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I have heard contradicting views that both parties say are research based. Specifically, I am looking for research on which teaching methods (direct instruction or student centered approaches) are most effective in high school mathematics (grades 9-12). I went to a workshop about a year ago that said direct instruction is proving to be more effective, but every curriculum and instruction department in academia focuses on teaching pre-service math teachers student-centered approaches. What does the research say? Searching google scholar does not seem to yield any useful results.

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Abstract from Alfieri, Brooks, Aldrich, "Does Discovery-Based Instruction Enhance Learning?", Journal of Educational Psychology, 2011:

Discovery learning approaches to education have recently come under scrutiny (Tobias & Duffy, 2009), with many studies indicating limitations to discovery learning practices. Therefore, 2 meta-analyses were conducted using a sample of 164 studies: The 1st examined the effects of unassisted discovery learning versus explicit instruction, and the 2nd examined the effects of enhanced and/or assisted discovery versus other types of instruction (e.g., explicit, unassisted discovery). Random effects analyses of 580 comparisons revealed that outcomes were favorable for explicit instruction when compared with unassisted discovery under most conditions (d = –0.38, 95% CI [–.44, –.31]). In contrast, analyses of 360 comparisons revealed that outcomes were favorable for enhanced discovery when compared with other forms of instruction (d = 0.30, 95% CI [.23, .36]). The findings suggest that unassisted discovery does not benefit learners, whereas feedback, worked examples, scaffolding, and elicited explanations do.

Clark, Kirschner, Sweller, "Putting Students on the Path to Learning: The Case for Fully Guided Instruction", American Educator, Spring 2012, also make the following points: (1) less-skilled students learn more from guided instruction, more-skilled from self-guided discovery (although if allowed to choose, each group will pick as a preference the type they learn less from), and (2) per Richard Mayer, the cycle of self-guided instruction has been disabused, and then resurrected under a different name every decade or so since the 1950's (and each generation of proponents seems unaware/disinterested in the findings that came before).

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    $\begingroup$ Hmm.. that is interesting. Most students in public schools will fall into the category of "less-skilled". So, why do we continue to teach pre-service teachers strictly student-centered methods? $\endgroup$ – MathGuy Oct 2 '17 at 18:35
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In the recent MAA publication "Insights and Recommendations from the MAA National Study of College Calculus" active learning is one of the 7 characteristics of successful Calculus programs. I would probably start with Chapters 3 and 8 and the references therein. For example, on page 97 you can find:

A meta-analysis of 39 studies in multiple STEM fields found that small-group learning had a positive impact on achievement, persistence, and student attitudes (Springer, Stanne, & Donovan, 1999)

and

These studies have consistently found that students from [calculus] reform courses developed stronger conceptual understanding and were more likely to persist in STEM fields while showing little or no negative impact on procedural fluency (Chappell & Killpatrick, 2003; Hurly, Koehn, & Ganter, 1999; Joiner, Malone, & Haimes, 2002).

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    $\begingroup$ Thank you. This seems to be specific to college calculus. I wonder if the same applies to 6-12 mathematics. $\endgroup$ – MathGuy Oct 2 '17 at 18:37
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    $\begingroup$ Perhaps something that should be clarified is if the fundamental principles are expected to be found via self-discovery, or if the group-work is a supplemental to the initial direct presentation. The research I see says those are very different cases, but it's easy to confuse the two. $\endgroup$ – Daniel R. Collins Oct 2 '17 at 21:32
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I suggest reading the AMS blog posts about active learning [which I think can serve as a suitable substitute$^{\star}$ for what you refer to as "student-centered"] for which the 2015 series can be found here:

https://blogs.ams.org/matheducation/tag/active-learning-series-2015/

Here is one post that you might start with:

https://blogs.ams.org/matheducation/2015/09/10/active-learning-in-mathematics-part-i-the-challenge-of-defining-active-learning/

Excerpt:

"...if the experiments analyzed here had been conducted as randomized controlled trials of medical interventions, they may have been stopped for benefit."

So strong is the evidence supporting the positive effects of active learning techniques in postsecondary mathematics and science courses that Freeman et al made the statement above in their 2014 Proceedings of the National Academy of Science (PNAS) article Active learning increases student performance in science, engineering, and mathematics.

You may, in fact, find that reading through papers on active learning is more productive than the search term student-centered. See also the AMS Notices (2017) piece here with citation:

Braun, B., White, D., Bremser, P., Duval, A. M., & Lockwood, E. (2017). What Does Active Learning Mean for Mathematicians? Notices of the American Mathematical Society, 64(2), 124-129.


$\star$: Here is a later blog excerpt RE: active learning and student-centered approaches [emphasis added]:

A student-centered instructional approach places less emphasis on transmitting factual information from the instructor, and is consistent with the shift in models of learning from information acquisition (mid-1900s) to knowledge construction (late 1900s). This approach includes

more time spent engaging students in active learning during class

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  • $\begingroup$ Gotta love how "more time spent engaging students in active learning during class" is a teacher-centered statement. Learning is an activity and "active learning" is a tautology. There is no such thing as "passive learning." It is sad that many well-educated people don't know how to write, possibly even to think while writing. To be a good teacher, one must have this clear: "Students should spend more time engaged in learning activities." I would add, "especially outside of class." $\endgroup$ – user1527 Oct 15 at 3:47
  • $\begingroup$ OTOH, "to lend a passive hearing" to what the professor says during class is a waste of time (Yale Faculty Report 1828), and I agree with what I think is the intention of the authors you quote. Always enjoy reading your posts. +1 $\endgroup$ – user1527 Oct 15 at 3:47
  • $\begingroup$ @user1527 The perhaps unfortunate nature of this neologism is not lost on me; in this respect, it reminds me a bit of the term "relational thinking" in the math education literature. In the spirit of your remark: I am unsure as to how a person can think without it being relational [in the colloquial/common sense of the word]. $\endgroup$ – Benjamin Dickman Oct 15 at 4:17
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I think you need to consider what is really under each of those terms (student-based versus direct instruction). For example one of the first answers here assumes that student based equates to discovery method. If I self-study a textbook (reading the chapter, doing homework problems, grading myself, etc.), is that student based? (yes). But is it discovery method (no).

There are more than two simple choices for how to teach a subject. To even have a good hypothesis to test, a little more effort is needed on definition of the alternatives.

I do like that you have restricted the subject (HS math), but I would also consider that different methods may work better with different populations, especially student ability.

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    $\begingroup$ Absolutely. It would be impossible to include all of the parameters here, so I left it kind of open. In general, math teachers that use student centered approaches use discovery based methods, so that's kind of what I was looking for. But, I understand what you're saying. $\endgroup$ – MathGuy Oct 8 '17 at 3:53

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