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Most of the students I've encountered seem to have had the same sort of math education I've had, the standard lecture, book readings, homework problems and exams.

In my own experience and in my education classes, this method has been superseded by more modern, active strategies where students learn by doing.

Are there any studies that can give an estimate of how many K-12 math classes are taught in the traditional way and how many in more modern ways?

I've been looking around, but my searches have returned noise level results.

Additional:

This article might clarify some of the questions about what is a traditional lecture versus a more modern active learning approach.

https://www.pnas.org/content/111/23/8410

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  • $\begingroup$ How do you define traditional and modern? $\endgroup$
    – guest
    Aug 30, 2020 at 19:30
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    $\begingroup$ Note also that there is a huge (HYOOGE) amount of faddishness in educational methodology. It can be very lucrative to package something as "new" when it is not. $\endgroup$
    – guest
    Aug 30, 2020 at 19:47
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    $\begingroup$ @guest: The OP defined those terms in the question. $\endgroup$
    – user507
    Aug 30, 2020 at 22:21
  • $\begingroup$ Yeah, I guess so. Marginally. Maybe an improvement would be to say practice versus lecture, rather than generalizing "modern" and "traditional". As my second point definitely applies here. Look at the history of recitation, slate work, worksheets, etc. $\endgroup$
    – guest
    Aug 31, 2020 at 0:01
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    $\begingroup$ David, scrolling through your link, out of 69 entries for "active learning" only the 55th entry tries to define it as: "Active learning engages students in the process of learning through activities and/or discussion in class, as opposed to passively listening to an expert. It emphasizes higher-order thinking and often involves group work." Sounds like typical edu-speak BS to me. When I was in college, we had traditional lectures, but then we also had practice classes, solving problems "through activities and/or discussion" related to lectures. So, we had both without using fancy buzzwords. $\endgroup$
    – Rusty Core
    Sep 1, 2020 at 20:29

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I'm a physicist and only rarely get to teach math, but I suspect the situation is about the same in both fields. I've visited a fairly decent-sized sample of classes for adjunct and tenure-track review at the community college where I work. My observations from visiting these classes are of course not really what you asked for, but I suspect they're pretty representative of the US, because we're in a big metropolitan area (LA) and hire from all over the US.

The evidence supporting active learning in physics has been pretty definitive and largely unchanging AFAIK since about 1995, when I started teaching. See Von Korff for a meta-analysis. The evidence in math seems somewhat less definitive, but we've had other questions on this topic here, which you can look for.

What I generally observe when I visit classrooms is that about 3/4 of faculty do nothing but straight lecture. The other 1/4 do mostly straight lecture but also make some cursory, ineffective use of practices that are spin-offs from research-based active learning, e.g., computer polling or gamified quizzes.

My impression is that the evidence-based movement toward more effective pedagogy got going a little ca. 1995-2000 and then died out -- not because the evidence had changed but because of other factors:

(1) Faculty don't know about the evidence and have never seen evidence-based practices modeled. In math, I think the evidence is also not as definitive as in physics.

(2) The techniques take practice to do effectively. (I have also seen them modified and misapplied by touchy-feely social justice types in a way that degrades intellectual standards and disrespects the legitimate role of the written word.)

(3) Many students will complain, which can be devastating for adjuncts and non-tenured faculty.

(4) The advent of ratemyprofessor, mymathlab, and chegg have caused a breakdown in faculty's ability and willingness to realistically evaluate students' level of mastery, so bad results of traditional practices don't get perceived as bad results.

I think evidence-based teaching in physics never got going at all in K-12, and survives today at the undergrad level only in some specific places that have their own educational research programs. Examples would be UW and possibly Harvard.

I'm sure there are quite a few math teachers at the high school and community college level who spend some significant percentage of class time on techniques like think-pair-share and are very effective with them, but I don't think there's any significant number of people doing the kind of systematic, wholesale active learning approach that you may see advocated in your education classes. It would be interesting to see studies comparing the effectiveness of that kind of more modest mixed format with more aggressive active-learning techniques.

Von Korff et al., "Secondary Analysis of Teaching Methods in Introductory Physics: a 50k-Student Study," Am. J. Phys. 84, 969 (2016), https://arxiv.org/abs/1603.00516

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  • $\begingroup$ I think there's a side variable of conflating clickers or inquiry based learning or even group work, versus the more fundamental issue of active versus passive. Practice versus lecture. $\endgroup$
    – guest
    Aug 31, 2020 at 0:06
  • $\begingroup$ Have always been a fan of "active" and it is quite possible to do that with old school techniques, like breaks in the lecture to have class work an example. Or three. Would you learn best from listening to the wrestling coach non-stop for 50 minutes. Or better if practice and explanation were mixed? In addition to attention span, there's a big difference in watching something and performing it. And you feel it when you act. But it doesn't mean "clickers" per se. It means more TEACHING and less "professor", $\endgroup$
    – guest
    Aug 31, 2020 at 0:07
  • $\begingroup$ What is "evidence-based teaching"? $\endgroup$
    – Rusty Core
    Aug 31, 2020 at 19:14
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    $\begingroup$ @RustyCore The phrase indicates teaching practices which have a robust body of research supporting them. $\endgroup$
    – Steven Gubkin
    Sep 1, 2020 at 22:13
  • $\begingroup$ I like the observations and list of reasons why classrooms are not usually flipped (which I use here as shorthand for OP's "modern, active strategies"). Here's another suggestion for your consideration: As a math instructor I spent several years pursuing claims about flipped-classroom benefits and never saw any convincing evidence for it (and much against it, e.g., in high-quality large-scale experiments). At those point I've abandoned spending any further time time pursuing those claims. $\endgroup$
    – Daniel R. Collins
    Sep 3, 2020 at 16:34

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