Category: research
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Constructivism is a theory of learning, not of labeling
I deeply believe that knowledge is constructed in relationship to what we already know. Understanding means constructing a web of connections, ideas, experiences, etc. So I am certainly a constructivist in mathematics, although I tend to see individual children as learning through not only their own experience, but through engagement…
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Concrete Representational Abstract (CRA) in mathematics
In response to a Twitter inquiry, I decided to write up some longstanding thoughts on the Concrete Representational Abstract (CRA) sequence that is popular particularly in designing instruction for learners with disabilities. First, what is CRA? Here, from a researcher who done several studies on CRA with students with disabilities…
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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 Education, 47(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…
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Disability, invisibility, and equity in mathematics (part one)
A recent post by my friend and colleague Andrew Benjamin Gael rightly critiqued the recent NCTM conference for omitting disability in current calls for equity. The recent Executive Summary of the Principles to Actions doesn’t mention disability or special education at all. Andrew asked why, and then went on to…
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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.…
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