Creativity

The head of the math department asked us to write about “creativity in the classroom,” presumably creativity both that we as teachers demonstrated and opportunities for our students to be creative.  It was an interesting exercise, though, and I thought I’d post some of my responses here (incomplete though they no doubt are since I did them off the top of my head).

Students

I think creativity in my classroom on the students’ part shows up when they work on ISPs without any more help than is written in the project guidelines; when I answer their questions with another question, forcing them to think more or seek help from a student; and some, when they work ahead or at their own pace, ignoring my “lectures”.; or when they come up with non-traditional proofs or different ways from the “traditional” ones to solve a problem.  I think I encourage that tendency by keeping my explanations minimal and open-ended and by continuing to hammer home the idea that there is nearly always more than one “right” way to do things.  I also encourage creativity by periodically asking students to do the same problem more than one way (like on the Diff Eq midyear exam this year)–which is not explicitly “free creativity” I guess, since we’ve usually sketched out the general outlines of the different ways, but it does reinforce the idea that there’s more than one “right” way to do things.  I also think my kids get to show more creativity than a lot of kids in math courses because, except when preparing for the AP, I *never* use multiple choice questions on tests or quizzes, which means they get to show what they *do* know as opposed to what they don’t.

Self

I think I show creativity in the classroom in a number of ways, including

• the whole lab format of the class;
• coming up with questions on the spur of the moment to help guide kids to thinking more instead of simply answering their questions (sudents don’t realize it, but simply answering their question is usually easier, in fact);
• with providing ISPs;
• with providing exercises like the ones in math 3 that are brainstorming exercises to see if students can derive formulas on their own from basic principles (deriving the formula for arc-length) or the initial brainstorming exercise on “how could find area under a curve that wasn’t one for which you had a formula” on the first day of class
• not just having ISPs but in developing such very different ones.
• in developing the math 3 course and approach itself as well as all its successor courses (though DBF has modified the courses he’s taken over)

This is not creativity “in math”, but it’s creativity in teaching:

• letting students periodically write on the “What Irks Me about Dr. Raulston” list;
• letting different sections (of math 3 this year) choose which topics they want to do when the order doesn’t really matter;
• using the computers and calculators as “personal tutors” to check answers I make them figure out by hand (as opposed to my just telling them the answer or supplying it);
• making them work as a group to compare answers to review problems instead of just supplying the answers;
• using the text A Very Short Introduction to Mathematics as an enrichment text in math 3 this year.

Individualization of instruction

Does individualization of instruction count as “creativity”? I don’t know.  But in case you think it might…some examples of that would include

• the time Charlie Caplan complained so much  that he’d only done badly on a test because of “calculation errors” and he would have done great if it had  been “all theory”; so, the next test he got was all theoretical–and different from the other students’
• letting Max (and others in previous years) take the class on his own 2nd period so he could still take the class and get in his fine arts requirement
• maybe even giving tutorials on facebook or on gchat?  That’s probably pretty creative right now though it will probably get more common later
• using a facebook group to send group information about homework and quizzes and tests and stuff.  You can do that other ways, of course, but students are so much more interested in using facebook than email or the sjs discussion forums (at least, my juniors and seniors are).

Voluntary feedback

I sent some of this post to a student who has had both me and other math teachers recently to get her opinion as to how accurate my comments were.  I routinely ask questions designed to prompt students to reflect on their experience in my courses as well as on the course objectives–the most recent example was my asking students to think about and then comment upon algorithmic and non-algorithmic approaches to math courses, the advantages and disadvantages of each.