Structuring Boardspace to Facilitate Repeated Reasoning

• Published in: The Mathematics teacher Vol. 114; no. 3; pp. 196 - 204
• Main Authors: DeLeeuw, William, Otten, Samuel, Dundar, Ruveyda Karaman
• Format: Journal Article
• Language: English
• Published: National Council of Teachers of Mathematics 01-03-2021
• Subjects: Common Core State Standards; Concept Formation; Educational Technology; Geometric Concepts; Geometry; Grade 6; Instructional Effectiveness; Lesson Plans; Mathematical Concepts; Mathematics Instruction; Teacher Student Relationship; Teaching Methods; Thinking Skills; Visual Aids
• ISSN: 0025-5769
• DOI: 10.5951/MTLT.2019.0360

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given mathematical topic, some students may perceive the structure or regularity, whereas others do not yet "get it." It is a teacher's job to help students notice and analyze the structure and patterns in mathematical entities, and they must also be able to express them through mathematical statements or visual representations. These two practices, though challenging, can be mutually supportive because students may notice patterns first and express regularity in repeated reasoning later. This article discusses how the planful use of boardspace can help move the structure and regularity to the visual realm and thus make it more readily perceivable by more students. Although the authors recognize that different types of boards (e.g., whiteboards, blackboards, SMART boards™, poster paper, etc.) vary in their specific advantages and disadvantages, they refer to their general purpose as a mode of visual display accessible by the whole class. They discuss some of the purposes of board use and illustrate these ideas with two examples of lessons in which the planful use of boardspace provided students with the opportunity to see the mathematical structure and regularity.