Research, Reflection, Practice: Children's Mathematical Understanding and Invented Strategies for Multidigit Multiplication

Abstract

Sharon, a fourth grader, was trying to solve a multiplication word problem: “A science lab has 37 ants. Students observed that each ant has 6 legs. How many legs do the ants have altogether?” She tried to recall the formal algorithm for multiplication. Setting up a table by 7s, she said, “Seven times six is 7, 14, 21, 28, 35, 42. Forty-two, put down two and carry four. Four plus three is seven. Seven times six is 42. So the answer is 422” (see fig. 1).