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So many articles that are written to help teachers improve their teaching are often from a perspective well beyond the classroom, and come off sounding condescending to teachers. This article is not one of those. This one is so teacher friendly and classroom familiar that when I first read it I couldn’t wait to get back in the classroom to look more closely at my own teaching. How often, I wondered, did I interrupt a child discussing their workable strategy so that I could show my more efficient strategy? Did I notice what that did to a child? How often did I begin actually writing steps to a problem, and not letting the student do it? What image of learning was I giving a student by doing that? And that was just the beginning of the article.
Once upon a time in teacher education we learned about Bruner and Piaget, and others who built on their foundation – but all of us for quite a number of years knew the foundation sources of our craft. That is no longer the case. This article should be one that doesn’t disappear over the years, but becomes a foundation for others to build on; it will be useful for many years.
Putting a twist on a popular mathematical tool, this collection
of activities shows how putting a number 1 in the bottom-left cell and a 100 in
the top-right cell can better support student reasoning.