Deborah Meier Is Right About Math

Deborah Meier:

The public’s much-criticized lack of interest in advanced math may, in fact, betray their good sense, not their bad. Calculus-driven math may be foolish-driven math, that mis-prepares us, leaving us disarmed before the realities of our world. Perhaps a “statistics-driven” math would be equally tough and “advanced” but more suitable for a democratic citizenry?

I’m convinced the Algebra I > Geometry > Algebra II > Precalculus > Calculus train is useful only to the students who ride it all the way through Calculus, where all of Algebra II’s abstract gamesmanship finally pays offAnd pays off big.

Other math teachers feel free to drop some disagreement on me but Algebra II needs to earn its way as an elective and accede its place on state college prereq lists to Statistics, which, for anyone majoring outside the hard sciences, is more relevant, more useful, and often more fun.

[via the Teaching Excellence Network’s strong new blog]


  • Roger Schank takes fewer prisoners than I do over at The Pulse.
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Well said. Having taught AP Stats for years, I saw far more value in knowing and understanding statistics than in knowing how to find the area under the curve.

    Not that there isn’t a special place in my heart for related rates problems, but you don’t exactly have to find the speed at which water is draining from a funnel on a daily basis.

    You may, however, have to sort out what’s real when politicians or the sensational news media throw out a misleading infographic or “average” of something-or-other.

  2. Maybe the reason that Algebra II and the rest are on the “required” list is because they would like more folks doing hard science/sciences in college (which goes back to the desire for more engineers, etc. because we don’t have enough of those, blah, blah, blah).

    I remember when they started requiring we take some course with “advanced” math at CSU back in the 1980s (thank god my husband missed that, he never got past fractions in math, but aced the logic portion of the LSAT). Fortunately they offered classes in Social Sciences that could meet this requirement within palatable subject matter. I took classes in political science statistics, which led jobs in public opinion polling, bank finance. Really, you can go pretty far with just a basic knowledge of statistics, and a lot of common sense. I wanted to kick myself when I working in banking because I had relegated most of my basic Algebra knowledge to the trash heap pile in my brain, and FINALLY, the order of ops stuff was useful, etc. when doing Excel formulas.

    In my experience there are lots of different math skills that you can have and that are useful. Few of us possess all of them, but most of us have some facility with some of them. My dh can figure out things involving logic (especially if it’s language based) like nobody’s business. My son has a really beautiful number sense, but if it’s language based (a word problem) forget about it. I have a reasonable intuitive feel for statistics and what is meaningful. Would I be more employable if I was an engineer? Hmm, don’t know.

    Dan, I you talk about using the online community for teacher support, I have an idea, it would be very interesting for me as an elementary teacher to discuss what/how I’m teaching with high school math teachers like yourself. I have posted a couple pieces recently, and got some nice feedback from Jackie B. Could we think about expanding this (by pimping on your more largely read blog) this summer? Just a thought?

  3. Summer’s a time for reinvention. I’d enjoy taking this forum in some new directions for a season. I’d Skype you if I did that. Let’s chat, though.

  4. As an elementary teacher I always question my knowledge and ability to think about what makes the most sense in high school. (Interestingly, going the other way is the opposite. High school teachers need to be involved in helping us figure out what to teach to prepare kids for those years.)

    I love teaching math and am fascinated by the subject. However, I didn’t take any higher math after high school because I couldn’t stand it then. I think I would have enjoyed statistics much more and it would be a lot more useful to me as a person and as an elementary teacher.

  5. Due to state mandates, we’re adding a required fourth year of math, and we’ve been discussing what’s appropriate for those who passed Algebra II but don’t want to go on to Pre-Calculus. I’ve been trying to push for Statistics. Are there any journal articles that mention this (or could you write one?) It’d help for a credibility push.

    I wouldn’t take out Algebra II though — there’s a good chunk of basic things that (our students at least) don’t understand until then, and a couple essential concepts for a real statistics class (like say, logarithms) that don’t get hit until then.

  6. I think Geometry should be replaced by Stats as a graduation requirement, so that Algebra I and Stats would be required of all citizens – those are the courses needed for a minimally informed electorate. Algebra II and Geometry should be for college-bound students.

  7. I agree with you, though I have to say my HS experience with Calculus was mind-blowing in a way that even English (my first and only real love, the only subject that truly understands me) was only able to approximate. It is of course more democratically useful for people to be able to debunk stupid newspaper poll articles but there is something truly beautiful about Calculus that I wish I could convey to every single person on the planet. Which is more important: truth or beauty?


  8. “Algebra II” is an inappropriate use of coordinate geometry, that kids, if anything, memorize until they are done with whatever rite of testing passage your state inflicts on them. Trig, often inexplicably included in the same year, is an even more disjointed and unmotivated definition-driven exercise in symbol manipulation and rule memorization. Finally we get exponentials and logs thrown in there, which are not algebra, but I guess they have to go somewhere.

    I have to teach “Algebra 2 with Trig” next year and am dreading it. It’s going to take my angst about trying to cram quadratics and exponentials down throats to whole new realms of anxiety.

    Luckily I will have tenure next year and feel a little more free to be a little more subversive. Read: keep the instruction problem-based and don’t be afraid to leave a little of the more pointless shit out. In New York it’s not necessarily required for graduation, but is required for the test that gets you a “regents diploma with distinction”, that most college bound kids need. Do I think we should replace it with an option for a decent statistics course? Hells yeah. Or a personal finance course, or a math/science history course, or basically anything, because anything would be more useful to most kids.

  9. (Admitted bias – I teach AP Stats as well as Intro to Stat at the university level)…

    I fully agree that statistics ranks among the top of the “needed courses” at the HS level. Almost every major (outside of the hard sciences) requires at least 1 quantiative analysis course. I would love to see more of a push for statistics from my department rather than trying to push everyone into the pre-calc>calc track.

    However, I would strongly disagree with the removal of Geometry. In my opinion, outside of Stat, Geometry is the next most used math course – anytime you do home remodeling, you are figuring surface area, volume, angles, etc. I would hate to see the houses built by a population with little Geometry knowledge.

  10. There are times I feel we throw around the ‘A’ word and aren’t necessarily talking about the same thing. In primary school one thing kids don’t get is a set of formal mathematics notational rules (sometimes known as algebra).

    Next up the difficulty scale is a systematic way to solve a set of linear equations (sometimes known as algebra). In Singapore Math this is done with bar models as early as grade 3 (but they don’t call it the ‘A’ word).

    Somewhere you want to throw in a way to work with slope and the equation of a line (sometimes known as algebra).

    My point is that the early stages of algebra can be thought of as foundational for later algebra or they can be thought of as an endpoint that most people will need proficiency with. And oh by the way, this early stuff can be taught in a non algebraic manner if your prism is that this is an end point.

    How you teach this early stuff may well be radically different when you make this distinction. For example a carpenter works with slope all day long without ever thinking of it in the same way that an engineer does.

  11. Yo Nate, absolutely, man. Calculus just wrecked me in ways which strike me continuously even now, years after the fact. If I could guarantee every Algebra II student that experience I wouldn’t have written this post. The Algebra II > Precalculus > Calculus route has still gotta be pushed, but more towards kids who demonstrate an aptitude for Algebra and an interest in hard science.

  12. Calculus, as others have said, is beauty. Calculus + Physics was the most incredible and awesome experience of my schooling.

    I wish I’d had stats over Algebra II. I used nothing I learned in Algebra II in PreCalc or Calc, and all I can remember of that course now is passing notes on my TI-83. (Texting for an older generation?) So from a personal “I wish I knew this now” perspective, it makes total sense.

  13. Look to the WNCP (Western and Northern Canadian Protocol) in Math. I think that they are getting things in order!

  14. (Background: Chemistry teacher.)

    I never understood why it goes Algebra I > Geometry > Algebra II.

    I can see far more value of having Geometry on one set of tracks and Algebra I > Algebra II on the other.

    Most students who do well in an Algebra > Calculus mathematics chain, also do well in Chemistry as the two come from similar origins.

    Most students who do well in Geometry but did not do well in Algebra I, struggle in Chemistry because it is similar to Algebra I and not to Geometry.

    Of course, I’m probably at the only school that had the poor sense to make Algebra II a co-requisite for Chemistry, rather than a pre-requisite. So I get a lot of students who scraped by in Algebra I, did well in Geometry, and are now in Chemistry/Algebra II concurrently and are having a nervous breakdown because “scraping by” in Algebra I and Geometry did not prepare them for either Algebra II or Chemistry.

    However, the students that do well in Chemistry/Algebra II concurrently, would be poorly served if their experience was discounted.

    Perhaps an either/or on the college admissions thing? Either a stats track OR an Algebra track?

  15. Or, as a follow up on my previous post … why not:

    Geometry > Algebra I > Algebra II > (I forget what goes here) > Calculus ?

  16. Students have 4 years for high school. Chemistry will usually come Junior year (with physics or adv biology Senior). Algebra in 9th, Geometry in 10th, and that means Chemistry and Algebra II together in 11th grade. That’s probably true in more high schools in America than not. (the integrated option is used in many schools, however)

    Education Trust reports that students who are successful in Algebra II in high school are twice as likely to graduate from college compared to those who don’t. They attribute this not to the specific content of the course, but to the common rigor. The same wouldn’t be true of statistics coursework which could be quite different in two different classrooms in the same school.

    What’s more important is figuring out how to teach the sort of rigorous content to all students than sorting them into tracks. Wouldn’t most of us want our own kids in the “track” that is twice as likely to actually graduate from college?

    Deborah Meier is incredibly wise about education, but changing the one universal high school course sequence –Alg,Geo,AlgII– that correlates to college success (and much greater job opportunities) is going to need better arguments than “I didn’t get anything out of the class” or “The kids don’t have the aptitude”.

  17. Joel you state, “Education Trust reports that students who are successful in Algebra II in high school are twice as likely to graduate from college compared to those who don’t.” Remember correlation does not imply causation. There are many factors which contribute to a student being successful in Alg II.

    Also, there are some school who are teaching Physics first.

  18. Joel says:
    They attribute this not to the specific content of the course, but to the common rigor. The same wouldn’t be true of statistics coursework which could be quite different in two different classrooms in the same school.

    My response:
    That depends on the course. If the school teaches AP Statistics, the teacher is required to complete an Audit in order for the students to receive AP credit. While the AP course is mathematically easier (other than a bit of knowledge about logs), it requires logical thinking and clear communication skills. (Which BTW are very important skills in the real world yet lacking in many math classrooms)

    However, your comment also applies to any course in the school. I also teach Geometry and I know the rigor in my classroom differs from other teachers in my school, even though the content is the same.

  19. Jackie & Druin–thanks for the comments. I appreciate the reference to Physics First article. Interestingly, their research–looks like a high school physics teachers organization–noted that only about 3% of schools were teaching physics first with most following the common practice of biology then chemistry (with only about 30% of students taking physics–I’m not sure if that’s 30% of the 70% still attending high school as seniors or what).

    I understand the fallacies of simple correlation arguments; however, Algebra (to a lesser degree) and Algebra II with national studies seem to hold up as universally significant courses which are more independent of the school (or classroom) in which they are taken. Most teachers I’ve known–and I’ve been working in public schools since 1975–want their own children to attend and graduate from college. My own boys took math all the way through high school in part because I know it puts them in with the group that has twice the chance of graduating from college–for whatever reason.

    I believe the biggest single factor for a student being successful in Algebra II or any higher level math class is the teacher they have for that class, and to a lesser degree the teachers they have had since pre-algebra.

    AP is another attempt to insure rigor; however, many students don’t have an opportunity to take AP courses–and many of those that do don’t take AP credit. The challenge I see isn’t with the top 10-15% of students (commonly in AP), but rather with getting 60%, 70%, or 80% of the freshman class to successfully understand rigorous coursework such as is found in the vast majority of Algebra II courses in American high schools.

    I don’t know why Algebra II would be more consistent than other courses, but I might speculate that there is a fairly consistent use of common text books and content standards–math teachers agree on what consists of Alg II. I don’t think that’s true for statistics, English Literature, U S History, Composition, Economics, Music, Art, or even the sciences.

    Certainly it is difficult for a high school to justify why it is that Geometry in room 200 has different standards / rigor / learning results than Geometry in room 201. Here’s a role for common End-of-Course exams.

    I do by the way completely agree and value the worth of a quality statistics high school course –well taught with high standards and even higher support — would be for each and every student. These are key real world skills.