kitchen table math, the sequel: let's not and say we did

Monday, August 29, 2011

let's not and say we did

Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering.
How to Fix Our Math Education
By SOL GARFUNKEL and DAVID MUMFORD
Published: August 24, 2011
Robert Pondiscio responds.

For the most part, it appears, Joanne Jacobs' readers aren't impressed. I'm especially partial to this comment:
I’m currently teaching quantitative literacy at the community college level. The vast majority of students who take it need either this class or a basic stats class to fulfill a graduation requirement.

I have taught this class for several semesters over the past few years. My impression: Most students don’t really care for the class, despite its “relevancy.” It seems that not a few felt misled by their advisers, thinking that they were enrolling in an “easier” math class. They tend to wish that they had enrolled in the basic stats instead, because it is more straightforward as a math class.
That reminds me of the time C. said, back when he was age 10 or so: "They don't understand, Mom. When you make math more fun, it's more boring."

12 comments:

MagisterGreen said...

That reminds me of the time C. said, back when he was age 10 or so: "They don't understand, Mom. When you make math more fun, it's more boring."

That's because when teachers or curriculum "experts" describe something as "more fun," they tend to be describing how it appears to them. To the kids, it usually appears quite different.

geo targeted search engine optimization said...

i miss college.

SteveH said...

"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."

The Common Core Standards were developed based on a workplace analysis. Of course, the analysis boiled everything down to one size fits all in high school (pseudo-algebra II). Then again the analysis in this article amounts to:

"For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation?"

That, of course, is not the question. The question is what math is required for each career path? You may not agree with those requirements, but they are defined by each college department. The goal of high school is to provide curriculum paths to meet those requirements. What sort of finance or programming knowledge might be useful is a different discussion.

"Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering."

What could these things possibly be without algebra? It becomes non-math. Interesting, maybe, but not something that will open career doors.

"It is through real-life applications that mathematics emerged in the past, has flourished for centuries and connects to our culture now."

But that's not what they are proposing. They are proposing top-down courses that do not go down. They avoid math.

My opinion is that the goal should be a rigorous course in algebra for all students. After that, I think the choices should open up for courses in finance or engineering. However, students should understand exactly what math they need for any of the college degrees they might want. As with things like Project Lead The Way, most students serious about science, math, or engineering do not have time for these courses. Fancy high school courses in finance won't help nursing students pass their college trig requirement.

Amy P said...

"Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering."

For a vocational track, how about pairing the traditional math sequence with a separate series of overlapping applied courses, rather than cannibalizing the time available for the math?

Allison said...

Steve said this in a different way, but I'd like to highlight it.

A sequence of finance, data analysis and basic engineering without algebra, geometry, and calc can *only* be a rote memorization class, where you plug and chug into formulas.

You cannot understand let alone derive the algebra for compound interest without algebra. You cannot understand let alone derive Newton's laws without at least algebra 2, and should be learning it in terms of calculus. You can't understand the notion of a null hypothesis if you haven't been taught the abstractions of algebra and beyond.

Weren't we supposed to be teaching critical thinking skills? Are the "let's replace math with nonmath" people actually allied with the constructivists somehow? Why aren't the railing against this?

Allison said...

Why did they bring these up as examples? They are terrible examples.

"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."

This is the part that's most insane. There is no possibility of understanding how mortgages are "priced" with you don't know how to solve a quadratic equations. There is no possibility of understanding the statistical results of a medical trial without understanding the t-test, which requires understanding regression, pairwise independence, sample mean, and is built on top of law of large numbers, something like chebychev's theorem, least-squares, maximum likelihood, etc. all of which require algebra, geometry, and calculus, plus a good deal more probability theory and overall, a lot of abstraction.

The "understand how a computer is programmed" line isn't something I even can parse. If they mean at the level of electrons and doping, well, you need some complex numbers there. At the level of Integrated circuits, you need some complex numbers there. At the level of binary, you need some pretty abstract math, and probably have learned about groups in order to have learned about rings and fields and modulo arithmetic. At the level of languages, you need to understand operator theory and linear algebra well enough to understand state evolution.

Now, it may be that most people don't need to know any of these things either. But that kinda undermines the argument for the need of a less abstract math sequence, doesn't it?

Anonymous said...

Maybe going back to traditional math, without calculators, in ES would prepare more kids for abstract math. Demand solid math knowledge of ES-MS teachers, use teacher-centered instruction and a good curriculum (Singapore or Saxon). The recent/current programs certainly aren't working well.

momof4 said...

In ES-teacher lingo, making math more "fun" (probably touchy-feely and/or artsy-crafty) may well mean making it less mathy, since many teachers at that level really don't like math or know it well. BTW, my kids all attended high-performing schools (smart kids) in nice suburbs.

Catherine Johnson said...

A sequence of finance, data analysis and basic engineering without algebra, geometry, and calc can *only* be a rote memorization class, where you plug and chug into formulas.

Not even!

A year of "data" without algebra or calculus is going to be a year of counting stuff and drawing bar charts.

Catherine Johnson said...

There is no possibility of understanding how mortgages are "priced" with you don't know how to solve a quadratic equations.

Really?

Amy P said...

"A year of "data" without algebra or calculus is going to be a year of counting stuff and drawing bar charts."

Right. In the wrong hands (i.e. out in the real world) this is just going to be cover for dumbing down. A really rigorous personal finance course does have its place in the high school environment (and that would cover a lot of what he's talking about), but that should be in addition to traditional math.

I think there may be some confusion of artsy-craftsy and actual applied work. There are superficial similarities, but they are different. In the first case, you wind up with a poster or a kleenex box or a diorama and you use up a lot of markers, glitter glue, and poster board, whereas in the second case, you might wind up with something actually functional, that somebody might actually buy (nobody in the history of man has ever bought a school project kleenex box), something that ideally will last and be used a long time. For examples, see some of the better projects at Instructables.

Catherine Johnson said...

A really rigorous personal finance course does have its place in the high school environment (and that would cover a lot of what he's talking about), but that should be in addition to traditional math.


A really rigorous personal finance course would be a heck of a lot preferable to Project Lead the Way, that's for sure.