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I have seen both of these in different research publications, but after searching for a while, I was not able to find the difference. I'll appreciate it if you explain the difference and give me some references to learn more about the difference.

Some links to publications about Active learning:

https://eric.ed.gov/?id=ED449714

https://eric.ed.gov/?id=ED424243

https://eric.ed.gov/?id=ED336049

Some links to publications about engaged learning:

https://www.questia.com/library/journal/1P3-827165091/engaged-learning-are-we-all-on-the-same-page

https://eric.ed.gov/?id=EJ871317

https://search.proquest.com/openview/ee56bfc90cac37ad96a4f6be61918f02/1?pq-origsite=gscholar&cbl=29705

http://www.tandfonline.com/doi/abs/10.3200/CTCH.55.1.5-18

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    $\begingroup$ @AliceD, Just added the publications about both topics. $\endgroup$ – user2521204 Jul 27 '17 at 21:04
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    $\begingroup$ Could you synthesize how each of those publications talk about the idea and what preliminary conclusions you've reached? $\endgroup$ – Seanny123 Jul 27 '17 at 21:10
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    $\begingroup$ @Seanny123, Wikipedia defines "Active learning is a process whereby students engage in activities, such as reading, writing, discussion, or problem solving that promote analysis, synthesis, and evaluation of class content. Cooperative learning, problem-based learning, and the use of case methods and simulations are some approaches that promote active learning." As far as I understand, they are talking about the same thing. I do not understand the difference; that's why I am asking you help me understand the difference. $\endgroup$ – user2521204 Jul 27 '17 at 21:30
  • $\begingroup$ maybe engagement has intrisic motivation $\endgroup$ – DesignerAnalyst Jul 31 '17 at 7:53
  • $\begingroup$ @DesignerAnalyst, Do you have any reference about this? $\endgroup$ – user2521204 Jul 31 '17 at 11:14
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One of the publications on engaged learning that you provide (the "Engaged Learning: Are We All on the Same Page?" one) seems to answer your question (here is a fuller version of it). The quote that addresses your question is given below (bold added).

Many of these concepts of engagement cover ground similar to that covered by initiatives in higher education known by other names:

  • Engagement with the learning process is similar to active learning.
  • Engagement with the object of study is similar to experiential learning.
  • Engagement with contexts generally is similar to multidisciplinary learning.
  • Engagement with social and civic contexts is similar to service learning.

Thus, the engagement seems to encompass active learning in that active learning is the piece of engagement related to the learning process.

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  • $\begingroup$ So, do you think we can argue that "engaged learning" can be defined as engagement with the learning process, and coc=nclude that "engaged learning" is the same as "active learning"? $\endgroup$ – user2521204 Jul 27 '17 at 21:39
  • $\begingroup$ Hmm: all semantics really. If "engaged learning" is not elsewhere defined (or commonly defined in the field) than one could presumably create the definition to represent this situation. Caveat that this is a psych forum, and that questions on educational semantics may not be able to be authoritatively answered here. $\endgroup$ – mfloren Jul 27 '17 at 21:41
  • $\begingroup$ Do you know any other Q&A website that can help me find answers to my learning science related questions? $\endgroup$ – user2521204 Jul 27 '17 at 21:45
  • $\begingroup$ May be able to try matheducators.stackexchange.com. Perhaps phrase it as "teaching a math classroom" or something like that? I'm not familiar with their community, so I couldn't tell you. There's also a cseducators.stackexchange.com, though I have a feeling this question would get less traction there. $\endgroup$ – mfloren Jul 27 '17 at 21:47
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    $\begingroup$ Of course. I should add that, in answer to your original question, yes, you could easily define it that way based off of this article. It would just be confusing if someone read your article next to an article where someone defined it a different way (and look bad on you if that other article were very well known). $\endgroup$ – mfloren Jul 27 '17 at 21:52

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