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There have been many innovative teaching methods tried from time to time. Twenty years ago was Calculus reform, now is flipped classrooms. We also have a resurgence of the Moore method under the name of IBL. Those are the ones I am most interested in.

Universities have had computerized grade information for twenty years perhaps. I assume it should be relatively easy to do longitudinal studies to determine the relative efficacy of these various methods. Are there such studies? Where are they? Where is the data? What are the conclusions?

Edit: I found this using Google: http://www.colorado.edu/eer/research/documents/IBLmathReportALL_050211.pdf

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    $\begingroup$ IBL is probably more difficult to implement than direct instruction, and more demanding on teachers and students. I'm note sure if you can equate "better grades" with "more efficient teaching method", it might be that poorly implemented IBL is dragging the average down. $\endgroup$ – Dag Oskar Madsen Apr 3 '15 at 1:15
  • $\begingroup$ @DagOskarMadsen It's a good point, but there should be enough data to weigh by quality of instructor. $\endgroup$ – Felipe Voloch Apr 3 '15 at 1:19
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    $\begingroup$ I would like to register agreement with Dag Oskar Madsen that the question is beset by more and harder methodological issues than I think you're giving it credit for. A dip into the math ed research literature will reveal this quickly. (For example: how do you measure the quality of an instructor.) $\endgroup$ – benblumsmith Apr 3 '15 at 12:40
  • $\begingroup$ Agree with the issues of this not being easy problem to crack (confounding variables, bias, lots of small crappy studies few large good ones, Hawthorne effect, etc.) And it's not just a math problem but teaching research in general. $\endgroup$ – guest Dec 7 '17 at 17:39
  • $\begingroup$ One outside the box idea is to look at non-traditional ed school areas for insight. Sports training and military training come to mind. You may get some insights on methodology and even on measurement. Also, the sample sizes tend to be large. $\endgroup$ – guest Dec 7 '17 at 17:39
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Like Joseph O'Rourke's answer, this one won't be complete, but, here's another possibly useful reference:

Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students' learning. In F. K. Lester, Jr., (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371 - 404). Charlotte, NC: Information Age Publishing.

It makes an attempt to synthesize a large amount of research over a long period of time. It is not aimed at the collegiate level at all, so it does not specifically address IBL. (At the primary and secondary / K-12 level, the set of ideas behind IBL have been implemented in several different ways under several different names, and are not associated with the name of Moore. But the relevant ideas are evaluated by Hiebert and Grouws - specifically they attend to the question of how much math education should obligate students to struggle / grapple with the content.) It is also too old to mention the flipped classroom, which idea has really only attracted widespread interest inside of the last few years.

As an aside, I would like to say that I think the research problem you're posing here is much harder than you're giving it credit for. Variation in implementation is a serious issue because a teaching method that is effective in one instructor's class may be worse than nothing in another's. For example, anecdotally, from my years as a classroom teacher at a large public high school, both the strongest and the weakest lessons (IMHO) at the school were "constructivist" (which was the relevant name for an IBL-like pedagogy). I would have expected no significant difference in average outcomes of "constructivist" vs. "traditional" classrooms at that school. Measuring outcomes is another methodological hurdle.

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  • $\begingroup$ This thought is way too anecdotal to merit inclusion in the answer but: it has seemed to me that researchers who want to prove the inefficacy of a method always aim to include bad implementations in their dataset, whereas people who want to show efficacy always attempt to restrict to implementations that they judge are faithful to their vision of the method. This makes the research less unanimous than you'd think it would be. Basically, everybody is studying what they think the method is: if they think it is bad, they find something bad to study, etc. $\endgroup$ – benblumsmith Apr 3 '15 at 13:29
  • $\begingroup$ Sorry if I gave the impression I thought this was easy. I realize it isn't. What's the alternative? There certainly isn't an a priori theoretical proof that method A is better than method B (for reasonable values of A and B). So now we are making decisions based on anecdotal evidence or worse, e.g. in the case of flipped classrooms, on what is cheaper. $\endgroup$ – Felipe Voloch Apr 3 '15 at 13:35
  • $\begingroup$ I totally agree that methodologically serious research about the effectiveness of pedagogical methods is necessary to inform policy decisions. And a huge amount of research does already exist and is continuing to be done. I was just cautioning against the sense (that I guess I wrongly imputed to you) that this research could be expected to resolve the disagreements to everybody's satisfaction in a reasonable amount of time. $\endgroup$ – benblumsmith Apr 3 '15 at 13:47
  • $\begingroup$ I did use the word "easy" in my question but was more to do with obtaining the data. $\endgroup$ – Felipe Voloch Apr 3 '15 at 14:03
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To state a theorem and then to show examples of it is literally to teach backwards.—E. Kim Nebeuts


This is hardly an answer to your question: I cite just one paper, emphasizing engineering rather than mathematics education, focusing on IBL, and the work is from 2006. Nevertheless...

Prince, M. J. and R. M. Felder (2006). "Inductive teaching and learning methods: Definitions, comparisons, and research bases." Journal of Engineering Education. 95(2): 123-138. (PDF download.)

Their paper opens with the quote above. They examine a range of IBL-like teaching techniques:

"Inductive teaching and learning is an umbrella term that encompasses a range of instructional methods, including inquiry learning, problem-based learning, project-based learning, case-based teaching, discovery learning, and just-in-time teaching."

They survey the literature evaluating each teaching method. They cite some longitudinal studies (in chemical engineering) and meta-analyses of ~80 separate research studies. They conclude:

"While the quality of research data supporting the different inductive methods is variable, the collective evidence favoring the inductive approach over traditional deductive pedagogy is conclusive."

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The calculus reform died without anybody noticing it and, that I know of, there were no longitudinal studies. In one case, though, if not an a longitudinal study, there was an evaluation and what followed was interesting.

In 1988, I was the principal investigator of a small NSF calculus grant predicated on two ideas:

  1. The very length of the standard Pecalculus 1 - Precalculus 2 - Calculus 1 sequence is of and by itself a major problem.
  2. The content of the sequence would be integrated in a two-semester sequence by way of a systematic use of polynomial approximations.

After a few years, in the words of the school's Office of Institutional Research, it was established that

Of those attempting the first course in each sequence, 12.5% finished the [conventional three semester 10 hour] sequence while 48.3% finished the [integrated two semester 8-hour] sequence, revealing a definite association between the [integrated two semester 8 hour] sequence and completion (chi2(1) = 82.14, p < .001).

Furthermore, the study mentioned that the same number of students in both sequences passed Calculus 2 but that the numbers in both sequences were too small to be meaningful.

So what happened next? The integrated sequence died within the next few years and no one was talking.

And then, a few years later, the school did a longitudinal study of the entire Arithmetic - Basic Algebra - Intermediate Algebra - Precalculus 1 - Precalculus 2 - Calculus 1 sequence. And, here again, the rather dismal evidence was immediately forgotten.

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