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ERIC Number: EJ1020246
Record Type: Journal
Publication Date: 2013-Aug
Pages: 8
Abstractor: ERIC
ISSN: ISSN-1073-5836
Norms and Mathematical Proficiency
Kastberg, Signe E.; Frye, R. Scott
Teaching Children Mathematics, v20 n1 p28-35 Aug 2013
To challenge students' reasoning and to align with a physical fitness unit that students were studying, teachers and authors, Scott Frye and Signe Kastberg adapted a ratio comparison problem from Susan Lamon, "Ratio and Proportion: Connecting Content and Children's Thinking," (1994) to include athletes and doctors who share pizza. In Frye's sixth-grade class, "persisting" and "challenging" and "questioning" were expected behaviors in all academic discussions. In mathematics class, however, these norms took on new dimensions as "sociomathematical norms", or expected ways of engaging in mathematical discussions. These particular ways in turn contributed to students' "mathematical proficiency." Sociomathematical norms for participation can be fostered when students' attention is focused on contributing to mathematical discussions, understanding one another's ideas, and exploring the merits of those ideas. Social norms develop across all disciplines. Although challenging and questioning would be considered a social norm, the students' discussions that focused on identifying and understanding differences in solutions and processes and evaluating their efficiency were sociomathematical norms. The development of mathematical proficiency can emerge from teachers' efforts to establish sociomathematical norms. Encouraging and drawing attention to students' comparison and evaluation of mathematical ideas is an important first step. In Frye's class, the discussion and comparison of students' solutions helped build mathematical proficiency. Because students were supported in persisting, representing, and sharing their findings and methods--as well as debating the differences in findings and solution methods--they developed strategic competence, adaptive reasoning, and productive dispositions. Frye's story illustrates how attention to students' discussion of their findings and processes can help develop sociomathematical norms and mathematical proficiency.
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Elementary Education; Grade 6
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A