Linear Algebra Journal Is there any journal which has significant material on the teaching of linear algebra. I am investigating the most effective way to teach a course on Linear Algebra.
What are the most important things students should learn on a first course?
What are the main questions in this field?
 A: The College Mathematics Journal dedicated one issue to linear algebra, it was
Vol. 24, No. 1, Jan., 1993.
Maybe some papers from this volume can be interesting for you:

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*Teaching Linear Algebra: Must the Fog Always Roll in?
David Carlson.
The College Mathematics Journal, Volume 24, Issue 1 (Jan., 1993), 29-40
jstor
different link


*The Linear Algebra Curriculum Study Group Recommendations for the First Course in Linear Algebra
David Carlson, Charles R. Johnson, David C. Lay and A. Duane Porter.
The College Mathematics Journal
Vol. 24, No. 1 (Jan., 1993), pp. 41-46.
jstor different link
A: Here's a list of some journals dedicated to teaching mathematics, so it is quite possible that you'll find papers on teaching linear algebra there, too. I am making this CW, so that other users can add more journals to the list. (I hope such a list is not completely off-topic for a question like this.)

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*Educational Studies in Mathematics link Wikipedia

*International Journal of Science and Mathematics Education link

*International Journal of Mathematical Education in Science and Technology link

*Journal for Research in Mathematics Education Wikipedia

*Journal of Mathematics Teacher Education Wikipedia

*Research in Higher Education link

*ZDM The International Journal on Mathematics Education link
A: Maybe the following isn't helpful, but anyway: 
(1) To figure out what the main questions are in linear algebra and which topics to include in a first class, I would simply go find a stack of linear algebra books (hopefully you have access to a nice library) and looks through them and try to identify the topics covered. I would also try to pay attention to how the books get the the same results in different ways.
(2a) Maybe then you could simply just ask yourself how you best learn and try to design your class around that. Students have different preferences, so I usually choose things the way that I like. However, if your preferences is say a very dry, purely abstract treatment, doing no examples, then you might want to ask yourself whether it is likely that your students might appreciate that. As a general principle (that I am sure many people would disagree with) that I have is that I teach best when I figure out what is working for me. I teach the best, when I find the method that I am most comfortable with. If I am trying too hard to be someone that I am not, then that just effects my teaching in a negative way. You might then ask: but shouldn't we evolve and learn new things as teachers? Sure, but if this is the first time teaching a class, you have to start somewhere.
(2b) In stead of going to journals right away, I would also try to contact people who have taught the class in the past and ask for their recommendations.
(2c) You might also be able to find some students who have taken linear algebra and ask them how they think they leaned best in the class.
