Chapter 2: Framing the Research on Digital Technologies and Student Learning in Mathematics

Today, U.S. schools are challenged to improve students’ school to K−12 mathematics education while enhancing their problem solving and critical thinking skills. Problem solving is a mathematical process integral to all mathematics learning that supports students in constructing new mathematics knowledge while concurrently developing key metacognitive skills of planning, evaluating, modifying, and reflecting when solving problems (National Council of Teachers of Mathematics [NCTM], 2000).

A primary goal of mathematics education is to promote competent problem solving practices. Mathematics educators strive to create problem solvers who are flexible thinkers capable of using a range of techniques and processes to approach novel problem situations (Schoenfeld, 1992). Technological tools provide one means for realizing this primary goal. Digital, silicon-based technologies are sometimes referred to as mind tools or objects for engaging students in critical thinking and higher order learning, sometimes portrayed as “ideal tools for knowledge construction” (Harvey & Charnitski, 1998). Spreadsheet capabilities provide students with mind tools that encourage the building of mathematical models to represent and understand quantitative relationships. Dynamic geometry software supports student explorations and development of mathematical arguments about geometric relationships. Many virtual manipulatives provide a dynamic environment for student exploration of mathematical ideas and affords them with opportunities to experiment, conjecture, and engage in higher level mathematical thinking.