In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the…

In what unique ways can mathematics tasks contribute to pre-service teachers' understanding of subject matter and pedagogy? And what school mathematics tasks can usefully be included in a pre-service program? To contribute to answering these questions, we report on the selection and choice criteria for mathematics tasks that we use in an…

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…