Moss & Beatty (2010): Knowledge building and mathematics
The purpose of Moss and Beatty’s study was to test the
possibility of young students’ engagement in theory development in the context
of mathematical problem solving. Three classes of grade four students were
introduced to pre-algebra and participated in solving a series of difficult
problems online.
This article introduced a learning context called Knowledge
Forum. This is an online forum to provide an authentic context for
collaborative problems solving and extended mathematical discussions while
students worked on an open-ended school-based generalizing problems. In this
context, the teacher posts a problem but then is ‘absent’ from online
discussions. Instead students figure out solutions.
Knowledge Forum is based on Knowledge Building which is
inquiry-based and centered around theory development. Knowledge Forum is based
on two principles: democratization of knowledge and epistemic agency. Democratization
of Knowledge counters traditional math classrooms were the teacher is the
holder of knowledge and ‘high’ students’ contributions are favored compared to
students who are struggling. Instead, Moss and Beatty found that all students,
including ‘low’ or struggling students used Knowledge Forum. Low students who
might not speak up in class contributed, albeit they spent more time signed in
and reading online posts than introducing new mathematical generalizations. Epistemic
agency describes the responsibility that the group assumes for ownership of
ideas that are given in public life in this online environment. Moss and Beatty
found that students took responsibility for contributing ideas, monitoring one
another’s contributions, asking for clarification with the goal of moving theory
forward.
In their discussion, Moss and Beatty make distinction between
Knowledge Building and community of learners. A community of learners (Lambert,
1998 qtd. in Moss and Beatty, 2010) is when students engage in justifying and
critiquing mathematical explanations with the goal of acting as an expert. In
contrast, Knowledge Building favors theory development –that is the collaborative
production of new ideas. Students spend less time justifying and critiquing and
even when they do justify and critique the aim of such activity is the production
of new ideas. Democratization then is more than the legitimization of
individual ideas but an understanding that knowledge building requires multiple
voices, multiple perspectives, even not-very-well-worked-out perspectives in
order to extend understanding and produce new knowledge.
STOP: This article appealed to me because it was written
very clearly. Also, I have been considering creating an online forum for grade
6 and 7 students throughout the Surrey SD who attend the Challenge program. The
biggest question we are asked is ‘what comes next after Challenge?’ Also, some
our low income schools have so many learning needs, are so poorly supported
that ‘high’ students are bored, left to their own devices and do not have
opportunities to participate with open-ended math with like-minded peers. This could
provide continued challenging mathematical material and promote intellectual
risk taking. I wondered about posting solutions and role of teacher and so this
article showed me that I can teach an eight-week module and that it is possible
for students negotiate meanings amongst themselves. The distinction between
community of learners and knowledge building particularly interests me. The
former seems almost like ‘make-believe play’ where one is ‘acting’ like an expert.
For some, this idea is enough to motivate students-they have the buy in but I can
see how for other students, acting like an expert does not appeal to them. I
think this article also shows me that I would have to be somewhat focused on a
topic; for instance, the pre-learning to the online forum was about linear
functions-activities were all centered around this. The article included sample
activities and I have done some of these. This article prompts me to want to
create a proposal for a class--I have to really think about to focus on for
grade 6 and 7s. Since many of you have taught this age group what would you
focus on? (Geometry? Patterning and Linear Functions since it leads to generalization
which is central to mathematics?) Also, Knowledge Forum was text-based but I
wonder how students could show learning with multiple representations-for
instance, students could draw solutions, post videos etc. I wonder what this would
enable? What new problems could arise from multiple representations? – for instance,
it could be more difficult to critique multiple representations than just text
explanations.
*of course, what about students just googling solutions?
I would love to hear your thoughts!
ReplyDeleteI love the idea of an online Knowledge Forum. I use a basic form of this with my entire class by posting problems and letting students share their solutions. I generally don’t have to act as “the expert” because students have gotten very good at having online conversations and showing different ways to solve the problems posted. At the beginning of the year, I was using online resources for the problems and did encounter “googling” the answer. Now, I pick a topic and try to design a real-life problem that involves the subject. Recently, I asked students if a boat with a 30m mast could go under a 25m high bridge. The discussion was great!
I think both patterning and geometry are great topics to focus on as they are very rich with potential for problem solving.
With multiple representations, you will encourage and stretch all your students to look at problems from a multitude of perceptions. I try to ask students to solve all their word problems in 2 different ways. It promotes creative thinking, I’ve found.
I think that your idea of an online module could be a great opportunity for intellectual risk taking. Is there a way that you could introduce an element of social justice or "citizen's math" into it? This builds on the ideas of democratizing knowledge and intellectual community. It also puts an ethic of a common shared goal that encourages cooperation. I think that geometry or linear functions could work. These two areas tend to be what I focus on when I create extensions for grade 7s.
ReplyDeleteIt might be interesting to have students design an extension module as well. They might have some different ideas about how to digitally "share" their thinking.