On the first day of school, I gave my students notecards with their table number. On that card, I asked for their name, 2 examples of everyday problems, and 2 examples of everyday creativity. I gave minimal guidance about what an “everyday problem” or “everyday creativity” is. I took the results and turned them into posters.
I ask my students about everyday problems because I know that I use mathematical thinking all the time, especially in teaching. I believe all of my students can benefit from the abstract problem-solving skills developed through mathematical thinking. Unfortunately, talking about these skills is perhaps even more abstract than the math, and convincing students that they are developing these skills proves rather difficult.
During my first year teaching, I tried asked my students to reflect on their work by naming a problem-solving skill that they used and describing a real world problem that could be solved with that skill. This task proved incredibly difficult for students, and I floundered when trying to explain or demonstrate what I was looking for.
This poster is my new approach. It sits on the wall all year long, reminding students that just like we solve problems in class, we solve problems in everyday life. I hope that they find it perplexing. What do they notice on the poster? What questions do they have? What does this say about the transfer and utility of mathematics?
Over the summer, I read Are You Smart Enough to Work at Google? by William Poundstone. I was really just looking for fun puzzles and riddles, but I stumbled upon a surprising perspective on creativity. Twice, Poundstone referenced definitions of creativity.
On page 28, he presents Torrance’s 1962 definition of creativity:
“Creativity is production of something new or unusual as a result of the processes of:
- sensing difficulties, problems, gaps in knowledge, missing elements, something askew;
- making guesses and formulating hypotheses about these deficiencies;
- evaluating and testing these guesses and hypotheses;
- possibly revising and retesting them; and
- finally, communicating the results.”
Later, on page 30, Pounstone presents the following as a sort of consensus definition:
“Today’s psychologists usually define creativity as the ability to combine novelty and usefulness in a particular social context.”
You could take “creativity” out of either of those definitions and replace it with “problem-solving” without anyone noticing.
As a result, I wonder: When is creativity useful (in the so-called real world)? Is creativity fun? Does the synonymous nature of creativity and mathematics/problem solving present an opportunity? How can we leverage creativity to teach problem solving and mathematical thinking?
Most common student responses to my opening day questions:
Everyday problem: getting out of bed
Everyday creativity: doing makeup
Both a problem and a source of creativity: coordinating outfits
Mister, is this right? 
The idea of a “consensus definition” was advocated for in a major way in work by TM Amabile about three decades ago. EP Torrance’s work is still widely cited, but his “tests for creative thinking” are widely considered to measure a construct known as Divergent Thinking, which serves (at best) as an estimate for Creative Potential. One must be careful in reading studies about creativity — often they are just trying to assess the divergent thinking constructs found in Torrance’s tests. As for “everyday creativity” (sometimes called “little-c creativity”) some dispute that this would even be considered creative; they want only to admit what could be called “eminent creativity” (AKA “Big-C Creativity”). In the context of education, you may be interested to read about the more recent “mini-c creativity,” and how it relates to learning.
If you want some intellectual vindication concerning everyday creativity and the relation to problem solving: Check RW Weisberg’s (2006) textbook (e.g., “…it seems reasonable to adopt as a working assumption the premise that creative thinking is an example of problem solving,” p. 581). It is long, but very clear with a nice mix of other theorists’ ideas (properly cited) and thought-provoking case studies. The book does not really necessitate being read in order, but it certainly could be, especially if you want to trace how he (carefully) arrives at the pulled quotation above.
More generally, you might take a look at either of the following:
1. http://matheducators.stackexchange.com/a/4104/262 An overview answer (written by me) to a Math Educators (MESE) question about creativity. For full effect, first read the entire answer, then go back and start hunting through the links.
2. http://www.newyorker.com/books/joshua-rothman/creativity-creep A recent (Sept 2014) article in The New Yorker about certain aspects of creativity (that I found to be pretty well-written!).
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