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I heard that there were some studies on what is the best order for teaching math. But I cannot find any papers (probably my English is too poor to google this paper correctly). As I heard idea was: take two groups. For the first group teacher gives theory and examples and after that students start to solve problems. For the second groups teacher firstly gives problems and students try to find a way to solve them. After some attempts teachers shows theory and explains it.

Has anyone seen these kind of research?

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    $\begingroup$ It seems misguided to try to give a one size fits all answer independent of level, specific content, and nature of students, among many other factors. What works with highly motivated university mathematics students is likely not the same as what works with poorly motivated middle school students, to put an extreme example. $\endgroup$
    – Dan Fox
    Commented Jul 7, 2023 at 14:37
  • $\begingroup$ I think every teacher I've ever had, in all domains, not just math, combined the two approaches: first practice, then theory, then practice again. $\endgroup$
    – Stef
    Commented Aug 4, 2023 at 12:15

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A go-to article for me is the following. Short overview article with extensive endnotes to further supporting literature:

Clark, Richard, Paul A. Kirschner, and John Sweller. "Putting students on the path to learning: The case for fully guided instruction." American Educator 36.1 (2012): 5-11.

Our goal in this article is to put an end to this debate. Decades of research clearly demonstrate that for novices (comprising virtually all students), direct, explicit instruction is more effective and more efficient than partial guidance. So, when teaching new content and skills to novices, teachers are more effective when they provide explicit guidance accompanied by practice and feedback, not when they require students to discover many aspects of what they must learn. As we will discuss, this does not mean direct, expository instruction all day every day. Small group and independent problems and projects can be effective—not as vehicles for making discoveries, but as a means of practicing recently learned content and skills.

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    $\begingroup$ What is the strongest critique or contrary position, if any? Typically a debate has two sides a good answer discusses both of them. $\endgroup$
    – Tommi
    Commented Jul 7, 2023 at 5:53
  • $\begingroup$ @Tommi This is not necessarily the strongest contrary position, but Hmelo-Silver, Duncan, and Chinn responded to a 2006 article of Kirschner, Sweller, and Clark. In the 2006 article, Kirschner et al. criticized what they called “minimally guided instruction.” Hmelo-Silver et al. claim that inquiry-based approaches do involve guidance and cite research on the effectiveness of these methods. $\endgroup$
    – Justin Hancock
    Commented Jul 7, 2023 at 8:59
  • $\begingroup$ Thanks @JustinHancock. That would be worth an answer, if Daniel does not edit it into his. $\endgroup$
    – Tommi
    Commented Jul 11, 2023 at 7:29

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