ERIC Number: EJ1329811
Record Type: Journal
Publication Date: 2022-Jan
Pages: 10
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0025-5769
EISSN: N/A
Available Date: N/A
Contemplate Then Calculate
Lucenta, Amy; Kelemanik, Grace
Mathematics Teacher: Learning and Teaching PK-12, v115 n1 p16-25 Jan 2022
Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word "shortcut!" So, the question is, how do teachers reduce students' knee-jerk reactions to follow procedures and algorithms and increase their capacity to pause and notice mathematical structure to find shortcuts? One response is to develop their capacity to think structurally. In this article, the authors will explore what it means to think structurally and introduce an instructional routine, Contemplate Then Calculate, to engage students in and develop structural thinking so that teachers can implement it with their students.
Descriptors: Mathematics Education, Mathematics Instruction, Teaching Methods, Computation, Thinking Skills, Mathematics Skills, Problem Solving, Task Analysis, Learning Strategies, Elementary School Mathematics, Secondary School Mathematics
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 - Evaluative
Education Level: Elementary Education; Secondary Education
Audience: Teachers
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: 1238157
Author Affiliations: N/A