Sociomathematical Norms, Argumentation, and Autonomy in MathematicsAuthor(s): Erna Yackel and Paul CobbSource: Journal for Research in Mathematics Education, Vol. 27, No. 4 (Jul., 1996), pp. 458-477
Sociomathematical norms are the normative aspect of mathematical discussions that are specific to a students’ mathematical activity. In this paper, Yackel and Cobb use sociomathematical norms in order to account for how students develop a mathematical disposition; that is how students develop specific mathematical beliefs and values and how they become intellectually autonomous in mathematics. The theoretical perspective is based on constructivism, symbolic interactionism and ethnomethodology. According to this framework, learning in mathematics is not about transmitting knowledge but rather about participating in a culture of mathematics. The development of an individual’s reasoning and sense-making cannot be separated from their participation in the interactive making of taken-as-shared mathematical meanings.
The relationship between teachers and students involves reflexivity as students contribute to classroom discussions and teachers legitimize responses. As this happens students’ understandings evolve and teacher’s interpretations of students’ understandings also evolve. For instance, in a grade 2 classroom students are encouraged to solve problems in a ‘different way’ in order to decompose numbers in several ways. This is not explicitly defined for students but as they respond to teacher and listen to others’ responses they learn what constitutes a ‘different way.’ Also, although elegance or sophistication of students’ responses are not explicitly discussed, students and teacher develop ideas about mathematical solutions that are more efficient than others. Also, reflexivity is highlighted as the teacher’s notions of student understandings evolve.
Explanations and actions in mathematics should be based on mathematical thinking rather than status-based; the goal is for students to base their reasoning on mathematical thinking rather than rely on social cues. The goal is intellectual autonomy.
STOP and Question:
This paper talked about sociomathematical norms that characterize an inquiry mathematics classroom. For example, offering a different solution or treating an explanation as an object for discussion. What sociomathematical norms do you think constitute and inquiry mathematics class? What do you think hinders students from adhering to sociomathematical norms (adopting mathematical ways of knowing)?
This article is similar to my article and reading your reflection helps me to understand the main point of both articles entirely. From my point of view, student’s beliefs of the mathematic classroom and their expectation from this class is the primary reason that hinders them to adhere to the socio-mathematical norms. Students usually believe that in math class teacher must teach and they must take notes and listen carefully. Since the public’s opinion of mathematics is a hard topic, most of the students even do not expect to get the point of a lesson in the class. So it is very unusual and unexpected for them to participate in the teaching process and to think mathematically. Sociomathematical norms mean thinking mathematically and discussing mathematics in the classroom, so when students believe that they cannot understand the math, how they can be involved in mathematics classroom and mathematics thinking?
ReplyDeleteI believe asking students to participate in mathematics discussion is a new method or even a new culture that takes time and practice to be implemented. Therefore, first of all, students must understand that math is not impossible and they can learn it. Then, after a while, these students will be involved in math discussion and teaching process.
These are interesting questions. First, I think that some sociomathematical norms for an inquiry classroom would spread across other subject inquiry classes. In fact, inquiry mathematics may naturally evolve into multidisciplinary discussions. Agreements about communication and collaboration such as suspending judgement, attempting to communicate solutions, taking risks, the right to pass, etc.. could be a starting place. I think that developing a conscious culture in mathematics could take a lot of time and be frustrating for some students. However, I also think that the philosophy of everyone as a developing mathematical thinker and working in a community of inquiry would be advantageous and rewarding in the long run.
ReplyDeleteIn response to your second question, if the sociomathematical norms set by the teacher do not match the ways in which a student is skilled in communicating, the student may have difficulty. Everyone has different ways of making sense of mathematics. This reminds me of a student I taught who was kinaesthetically a genius, but had much difficulty with auditory processing. To work with him, I, and other students, adopted a way of drawing and moving objects to show examples of mathematical thinking. I also think problems can evolve when students are not aware of what sociomathematical norms teachers expect/endorse.
These are interesting questions. First, I think that some sociomathematical norms for an inquiry classroom would spread across other subject inquiry classes. In fact, inquiry mathematics may naturally evolve into multidisciplinary discussions. Agreements about communication and collaboration such as suspending judgement, attempting to communicate solutions, taking risks, the right to pass, etc.. could be a starting place. I think that developing a conscious culture in mathematics could take a lot of time and be frustrating for some students. However, I also think that the philosophy of everyone as a developing mathematical thinker and working in a community of inquiry would be advantageous and rewarding in the long run.
ReplyDeleteIn response to your second question, if the sociomathematical norms set by the teacher do not match the ways in which a student is skilled in communicating, the student may have difficulty. Everyone has different ways of making sense of mathematics. This reminds me of a student I taught who was kinaesthetically a genius, but had much difficulty with auditory processing. To work with him, I, and other students, adopted a way of drawing and moving objects to show examples of mathematical thinking. I also think problems can evolve when students are not aware of what sociomathematical norms teachers expect/endorse.