Research in Mathematics Education, 6, 15-20+115-122.
Summary/Analysis:
This summary pertains to a chapter entitled “Creating an Environment for Learning Mathematics: Social Interaction Perspective.” It explains a problem based approach to teaching math where the students participate in dialogue about how to solve various problems, share different approaches with the class, and determine which strategies work for each particular problem. The author begins by explaining how this method is different from the traditional math classroom in that students are the ones developing ways to solve problems instead of being told how to do so by the teacher. She then goes on to explain how important it is to establish classroom norms for how to collaborate and talk about mathematics. This takes place on two levels: actually talking about the math and talking about how to talk about the math. In the first, the students take the lead and the teacher serves as a facilitator. The teacher poses questions to push student thinking, but the students take the lead. In the latter, the teacher leads the conversation. In both cases, students must be taught that everyone’s thinking is respected and the environment must be one in which they feel safe to share.
I found this article relevant to my teaching, because the math department at my school is currently working in our respective classrooms to establish the type of learning environment that Woods describes. We have discussed how essential it is to be explicit in our teaching of class norms, from how to share our ideas to how to respectfully disagree. In order for this to happen, the teacher must know each student very well and be able to predict how students will respond and/or react to each other. The teacher must also be able to think quickly to mediate class discussions so that students feel safe to make mistakes and are willing to listen to other’s thoughts and feedback about different methods of solving problems. I especially related to her method for making sure all students are equally prepared for class discussion. Every student works in a dyad to develop a method to solve the problem. During this interaction, students are expected to assert their opinions while explaining and justifying their work to their partners. They then have to agree upon an answer and a method for getting it. After all pairs have the opportunity to solidify their thinking, pairs are called to the board to share their ideas. If a pair comes up and is not able to justify their thinking, they are given a chance to go back to their seat to quietly continue discussion while a new pair comes up to share. I appreciated this, because the first pair is not being let off the hook. They are still being held to the expectation that they will have to share, but the teacher is allowing them a safe space without judgement to be able to better prepare their ideas. This is something I plan to implement into my class norms as I begin problem solving with them this week.
Relevant Quotes/Concepts:
~“The expectations for children's actions in the mathematics class were quite
different from their previous experiences in school and in this classroom in other
subjects (Wood, Cobb, & Yackel, 1990). In those situations, the students were
expected to learn what the teacher wanted them to know rather than express
their own thoughts (Edwards & Mercer, 1987; Weber, 1986)” (16).
“Teachers should provide students with instructional activities that will
give rise to problematic situations” (16).
“Children's actions, which are logical to them but may be irrational from
an adult perspective, should be viewed as rational by the teacher” (16).
“The nature of the teacher and student interaction that occurred within the
whole-class discussion was crucial to establishing the social norms that were
necessary for developing a setting in which the children would feel psychologi-
cally safe to express their mathematical thinking” (17).
“Teacher: You two work on it. ... You whisper and figure it out for yourselves. Obvi-
ously, you don't have it all quite worked out well enough to explain it to us. You
got one answer but you're not sure how you did it.
She turned to address the class as she made the last statement and called on
another pair. In this way, she has made it very clear that when students explain
their answer, they must have agreed on the answer and solution in their small
group before attempting to explain it to the whole class” (18-19).
Text Sources:
Barnes, D., & Todd F. (1977). Communication and learning in small groups. London: Rout-
ledge & Kegan Paul.
Bishop, A. J. (1985, April). The social dimension of research into mathematics education.
Paper presented at the annual meeting of the National Council of Teachers of Mathematics,
San Antonio.
Cazden, C. (1988). Classroom discourse: The language of teaching and learning. New York: Heineman.
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2 comments:
Cara~
This is a fascinating post! I love the details you brought in about the study itself and how the different strategies rolled out in the classroom - and the way you reflected on them and connected them to your own work!
I'm curious - did they collect any data on how students experienced this dyad approach, and did they come to any particular conclusions about it? It sounds fascinating!
I am really interested in the structures that can be put in place to facilitate group discussion and collaboration when problem solving together. I have done challenge problems in my own class where the students are given freedom to work on a problem together and then write individual write ups. I have always struggled to have the discussions be meaningful, and reading this article may help me. I created a Wiki for challenge problems if you would like access. I just need to send you an invite.
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