"I am talking about a culture of schooling in which more importance is placed on exploration than on discovery, more value is assigned to surprised than to control, more attention is devoted to what is distinctive than to what is standard, more interest is related to what is metaphorical than to what is literal."
"What Mathematics Education Can Learn from Art: The Assumptions, Values, and Vision of Mathematics Education" presents readers with a seemingly radical idea about a new method of mathematics teaching. Dietiker suggests that mathematics classrooms are often "too tidy" and society assumes that math should be precise and carefully deduced. Instead, she presents, we should be thinking about mathematics as story.
"Interpreting mathematics as a story repositions mathematics curriculum from an instruction manual or a collection of facts to a form of art, intentionally crafted to offer aesthetic experiences for a set of students, whether positive or negative." (2)
In her years of teaching and working with educators, Dietiker has experimented with incorporating narrative and the information we know about story into the mathematics classroom in what she calls "Mathematical Adventures". Textbooks are traditionally the source of information and practice questions, resulting in students who can solve very specific types of problems and become bored when faced with the same types of questions over and over again.
"I wondered why many of the teachers I met through professional development, who had earned by respect, rarely questioned their textbooks." (4)
Stories teach lessons about life, so why do we not use stories in math? Mathematical stories must also have characters and plot points and setting that move the story along. Questions can be asked to guide the process, such as "How might this mathematical story compel a student/reader in parts of the lesson to be interested in the final outcome?"
While I was reading the article, I stopped at many points mentioned above, and I kept thinking about a method I use in my own classroom that I call "Smudge Math". Working in groups, I present students with the information we are learning that day, but rather than saying "The quadratic equation can be factored to look like this.", instead I say, "I know that this quadratic formula can be factored, and the factor looks like this, but I can't quite remember what goes in those blanks that have been smudged out...you need to figure it out!" We start with a lot of assistance, so most of the factored form is filled out, but as we progress through types of problems, I give less and less information, and students draw on the vast experience they have to come up with an answer. I love this because it makes them think! I hate the idea of math class being experiences where students copy the work on the board and then replicate it in various forms -- tests, quizzes, assignments....we need students who are capable of critical thinking and problem solving! Engaging them in story and challenge changes the task from "completing the question" to "going on an adventure", which I think is extremely beneficial!
This week has me thinking on integration. I was struck by Dr. Gerofsky’s comment in the introduction that worksheets and teacher lectures are not bad, they’re just not enough. Embodied and theoretical mathematics need to be integrated meaningfully. It’s not one or the other.
ReplyDeleteI immensely enjoyed the article by Dietiker. One part that stood out to me was part of a quote from Eisner (2002). I think it stood out because I noticed the binary way that science and arts were compared. “Science was cognitive; the arts emotional. Science was teaching, the arts required talent. Science was testable; the arts were matters of preference. Science was useful; the arts ornamental.” Eisner goes on to explain how the shift toward science was about tidying up a complex system, but as Dietiker proposes, “coming to understand a mathematical idea is generally not a tidy affair.” That was a stop for me. How much of the way we teach mathematics is about trying to make the subject tidy? When it feels messy, do we feel uncomfortable? I wonder how much this is about control?
I love the way Dietiker unpacks mathematics as story… “without mathematical action, the story has no plot!”
Lovely post and discussion, Fiona and Joy! This idea of 'tidiness', order and control is a big one to consider when we think about math (and science) education. David Pimm, Brian Rotman and a few others have asked the question, "What is the desire of the mathematician?" As educators, we might also ask, "What is the desire of the math teacher, and the math student?" Completion, wrapping things up nicely, tidiness, order -- those are some of our desires, for sure, in things like worksheets and textbooks. So what about 'wild pedagogies' for math -- math in the wild? Can we hold desires for both some degree of control and some degree of wonderment, openness and inquiry in the wild?
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