ERIC Number: EJ1484319
Record Type: Journal
Publication Date: 2025
Pages: 5
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0025-5769
EISSN: EISSN-2330-0582
Available Date: 0000-00-00
What Do You Mean by the "Fancy 1?"
Laura B. Kent; Tammy Skelton
Mathematics Teacher: Learning and Teaching PK-12, v118 n9 p708-712 2025
Effective mathematics teaching practices include not only probing student thinking and selecting student strategies to share but also facilitating discourse and encouraging reflection about important mathematical ideas (National Council of Teachers of Mathematics [NCTM], 2014, pp. 36-37). Encouraging students to use precise academic vocabulary to communicate their own strategies helps to align their thinking with conventions and mathematical notations. Students do not always know why their strategies work, and a vital role of the teacher as the facilitator of learning is to equip students to communicate their ideas with accurate terminology. In this scenario, the teacher recognized an opportunity to formalize what one student called the "Fancy 1" when describing a strategy for solving a proportion problem. Posing problems that elicit informal scaling strategies provides opportunities for the introduction of the Identity Property of Multiplication, as halving and doubling the same quantity is the same as multiplying by one. Notating these strategies using equations that show that multiplying and dividing by the same number is the same as multiplying by one can facilitate connections between these scaling strategies and the Identity Property of Multiplication. Highlighting properties of operations is an important aspect of analytical and structural aspects of algebraic reasoning (Kieran, 2022). This article describes a sixth-grade lesson in which the Identity Property of Multiplication was introduced and formalized as part of a unit on ratio reasoning and percentages. The teacher, Mrs. S, used problem posing as her primary instructional practice to elicit student thinking and encourage diverse approaches to solving the problem.
Descriptors: Grade 6, Mathematics Education, Multiplication, Language Usage, Learning Strategies, Educational Practices, Problem Solving, Teaching Methods
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: publicationsdept@nctm.org; Web site: https://pubs.nctm.org/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Elementary Education; Grade 6; Intermediate Grades; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A

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