Andrew Hacker’s provocative weekend op-ed in the New York Times (“Is Algebra Necessary?”) wondered why schools insist on subjecting students to the “ordeal” of algebra. “There are many defenses of algebra and the virtue of learning it,” Hacker wrote. “But the more I examine them, the clearer it seems that they are largely or wholly wrong.” Making algebra mandatory, along with other more advanced math subjects leads to failure and dropping out, which “prevents us from discovering and developing young talent,” he argues.

“The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason. Shirley Bagwell, a longtime Tennessee teacher, warns that ‘to expect all students to master algebra will cause more students to drop out.’”

Well, sure. But expecting competence in any reasonably advanced subject–biology, physics, or English composition–will likely have the same effect. What Hacker is arguing might well be termed Barbie Syndrome: years ago, a talking Barbie doll uttered the infamous phrase, “Math class is tough!” Mattel pulled the doll off shelves, but Barbie might have received a sympathetic pat on the back from Hacker, who proposes a different math curriculum that mirrors the quantitative reasoning most of us will need on the job:

“Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call ‘citizen statistics.’ This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives. It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.”

“There’s a strong argument to be made that math is taught poorly in many schools, with little attention paid to how most people are likely to use numbers in the real world,” Dana Goldstein points out. But Goldstein correctly perceives that any argument about who should learn what is ultimately about tracking. “A great teacher can often spark interest in a subject a student thought she would never enjoy. One reason to have more rigorous academic standards is to leave open the possibility of that magic happening more often for more young people, and to make sure unfair streotypes about who is ‘academic’ don’t prevent kids from discovering unexpected passions,” she writes.

Dan Willingham points out that Hacker is simply wrong in several assumptions. “The inability to cope with math is not the main reason that students drop out of high school, he writes. “Yes, a low grade in math predicts dropping out, but no more so than a low grade in English. Furthermore, behavioral factors like motivation, self-regulation, social control as well as a feeling of connectedness and engagement at school are as important as GPA to dropout [rates]” he notes. Willingham also dismisses Hacker’s argument that too much of what students learn in math class doesn’t apply in the real world.

“The difficulty students have in applying math to everyday problems they encounter is not particular to math. Transfer is hard. New learning tends to cling to the examples used to explain the concept. That’s as true of literary forms, scientific method, and techniques of historical analysis as it is of mathematical formulas. The problem is that if you try to meet this challenge by teaching the specific skills that people need, you had better be confident that you’re going to cover

allthose skills. Because if you teach students the significance of the Consumer Price Index they are not going to know how to teach themselves the significance of projected inflation rates on their investment in CDs. Their practical knowledge will be specific to what you teach them, and won’t transfer.”

Willingham says Hacker’s op-ed also “overlooks the need for practice, even for the everyday math he wants students to know.”

“There are not many people who are satisfied with the mathematical competence of the average US student. We need to do better. Promising ideas include devoting more time to mathematics in early grades, more exposure to premathematical concepts in preschool, and perhaps specialized math instructors beginning in earlier grades.”

Hacker’s suggestions “sound like surrender,” Willingham concludes, and I agree. It’s hard not to detect a whiff of defeatism–a shrug, a wave, and the weary suggestion that, “Hey, not everyone can be good in math. It’s OK” in Hacker’s putatively sensible piece. But let’s try a more vigorous focus on math–*with computational mastery and conceptual understanding given co-equal status*–before we throw up our hands and suggest that Barbie drop algebra and switch to “citizen statistics” in 8^{th} grade.

**Update: **“I think it is dumbing down math — so far down that it will close the door on many careers,” writes Joanne Jacobs. “But it’s better to teach some math than stick unprepared, unmotivated students in dumbed-down classes labeled ‘algebra’ and ‘geometry.’”

**Update x+2: **Sherman Dorn weighs in.** **

It seems to me that the argument being made by Hacker is one we’ve seen many times before in modern education culture; namely the “Well, we can’t seem to figure out how to teach it effectively, so let’s not bother anymore.”

Comment by Glenn — July 30, 2012 @ 1:29 pm

Hacker sounds to me like he has bought into the idea that intelligence is based on innate characteristics and thus immutable so why try to get better. I think this is probably one of the most toxic beliefs in the American school system.

Comment by DC Parent — July 30, 2012 @ 3:49 pm

High school algebra isn’t difficult. Yet many students taking tests like the COMPACT test (see link to sample test below) score so poorly that they end up taking remedial math in college.

http://www.act.org/compass/sample/pdf/numerical.pdf

Nothing on this test is even vaguely challenging to someone who “gets” basic algebra. But apparently many students do not get it.

This suggests two things: (1) that the math curricula do not adequately prepare students for algebra, so that when they reach it, they throw up their hands; and (2) that students aren’t used to struggling even with moderate challenge, so they give up at the outset.

There’s much concern about pushing the kids past their comfort level, past their “zone of proximal development”–but real learning requires vigorous challenges. When it comes to math, you have to struggle with certain problems before they become second nature.

We have to give kids solid instruction and stop coddling them–the opposite of what Hacker suggests. The students, for their part, must get used to tackling difficult problems. Without that willingness, they’ll reject anything substantial as too hard.

This doesn’t mean that all students will do well in math. But for crying out loud, high school algebra and geometry should be within most students’ grasp.

Comment by Diana Senechal — July 30, 2012 @ 5:19 pm

A recent article from City Journal noted, “In math, the CCSS delay Algebra I from eighth until ninth grade and use an experimental method of teaching geometry that has not succeeded anywhere. There is no better authority on math than the National Mathematics Advisory Panel, which reviewed 16,000 research studies before issuing its final report in 2008. The NMAP found that algebra was the key to higher math study and that more students should get to Algebra I by eighth grade. In testimony submitted to the Texas state legislature, Stanford University professor emeritus of mathematics R. James Milgram, who conducted one of the Pioneer reviews, described “a number of extremely serious failings” in the national math standards, noting that they reflected “very low expectations.”

Yes, we should have all eighth graders take (and succeed) in Algebra I but they must first have a solid grounding in mathematics K-7. The lack of this elementary foundation in math is the reason Ken and Barbie drop/fail Algebra I, not because they’re “not good at math.”

So, Robert and Diana can tell you one strategy that would promote greater math success with K-7 students, and it’s the antithesis of whole group instruction, isn’t it, guys?

Comment by Paul Hoss — July 30, 2012 @ 9:46 pm

Paul,

No, this “strategy” isn’t the antithesis of whole-class instruction. It requires sustained, challenging lessons.

We’ve argued about this for a long time–but why would anyone seek to fragment the instruction instead of giving a sustained and focused lesson? High school and college courses do the latter, and with good reason; the topics require time and attention.

If you put the subject matter first, and form the pedagogy around it, you’ll agree, I think, that the more complex the topic, the more instructional attention it needs.

In any case, this is tangential to my earlier points: that students need a strong mathematics curriculum and need to learn to struggle with difficult problems.

Comment by Diana Senechal — July 30, 2012 @ 11:08 pm

I speculate Mr. Hacker does not shoot free throws, throw a 5 yard out pattern, or play a 12 bar blues line, either. Every one of these celebrated (and well compensated) skills require hours and hours of grueling, ‘boring’ practice, the very same a student must employ to succeed mathematics.

Comment by Peter Ford — July 30, 2012 @ 11:38 pm

I had the impression that Hacker was not arguing that algebra shouldn’t be taught, but that expecting scores attained by only 4 percent of female and 8 percent of male students was setting too high a barrier for entrance to college.

Comment by Harold — July 31, 2012 @ 12:56 am

Diana,

And different students experience different troubles at different points in a lesson or sequence in lessons.

Math is perhaps the most sequential discipline students experience in school. If a student doesn’t master the prerequisites and the teacher keeps progressing through the sequence, students will be lost. Conversely, if a student masters it immediately or already knows it before the teacher presents it (not an impossibility with some bright kids), that student will be bored. They all learn at their own pace yet too many teachers are unwilling to acknowledge this reality, perhaps because it would require more work on their part. Schools should exist for students, not teachers that are supposed to serve the students.

Comment by Paul Hoss — July 31, 2012 @ 5:34 am

Paul,

My point is that as the topics get more complex, they need more instructional time. This is not a selfish teacher-serving notion. If I had kids, I would want them in a class where the teacher could give sustained lessons instead of going from group to group. Of course, if the instruction is far beyond or behind the student’s level, that’s no good. But there are ways to prevent this from happening.

I know of a Core Knowledge (or partly CK) school in New Mexico where the students may take a math class for a different grade level. So, Rebecca may be in fifth grade, but she may take sixth-grade math, if she’s ready for it. This makes a lot of sense to me. My friend’s daughter attended the school and did just that.

Yes, even so, some students may accelerate and others may fall behind. But you can work with a range of levels when it’s reasonably narrow. Also, the kids can learn to seek out assistance when they need it–something they should learn to do anyway.

Tell a college professor to “differentiate” a calculus class to accommodate students who haven’t had trigonometry yet (and perhaps a few who never really learned their arithmetic). He or she will laugh. There’s such a thing as teaching a course. Not ready for it? Be prepared to work extra hard, or else take a different course.

Comment by Diana Senechal — July 31, 2012 @ 7:29 am

I agree with the NYT article. What is the point of learning Algebra or making kids read Dante’s Inferno? Our schools are full of either conservative, stale thinking that bores students to death or overly sympathetic thinking that sees building self-esteem and student-directed learning as the goals. Students are failed by educators with few fresh and intelligent ideas imho.

Comment by Jim — July 31, 2012 @ 11:40 am

Diana,

I am disappointed you have not read my book. I addressed a number of the issues you raised above. If you’d like, I’ll send you a copy. It is but, Common Sense.

Comment by Paul Hoss — July 31, 2012 @ 1:20 pm

I saw Hacker’s column as the race to the bottom mentality that if some concept or coursework is not equally accessible to all students, it needs to be disallowed. That anything else is to deny equal opportunity to credentials.

It reminded me of the Lumina Foundation’s work on a Diploma Qualifications Profile for higher ed as well as AACU’s inclusion project. Bringing that down into K-12, which the UDL mandates seem to do, is a prescription for hardly anyone to know anything unless it is coming from home.

The ultimate fostering of inequity.

Comment by StudentofHistory — July 31, 2012 @ 2:17 pm

While we’ve all gotten caught up in The Perfect PK-12 Curriculum discussion (as though, apparently, once such schools begin preparing STEM-proven graduates, the sci-tech sector will be pouncing on 18-year-olds for their entry-level positions), I’m afraid we may have forgotten what institutional competencies proven math achievers demonstrate. Take the content out of it altogether, and here’s what we have proof such kids can do:

1. Understand, recall, and employ (not to mention have an appreciation for the value of) smaller, more fundamental procedures automatically on the way to achieving solutions to complex problems.

2. See even the most time- and frustration-intensive problems through to completion. (And, when they can’t complete them, seeking experts for assistance, usually outside the ‘work day’, in-class time.)

3. Put aside their own interests and questions of ‘Why should I DO this?!’ or ‘What is this even FOR?!’ so they can work through numbers 1 and 2.

Though I can’t speak for everyone’s collegiate, professional, or spousal/parental/tax-payerly experiences, I know that mine all regularly expect me to do numbers 1, 2, and 3. And as a hiring manager I might actually be more concerned about a candidate’s dependability relative to 1, 2, and 3 than I their level of expertise, as I know I’ll likely have to do some re-training & -installation there anyway.

So yes, ‘totem’ (per Hacker) or not in light of how it’s actually used in practice, my belief is that level of proficiency in math indicates a number of institutional qualities that predict success at a number of tasks.

I often bring this up to educators when talking about math issues in their buildings, especially when they wonder why Algebra II gets so much importance as an academic benchmark, especially when, ‘Hey, I’m a successful, happy adult, and I’ve never used that stuff once!’ First, I remind them about NCES/Adelman’s study ‘Answers in the Toolbox’, which, based on a very well-done longitudinal look, showed how a student’s level of academic intensity is the single best predictor of college success (or not). That, I explain, likely set the bar. What it means, though, is not as simple as ‘content in-success out’. When they question that, I ask them to think of the kids they know at their school who are in Algebra II or higher. Once pictured, I ask, ‘Do you think they’ll someday graduate from college?’ [Answer almost invariably yes.] ‘Why? What is it about them that makes them college-ready?’ The list that then follows has nothing to do with that student’s math proficiency, as I’m sure everyone reading can imagine.

When we’ve responded as an enterprise, then, by figuring out how to increase math proficiency by making it more palatable or real-world-relatable for students, I fear we may actually have missed the point about all it tells us about a student’s appreciation for fundamentals, stick-to-it-iveness, or working on something that is (let’s face it) meaningless in a directly practical sense. And as these things are what make people ultimately hirable in the job market and durable college students who will make it through all the bumps to achieve 4-year degrees, there’s no way I believe we should back off of such requirements.

Now what we need to do is figure out how such a message can be made more attractive and getting students/teachers to buy in. For simply: widely differentiating math instruction/assessment, making math more real-world-relevant, or steering math instruction through tech-based games to build engagement are sure to continue falling flat, especially as one moves into more advanced levels.

And, by moving the lines around, we may never get a student’s math performance to tell us all the useful things it has in generations past.

Comment by Eric Kalenze — July 31, 2012 @ 2:55 pm

“Widely (differentiating) individualizing math instruction/assessment falling flat?” If it does, our schools will continue to fail, especially for our less privileged.

With the technology finally available to realize this type of pedagogy, there are no longer any acceptable excuses.

Comment by Paul Hoss — July 31, 2012 @ 7:00 pm

Hacker’s logic on college entrance was just bizarre. Clearly more than 4% of young women and 9% of young men go to college, so a 700 on SAT math isn’t needed to go to college (only to an “elite” college). And though that statistic would suggest that women would have a harder time getting into college than men because of math, women now outnumber men at most colleges, elite or otherwise.

He also shows a pretty shaky understanding of math if he thinks that you can effectively teach students about the consumer price index without algebra. If you don’t understand that “7 times something equals 14″ is really the same problem as “something equals 14 divided by 7″ any real world application of numbers is going to be a long hard slog.

Comment by Rachel — July 31, 2012 @ 11:04 pm

Paul,

What is your book, and where can we get it? (I googled you, but couldn’t find it.)

Comment by Anonymous — August 1, 2012 @ 8:56 am

The book is titled Common Sense: The Missing Link in Education Reform (written by a teacher) available on Amazon and Kindle.

Comment by Paul Hoss — August 1, 2012 @ 11:35 am

Mr. Kalenze, you captured what is my vision as a math teacher: students learn, grow and prosper THROUGH the knowledge, skills, and reasoning of mathematics.

Mathematics (coupled with science) provide students the unique opportunity to employ and sharpen steps “1,2 & 3.” That you persist until you get the ‘right’ answer becomes an ethic you can employ in every other aspect of your life, and mathematics gives you that opportunity better than any other field of study at the elementary/secondary level.

Comment by Peter Ford — August 1, 2012 @ 10:27 pm

Rachael: “Hacker’s logic on college entrance was just bizarre. Clearly more than 4% of young women and 9% of young men go to college, so a 700 on SAT math isn’t needed to go to college (only to an “elite” college).”

Come on Rachael, when Harvard and Rice set a standard, all the parents and high schools will try to meet it and will feel like failures if they don’t:

http://www.nytimes.com/2012/07/29/books/review/teach-your-children-well-by-madeline-levine.html?ref=review&pagewanted=all

Comment by Harold — August 3, 2012 @ 12:16 pm

As a teacher, to some degree I agree that algebra is not for everyone, even basic algebra…..But my wishful thinking mind keeps trying to convincing me that I need to try harder because of the supposed benefits that algebra can bring to an otherwise algebra-untrained brain…..Still debating

Comment by Emmie Nati — March 1, 2013 @ 9:51 pm