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I'm new math teaching assistant in faculty of engineering in Egypt. And after one term only, I found 3 big problems here:

1) There is no help in teaching me how to teach. It's up to my own skills.

2) There is no obvious goal for teaching math. what is important to focus on? proofs, concepts, or applications ?

3) Fresh students who came from school lack almost all concepts behind calculations. They don't know what is the "Concept" of any of the math topics from school. They can only make calculations. In addition, the majority of them lack creativity and curiosity, they just want to know what make them pass in exam!.

I want to know what to start with?

What is the most important to know about when I teach math? Any source talking about best way to teach math?

What is my mission when I teach math for engineering students ? to build proof constructing mind ? to focus only on applications ? to mix between proofs and aps. ?

And finally, how to deal with the problems created in school phase ?

I'm grateful for your help. :)

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closed as too broad by Benjamin Dickman, Joonas Ilmavirta, DavidButlerUofA, Ben Crowell, user173 Jul 18 '15 at 1:28

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ The situation sounds quite far from ideal, but the post (containing numerous questions) is surely too broad for MESE. Maybe the best place to start would be by asking some of these questions of approachable coworkers (or previous/current math TAs). $\endgroup$ – Benjamin Dickman Jul 13 '15 at 5:35
  • $\begingroup$ I don't think 'where should I start' is too broad. Admittedly, the additional questions tagged on to the end should probably be different questions (and probably already are). $\endgroup$ – Jessica B Jul 13 '15 at 7:18
  • $\begingroup$ You haven't told us which course you are teaching. Surely the goals for a course depend significantly on what the course is. $\endgroup$ – mweiss Jul 13 '15 at 14:45
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    $\begingroup$ @mweiss The goals of a single course can vary widely depending on uni, department and lecturer, and maybe also cohort of students. $\endgroup$ – Jessica B Jul 13 '15 at 15:03
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    $\begingroup$ @JessicaB yes, certainly. My point was not that the goals depend solely on the course, but that that it is almost impossible to answer this question without knowing what course is being taught. $\endgroup$ – mweiss Jul 13 '15 at 15:35
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I would start with a discussion with the Engineering department about what it is they want the students to learn. Teaching different skills will need different methods, so you might as well start with learning what will help you most in the short term. Personally, my experience suggests proofs are likely to be very low priority, with a focus on calculation being what is needed for later use, and a focus on applications needed to keep the students happy. This might be very different in your context though.

In terms of learning how to teach, there are some useful resources around, if you know where to look. One I recommend is a small book by Alcock and Simpson. It isn't exactly written for your situation, but I think it is helpful in explaining how things look from a student's perspective (especially when it comes to understanding concepts).

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  • $\begingroup$ Thank you very much, I downloaded this book and from its contents I see that it's very good starting resource. Thanks a lot :) $\endgroup$ – Mohamed Mostafa Jul 13 '15 at 19:01
  • $\begingroup$ Perhaps a more focused question than "what it is they want the students to learn" is "what other courses have your course as a prerequisite?" That should give you an idea of what will be expected of your students after they finish your course. $\endgroup$ – Andreas Blass Jul 14 '15 at 3:24
  • $\begingroup$ @AndreasBlass I would go the other way round. Knowing what courses come later does not tell you what the students will be expected to have already mastered for those courses. I annoyed a lot of my linear algebra students because I thought that those going on to engineering were expected to be able to find the matrix of a linear map, but I discovered (too late) that they were really just expected to memorise a small number of specific maps. $\endgroup$ – Jessica B Jul 14 '15 at 7:18
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I think you need to build a support network locally. Even if it means going outside the university to a nearby university, you will need mentors, fellow TA's, administrators, and others to help you not just understand and solve the problems you currently see, but to anticipate problems and improve your efforts as a teaching assistant.

Even going outside your department, there should be SOMETHING available at your university. Even if you are the only TA for math for the engineers, other teaching assistants may be able to answer your specific questions even if they are outside the field of the questions.

Point 1): there IS help teaching you to teach; you have to find it. Asking here is a good start, as there are some online resources that you can find with a web search. However, you will need to consult people as many answers depend on the immediate or near environment. (To show off my ignorance, if you have to teach an example of the pigeonhole principle by having students put on or take off hats, and you have a class full of women wearing burkas or some prohibition where wearing hats is socially unacceptable, then my hats example would not be appropriate. I don't know the cultural norms in your area, so stuff I say may turn out to be singularly inappropriate.) You need to develop (and become) local resources.

Point 2) There are obvious goals, they just are unclear and not well formed. An obvious goal is that the engineers need to learn the stuff to either perform certain skills or to acquire material that depends on the stuff you are teaching. If you don't know what they need, find out. However (and I think this is more important) you need to teach them how to recognize what is and what isn't useful, and how to acquire and apply more knowledge. They will be addressing various engineering problems and related problems, and your job gives you an opportunity to address both kinds. They will be better practitioners if they not only can do the calculation/process/design, but decide when and how it should be done, and where they can go to look up the stuff they need to do it. As a brief example, in showing how to do calculations for stresses experienced on a trestle bridge built for a pipeline, they need to consider the weight of both the full and the empty pipes, so they need estimates for the volume and mass of material in the pipe, as well as the mass of the pipe itself. (Borrowed from an incident in which poor design principles were revealed.)

Point 3) In my experience, you can't awaken curiosity on call; it happens or it doesn't. You can try to use some other motivations to help drive the teaching. However, if you can recognize a motivation of your students, state that motivation, get them to agree that it is a motivation, and then show how that motivation drives the lesson you are about to give, that may be a good replacement for independent curiosity. Here you will need examples from the field to provide motivation for you to take this kind of approach.

Good Luck.

Gerhard "Local Support Is Very Important" Paseman, 2015.07.13

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  • $\begingroup$ Really nice ideas. You helped me a lot. Thanks a lot :) $\endgroup$ – Mohamed Mostafa Jul 13 '15 at 19:03
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"What is my mission when I teach math for engineering students?"

I think it is possible to zig-zag between applications and appreciation of the history and the beauty of the mathematics underlying those applications. An example is the "simple suspension bridge," which follows a catenary. There is interesting history here, in that Galileo realized the curve was not a parabola, but he did not derive its analytical shape. In fact, the two curves are very close, but the catenary follows $y = \cosh(x)$:


          enter image description here
          (Catenary: black. Parabola: red. Image (detail) from Wikipedia.)
One could connect to architecture via the inverted catenary arch:
          CasaMila
          (Gaudi Casa Mila.)
This is just one topic, with deep and rich material. But I believe, with effort, most topics of interest to engineering students have similar rich history and mathematics behind them.

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  • $\begingroup$ @MohamedMostafa If you like the post, I would recommend "upvoting" it by clicking the up arrow at the upper lefthand corner of the post. $\endgroup$ – Steven Gubkin Jul 13 '15 at 20:49

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