Susan’s article attempts to “establish a description of the
mathematical word problem as a linguistic genre, particularly considering its
pragmatic structure... [she hopes] to find clues to the unspoken assumptions
underlying its use and nature as a medium of instruction.” While I don’t have
enough background in linguistics to understand much of the article (see the
L-tense and M-tense section!), I appreciated some new perspective she brought
to how we see word problems.
In particular, Susan points out that since word problems
generally don’t refer to real life situations, they could be considered to be
works of fiction. The section in which she points out how authors of word
problems try to convince students to believe the underlying facts they will use
to approach the problems is quite humorous. Susan wonders (as many students
often do) what the purpose is of these works of fiction (aside: what is the
purpose of any work of fiction?)
Last year, we decided the midterm exam for our Grade 8s
should be a task based exam. The most revealing task we gave them was also the
simplest. We gave students different sized boxes and measuring tapes, and they
had to find their surface area. We watched on with surprise as our top students
who could have easily have found surface area of a rectangular prism with a
formula struggled to use the measuring tape carefully and correctly. This was a
meaningful problem solving task that students can connect to “real life”
(wrapping a present, painting a room) much more directly than in a fictional (Kevin
is painting a room…) problem. Perhaps if students were given the time to undertake
more tasks such as these, they would develop meaningful problems to them
instead of invented stories when asked to come up with their own math problems.
Math is a beautiful language, yet its beauty may not be appreciated by some students in the form of word problems. I think it's because some students find it difficult to translate plain English of a math problem into mathematically meaningful symbolic notations. Such translation is a big challenge for some of my students who are either native or non-native English speakers when they do word problems.
ReplyDeleteIn response to the task-based exam, I think some students (and probably even some teachers) are so used to solving math problems by paper and pencil that they may find it "awkward" to solve them using a hands-on approach. This is like a person learning how to ride a bike for the first time. He/She may find it awkward to control his/her bike on the first few attempts. However, after some practice, the students (or the beginning cyclists) will eventually grasp the new way of doing things and see the benefits of doing the same task in different ways.
David, I love your story of the task based exam. That sounds wonderful. This has all caused me to think a bit. I am certainly guilty of trying to inject humour into word problems. Why? It's my attempt to draw the students in to something that is otherwise just another dry math problem. I'd argue that a chuckle of acknowledgement is at least some level of engagement. Granted, I teach extremely reluctant adults: I'm trying to win them over by any means possible. Perhaps that's simply my purpose. Another strategy like your task based test hadn't ever occurred to me. Thanks!
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