What Math(s) Ed literature is accessible to the working math(s) educator?

Question

This site is - as far as I'm aware - for what I would term working maths educators. That is, on the whole the users of this site are not researchers in mathematics education. Rather, we are the people who get on with the work of providing mathematics education every day.

That said, there are some people out there who do actual research on mathematics education. There are more who study education in general. I have a hope that some of the results of this would be useful to people like me, but I find it hard to get hold of stuff that I can directly use. In particular, what I want is ideas on how to improve my teaching that:

1. Are based on actual research. That is, its effectiveness has been proved. (Of course, this might be that it has been proved to be effective in teaching Australian Skiers how to do Differential Topology, but that's still better than "It sounds like a good idea so let's give it a try.")

2. Are practical. I've heard my fair share of general theories of learning and education and general theories are not all that useful to me because it takes time to translate them in to things that I can actually do in my lecture hall. Moreover, the opportunities for experiment are somewhat limited because if I get it wrong, the students tend not to come back for a second attempt.

3. Are mathematical. Here the problem is that many techniques are subject-specific and what works well in a history class or philosophy class may not be so good in maths ("Get in to groups of three and discuss the Gauss Elimination Algorithm.").

What I'm looking for is a way in to the maths education literature. I don't really want to start reading random articles because I don't have the necessary background to evaluate them. Maybe eventually I'll get to that level, but for the moment I need some guidance. However, although short of time and expertise, I do have a reasonable level of intelligence and motivation so I think that if someone could provide me with a road map then I'd do a reasonable job of finding my way from that.

Note that I don't want a list of all maths education departments or journals. I want a recommended initial reading list. But also that should be knit to practice since I don't want to become a maths education researcher myself, just that I want to make use of the fact that they exist.

So, where do I start reading?

Answer 1

For those with a background in mathematics, perhaps the following source would be of use:

Curtis C. McKnight (Ed.). (2000). Mathematics education research: A guide for the research mathematician. American Mathematical Soc.. Link.

A review of the book can be found on the MAA website here.

From this latter link:

In a nutshell, this book is a guide for reading and evaluating mathematics education research, especially undergraduate mathematics education research. Its purpose seems to be to encourage research mathematicians, who do much of the teaching of undergraduate mathematics, to use education research to actually inform their teaching. In order to use this research, though, mathematicians need to know how to find and evaluate the research already done, and this is the focus of this book.

There is plenty more to the review, and the book itself is quite readable. (Unfortunately, only part is available through the Google Books link provided above; please edit in a full link if you find one!)

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I might add that the MAA has a page on Teaching and Learning. You could also search the site for education to find relevant links. For example, the second result is the "Searching for Common Ground" reference provided in a separate answer here from M Jansen.

Answer 2

I very much welcome connections of research and teaching, although results from research still need or be interpreted in your specific situation. Let me give an example.

It might happen that your students can state the correct definition of a subspace of a vectorspace, but if you ask them if a specific set is a subspace, they "try guessing". There is no research that says "you should introduce the definition of a vector space in a specific way". However, there is research on how students work with definitions. Math educators mostly agree that for a given object or property, people usually have a picture in mind (maybe many pictures). We call this their concept image. The students also might have a concept definition in mind, hopefully the definition you gave to them. This distinction might help you see if your students try to compare the given subset with other subspaces they know, so they would work with their concept image only. The question of how to introduce definitions thus becomes the question of how to help your students to work with definitions.

If this example somehow matches your interest, I would suggest you to read the book Ideas from Mathematics Education, (free download) by Alcock and Simpson. It was written explicitily for mathematicians. Both authors worked are researchers in mathematics education and they collaborate with teachers and researchers in mathematics. Concerning concept image and concept definitions they have recommendations for the examples you choose, what to emphasize when you work with definitions, etc.

Answer 3

I am a mathematics educator who conducts research on teaching and learning, and I also teach mathematics courses that are mathematics content courses for future teachers. I endorse the references given here! Great ideas.

Another option: Mathematics and Mathematics Education: Searching for a Common Ground.