I don’t blog all that often, and my subjects are usually very specific, so it was oddly coincidental when two of my favorite targets, Scabs for America, er, “Teach for America,” AND a misguided online content provider known as Conceptual Math, (which seems to be some kind of unwieldy appendage to a midtown advertising agency, judging by the rampant use of hyperbole in describing its materials) have now joined forces to  bring you, well, why not let the press release explain it all:

UST THE TWO OF US:Teach for America (TFA) recently announced a new partnership with online math curriculum provider Conceptua Math to create a Common Core math curriculum for incoming TFA teachers.

The partnership will manifest in two movements. For the 2013-2014 school year, 90 TFA teachers (representing grades 3 through 8) and staff members will pilot Conceptua’s all-digital Common Core math curriculum. Following, new TFA recruits attending the 2014 Chicago summer institute (where incoming corps members receive teacher training for approximately 5 weeks) will receive access to Conceptua math curriculum if they are teaching grade 3-5 math classes in their permanent school placement. They will also receive access to the curriculum for the entirety of their two-year teaching commitment with TFA.

Scott Painter, TFA’s Managing Director of Math and Science Design, describes the switch to Common Core as “a fundamental shift in what’s being taught;” he believes that Conceptua is not just a good resource for developing content knowledge, but also helps teachers develop pedagogical knowledge.

So what’s in it for Conceptua Math? Over 300 Teach for America corps members will use their curriculum product this coming summer. And if the pilot proves successful, Conceptua Math could be looking at a much longer and more lucrative partnership with TFA.

Good Lord!

I think the last 4 words of the last sentence say it all: Conceptua Math gets novice teachers who are programmed to use their extremely mediocre (but no doubt expensive) materials, and in return TFA gets to tell the public that their teachers do get training in their subject areas, even though there is a less than even chance that a TFA recruit will actually be placed in either the subject area or grade level for which he or she was drilled during the 5 week long “boot camp” indoctrination. The implications are scary, to say the least: hundreds of impressionable soon-to-be “teachers” will be brainwashed to believe they can pop open a can of Conceptua Math and immediately set their charges on the course for full mathematics proficiency.

What more is there to say? Ashes to ashes, dust to dust, we all have to sell our souls sometime. That Conceptua Math was willing to do so while imperiling its “reputation’ speaks volumes about the desperate nature of educational industrial complex. That TFA would make such a blatant self-serving connection only shows how much propping up the organization requires to forge ahead in its discredited mission.

Education Reform has been around as long as there has been education, but today’s brand of “reformers” are a heck of a lot different than John Dewey, Carolyn Pratt, Maria Montessori or Herbert Kohl. No, today’s “reformer” is a loudmouth, self-promoting, mendacious media star who has little to no knowledge of what goes on in a child’s mind, and probably even less about what a quality education looks like. These “deformers” run scab organizations like Teach for America or are shills for big businesses and homophobic lawmakers, giving themselves oxymoronic names like “Students First.”

Still, these de-formers could have their use, if they would only wake up and smell the coffee. Herewith is my compendium of when I would be “in” with these folks, and when I’d be “out” with them. In this post, I’ll start with my favorite organization, Teach for America.

I’m “in” if TFA recruited everyone who was interested in teaching, not just those from elite (read “high priced”) colleges and universities, as we know that most of the the students in these institutions are there because they had the money to pay for it. 

I’m “out” when TFA claims that only teachers from elite universities should be placed in needy schools. As David Kirp pointed out in “Improbable Scholars,” teachers who studied at less prestigious colleges can be turned into shining examples of their profession with ongoing support and encouragement, much like those from only the elite (read “high priced”) institutions.

I’m “in” when TFA recruits “non-traditional” graduates to enter the classroom, including people of color, immigrants and students whose first language may not be English, and places them in communities similar to the one in which they grew up. Such recruits would have a vested interest in staying in these schools for the long term, not the 2 – 3 year stints that are typical of TFA’ers.

I’m “out” when TFA places teachers in communities in which the recruits have no connections or understanding of the culture, and have to spend most of their time and energy decoding the mores as they struggle with children and families to whom they are unable to relate.

I’m “in” when TFA helps to support all teachers, not just the ones they train in their abbreviated “boot camps.” These recruits should be paired up with experienced, enthusiastic teachers from whom they can learn and grow, and the mentoring teachers should be acknowledged for having the skills and expertise to help these novices as they start their careers in this underserved profession.

I’m “out” when TFA recruits are brought in as “scabs” to replace experienced and trained teachers who have the audacity to be working in a school that has been labeled as “failing” by some arbitrary set of standards.

I’m “in” when TFA gives financial help to recruits in getting their licenses and degrees. We know that many potential teachers shy away from the profession because of the poor salaries; helping them stay out of debt when they earn their degrees will certainly help ensure their longevity and commitment.

I’m “out” when public money is used to help recruits get their degrees, who then leave the profession after a few years, sticking the taxpayer with the tab and nothing to show for it.

I’m “in” when TFA uses actual research to advocate for policies that have been shown to be effective in schools, including teacher coaching, collaborative teaching and diverse forms of assessments.

I’m “out” when TFA accepts the discredited policies of high stakes testing, teacher pay for performance and opening for-profit charters in place of low-achieving underserved schools.

I’m “in” when TFA advocates for the actual profession of classroom teaching, and supports their recruits in making it a lifelong career.

I’m “out” when TFA counts among its “successes” ex-teachers who start a business or organization that ultimately demeans the profession of teaching. In fact, the most helpful thing that Wendy Kopp could do to restore any legitimacy to TFA is publicly disavow any connection to, or support for, Michele Rhee.

That’s my “in” and “out” list. What have you to add to that?

Several years ago, I almost got into a fistfight with a friend while attending a speech by Malcolm Gladwell at the NCTM annual conference in Salt Lake City. What began this near melee was Gladwell’s assertion that Pablo Picasso’s innovations somehow “peaked” in his youth, while Cezanne was the example of someone who gradually refined his work until it achieved the excellence it was remembered for. I took exception to this assertion, mostly because the description of Picasso’s career is completely untrue: Picasso’s work was innovational through the many decades that he worked, and he continued to innovate up to the end of his life. The narrative Gladwell had created was based on the auction value of each artist’s works: apparently, early Picassos were more value than later ones, therefore his work early in his career was more innovative.

Unfortunately, this correlation that Gladwell created was a complete crock: the value of an artist’s work is based on a lot of complex variables, including the availability of the pieces from that period (I wouldn’t be surprised to find that PIcasso’s early work is scarcer than his later work), the buyers’ tastes (believe it or not, different styles of art go in and out of fashion like everything else, affecting their auction prices) and, last on the list, whether it was an example of the artist “at his best.” Clearly, Gladwell was out of his depth when it came to valuing artwork. If the facts don’t fit your story, don’t change the story; alter the facts.

Of course, this kind of irresponsibility is rampant among journalists of all stripes; our latest example is by Annie Murphy Paul, who has written yet another book on learning called “Brilliance: The Science of Smart.” I’m not going to criticize something I have not (and will not) read, but I did see Paul’s (or is it Murphy Paul?) latest column on the Time website to know that when something looks and smells like BS, it most likely is. Let’s read one of her choice quotes:

“Indeed, many experts who have observed the wide gap between the math scores of American and Chinese students on international tests attribute the Asian students’ advantage to their  school’s relentless focus on memorizing math facts. Failure to do so can effectively close off the higher realms of mathematics: A study published in the journal Math Cognition found that most errors made by students working on complex math problems were due to a lack of automaticity in basic math facts.”

Where to begin? How about with the relentless use of the word “many,” which is used “many” times. “Many experts” are cited in the opening sentence – well, how many is it? Who are these “experts?” Did these “experts” really lay all the blame on the differences between Chinese and American students’ achievement in mathematics on math facts? And why is there no link to the article in Math Cognition, a journal which even I, a class A nerd of all nerds, has never heard of? Perhaps because the study was from, wait for it, 1999? Maybe it was the fact that the students were not actually working on complex math problems at all, but multi-digit addition problems? Maybe because the study looked at 3rd through 6th grade, and made no mention of how their data compared to Chinese students? This is a clear cut case of cherry picking data to fit a narrative. How Time allowed Murphy Paul to publish this packet of prevaricated nonsense is a mystery to me.

Addendum: When I alerted Murphy-Paul to the dubiousness of her claims, she both blocked me on her Twitter feed as well as blocked my emails. Well, I guess that puts her into a major Egyptian river (a.k.a. “da nile”).

There seems to be no shortage of “expert” advice when it comes to the “flipped classroom,” (which you can read about here, here and here) and as I read the enduring hoopola about classrooms that are adopting this style of learning, it gets me to dreaming: in what kind of alternate universe would this work? If you consider that one of the most visible proponents of  this ideology is the one and only Sal Khan, who makes his home in an upscale locale called Mountain View, California, then you’ll quickly figure out who stands to benefit the most from this type of “instruction.” Many of us, however, are not fortunate to live in a community where the median family income is over $100,000. (which makes it double the median family income in the United States, by the way) putting Khan in an entirely different universe from the one in which many of us live. Many teachers working in urban school districts are attempting to make things work in communities where resources are less generously distributed, which is better known as “THE REAL WORLD.” This world bears little relation to the ones modeled in the “flipped classroom.” So let’s pause for a moment and consider the world of those who advocate the “flipped classroom,” and compare/contrast it with THE REAL WORLD.

In the fantasy world of the flipped classroom, the student attends a school where s/he can drop into the school’s computer lab anytime s/he likes, so that s/he can watch the video lecture whenever s/he likes, either before school, after school or even in the 10 minute break before the class is scheduled to start. If s/he is involved in an afterschool athletics, arts or academic program, s/he will usually head  to a comfortable homes where, with some gentle prodding, s/he will fire up the latest model computer with a high speed internet connection and settle down in a quiet and private space to watch the 15 minute video on adding and subtracting fractions.

The student in this alternate universe pays rapt attention to the lecture, takes copious notes, and replays the parts which are difficult, unclear, or inaccurate (all of which are very likely.) The student arrives at the classroom where the teacher, who has ample supplies, plenty of  professional support, and a beautiful, sun drenched classroom, will engage the students in an engaging, properly differentiated problem solving activity based on the video that all the students viewed and eagerly digested before they came to class. Sounds pretty ideal, right?

In “THE REAL WORLD,” there is a computer lab, but it is not available during the day because the school is overcrowded and it gets used every period of the day. The student goes to an afterschool program which is in a crowded cafeteria that has no internet available, which is not a problem, because nobody has a laptop or tablet anyway. If somone did, it would be so old that it could not play the videos, or the internet speed would be so slow that it could not show the video all the way through. Perhaps the student attempts to view the video on a smartphone, but the screen is so small and the sound so bad that s/he can’t make out what is going on. There is a teacher available to help the student with his/her homework, but since that homework involves watching and taking notes on a video that can’t be viewed, the teacher is of no help.

In THE REAL WORLD, the child comes home to a small apartment where there is a single computer shared by the entire family. After waiting for his/her turn (because his/her siblings are also in “flipped classrooms,”), the student sits down to watch the video, but there are many other competing distractions once the computer is turned on: s/he checks his/her Facebook page, then uploads a  few Instagram photos, reads the last 50 tweets from a favorite celebrity, and don’t forget the 100,000,000 videos that are available on YouTube, 999,999,999 of which are far more entertaining than the one on fractions.

In THE REAL WORLD the student rushes through the video, but barely makes out what is going on because there is music blasting from the other side of the room. S/he watches it once, and then returns his/her attention to more important things, like playing video games. All this is moot if the student is not fully English proficient, because although the video may be viewable in Spanish, it is in an incomprehensible dialect the student can’t understand.

In THE REAL WORLD the student rushes to school on a train or bus, where all memories of last night’s video fades into the background. His/her teacher asks how many students watched the video the previous evening, and 8 kids out of the 35  have seen it; of those 8, perhaps 2 can recall in detail what it was about.

In THE REAL WORLD, the teacher, who is most likely not trained to teach mathematics, struggles to replicate the lesson on the video, since 90% of the class is unprepared, but the kids who watched it at home are bored, and the kids who didn’t watch it are also bored, because lectures, especially those about fractions are, well, boring!

In THE REAL WORLD, the teacher realizes that the notion of “flipping the classroom” is only doable in some alternate universe that one sees in textbooks and on half-hour sitcoms; the only point of intersection between THE REAL WORLD and that of the “flipped classroom” is that it involves children and learning, but little else. After 10 years of classroom experience, the teacher knows full well that s/he has absolutely no control over what takes place beyond the 40 minutes the student spends in the class each day.

When I ponder the notion of “Flipping the Classroom,” it reeks of so many other “inovations” which on the face of it, appear to be logical and seamless. The reality is that, like many other initiatives of this type, it can only succeed in some kind of strangely homogenous universe which bears little relation to reality, a universe which appears to be primarily suburban and most definitely middle to upper class. To be honest, anything done with these student populations to improve the quality of  learning would increase their test scores, because the variables are so easy to control.

In THE REAL WORLD, things are very different, and it’s not because the kids who inhabit THE REAL WORLD are any less capable. Those of us who have worked in this world know and understand that solving the challenges these students face will require a lot more innovation than assigning a YouTube video for homework. If the experts really thought they were changing the nature of education, they would start by figuring out how to make a “flipped classroom” work for those students who spend their time living in THE REAL WORLD. Until that time, it’s just something that happens ELSEWHERE.

Note: I am revisiting this post after viewing this completely sad video of students sitting in front of computers day after day, year after year, at something called the “Cornerstone Charter School” in Detroit. What kind of fond memories of learning will they take away? Will they have a single “aha” moment during their years sitting in front of a screen? Will they develop any “soft skills” like compassion, empathy, indignation or imagination? Or is this preparing them for the day when they themselves will occupy their own cubicles and screens, working 8 hour days with nothing to show for it beyond a minimum wage?

Watch the video and consider my thoughts.

I love visiting classrooms as part of my work as a teacher coach and curriculum designer, and one of the great perks is sitting down with students and asking questions while they are working on an assignment. Today was one such day: I was observing a 5th grade class where the teacher was concluding a unit on statistics, and the students were busy making corrections on a quiz they had taken the previous day.

I placed myself next to Julian, a young man whom I had watched for the previous 2 years while he was in the 3rd and 4th grade. Julian tended towards distraction, and on many occasion when I saw him drifting off into free flight, I would tap him on the shoulder as I strolled by, turn towards him and use the Robert DeNiro “I’ve got my eyes on you” signal from “Meet the Parents.” Julian smiled each time I used this little trope, and it became part of our bond.

I looked over Julian’s quiz, made some suggestions for corrections, and then asked him a few questions about the meaning of mean, median, range and mode. My questions moved into the hypothetical “meta” realm, where I asked things like “what if I only knew the median for this data; what would I know? What wouldn’t I know? We chatted for about 15 minutes, during which time I developed a new lesson idea: suppose you had the statistical information about 5 people, including the mean, mode, range and median. What kind of data could you assign to each person to get this set of statistics? Could someone create a completely different set of data which would yield the same set of statistics?

As I stumbled out of school at the end of the day, I was stopped by Julian’s mother. “I just wanted to thank you for the time you spent with Julian today,” she said, “he really appreciated the time you took to explain things to him.” I told her the truth, which was that I hadn’t “explained” much of anything, and that we were just having a little conversation. Nonetheless, she thanked me again.

All of which got me thinking: what makes “teaching” teaching? In between checking the homework, explaining the assignments, creating and grading the exams and all the other elements of teaching mathematics, what it all comes down to is those moments of intellectual intimacy, when two minds co-mingle and understanding emerges.

I don’t know if Singapore Math is any more “effective” than TERC or Chicago Math. I have my doubts that Khan Academy is going to have any staying power, and I am not yet convinced that technology will make kids any better at mathematics. What I do know is that the 5,000 years of history has shown that the most effective form of teaching takes place when someone taking an interest in a child, a conversation takes place, and eventually, understanding develops. It is the intellectual version of the “I and Thou” relationship about which Martin Buber has written. It is what we have all experienced at one time or another, and even though I am not a strong believer in the existence of a supreme being, when those moments take place, God is in the house.

As my loyal readers have probably caught on to by now, I am a die-hard skeptic of any curriculum that seeks to make math “fun and easy.” Actually, I have no problem with the fun part (although it is debatable what constitutes “fun” in mathematics, especially to a 13 year old), but anyone whose intention is to make math “easy” is beneath my contempt. By its very nature, mathematics is difficult and  frustrating, and anybody, ANYBODY who attempts to convince me otherwise is probably not actually doing or teaching mathematics.

Let’s look at just a few things that makes mathematics fundamentally annoying:

Ambiguity and Inconsistency: Those who are ignorant of mathematics claim that mathematics is inherently consistent and rule driven. These are the same people who claim to have an inability to fathom mathematics because they consider themselves “creative,” “people oriented” and “rule breakers.”  Mathematics is, however, by its very nature ambiguous, and it has a long history of creative minds that piled on idea after idea to construct this towering edifice of inconsistency and seemingly improbable ideas (really, there is a square root of -12? Are you kidding me?)  These ambiguities and inconsistencies surface over and over again in the field of mathematics, and anybody who isn’t willing to admit to and confront them is doomed to failure.

Lack of Precision: Yes, there is only a single correct answer to the problem 8 x 7 (according to a story by Robert Kaplan, it is not 53 or 57.) However, 8 x 7 is not mathematics, but its important  and superficial sibling known as “arithmetic.” A real mathematics problem asks us to consider whether there are more points between 0 and 1 or -? and +? on the number line (they’re actually the same, but that’s another matter.) Furthermore, much of the actual mathematics we use is probabilistic, whether it is involves predicting the value of my IRA when I retire to determining what the number of number of hours I’ll need to master the bassoon part on Ravel’s Bolero. Mathematics is not infuriating because it is so precise; rather, it offers up precision where none is available, and even when invoked, its precision can be startlingly imprecise.

Unclear and Inconsistent Methodology: Yes, there are standard algorithms for computing everything from the quotient of two multi-digit numbers (better known as “long division”) to calculating the sum of an infinite series. But this does not fall into the purview of actual mathematics; it is merely an advanced form of arithmetic. True mathematics involves interpreting or inventing procedures that apply not only to particular cases, but also varying those procedures so that they can be streamlined or made “elegant.” There is no “correct” way to perform “long division;” however, there are some ways that are more efficient, transparent and elegant.

Many years ago there was an outcry over a talking Barbie doll which, among her repertoire of mindless statements, rendered an opinion that “Algebra is hard!” Lost in the outcry over of a polystyrene doll uttering such a remark was the actual veracity of her statement. Algebra is hard, and so is much of real mathematics. Let’s just admit it and move on. Let’s remember, however, that just because something is hard, doesn’t mean it isn’t worth doing.

As many of you may (or may not) know, I have an exhibit on Governors Island in New York Harbor that will be on view until the end of September. For those of you not familiar with Governors Island, it was originally the home of the governor of NY when it was still a colony; in its 200+ year history it has been an army base, jail for Confederate soldiers and, from 1966 – 96, a Coast Guard base that housed approximately 3,500 soldiers and their families. Now under the ownership of the City of New York, it has become a multi-purpose space for arts and recreation.

In January, I applied to the Trust for Governors Island to obtain a space to install my exhibit, Mü-Math: The Mobile Unit to Promote Mathematical Thinking on Governors Island from Memorial Day to September 30th, when Governors Island will be closed to the public until the following spring. The exhibit is housed in a building that used to be apartment housing for soldiers with families: by New York City standards it is quite spacious, with two bedrooms, a large kitchen and living room.

The exhibit has about 10 different activities which are notable in that they are more like puzzles than the math you would find in a textbook, yet each is linked to powerful ideas about the nature of mathematical thinking. For example,the idea of algebra as pattern detection, interpolation and extrapolation is conveyed using a set of subway cars that show a number progression. Each week I try to add a new activity to spice things up; the latest idea, “Align the Avenues,” actually came from a visitor who presented me with a puzzle where the numbers 1 – 8 had to be put into a grid so that no two consecutive numbers would touch on the top, bottom, sides, or diagonals. I re-cast the numbers as “avenues” and turned the grid into the “Welcome to ______” road signs that greet drivers on our various highways and bridges, so that it now looks like this:

 Unfortunately, as I write this, I realize that the directions don’t specify the sides as well, but that can easily be corrected in the final version. Yes, I know the “solution” on the right is incorrect, but if you do decide to solve this on your own, please look at the solution carefully. There is real elegance to where certain numbers are placed, and it begins by thinking about which numbers have the fewest “neighbors” and how that should influence their placement. The solution also has an interesting train of logic that one must follow, because one “clue” leads to another, which leads to another, which finally solves the puzzle. As in any great puzzle, there are multiple solutions, but they all follow the same kind of internal logic.

Of course, if you’re hosting an exhibit on mathematics and problem solving which incorporates puzzles, you’re going to attract a certain number of “wise guys.” Here’s one that a character sprang on me (and a roomful of visitors) a few weeks back. He claimed to have invented it and uses it as a “test” to figure out whether one has the skills to be a leader. I flunked it with flying colors, so maybe my future is limited to being a self-described cognitive artist.

Why does it take a former political science professor to tell us what is patently obvious in the field of mathematics education? Andrew Hacker, a professor emeritus at Queens College and co-author of the “Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids — and What We Can Do About It,” tells us in a front page article in the Sunday New York Times that we should jettison our current high school math sequence in its entirety. In an article entitled “Is Algebra Necessary?” Hacker argues that forcing all students to march lockstep through the algebra – geometry – trigonometry tunnel is a waste of time and results in many students leaving school dispirited and disinterested. To me this is not a terribly daring position, and anybody who would disagree with Hacker’s proposition probably belongs to the faction that believes that “tradition” consists of subjecting our children to the same mind-numbing educational system that we and our elders suffered through because “it was good enough for us, so it must be good enough for them.” Judging from the negative responses, you might have thought that Hacker was demanding the downfall of the Occident, for the consensus seemed to be that we should fix things by getting better teachers (or better students, as I often quip.) I myself have taught algebra for many years, and even though I attempted to make a go of it, I can only agree with his assessment.

To begin at the beginning, let’s answer Hacker’s question, “Is Algebra Necessary?” with another question: “Is Cubism necessary? Are Shakespearean sonnets necessary? Is avant garde jazz necessary?” No, Virginia, none of these are necessary, and when it comes right down to it, neither is algebra. But that doesn’t mean any of them are irrelevant or unimportant.

But before I begin arguing the point, I think it is necessary to distinguish between “algebra” the noun, and “algebra” the verb. Algebra the noun consists of the symbols written down in textbooks, is riddled with lots of Xs and Ys (I once considered applying for the right to copyright the use of X and Y in algebra texts, in the hope I would get rich by receiving 1/100^th cent for every time either one appeared), and involves lots of “rules” that came down from some central authority, the most egregious of which is “FOIL.” This is the “algebra” that Hacker describes and that the majority of us who have attempted to learn and teach now decry.

If we understand “algebra” as a verb, then it could be very useful to most people. Algebra the verb, which I’ll refer to heretofore as “algebraic thinking,” represents a non-inconsequential step in human understanding. For what is algebraic thinking but the transition away from “case based” arithmetic, and into a generalized form which can be applied to any instance? Algebraic reasoning allows us to do such things as identify patterns and relationships (which can be compressed using symbols, but I’ll leave that to the textbook writers) that can be applied to a variety of situations.

For example, arithmetic tells me if I purchase 5 pounds of bananas for 60¢ per pound, I know the total price will come out to be $3.00. Algebraic thinking, on the other hand, tells me that if I multiply the number of items by the price per item, I will always get the total price, regardless of whether the items are bananas, magic beans or credit default swaps. The power of algebraic thinking is that I don’t have to go through the trouble of developing a new method each time I want to solve a certain type of problem: much like the venerable Swiss Army Knife, one tool, better known as an algebraic equation, can handle it all.

Algebraic thinking also gives me access to tools that can help understand the past, present and/or future through the use of patterns that can be recorded and generalized. For example, if I found myself afloat in a leaky rowboat and noticed that the water was rising at the rate of 2” every hour, it is safe to assume that after 8 hours, my boat will have taken on 16” of water, which could be especially disturbing if the boat is, in fact, only 12” deep. Algebraic thinking gives me the power to work out a variety of scenarios: if my boat has already taken on 10” of water, I might want to consider bailing very quickly, while if it was only at the 3” level, I would have a bit of time to play a few hands of solitaire before taking action.

Finally, having access to algebraic thinking puts me in better control of my life and can directly influence how I make daily decisions. As I write this, I am sitting on line with 300 other people to see “Shakespeare in the Park,” an annual ritual which involves queuing up at 8 am to wait until tickets are distributed some 5 hours later. By my last count, there are 300 people in line ahead of me, some, but not all of who will get 2 tickets apiece. The theatre holds about 1800 people and I just learned that 500 of those tickets are going to be distributed to residents of Brooklyn. Using algebraic thinking, I can put together a reasonable prediction that staying on line for the next 2 hours would be a reasonable course of action. (As it happened, I did end up getting a voucher which would entitle me to get two tickets shortly before the show begins; what time I should arrive to do this is yet another algebraic problem.)

So what are we to make of Hacker and his call to eliminate algebra the noun from the high school curriculum? Of course, some of Hacker’s assertions are debatable; when he cites that “most of the educators I’ve talked with cite algebra as the major academic reason” for students dropping out of high school, he is clearly confounding personal anecdote with actual data. On the other hand, as one of those teachers who has himself observed students suffer through factoring polynomials without an actual explanation of why this may be relevant to anything they might pursue later in life, I’ve come up with bupkis over and over again. To this I would wish a fond farewell to algebra the noun: nobody is likely to miss you.