Using Classroom Scenarios to Reveal Mathematics Teachers’ Understanding of Sociomathematical Norms

Abstract

The purpose of this study was to uncover the degree to which in-service teachers understand sociomathematical norms and the nature of that understanding without having to enter and observe their classes. We therefore developed five classroom scenarios exemplifying classroom interactions shaped by certain sociomathematical norms. We then administered these scenarios to in-service elementary school and grade 5-12 mathematics teachers and collected their written responses. We also collected data about what teachers believe about sociomathematical norms through a Likert-type questionnaire. We then analyzed the data using quantitative and qualitative techniques. First, the findings suggest that the teachers' understanding of sociomathematical norms is neither dependent on the level of schools teachers teach, or their background or demographic characteristics such as number of years they spent in teaching, specialty area, faculty graduated, highest degree earned, and gender. Second, what teachers believe about sociomathematical norms seem to be not parallel to how they analyze the scenarios illustrating sociomathematical norms. Third, use of scenarios was helpful in revealing how teachers think about sociomathematical norms. Finally, there are three cross-cutting themes to which all the teachers referred in common for all sociomathematical norms: opposition (opposition to the core of the norm), social facilitator (considering all targeted norms as supporting and regulating the classroom social environment) and condition-based (believing that interactions given in scenarios are only possible under certain conditions).

Mathematical Resilience, Habits of Mind, and Sociomathematical Norms by Senior High School Students in Learning Mathematics: A Structured Equation Model

“…Furthermore, for the sociomathematical norm instrument in this study, it refers to the following indicators: 1) experience of mathematics: contributing carefully and actively in discussion activities in the process of learning mathematics; 2) explanation of mathematics: understanding ideas and being able to explain their ideas from solutions systematically; 3) mathematical difference: identifying the similarities and differences in the ideas of several alternative solutions, as well as comparing the similarities and differences in the ideas of several alternative solutions that have been constructed; 4) mathematical communication: making sense as a basis for communication in the learning process and submitting statements to understand an idea in a language that is easy to understand; 5) mathematics effectiveness: finding the most effective alternative solutions and explaining the solutions to problems in a straightforward manner; 6) mathematical insight: interact in depth in discussion activities and use various sources in the discussion process to solve problems (Kang & Kim, 2016;Ningsih & Maarif, 2021;Widodo et al, 2020;Yackel & Cobb, 1996;Zembat & Yasa, 2015).…”

“…This is intended to explore the positive contribution of the affective domain in the learning process. The scope of study of affective has begun to develop, not only examining attitudes but examining several aspects such as beliefs and emotional reactions (Ignacio et al, 2006), mathematical resilience (Hendriana et al, 2019;Johnston-Wilder et al, 2018;Johnston-Wilder et al, 2015;Kooken et al, 2013;Thornton et al, 2012), habits of mind (Costa & Kallick, 2008;Dwirahayu et al, 2017;Matsuura et al, 2013;Yellamraju et al, 2019), sociomathematical norm (Güven & Dede, 2017;Maarif et al, 2022;Sánchez & García, 2014;Yackel & Cobb, 1996;Zembat & Yasa, 2015), and so on. These affective aspects must be developed and optimized in teaching and learning activities, especially mathematics.…”

“…Social interaction in learning mathematics is needed to develop their ideas in solving math problems (Kang & Kim, 2016). As long as students play an active role in building sociomathematical norms, they develop self-confidence and mathematical values that can be used as a basis for thinking actions in autonomous learning communities (Dickes et al, 2020;Zembat & Yasa, 2015).…”

Students' problem-solving ability: An analytical practice viewed from the aspect of sociomathematical norm

“…In line with the opinion of Ningsih & Maarif (2021) who stated that problemsolving is related to sociomathematical norms because these sociomathematical norms focus on how problem-solving should be done. The importance of sociomathematical norms is stated in Zembat & Yasa (2015), sociomathematical norms are an important part of educator knowledge in terms of supporting the mathematical development of students and shaping the quality of social interaction in the classroom.…”

Prescriptions Guiding Prospective Teachers in Teaching Mathematics

“…What is the nature of the knowledge that is specific to teaching?" Ma (1999) concludes that teachers should have deep knowledge at their teaching level instead of knowing advanced mathematics because no direct positive correlation exists between the formal education that teachers receive and their teaching (Askew, Brown, Rhodes, Johnson, & William, 1997;Zembat & Yasa, 2015). Teachers' knowledge should also be "connected" and "profound" (Ma, 1999).…”