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ERIC Number: EJ1044517
Record Type: Journal
Publication Date: 2014-Oct
Pages: 6
Abstractor: ERIC
Reference Count: N/A
ISSN: ISSN-0025-5769
Connecting the Dots: Rediscovering Continuity
Camenga, Kristin A.; Yates, Rebekah B. Johnson
Mathematics Teacher, v108 n3 p212-217 Oct 2014
The topic of continuity is typically not introduced until calculus and then reexamined in real analysis. Recognizing the connections between secondary school mathematics and the advanced mathematics studied at the college level allows teachers to better identify mathematical concepts in student ideas, motivate students by piquing their curiosity, develop a robust foundation for future student learning, and create opportunities for students to learn more about the process of doing mathematics. In this article, the authors examine the advanced concept of continuity of functions on the real line through the lens of middle and high school curriculum examples, connecting these examples to the development of continuity in calculus and real analysis. Although the authors are not advocating that teachers present these precise definitions of continuity to students before calculus, they believe that awareness of the definitions can help teachers recognize the precursors of advanced ideas in their own curriculum. A bibliography is included.
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: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A