Before I start offering my own perspective in that line, I want to state clearly and for the record: I did NOT read Baker's article in the same way that I read Andrew Hacker's article of a year ago in the New York Times.
I will state that, for the record, I agree with the vast bulk of what Baker says in his article, and that to do otherwise is to ignore the realities of what actually happens in real classrooms to real students.
Maybe it's that I'm a year older, maybe it's that I'm just not going to get riled up any more by someone claiming that math education is irreformable, and so therefore should be tossed out and replaced with...'a one-year "teaser course" in mathematics for ninth graders. A one-year course in all of the "big ideas in mathematics". Hm. Sounds familiar. (Believe me, I don't think Baker knows me from Adam, and he certainly didn't read my EduCon 2.5 proposal, but still...something in the aether, apparently.) And Baker writes with much more sympathy and understanding of the struggles of a typical mathematics student than Hacker did, in my opinion. He also did a much better job of bringing in big guns to support his position (e.g., Underwood Dudley, Steven Strogatz, Paul Burke, Michael Wiener). He also, and most importantly in my mind, reminded everyone of the history of math education in the 20th century, and how right up to Sputnik only a small cadre of students took advanced mathematics of any type, not just algebra 2.
Baker's complaint about math education (NOT MATH!), as I read the article, is that it lacks a fundamental narrative. That is, we expose our students to "hairy, square-rooted, polynomialed horseradish clumps of mute symbology that irritate them, that stop them in their tracks, that they can't understand." We do this for a variety of reasons: it's on the test, it's the next unit in the (Common Core) curriculum, it's what they need to take the next course, etc. We spend no time at all on the great story, which is of math itself and the power we humans have gained by its use. As a result, we produce large numbers of students who (mostly) think of math as that disconnected, irrelevant, annoying, frustrating subject. If you believe Baker's numbers from the Amplicate survey, 86% of respondents HATED algebra. Which is a smaller percentage than the number of respondents who HATED geometry. This is success? If you are going to complain about Baker's article, then I think you need to start there. It does no good to criticize Baker's rational functions example by drawing from other references defining rational functions, and then complaining that Baker's example is merely one of not finding a student-friendly definition. It's the CONCEPT that is the problem for students, not the wording.
Baker's take on the "robotic gecko" Algebra 2 book is priceless, and precise:
It's a highly efficient engine for the creation of math rage: a dead scrap heap of repellent terminology, a collection of spiky, decontextualized, multistep mathematical black-box techniques that you must practice over and over and get by heart in order to be ready to do something interesting later on, when the time comes. (p. 33)(By the way, this also offers something different from Hacker's complaints, and perhaps also why Baker's article made more sense to me than Hacker's. Hacker's article: math is too hard for kids, so we shouldn't teach it. Baker's article: math-as-taught lacks a compelling story, so we need to think about how to teach math so that its story can be told.)
From my colleagues, many of whom are feverishly working on new and better ways to teach rational functions, I can already hear the complaints: "Not in my classroom! In my classroom students learn to THINK!" "We do projects where students demonstrate their understanding (sic) of the material!" "I have a really good way to teach topic X, and my students Really Get It!" Is that so? Are you sure? Are your students so different from Amplicate's anonymous respondents? English has a narrative. History has a narrative. Learning a foreign language is a tangible goal, if no narrative. What is the story of mathematics? Do you talk about it? Do your students see the grand sweep? Or is it logarithms last week, and trig identities tomorrow?
So I'm on board with Baker's points, and his general plea for something different in math. And I'm feeling pretty good because for a magazine like Harper's to publish something like this is, honestly, nice to see.
But there's this little nagging voice in my head. Which says: what happens to those kids next? They've taken that "first year"/9th grade course; what now?
And then I read Jose Vilson's and Michael Doyle's posts on Baker's article, and they poke huge holes in my good feelings (deservedly so) and make that little nagging voice a loud screaming. Vilson puts it bluntly, and Doyle quotes it in big letters:
If someone said, “Let’s end compulsory higher-order math tomorrow,” and the fallout happens across racial, gender, class lines, then I could be convinced that this was a step towards reform.And that's really the heart of all of this, isn't it? We can't do what we need to do with mathematics education, which is reformulate it to make the required-for-everyone-part meaningful, and leave the higher-order stuff for those for whom, as Baker says, "Fourier analysis is a joy and a marvel, a way of hearing celestial music". We can't do it because, as Doyle puts it so well:
Algebra II has become a badge, one of many, that pretends to separate middle class white boys from, well, everybody else.Now, as a teacher in a suburban district, I feel this argument. In my bones I know this is right. In my bones, and as I've experienced, I know that students in the upper/upper-middle socioeconomic classes go to Kumon and Sylvan and Huntington Learning centers. They get all of that individual, expensive (I know because I've done it) tutoring. They meet with some kind soul once, twice, or more every week to go over homework, to prepare for tests, to have that someone explain - patiently, over and over and over again if needed - how one does X. How one factors quadratics, simplifies rational expressions, or whatever.
You can pass A2 without understanding a whole lot about mathematics, or even numbers, but the vast majority of careers that "require" A2 do not actually require that you actually use it--they just require that you have some kind of certificate saying you passed a course labeled Algebra II.
If your family has the cash, your family gets you the tutoring you "need". If not, good luck. Anyone wonder why the number of students from less privileged backgrounds drops as the math level goes up? I don't.
And let's not forget that college entrance requirements generally won't allow students to NOT take algebra 2 in all of its spiky decontextualized-ness. Or to not take the SATs/ACTs, which are (of course) exemplary assessments of critical thinking and creativity (with bubble-forms).
So here's what I predict would occur from an implementation of Baker's proposal. Almost every kid takes his 9th grade class. Gets a great overview of mathematics. Some, who are intrinsically interested in the subject, go on to the "college track" sequence, starting (perhaps) from a reformulated "algebra 2/precalculus"-type class, then calculus. Some, who have found other interests in mathematics this way, take a different path; perhaps through statistics, probability, or discrete math. And some have taken all of the math they're going to take. Great!
In an ideal world, kids would sort themselves in this way based on their interests.
Kids in track #1 ("calculus track"): These are the kids who love math, who love the challenge of it, and who see the abstractions of algebra and analysis as pursuits worthy of study.
Kids in track #2 ("statistics track"): These are the kids who recognize the importance and practicality of math, and who see utility for it in their futures.
Kids in track #3 ("one and done"): These are the kids who have had a good experience with math, who have seen the forest for the trees, but do not wish to go deeper as their interests lie elsewhere.
In the real world, though, college pressures, parental pressures, "Race to Nowhere"-type stuff, become issues. Here's my prediction for what would really happen:
Kids in track #1 ("calculus track"): Based on current college policies, this track would still have the leg up on college admissions. Parents of kids in upper socioeconomic strata would make sure (spend whatever $ necessary) that their kids were in this track and that they stayed there.
Kids in track #2 ("stats track"): may still get tutors for assistance. Not nearly as advantaged for college admission, but because they are taking meaningful mathematics all the way through high school, may be at less of a disadvantage.
Kids in track #3 ("one and done"): Any guesses about college for those kids?
Now of course, if this proposal REALLY were implemented, my other prediction is that the top-end (socioeconomically) kids who otherwise would have been in a public school will quickly bail for a traditional private school, offering "real math" and that all-important college advantage.
In either case, kids on track #3 - how do you ensure they have access to quality educational opportunities post-high school? And I'm not interested in hearing "Well, they only took 1 year of MATH, so they shouldn't." If you really believe that for a student to do well at "good university X" they have to pound their heads through at least precalculus, you'd be wrong. I will assert (without evidence) that student success in college is more about a student's work habits, overall knowledge base, and interpersonal and time management skills than whether or not they got a B in precalculus or an A- in algebra 2. Don't believe me? Ask yourself: how many math courses do students have to take to get a degree from a "prestigious" comprehensive university?
And now I feel rotten, because I'm back to the beginning. This is as far as I can think through it: Math education needs work, as Baker says. His proposed changes would alter student attitudes towards mathematics, which in my head is terribly important. But I believe he is naive to imagine that this reform would really change anything meaningful in terms of equity.
What I need to work on answering: where is the lever for change that I have control over? Where's the big red button I can push to help make things for EVERYONE better? Because I can't control issues of equity, which are ultimately preventing any meaningful changes from happening.
Actually, maybe I can. Maybe I can tend my own garden and do what I can do in my own school to make things more equitable. Hm.....