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The educational system in which I have studied focuses on teaching the theory/abstract theoretical courses before the applications.

For example, I spent the first 1-2 years of a 5-year engineering program only studying Mathematics, Physics and other basic courses before even getting any hint what the applied problems we will eventually try to solve are. In terms of tools, I first learned and programmed the individual methods and then I used "real-life" software for the first time.

Now, having seen applications, I look back to my basic courses and I think "that abstract topic was actually much simpler than I originally thought!". It feels like I was just stupid to not be able to fully understand or get interested enough into the abstract topics.

I would feel much better if my university has made me first work on some easy applications, trying to understand the context, the difficulties and the possibilities, then dive into theory and then have the advanced applications that require advanced theory. A kind of "iterative model". I understand that this would probably take more time.

However, I see that university education keeps being like this in the universities I have studied into (Greece and Germany). Strong theory first, applications later. Traditional, "sequential" model.

Does my "iterative model" observation, as a student, make sense from a teaching perspective? What is the current situation and trend in more "progressive" educational systems? If it is not already applied, why not?

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    first work on some easy applications, trying to understand the context The problem might be that there is no single context and you need different parts of an initially abstract math course in subsequent applied courses. Also, the point of such course is to teach you to think abstractly. The fact that after 3 years you found the concepts easy, in the right context, means also that you matured enough frmo a math perspective. BTW, Greek universities are notoriously difficult and abstract afaik. – PsySp Mar 14 '17 at 15:14
  • Maybe a "spiral" (easy application, followed by easy theory, followed by deeper application & theory etc) or a "sequential V-model" (setting a topic, getting from applications to theory and back to applications, then moving to the next topic) would be a better approach for the "no single context". (I invent the terms right now, I have no idea if they make sense) – MakisH Mar 14 '17 at 15:31
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    I think it makes sense but is very complicated. It is very welcome to show a "teaser" of why these concepts are relevant and I think it is done to some extent, but at the end I think it's not avoidable to learn these abstract topics. And when u learn them, then they would seem trivial in the certain context. – PsySp Mar 14 '17 at 15:33
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    In many cases, I think, such abstract courses are being taught by math or physics professors that, naturally, they do not pay much attention to potential applications besides some standard ones (teasers). It requires a lot of effort from the department (and the teacher) to teach in such a way you mention, and this is especially true in big engineering departments. Also, do not underestimate the power of pure math courses in engineering curriculum. – PsySp Mar 14 '17 at 16:09
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    In other words: you are learning (say) Linear Algebra not only to apply it to some subsequent courses later but also to learn what L.A. is about and it's properties. Since the applications of L.A. will eventually come in other courses, many instructors adopt the strategy of teaching you as much as possible of LA and just offer you potential "appetizers" in the way. – PsySp Mar 14 '17 at 16:12
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It isn't really a question of either or in terms of theory and practice. Instead, what is needed is theory and practice happening simultaneously in the classroom. The students learn a concept and then they used it immediately in some sort of authentic assessment. To have to what 1-2 years to use any sort of new knowledge is difficult for the average young adult learner and nearly impossible for a mature adult learner. Knowledge retention is most effect through teaching it to others and followed next by the application of it.

Within education, there is a big emphasis on learning by doing or being an active learning. This can take many forms such as the use of projects, problem-solving, presentations, etc. The point is that the students need to learn through actually doing or producing something through some sort of authentic real-world application. The real-world application creates the relevancy that most students need in order to process whatever it is that they are learning. This is particularly true for inexperienced students who have zero practical knowledge.

A major exception to this is the experienced student who returns to gain theoretical insights into their career. For example, if a teacher returns to school for a master's in education, they often experiences many "aha" moments when they see a connection between a theoretically concept and something that happened when they were teaching. Since these people already possess practical knowledge they are even better able to appreciate theoretical knowledge and create a bridge between the two.

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I highly recommend to teach practice first. You can derive understanding for the theory easier from the practice instead of doin it the other way round.

I give you an example from my bachelor programme: We had a course about data modelling and one lecture was about relational algebra. It was downright confusing for the majority of the class although we had courses in formal models before. The next lecture was about SQL and after that lecture and inlcuding SQL homework the topic of relational algebra was much clearer to the course participants. Hence it would have been wiser to put SQL first and relational algebra afterwards.

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    This is actually very subjective and it's debatable if it's the correct approach. – PsySp Mar 14 '17 at 16:00
  • So what? That applies to most replies here on this board which are marked as thread answers or get a lot of upvotes. Every answer is subjective if you cannot undermine it with empirical data, which most of the answers do not. – Bruder Lustig Mar 14 '17 at 16:18
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    Don't take it personal. I just wonder how you can highly recommend something that dozens of generations of teachers are not able to solve. High recommendation is slightly extreme for my taste in this case, that's all. – PsySp Mar 14 '17 at 16:27
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    I share your feelings and I like your example. But I really hope to eventually see an answer based on teaching as a scientific field, rather than intuition (from which I am also driven). :-) – MakisH Mar 14 '17 at 16:58
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    @BruderLustig Thanks. My point is that it is not very easy to generalize emphatically based on few examples. I can see merits to both practical and theoretical teachings, not narrowed by a single course. In my limited opinion as various math courses instructor, if I may, practical teaching has short term benefits (excites and motivates the student) but theoretical teaching has long term benefits. – PsySp Mar 14 '17 at 17:42

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