Author: Yackel, E., & Rasmussen, C.
Source: Yackel, E., & Rasmussen, C. (2002). Beliefs and norms in the mathematics classroom. In Beliefs: A hidden variable in mathematics education? (pp. 313-330). Springer Netherlands.
In this chapter, the authors investigate
how students’ mathematical beliefs and sociomathematical norms are changed in
mathematics classrooms from both sociological and psychological perspectives. They
analyze the comments from the students that are reflected on their mathematics activities,
and the dialogues among the instructor and the undergraduate students in
differential equations classes that the instructor use an inquiry approach.
According to the authors, what becomes normative relies on what
accepts mathematical explanations in classrooms. They describe two aspects of
acceptability of explanations. The first is that an explanation is acceptable when
it provides a clarifying function that makes clear other one’s thinking as one
of communications. The other one is that an explanation should be “about
student’ mathematical activity with entities that are part of their
mathematical world.” (p.325) One of examples the authors show in this article
is that the participated students dynamically recognized the criteria for the
acceptable explanations and adapted their answers when the instructor shifted
from a calculation orientation to conceptual orientation in his questions in
the differential equations class. In short, through the observations, the
authors conclude social and sociomathematical norms and individual beliefs have
strong relationships and evolve together in classrooms.
I
agree with the idea that the beliefs students hold and (social and) sociomathematical
norms are developing each other. Students might constitute own beliefs of
mathematics while socialmathematical norms change in classroom. But something
that was not included in this article, actually my curious point, is whether
teachers/instructors change their beliefs or not in classrooms. Do they fix
their beliefs? Or do they modify/adapt their beliefs with the development of
socialmathematical norms? I believe they also do so but they do not often
change their belief regard to the dialogues in the classroom.
Additionally, I think only teachers lead to
develop sociomathematical norms. Although the authors explain students also
constitute the sociomathematical norms in their interactions, no change might
be occurred in the norms if teacher is not in the classroom. This implies the
current sociomathematical norms are students-centered. Hence, my another question
is, can students mainly lead to develop sociomathematical norms with minimal supports
from teachers?
Finally,
because I am studying immigrants education, I am curious how students who study
math in their additional language interpret sociomathematical norms. Some of
them may not understand native students’ conversations which constitute
sociomathematical norms. In this case, I expect they recognize what “bad”
explanation is rather than explore “good” explanation from nonverbal communication.
But I do not think they can interpret it as well as native students.
Question:
What do you think about the classroom that
students proactively lead to develop sociolmathematical norms with just minimal
observations and supports from a teacher? Do you think it is dangerous? Or
effective to their autonomy, creativity etc.?
This is a very intriguing question. I see the central idea of education is that learning is not as a passive act of absorbing information, but is rather a sequence of active process with a focus on asserting control over one's own thinking. As such, not only are students able to contribute to the construct of sociomathmetical norms, but also are able to take the primary role in establishing the norms. Some may advocate that it is required in a successful problem solving process as Mathematics learning involves more than cognitive development. As you mentioned, Individual beliefs and disposition of teacher and students have its way to promote sociomathemetical norms. However, it is a challenge to actively change teacher’s role form the center of instruction to the co-builder of the norms. James talked about how students in Kenya took roles in student-led conventions and it inspired me to investigate to which extent of teachers can shift the responsibility of building learning environment to students.
ReplyDelete
ReplyDeleteI think that a classroom where the students have a lot of involvement and influence in establishing and maintaining norms is one where you will see students taking ownership over their learning. When given the opportunity, even elementary students can handle both establishing and maintaining the norms of the classrooms. Of course, boundaries and protocol should be established, sometimes by the teacher, but once established the classroom can function as a community. Giving students the opportunity to do so makes them more prepared for the world outside the school walls, where they are not teachers establishing norms, but rather societies and cultures. Often, students as a group are more effective with each other when a student has not adequately explained a problem: they ask questions, they ask for a pictorial representation of the problem, they ask for another way to solve the problem. Students are also capable of standing up for injustices they may see and teaching students to stand up for what they feel is right is an important lesson.