How to help kids use more complex strategies in multiplication? Give them harder problems.

Zhang, D., Xin, Y. P., & Si, L. (2013). Transition from Intuitive to Advanced Strategies in Multiplicative Reasoning for Students with Math Difficulties. Journal of Special Education47(1), 50–64. I love this article because it uses constructivism to understand the development of three kids with disabilities in learning multiplication, particularly drawing from the work of Siegler on how kids use multiple strategies over their course of their development with a new mathematical operation. Take-away- kids only switched strategies from counting when the numbers got big enough. Lesson to be learned is to stop giving kids only easy problems, because such problems actually encourage them to continue using less sophisticated strategies. (more…)

Designing intervention on the landscape of learning

In 1999, I was working as a special educator in an inclusive elementary school. My ideas about mathematics instruction were old-fashioned.  A few of my fifth-grade students had particular difficulties in multiplication, and it was hard to see what they could do—I was so focused on what they couldn’t do.   That summer I attended the Summer Institute at Mathematics in the City at the City College of New York.  One (of many) ideas that transformed my work was the idea of the landscape of learning.  (more…)

Designing intervention in operations

In Models of Intervention in Mathematics, edited by Cathy Fosnot and published by NCTM in 2010, Susan Jo Russell wrote a piece called “The habit of reasoning: Uncovering competence through focused instruction.” I love this piece because it gives a structure to how teachers can plan intervention with kids that builds on strengths. (more…)