Hi Katrin,

I co-authored a paper in relation to Signature Pedagogies in Mathematics Education. In my humble opinion it might be of assistance. The reference details are

Larkin, K. Jamieson-Proctor, R. & Finger, G. (2012). TPACK and pre-service teacher Mathematics education: Defining a signature pedagogy for Mathematics education using ICT and based on the metaphor ‘Mathematics is a Language’. Computers in the Schools - Special Issue: Technology and Signature Pedagogies. 25(1):207-226. DOI: 10.1080/07380569.2012.651424

Regards, Kevin.

I don't think I'd agree. I am very concerned and interested in math teaching; I teach programming and algorithms to University art students, and they have often been crippled mathematically by fears and misapprehensions passed to them by previous teachers and students. So I do almost NO math, but we still get a lot of programming done.

Thanks for the paper - there's also one by Passey at the beginning of the issue that looks interesting. But I don't think you can call mathematics a 'language' in the same way that English or German are. The problem is that the language of math is designed specifically as a shorthand for concepts that CAN be expressed in English, at least at early stages. So the symbol '=' can be replaced by 'is equal to'; more of a lexeme than a grammer element and not the point of confusion.

I'd say that the concepts underlying mathematics can be taught in a more abstract but also concrete way, using real world projects, cases, studies. Abstract because the math concept is somehwat hidden by the statement fo the problem, but concrete in the mind of the learner because they are doing something they understand. So, for instance, 'Today we're going outside and do some surveying'. After that it makes sense to try to get them to write it down somehow, to devise a system. Which is what math is.

I'd start with ideas. Small kids can actually understand more of that than you might think, and have fun with it. I used to talk to my own children about things like trans-finite numbers (didn't call them that) in the car on trips. (We also watched movies).

I could be mistaken, but I've seen the problem as one of mathematicians generally being people who never really had trouble with math. Generations of us have been taught in a similar way, and there's been a kind-of natural selection taking place. Now mathematicians can't communicate the beauty and simplicity of the concepts, and can't see where the students have problems at all. They never had them. I've completely discarded the concept of a proof being beutiful since it is a very unaccessible and abstract beauty that serves to seperate some from others. Talking about concepts first can allow the group to join together. Don't even have to call it math until later.

I quite like the concept of signature pedagogies, but I'm not convinced it can (or should) be applied to all disciplines.

While I'd agree that mathematics has a language associated with it, I'm having trouble getting my head around the notion that mathematics *IS* a language. I come from a background of computer science, where we have many languages, but I still wouldn't advocate teaching a programming language in the same manner as one teaches a natural language.

Schulman said signature pedagogies are: “types of teaching that organize the fundamental ways in which future practitioners are educated for their new professions” (p. 52)

Fair enough.

But he also said: “Signature pedagogies, by forcing all kinds of learning to fit a limited range of teaching, necessarily distort learning in some manner. They persist even when they begin to lose their utility” (p. 56)

Is mathematics a profession? Outside of the academy, what does a professional mathematician do?

Hi have a look at this article which is quite nice, Shulman, L., (2005). Signature Pedagogies in the Professions, Daedalus: 134,3; Proquest Science Journals, 52-59.

Thanks Natalie!

That's actually the paper I cited at the very top. :)