President's Choice: Mathematical Insight: Changing Perspective
Selected by Lee V. Stiff.
Encouraging Preservice Mathematics Teachers as Mathematicians
An assignment that asks preservice secondary mathematics teachers to make connections between the mathematics they know and the mathematics they will teach. It describes how one preservice teacher's project resulted in a physical representation of the statement and proof that the sum of cubes of the first n natural numbers is equal to the square of their sum.
What Else Can You Do with an Open Box?
Catherine Miller, Douglas Shaw
Starting with the classic Open Box problem, we present extensions of this problem that can be used in high school mathematics classes. We also challenge high school teachers to use this process of problem analysis in their own practice as a way to enrich the content of their lessons and as a means of individualized professional development.
Shifting from Traditional to Nontraditional Teaching Practices Using Multiple Representations
Algebraic reasoning skills can be enhanced by building connections among symbolic, tabular, and graphical representations. But how do classroom teachers change traditional teaching practices to foster the use of different representational forms? This article explores how I learned to incorporate representational fluency in teaching and assessment. It builds on ideas from classroom practice and advocates making small changes in teaching practices to foster connections between representations.