SOCIOMATHEMATICAL NORMS, ARGUMENTATION, AND AUTONOMY IN MATHEMATICS
By Erna Yackel And Paul Cobb
In order to make sense of mathematics learning and teaching, the authors put forward a framework to interpret students’ learning from the perspective of sociomathematical norms. Sociomathematical norms, described by the authors, are unique to mathematics, in contrast with social norms which are general across all subject areas. “For example, the understanding that students are expected to explain their solutions and their ways of thinking is a social norm, whereas the understanding of what counts as an acceptable mathematical explanation is a sociomathematical norm” (p. 461). In this paper, the sociomathematical norms of mathematical difference and mathematical sophistication are established. The central idea of sociomathematical norms is that the normative aspect of mathematics discussion in classrooms is co-constructed by the teacher and students, which opposes the notion that mathematics learning is context-free. The author argues that what becomes mathematically normative in a classroom is shaped by the teaching goals, understanding of constraints, and negotiation among the classroom participants.
Further, the author illustrated how different sociomathematical norms regulate mathematical argumentation and provide extensive learning opportunities for both the students and the teacher. Whiles students consistently contribute to the classroom discussion by explaining their solutions, the teacher is offered opportunities in turn to develop notions of what is sophisticated and efficient for the children. The paper also discussed the link between sociomathematics norms and being autonomous learners. The author explained that autonomy takes place when students take responsibility to an extent beyond “being a student”. Such a transition requires awareness of sociomathematical aspects created by students and teachers. This is also noticed in many inquiry-based approach classes I have observed.
The authors argued that “initially, students' explanations may have a social rather than a mathematical basis.” (p. 467) While I had a very vague conception of the mentioned process, I experienced an enjoyable enlightenment reading this paragraph. One particular example was used for clarifying how the teacher and students interactively constitute what counts as an acceptable explanation and justification. In example 4, a student changed her answers and challenged the mathematical basis for explanations. The teacher explicitly acknowledged that “she changed her answers on the basis of her interpretation of the social situation rather than on mathematical reasoning, the teacher invents a scenario to clarify his expectations for this class.” (p. 468). I sense that this practice of the teacher was surprisingly effective and powerful since it created a concrete case that every student can comprehend and refer to.
Question:
The author distinguishes sociomathematical norms from social norms. How do you think norms in math classrooms differ from norms in other subjects?
There are more norms that different school subjects have in common than differences. I think there are many norms that are associated with other subjects that also apply in mathematics classrooms. Norms like in English or Socials, you may be asked to support your opinion with evidence, and in mathematics class, you would be asked to support your solution. You may be expected in English to use correct spelling and grammar. The same is true in my mathematics classroom. Establishing criteria for assignments and expectations is also occurring in many classrooms. Even in regards to behaviour, expectations and norms are remarkably consistent. Perhaps this is because my class writes their own “norms” at the beginning of the year and do so in many of their classes. The student-generated norms are remarkably consistent across subjects. Certainly, some norms are specific, such as using bar models (pictorial representations) in their work in many units, not being allowed to use a calculator, how the teacher interacts and provides feedback to students, but I think there is more in common than not.
ReplyDeleteI suppose the norms in mathematics classrooms is covered by the belief of a teacher’s magical word: “mathematically”. And this word strongly relies on the interpretation of the teacher that what mathematics is. I think most mathematics teachers believe mathematics requires writing with using numbers rather oral explanation, and students’ accuracy based on the textbooks rather their uniqueness. Although other subjects might have similar norms, I guess, mathematics is more restricted to follow the norms. For instance, new students such as transfer student need to understand the norms about what the other students have learned in the classroom as much as the mathematical knowledge. However, the other subjects might require the knowledge rather than the norms (but we have to investigate it).
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