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ERIC Number: EJ1016716
Record Type: Journal
Publication Date: 2013-Mar
Pages: 9
Abstractor: ERIC
ISSN: ISSN-1072-0839
Restoring Order to Permutations & Combinations
Kimani, Patrick M.; Gibbs, Renamarie T.; Anderson, Sarah M.
Mathematics Teaching in the Middle School, v18 n7 p430-438 Mar 2013
Numerous research articles and curricula standards maintain that learning is optimized when students are actively involved in the learning process by assimilating information and constructing their own meanings. The authors' experience with teaching probability concepts has shown that students struggle with concepts of counting. These struggles affect students' ability to find sample spaces and probability. In particular, students have difficulty making sense of permutations and combinations. They often have trouble with the meanings of these concepts, with their relationships, and how and when to use each concept. The authors have found that students lack the conceptual understanding necessary to succeed in making sense of these ideas. Their observations of students' struggles with counting concepts are consistent with what others have identified (e.g., Annin and Lai 2010; Sriraman and English 2004). To combat this lack of foundational understanding, they use a student-centered problem-solving approach to engage sixth-grade students in making sense of counting problems. In this article, the authors share how they teach the fundamental counting principle (FCP) and use it as a crosscutting and unifying theme for all other counting concepts. 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: Middle Schools; Grade 6
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A