A mathematics learning environment is a complex conglomeration of factors, rules, interests, identities, and ideologies ranging from institutional, communal, and individual. Players in this space experience success differently and at different levels. Researchers and educators have always struggled with maximizing learning, reducing gaps in learning among learners, and creating lasting experiences for the learners. On my epic to discovering how different and similar mathematics classroom discourses can be; I converse with social constructivists; social humanists, symbolic interactionists, and ethnographers who believe that knowledge is situative and students develop it through interactions, actions, values, choices, and sharing. I have noticed that every player in the mathematics learning and doing space is tuned differently depending on their historical and current contexts, training, and belief systems. I borrow from Rubbin (2007) and Yackel & Cobb (1996) to foster a framework for my arguments and definition of a mathematics classroom. I define a mathematics classroom as a learning community with an adaptive microculture that could impede or enhance learning. The adaptation of the microculture depends on factors such as teacher in-service training, students' dynamic identities, policy reforms, institutional culture and ideology change, and individual leanings.
To account for the development of students' mathematical beliefs and autonomy in a mathematical class, Yackel and Cobb (1996) presented the sociomathematical norm's framework. They relied on social constructivism, symbolic interactionism, and ethnomethodology in crafting their lenses and marking the differences between social and sociomathematical norms in a mathematics class. They believed that social and cultural processes play an integral role in students' development and sense-making of mathematical knowledge (Yackel et al., 2001). Yackel and Cobb defined sociomathematical norms as norms specific to mathematical aspects of students' interactions. They believed that the sociomathematical norms provide a lens to analyze the mathematical aspects of teachers' and students' interactions in a mathematics classroom. These sociomathematical norms are intrinsic aspects of the mathematics classroom microculture that help to analyze sophistication, efficiency, and similarities and differences in mathematical arguments. How would students develop and internalize these sociomathematical norms? How do sociomathematical norms influence mathematical classroom discourse?
Yackel and Cobb (1996) provide a basis for defining and setting up productive classroom discourse; their definition of a class microculture and their underpinning of social and cultural activities in the class are in line with Holland et al. (1998) figured worlds that are central to the positioning of the students as valuable and active contributors to the classroom body of mathematical knowledge development (Gee, 1999; Rubbin, 2007).
Rubbin (2007) addresses differential learning by presenting students' identities amid figured worlds and their effects on classroom discourse. Discusses the out-of-class discourses that affect the in-class discourse. I sometimes wonder how complex it is for students to discern the different discourses, to know what to carry into the class, and when to rely on which for their positioning in the class mathematical activities. I sympathize with students whose worlds are shaped and constrained by dilapidated urban neighborhoods characterized by a dense population, overstretched social amenities, underfunded schools, and a polluted environment with toxins from neighboring industries (Tate, 2008, Hogreb et al., 2012, Anderson, 2014). I wonder how this positions students from this sociocultural, political, and socioeconomic background in a mathematics classroom discourse.
Rubbin's (2007) and Yackel & Cobb's (1996) articles draw from social constructivism to argue that mathematics learning occurs as a result of in-class student interactions shaped and constrained by political, socioeconomic, sociocultural, and ideological disposition within and without their learning institutions. To me, it's not okay to explicate classroom discourse and student mathematical knowledge development and sense-making without exploring such factors. Holland et al. (1998) argue that these factors constitute the figured worlds. They dictate the teachers' and students' identities, values, and actions they embody in any mathematical classroom. I am therefore bothered by how figured worlds impact mathematical classroom discourse. Join me as I try to build knowledge around these research questions: i) To what extent do students' out-of-class experiences affect their in-classroom interactions? and ii) To what extent do target training and math coaching improve in-service mathematics teachers' pedagogical content knowledge and figured identities, and how does this impact their mathematics classroom discourse pedagogy?
References
Gee, J. P. (1999). Mind and Society: A Response to Derek Edwards’‘Emotion Discourse’. Culture & Psychology, 5(3), 305-312.
Hogrebe, M. C., & Tate IV, W. F. (2012). Geospatial perspective: Toward a visual political literacy project in education, health, and human services. Review of Research in Education, 36(1), 67-94.
Holland D., Lachicotte W., Skinner D., & Cain C. (1998). Identity and agency in cultural worlds. Cambridge, MA: Harvard University Press.
Rousseau Anderson, C. (2014). Place Matters: Mathematics Education Reform in Urban Schools. Journal of Urban Mathematics Education, 7(1), 7-18.
Rubin, B. C. (2007). Learner identity amid figured worlds: Constructing (in) competence at an urban high school. The Urban Review, 39(2), 217-249.
Tate, W. F. (2008). Putting the" Urban" in mathematics education scholarship. Journal of Urban Mathematics Education, 1(1), 5-9.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for research in mathematics education, 27(4), 458-477.
Yackel, E. (2001). Explanation, Justification, and Argumentation in Mathematics Classrooms.
My journey to discover; is preceded and trailed by geospatial factors.