In Brown
and Walter's article "Problem Posing in Mathematics Education" they
discuss the recurrent themes that should be a part of a student’s mathematical
experiences if “learning mathematics is to be viewed as an act of liberation.” They call these themes sensitivities, and in this article in particular, shy away from the
mathematical content, and instead focus on the pedagogical issues. Each of these sensitivities revolves around the idea that mathematics is, at
its essence, a “problem-solving activity.” Filled with examples and anecdotes
from their team-teaching experiences, this article was an engaging look at how problem-posing
can motivate and involve students, giving them a voice in an, otherwise externally-imposed,
curriculum.
In
their discussion of the efforts that go into creating an atmosphere of
problem-posers, they describe three layers: context, posing, and solving. Typically, a teacher would provide a problem
given a particular context, and the students would be asked to solve it. In
problem posing, a context, or scenario, is provided for which a problem is to
be posed. This gives the students creative
reign over what kind of question they might ask of the scenario. Brown and Walter hope that these individual
efforts, creative endeavors, and opportunities to explore problems of their
own choosing will result in students who take more responsibility for their
learning.
I
once taught an extracurricular problem-solving course in mathematics. The engagement and creativity that students exhibited
was truly impressive. Looking back on my
choice of problems, I think that it was their open-ended nature that was a
major contributor to the high levels of engagement. Giving students the choice of how they might
attempt the problem was reflected in their range of answers and opened up the
door for inspired learning and creative discourse: students defended their own methods
and learnt from their classmates.
Open-ended problems could be a good gateway to developing the
independence and confidence needed for students to pose their own
problems.
This article reminds me of the article that I read in that the environment for problem-solving needs to allow the students to explore unique methods and defend their methods when discussing them with classmates, although Schoenfeld refers to it as creating a community and is mostly focused on problem solving. In my teaching experience with 8, 9 and 10 year olds, I find that posing problems is often quite challenging for them. I believe that it would be great to have them do this more frequently. I would then extend this posing of problems with a problem exchange in order to have them pursue more challenging problems and also have an understanding of the need to be focused and clear with their problem posing. I am left wondering how specific the scenario or context is? I wonder how you could appropriately guide them towards your topic of choice without inhibiting their creative reign?
ReplyDeleteI am delighted to know that Conrad's students were engaging and creative when working on open-ended mathematics problems. Often times, engagement and creativity seem to disappear at the time of carrying out the dirty work. By dirty work, I mean the actual act of translating their thoughts and ideas on to a paper. That is, representing their line of mathematical thoughts into mathematical expressions, symbols, or relationships. I think that this is the step where we lose so many students. How can we identify or provide tools (to the teachers) that would plug this ever expanding gaping hole?
ReplyDelete