NotesFAQContact Us
Search Tips
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ1044627
Record Type: Journal
Publication Date: 2014-Nov
Pages: 6
Abstractor: ERIC
Reference Count: 7
ISSN: ISSN-0025-5769
"Both Answers Make Sense!"
Lockwood, Elise
Mathematics Teacher, v108 n4 p296-301 Nov 2014
Formulas, problem types, keywords, and tricky techniques can certainly be valuable tools for successful counters. However, they can easily become substitutes for critical thinking about counting problems and for deep consideration of the set of outcomes. Formulas and techniques should serve as tools for students as they think critically about counting problems; they should not become students' only mechanisms for counting. Counting is, ultimately, about enumerating a desirable set of objects, and this goal should not be lost on students. Teachers should encourage students to ground their work in the set of outcomes that they are trying to count and to use problem types, keywords, and formulas as resources in that work. The practice of systematically creating lists can help students build a foundation for more complex counting problems that they may encounter. By encouraging students to consider sets of outcomes as they count, teachers can help students ground their counting procedures and strategies in something concrete, enabling them to think and work in accessible contexts. Doing so can foster a perspective of counting as a meaningful and flexible activity rather than a mindless application of formulaic rules and procedures. With a robust understanding of how their counting processes structure and organize the set of outcomes, students can be more equipped to develop into successful counters and combinatorial thinkers.
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: High Schools; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A