-century skills. Finland implemented reforms in the 1990s and early 2000s that embraced the tenets of these movements

In other words, Finland does well on the PISA test because PISA reflects Finland’s educational goals (interestingly, **many Finnish mathematics university professors think those goals leave Finnish students woeful underprepared for college math, but that’s a whole separate discussion**).

Over 300 Finnish college mathematics professors signed a statement decrying the adoption of a ‘constructivist’ mathematics curriculum. I have no idea what percentage of Finnish mathematicians that is, but Finland’s population is smaller than Massachusetts’, so it’s probably most of them.

Of course, the other thing to remember is that U.S. students, once we account for poverty, seem to do extremely well on the PISA exam, which tests precisely the sort of applied math approach the authors call for. Call me conservative, but I’m not sure this is the most pressing educational issue right now.

To say in one sentence that we shouldn’t teach algebra’s “abstract ‘x'” because it loses kids, and then say we should teach how computers are programmed? Supreme ignorance. Computer programming is *nothing but* “solve for X”, and always has been.

As for e=mc^2, you could teach the young layman everything they could understand about it in 5 minutes (Niel deGrasse Tyson did exactly that in his PBS show). Doesn’t mean they’ll understand what it *means*, only that they can repeat a string of letters and numbers just as if they were still watching Sesame Street.

Most adults have forgotten the context of their algebra classes by the time they start complaining about them. High School Math classes are *full* of (semi-)practical real-world problems, they very problems that became the reason why we had to invent/discover the maths in the first place. Thing is, after working with the variables and formulas for so long, and then NOT working with them for even longer, we’ve (as adults) have forgotten the context that was included in the class, so we recall the formula and go “why the hell did I have to learn that” and think everything needs to be thrown away.

Now, that doesn’t mean that I think that for those not going to university that they should still be on a calculus-track curriculum. In fact, many of the things he talks about used to be included in “home economics” classes back in the day, only those classes disappeared as more and more schools over-focused on meeting university-targeted graduation requirements.

*Either* solution alone (all home-ec, or all calculus-track) is wrong. Different types of kids have different needs, and it would be better for all if we found away to address that…but of course, the only way to address that is to throw “standards” out the window and stop treating kids like factory products and national symbols.

i wouldn’t say that. i suppose a Turing machine (or lambda calculus, for that matter) might be entirely reduced to nothing but “solve for X”, but that doesn’t make them

easier.lambda calculus can also be reduced to INTERCAL — or brainf*ck — but those aren’t improvements, either. computer programming is more an exercise in writing out

obnoxiouslyspecific descriptions of a problem or its stepwise solution process, or both. it uses a mode of thinking that’s probably common to both it and mathemathics (and symbolic logic), but trying to do it by means of simple algebra isn’t likely the most useful approach.