We report results from a mathematics content course intended to help future teachers form a coherent perspective on topics related to multiplication, including whole-number multiplication and division, fraction arithmetic, proportional relationships, and linear functions. We used one meaning of multiplication, based in measurement and expressed as an equation, to support future teachers' understanding of these topics. We also used 2 types of length-based math drawings–double number lines and strip diagrams–as media with which to represent relationships among quantities and solve problems. To illustrate the promise of this approach, we share data in which future secondary mathematics teachers generated and explained without direct instruction sound methods for dividing by fractions and solving proportional relationships. The results are noteworthy, because these and other topics related to multiplication pose perennial challenges for many teachers.
Andrew Izsák, Department of Education, Tufts University, 203 Paige Hall, Medford, MA 02155; Andrew.Izsak@tufts.edu
Torrey Kulow, Portland State University, College of Education, Curriculum and Instruction, PO Box 751, 1900 SW 4th Ave, Rm 290U, Portland, OR 97207-0751; firstname.lastname@example.org
Sybilla Beckmann, Department of Mathematics University of Georgia, 501 Boyd GSRC, Athens, GA 30602; email@example.com
Dean Stevenson, Prince William County Schools, 14715 Bristow Rd, Manassas, VA 20112; StevenDL@pwcs.edu
Ibrahim Burak Ölmez, University of Georgia, 105 Aderhold Hall, 110 Carlton St, Athens, GA, 30602; firstname.lastname@example.org