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ERIC Number: EJ1070867
Record Type: Journal
Publication Date: 2015-Apr
Pages: N/A
Abstractor: ERIC
ISSN: ISSN-0025-5769
Conceptual Precalculus: Strengthening Students' Quantitative and Covariational Reasoning
Madison, Bernard L.; Carlson, Marilyn; Oehrtman, Michael; Tallman, Michael
Mathematics Teacher, v109 n1 p54-61 Aug 2015
Research over the past few decades points to ways precalculus and calculus courses can be strengthened to improve student learning in these courses. This research has informed the development of the Algebra and Precalculus Concept Readiness (APCR) and the Calculus Concept Readiness (CCR) assessments. In this article, the authors present three sample tasks from these instruments--the Oil Spill problem, the Free Throw problem, and the Ladder problem--that require an understanding of functions to represent the relationship between quantities. Commentary on student responses serves to identify foundational reasoning abilities and may help teachers develop curriculum to support student achievement.
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: N/A
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: DUE-1122965