The Declining Quality of Mathematics Education in the US

Leland McInnes:

Mathematics education seems to be very subject to passing trends – surprisingly more so than many other subjects. The most notorious are, of course, the rise of New Math in the 60s and 70s, and the corresponding backlash against it in the late 70s and 80s. It turns out that mathematics education, at least in the US, is now subject to a new trend, and it doesn’t appear to be a good one.
To be fair the current driving trend in mathematics education is largely an extension of an existing trend in education generally. The idea is that we need to cater more to the students to better engage them in the material. There is a focus on making things fun, on discovery, on group work, and on making things “relevant to the student”. These are often noble goals, and it is something that, in the past, education schemes have often lacked. There is definitely such a thing as “too much of a good thing” with regard to these aims, and as far as I can tell that point was passed some time ago in the case of mathematics.

4 thoughts on “The Declining Quality of Mathematics Education in the US”

  1. Thank you for sharing this Steffen. In particular, the comments following the opinion piece were interesting. One of them referred to RME and a quick Google turned up this link .
    Apparently the Netherlands have been using RME for decades. Netherlands students typically outperform American students on TIMSS, although not at as high a level as Singapore, Japan, South Korea, and Hong Kong. Is there anyone with more extensive knowledge of RME who can confirm that it de-emphasizes traditional US algorithms and explain some of the key elements of the approach?

  2. Thanks Tim for pointing out the educationupdate reference.
    So, we now have to-be Ph.D. in Math saying back to basics with algorithms (and agreeing with the weather lady cited on SIS:
    Then we have a husband and wife math Ph.D. team singing praises of the Netherland’s version of discovery math (RME) in teaching their 8 year-old numeracy and discrediting the algorithmic approach.
    So, it does seem obvious — it always has to me — that the answer to which approach we should take is probably “both” under different set of factors, at different times in a child’s developmental life.
    It does seem to me that the answer to all questions of educational curriculum is to take the eclectic approach.
    Is there research to tease these factors out, or are we stuck with the typical research by advocates of one extreme or another?

  3. I’m the author of the article referenced here. I would just like to be clear that, ultmately, I’m in favour of an eclectic approach as well. I think discovery is a good way to teach math (though it suffers from the difficulty that, to work well, it requires a teacher with a deep understanding to guide the students in profitable directions). The problem is when it is done to the exclusion of proficiency in basic skills. For example, it is hard to explore algebra and algebraic manipulation unless arithmetic is second nature to you.
    Ultimately, however, my real objection is to what was mentioned later in the video – the overly applied aspect of teaching math. Again, I’m not suggesting a reversal, I favour a somewhat eclectic approach on this point as well: demonstrating the applicability of mathematics is important, particularly in motivating further mathematical developments. If the focus becomes solely on application, however, then the teaching of abstraction is lost. Mathematical techniques become tied to certain kinds of application, when the real power of mathematics is its ability to generalise and apply to situations that, on the surface, do not appear similar at all. Managing to abstract away from the particular details and perform mathematics independently of the specific situation is something that also must be taught. Indeed, I suggest that it is one of the most important things that mathematics can teach.

  4. I think I agree with Leland’s position but I’m not sure.
    I’m not a mathematician. In college, I had courses in differential equations, advanced calc, abstract algebra, mathematical statistics, mathematical logic and such. Certainly nothing particularly deep.
    The abstractions were fun, the proofs had beauty but there was no question in my mind that the students from the engineering school had a far deeper understanding of some of this material than I, because the math had a practical side for them and fit into the web of their engineering studies.
    It was different in statistics courses because this math had deeper connections to the experimental sciences, in which I was studying.
    “What does this really mean?” and “how can I use this?” are the questions I most frequently ask when confronted with abstractions. These are questions of applicability and usefulness.
    It seems when we are talking of arithmetic in schools, we are talking about elementary school (grades 1 thru 5). If one agrees with Piaget’s stages of development then abstract reasoning doesn’t/can’t develop until a child is 12 years old. Before that, Piaget’s says that the kids are in the concrete stage (from 7 to 11). This would imply to me, at least, that, in the early years, pushing the concrete and practical is most appropriate, while the abstract must await further maturation.
    That does mean that mastery of arithmetic should be a reasonable expectation in elementary grades. This in turn should imply mastery of its practical use.
    Here’s where I differ with Leland, I believe. Mastering the mechanics of arithmetic is basic, but one cannot say someone has mastered arithmetic if they don’t know when to use the arithmetic they are mechanically able to exercise. It’s neither “overly” nor “motivational” — it’s key.

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