ERIC Number: EJ1096287
Record Type: Journal
Publication Date: 2016-Feb
Integer Solutions of Binomial Coefficients
Gilbertson, Nicholas J.
Mathematics Teacher, v109 n6 p472-475 Feb 2016
A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation concisely and applying it with straightforward calculations. Delving deeper, however, reveals countless interesting connections, patterns (e.g., Pascal's triangle), and applications (such as those found in Cox et al.  and Lockwood ). What is particularly important about the two approaches presented here is that they are very different and yet they end up in the same place. Attending to what the situation represents (i.e., combinations) provides insights different from those that arise when we focus on the structure of the formula. Although the proof may be more complicated than many students can handle, the main ideas are still accessible.
Descriptors: Mathematics Instruction, Mathematical Formulas, Validity, Mathematical Logic, Problem Solving, Secondary School Mathematics, Computation, Mathematical Concepts, Teaching Methods
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: NCTM@nctm.org; Web site: http://www.nctm.org/publications/mathematics-teacher/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education
Authoring Institution: N/A
Grant or Contract Numbers: N/A