Dana C. Cox

Developing and Validating a Reliable TPACK Instrument for Secondary Mathematics Preservice Teachers

Abstract Within the realm of teaching middle and high school mathematics, the ability to teach mathematics effectively using various forms of technology is now more important than ever, as expressed by the recent development of the Common Core State Standards for Mathematical Practice. This article presents the development process and the results from 15 institutions and more than 300 surveys completed by secondary mathematics preservice teachers. The results suggest that technological, pedagogical, and content knowledge; technology knowledge; content knowledge; and pedagogical knowledge constructs are valid and reliable, whereas pedagogical content knowledge, technological content knowledge, and technological pedagogical knowledge domains remain difficult for preservice teachers to separate and self-report.

Screencasting as a Tool to Capture Moments of Authentic Creativity

In the context of working with preservice secondary mathematics teachers (PSMTs) in a course on mathematical problem solving with technology, we tested the potential of technology to both inspire and capture moments of authentic creativity in the mathematics classroom. In a case study of two PSMTs working in partnership to solve a task using Interactive Geometry Software (IGS), we documented a rich narrative based on four episodes of creativity. These four episodes can be characterized as moments of creative insight because they represent moments that inspired either the development of new solutions or strategies (Problem Solving Insights) or spurred new questions (Problem Posing Insights). At the heart of the case is a task that requires constant negotiation and discussion in a digital workspace. Capturing an authentic narrative can be challenging with verbalized thinking alone, as the articulation of insight is not always possible. Screencasts are a tool that captures verbalized thinking as well as on-screen activity. This case study illustrates the power that this tool has in preserving the authenticity of those moments, but also in creating a record of practice to which both students and teachers might refer when making learning processes explicit.

Engaging in Research: Why? How? Now!

Why should teachers engage in research studies? As a community, teachers and researchersare concerned with addressing critical issues in math education. NCTM’s web resources and conferences, as well as the pages of this journal, give evidence of a growing community and an expanding body of work supporting NCTM’s (2012) position of linking research and practice—a “border crossing” between the world of research and the world of teaching (Silver 2003). Despite these initiatives, an emerging issue remains: How do we work together to cultivate a two-way exchange of professional knowledge (Heid et al. 2006)?

Multiplication principle problems and permutation problems

How many different outfits are possible when assembled from three pairs of pants and five shirts? In how many different ways can four students be arranged in a line?