Algebra pays

Learning algebra is essential for low-income minority students who hope to go to college, writes Ryan Hall, who teaches eighth graders at Williamsburg Collegiate Charter School in Brooklyn.

 Algebra requires students to learn how to see patterns, how to generalize these patterns into rules, and most importantly how to make connections and solve problems.

If nothing else, mastering algebra is like doing push-ups, Hall writes. “Algebra makes your brain stronger.”

Math isn’t just for “math people,” Hall writes. All students can master algebra if they’re willing to “struggle and persevere.” His school devotes two hours a day to math. Teachers are coached on planning and executing lessons.

For every two-hour lesson plan I deliver, I spend many hours preparing that plan to ensure that it is flawless for my students. And we are driven by data. We assess regularly to know who is getting it and who is not, and then we intervene with supports for any students who need them.

But hey, these are kids. So we also play games like algebra Pictionary and algebra Taboo to help students learn vocabulary and practice communicating. We race to see who can factor the most polynomials in a minute. We have “Mathletes” practice at lunch and compete on Saturdays.

When his students said they should get paid for going to school, he devoted a class to calculating how much extra they’d earn as adults if they succeeded in class.

We basically found the additional income of having a college degree over the length of a normal career, and then divided that by the total hours they spend in classrooms from K through 12. They were amazed at how much they actually “earn” — and of course, they were even more invested after that.

Two hours day for math? It’s not surprising that 98 percent of his eighth-grade algebra students passed New York’s Regents exam.


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  1. Two hours a day on math, no wonder that 98% of the students under this instructor passed their regent’s exam.

    Math in general teaches critical thinking, problem solving, and analysis skills, which are needed no matter what future career a person might have.

    Of course, I’m in favor of improved math for students in Grades 1 through 5, which is where so many students fail to properly learn basics that they’ll do nothing but struggle in MS/HS math classes.

  2. Impossible! Everyone knows that only certain people are capable of learning math while the rest of the population is compelled to suffer through it.

    • I’m guessing with a name like “____ Collegiate Charter” and requiring 2 hours per day of math, this is a self-selected group of students. Those who can’t or won’t hack it presumably are less likely to apply in the first place, and less likely to stay if they do enroll.

      • Yes, many public schools are required to put their weakest kids into two hours of math–1 hour math, 1 hour intervention. It’s not unique to the charter, and it doesn’t lead to good math scores. It leads to exactly what you’d expect if you take kids who hate math and give them twice as much of it.

        Everyone knows that only certain people are capable of learning math while the rest of the population is compelled to suffer through it.

        If by “certain people” you mean people with a certain level of cognitive ability, yes. Or perhaps you think it’s silly to assume that kindergartners can’t learn calculus.

        • Cal, don’t be a goof. You know exactly what I’m saying. And if you don’t, well, I doubt you’d understand if I dumbed it down a bit.

          • Right, because having three credentials that I tested into makes me really, really dumb.

            I know exactly what you’re saying. You think that everyone is capable of advanced math. You’re wrong.

  3. Algebra is a current discussion topic on the Kitchen Table Math website (link @ left); specifically the prior necessity of mastering long division and fractions (incl decimals). Age~10 performance on the latter is a strong predictor of HS math success, which is logical because long division and fractions are the first abstractions students encounter and algebra (and its successors) are in the abstract world.

    I don’t think that all students, even all college-prep students, are ready for algebra in 8th, though; I’d prefer kids with significant weaknesses get extra help in the pre-algebra area in 8th and go on to algebra in 9th. Getting more ready for 8th (or 6-7th) is great, though. I’m with Bill on the need for serious improvement in k-5.

  4. What procedures do these people call “Algebra”? Once people can solve equations of the form “a = 7 3/10 – 2 3/4 => a = ___” (i.e., subtracting fractions, by age nine for most kids if a loving homeschooling mom has moved at a relaxed pace) they are ready for the materal people call “pre-Algebra” or ” Algebra I” (solving linear equations in one variable, solving and graphing linear inequalities in one variable, solving and graphing linear inequalities in one variable with absolute value, equation of the line in two-space).

    Two hours a day is an overdose, guaranteed to generate an allergic reaction. Give me one hour a day, four or five days a week for a 32 week school year, with 25 kids who can do this…

    a = 7 3/10 – 2 3/4 => a = ___

    and I will give you at least 20 kids who can do this…

    {p1(45, -120), p2(115, 48)} subset L1
    {p3(30, -24), p4(-30, -104)} subset L2


    m((p1,p2)) = ___ (slope is a function from intervals to reals)
    d(p1,p2) =___ (distance is a function from pairs of points to reals)
    u(p1,p2) = ___ (midpoint is a function from intervals to points)
    L1 = ___ (point-slope form)
    L1 = ___ (slope-intercept form)
    L 1 = ___ (intercept form)
    L1 = ___ (vector form)
    L1 intersect L2 = ___

    and at least five who can do this…

    L1 = ___ (determinant form)

    No sweat, no tears. School is a huge waste of time. Most kids learn to add and subtract fractions by fourth grade, and we march them in circles (“Consumer Math”) for four years until the stragglers catch up.

  5. Cardinal Fang says:

    Williamsburg Collegiate is a grade 5 – grade 12 charter school whose students are virtually all poor and either black or Latino. Admission is by lottery, local students preferred. Parents have to agree to monitor their child’s homework and do some volunteering at the school.

    While the Williamsburg parents are required to be much more involved in their kid’s school than other local parents, I doubt that even a majority of the entering fifth graders can subtract fractions.

  6. Malcolm,

    When I go to the deli counter and the clerk cannot determine what 3/4ths of a pound of corned beef is (due to the fact the scale is digital), I’d have to say that person received some pretty lousy instruction in math (based on observation).

    So many persons are ‘math phobic’ in our society today it’s not even funny, and if we’d start at a younger age with students mastering the basics of (add, subtract, multiply, divide, fractions, and percents) via the old ‘drill and kill’ method (which is the way I learned it), I don’t think we would have so many persons under 25 unable to handle math I consider to be grade school in nature.

    Perhaps my standards are too high, but the six concepts above I learned LONG before I entered middle and high school.

    Anyone like to disagree here, please comment.

    btw, I’m not talking about students who have a defined disability related to learning, I’m just talking about the plain old student here.

    • Ah, yes, the “I’m just an ordinary guy and I can get this stuff” approach. You long to be told that you’re just so much smarter than everyone else, while secretly you know that you’re totally smart.

      Yes. You are special. The very fact that you engage on this blog means your IQ is probably over 115, and that means your own experience is completely useless. And yet over and over again, in each post thread, you talk about what YOU could do, just in the hopes that someone will tell you that you are smart. You’ve been told. Can you stop talking about yourself now?

      Your standards are too high. Kids with lower than average cognitive abilities can’t do what you did LONG before you entered middle and high school. Got it?

      • Stephanie says:

        As someone who helps many children who do struggle greatly with math, I have to disagree with your comment that, “Kids with lower than average cognitive abilities can’t do what you did LONG before you entered middle and high school.”

        Given practice, patience, and good instruction, almost ALL kids I work with can meet the expectations I have for everyone. The main difference is they may need more time and practice to do it than others. They usually did not memorize the basic facts which leads to problems later when they try to do long division or fractions. Even their parents will want to give up and move on, but my experience has taught me to be stubborn and stick it out. Never give up on a child.

        • I would never give up on a child. I just want to teach him at his level, not the level that politics mandate.

          • (Cal): “: I would never give up on a child. I just want to teach him at his level, not the level that politics mandate.
            Government subsidization and operation of school generated this mess. The State cannot subsidize education without a definition of “education”. Control by remote authorities implies standardization and the one-size-fits-all pace of US K-12 schooling that kills student motivation.

        • Does your experience suggest that better curriculum (traditional/Singapore vs. spiral types) and explicit instruction, starting in kindergarten, enables more kids to acquire solid arithmetic skills?

          To me, it’s a given that some kids need more time, more explanations and more practice than others – despite the current educational practice of dumping everyone into the same classes; thereby losing the bottom end and boring the top end.

          • The human and canine IQ curves overlap. Some influential factors (“causes”) such as genetics and the home environment do not lend themselves to policy manipulation. Student motivation matters critically to overall system performance. Policymakers can (maybe, if not bound by interest groups) shape the institutional structure so that it better accommodates variations in student interests and abilities. Policies that expand the educational options available to parents and that directly enhance student motivation (e.g., credit by exam, with early out, self-paced, self-selected curricula) will enhance overall system performance.

            Einstein was a smart guy. He did not have to travel at the speed of light to understand relativistic physics. He did not have to be normal to understand the effects of compulsion on normal humans. It’s not benign.

        • Stephanie,

          But, what expectations are the ones you have for ALL the students? Are they as high as you think they are? P.S. – You’re gorgeous! 🙂

          • If we lay down a clear track and let students move at their own pace, our “expectations” are only that they stay on the track, not that they reach some predetermined point by age X. Our expectations for ourselves are that we motivate them to stay on track. Nothing better indicates the priority that insiders place on the US K-12 school system as an employment program for dues-paying members of the NEA/AFT/AFSCME cartel than the measurement of education in units of time. “A year of Algebra” makes as much sense as “a pound of friendship”.

            Instead of “12 years of Language Arts” why not define the Language Arts curriculum as performance on standardized tests of reading vocabulary, reading comprehension, and essay exams (book reviews) on any __X__ books from a list of __Y__ titles, at or before age __Z__.

            Similarly, for Math, we could lay down a sequential track of skills and allow students to buy their freedom by attaining profiiency at some determined level. Even if you set the bar quite high (say, fractions by age 8, equations of conic sections by age 14, integration and differentiation of polynomial, exponential, and trigonometric equations, by age 18), you would find that performance would increase enormously over the current level. Students will work for freedom if we are honest about the task.

  7. Bill,
    Do you like music? I don’t play any instrument, can’t read musical notation, will clear a room if I try to sing, but I love to listen. I know three people who actively dislike classical music. They have in common parents who made them attend piano lessons early in life.
    Of course people are Math phobic. Two hours per day for 12 years of something you dislike?
    Albert Einstein
    “Force and Fear Have No Place in Education”

    To me the worst thing seems to be for a school principally to work with methods of fear, force and artificial authority. Such treatment destroys the sound sentiments, the sincerity and self-confidence of the pupil. It produces the submissive subject. . . It is comparatively simple to keep the school free from this worst of all evils. Give into the power of the teacher the fewest possible coercive measures, so that the only source of the pupil’s respect for the teacher is the human and intellectual qualities of the latter.

    Albert Einstein
    “Autobiographical Notes”
    __Albert Einstein: Philosopher-Scientist__, Paul Schilpp, ed.

    It is, in fact, nothing short of a miracle that the modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry; for this delicate little plant, aside from stimulation, stands mainly in need of freedom; without this it goes to wreck and ruin without fail. It is a very grave mistake to think that the enjoyment of seeing and searching can be promoted by means of coercion and a sense of duty. To the contrary, I believe it would be possible to rob even a healthy beast of prey of its voraciousness, if it were possible, with the aid of a whip, to force the beast to devour continuously, even when not hungry, especially if the food, handed out under such coercion, were to be selected accordingly.

    • Cranberry says:

      know three people who actively dislike classical music. They have in common parents who made them attend piano lessons early in life.

      And yet, I know many people who love classical music, in part because they can read music, and hear subtleties which escape the musically uneducated. They have in common parents who made them attend piano lessons early in life.

      Anecdotes are not data.

      Albert Einstein was born in Ulm, Germany, in 1879. He attended a Catholic elementary school, then a Classical Gymnasium, and then, after failing the entrance exam the first time he sat it, the Zurich Polytechnic.

      I think his scale of “coercion” is set at a vastly higher level than the average American citizen.

      I do wish people would stop citing Albert Einstein in debates over education. You can’t form policy for most people on the basis of the extreme outliers.

      • People who can read music and play an instrument get more out of music than I do, likely. That does not negate the point about compulsion prvoking an allergic reaction.
        Anecdotes are data. The world is a pile of anecdotes. Statistics summarize data.

  8. Dave Schutz says:

    This is one of the best mash notes for algebra which I’ve seen:

    • It seems to be the same story over and over here: If a student hasn’t learned the basics of arithmetic, algebra is going to be a terrible struggle. If only we had a way to teach the multiplication tables. You know, something similar to the way we teach athletic skills, where you drill over and over until it’s automatic.

      Nah… sounds boring.

  9. Malcolm, I can play piano (learned to do so in middle school where music was a required course)…I can sight read and play by ear, but in the immortal words of charles emerson winchester in a MASH episode:

    I have hands David, hands that can make a scalpel sing.

    More than anything in my life, I wanted to play, but I do not possess the gift.

    I can play the notes, but I cannot make the music.

    I can play songs, and be technically proficient at it, but do I possess the love of music for what it is…no…

    Now give me a computer, virtual environments, and some operating system and I can do a LOT of stuff :)…


    Your comments are spot on, and some students WILL need additional time and teaching, but when they understand and the light bulb goes on, they’ll think:

    gee, this is easy, why am I making it so hard.

    To put this in prospective, I just spent the better part of the last 3 days trying to solve a problem with building some computer programs…figured it out sitting at a McDonald’s online this morning about 20 minutes ago.

    I’d like to be able to get something working inside of 30 mins or less, but in this case, it wasn’t possible, until I understood WHY the stupid things wouldn’t install properly.