
05239847
j
2008a.00025
Milou, Eric
Schiffman, Jay L.
The spirit of discovery: The digital roots of integers.
Math. Teach. (Reston) 101, No. 5, 379383 (200708).
2007
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
B50
F69
discovery learning
teacher education
mathematical concepts
mathematics skills
faculty development
problem solving
secondary school mathematics
number concepts
number theory
Summary: In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed in this article was conducted with a group of preservice and inservice teachers, and the objectives included examining patterns, making conjectures, and using data analysis to construct scatter plots and tables, all in the spirit of discovering mathematics. This activity is based on a concept called the multiplicative digital root of an integer (Sloane 1973). (In this article, the term "integers," unless otherwise qualified, mean positive integers.) An activity of this sort can stimulate meaningful discovery by having participants collect data, harness technology, explore patterns, form conjectures based on the analysis of such patterns, use counting tools, and improve computational proficiency as part of their professional development. (Contains 2 figures and 8 tables.) (ERIC)