Firstly many apologies if this question is not appropriate for this forum; I am a mathematician and a mathematics education researcher. However, I am posting on this forum because I am doing research into the nature of written mathematics and good a grasp school students have of it. What I am looking to do is compare a sample of students' writing to the standards of professional formal mathematical writing. I was wondering whether anyone can help me identify a linguistic research methodology that accomplish this. I am aware that there indeed a method called the comparative method in linguistics but from what I could see this was to compare two different languages. I was hoping that someone could suggest something (possibly a variant of the comparative method) that I can use.

Many thanks for your help in advance.

  • The comparative method has to do, as you say, with comparing two languages to see whether they're related historically, and if so to what degree and in what ways. "Written mathematics" means mathematics already, doesn't it? There isn't much research into spoken mathematics, although David McNeill has done some interesting work in gestural mathematics. And is formal published mathematical writing what you want all math students to achieve? It's used (and understood) by a vanishingly small proportion of English speakers, who have very few jobs to offer successful students. – jlawler Aug 11 '16 at 18:54
  • The writing problem is summarized nicely in Davis and Hersh's The Ideal Mathematician, from their indispensable The Mathematical Experience. – jlawler Aug 11 '16 at 18:58
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    Thanks @jlawler. I had actually seen The Ideal Mathematician before but forgot about it so thanks for bringing it to my attention. – Nikesh Solanki Oct 4 '16 at 8:12
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    @jlawler My aim is that all mathematics communicate mathematics clearly and effectively. So I should say that I am comparing students' writing to what is considered good written communication by professionals rather than how mathematicians actually do write. Though you are correct that such language is used by a few, the point is that students develop an appreciation of modes of communication since whatever working world they eventually inhabit will have its own mode of communication. – Nikesh Solanki Oct 4 '16 at 8:15

You are not looking for "comparative method" (this one belongs to historical linguistics) but for corpus linguistics. The mathematical writings of your more or less experienced students and of professionals constitute a corpus. You can annotate it with all kinds of information (e.g., human judgements of the quality of writing, stylistic errors, linguistic information like part-of-speech (POS) tags, etc.) and then start some statistical analysis.

  • My thanks to both @jknappen and user6726, both of whose comments were extremely helpful. – Nikesh Solanki Oct 4 '16 at 8:18

It sounds like you're looking for a statistical stylistic analysis. In linguistics, students frequently haven't learned the subtle stylistic rules that professionals have inductively formed from reading numerous articles. Our prescription for students is usually to read journal articles (in the hope that they will pick up the rules). At a simple level, you could compare the probability of word X after word Y in student writing versus a corpus of professional articles. At a higher level of analysis, one could likewise discern professional usage patterns w.r.t. more abstract construction properties, such as passives, parentheticals, nominalized sentential clauses as opposed to finite ones. This kind of analysis is sometimes used to prove specific authorship in court.

  • Many thanks @user6726. Your response was very helpful – Nikesh Solanki Oct 4 '16 at 8:25

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