{"title":"Sociomathematical scaffolding as students engage in revising draft definitions, conjectures, and proofs","authors":"Kristen Vroom, Brittney Ellis","doi":"10.1007/s10649-023-10294-1","DOIUrl":null,"url":null,"abstract":"<p>Instructors manage several tensions as they engage students in defining, conjecturing, and proving, including building on students’ contributions while maintaining the integrity of certain mathematical norms. This paper presents a case study of a teacher-researcher who was particularly skilled in balancing these tensions in a laboratory setting. We introduce sociomathematical scaffolding, which refers to the scaffolding of normative aspects for mathematical discourse. We found that the teacher-researcher’s sociomathematical scaffolding entailed inquiring into the students’ intended meaning of their draft and then supporting students in revising their draft to adhere to mathematical norms. We illustrate this pattern in three episodes in which the teacher-researcher supported a pair of students to revise their drafted (1) definition of unbounded above sequences, (2) conjecture of the Archimedean Property, and (3) proof by contraction of the Archimedean Property.</p>","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":"36 1","pages":""},"PeriodicalIF":3.4000,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Educational Studies in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10649-023-10294-1","RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
引用次数: 0
Abstract
Instructors manage several tensions as they engage students in defining, conjecturing, and proving, including building on students’ contributions while maintaining the integrity of certain mathematical norms. This paper presents a case study of a teacher-researcher who was particularly skilled in balancing these tensions in a laboratory setting. We introduce sociomathematical scaffolding, which refers to the scaffolding of normative aspects for mathematical discourse. We found that the teacher-researcher’s sociomathematical scaffolding entailed inquiring into the students’ intended meaning of their draft and then supporting students in revising their draft to adhere to mathematical norms. We illustrate this pattern in three episodes in which the teacher-researcher supported a pair of students to revise their drafted (1) definition of unbounded above sequences, (2) conjecture of the Archimedean Property, and (3) proof by contraction of the Archimedean Property.
期刊介绍：
Educational Studies in Mathematics presents new ideas and developments of major importance to those working in the field of mathematics education. It seeks to reflect both the variety of research concerns within this field and the range of methods used to study them. It deals with methodological, pedagogical/didactical, political and socio-cultural aspects of teaching and learning of mathematics, rather than with specific programmes for teaching mathematics. Within this range, Educational Studies in Mathematics is open to all research approaches. The emphasis is on high-level articles which are of more than local or national interest.? All contributions to this journal are peer reviewed.
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