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?
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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.
Maybe some papers from this volume can be interesting for you:
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.)