strategic flexibility

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…)

New research on how learners in special education intuitively and accurately use indirect addition for subtraction

For far too long, the assumption has been that learners with disabilities cannot benefit from constructivist mathematics instruction.  This assumption, in my opinion, is based on the highly erroneous idea that kids with disabilities cannot think for themselves, but must be spoon-fed methods.  In my experience, this is not true.  First, kids with disabilities are a highly diverse group of learners, with different strengths and needs. Second, all learners construct knowledge based on their own experiences and knowledge. Unfortunately, many researchers in special education mathematics seem to misunderstand constructivist mathematics as discovery learning rather than the carefully designed and scaffolded instructional sequence that it is. Here is some new evidence to support that idea, particularly about subtraction. (more…)