ag7084@usma.edu

I have developed a framework that describes students’ habits in learning mathematics (How should I study it?), and practices in checking mathematical truth (How do I verify it?). My work stems from theories of college students' intellectual development (e.g. Perry, 1970), which state, in brief, that students begin with narrow, black-and-white, uncomplicated views of the world but slowly develop more complex, contextual, shades-of-gray views. I took these theories on "ways of knowing" and adapted them into "ways of knowing mathematics" to help frame students' intellectual understandings about mathematics. The results of my research is an evolving framework that describes stages of development of mathematical sophistication in undergraduates (much in the spirit of Piaget's description of the stages of learning of schoolchildren).

My poster displays the theoretical framework. My presentation is highly interactive – as people walk by my poster, I buttonhole them, ask them to bring to mind a student they know well, and we collaboratively discuss the framework, which describes five stages of sophistication in two separate categories. I therefore have the chance to give each participant some hands-on experience for the framework, and I provide them a summary sheet and contact information to enable further exploration.

References

Perry, W. G. (1970). Forms of intellectual and ethical development in the college years. New York: Holt, Rinehart & Winston.