Mathematics and Technology

In his Ted Talk about the future of mathematics education, Conrad Wolfram said, “I want to see a completely renewed, changed math curriculum; built from the ground up, based on computers being there, computers that are now ubiquitous almost.” Although I believe in doing mathematics with paper, pencil and the mind and I grew up learning good mathematics this way, I admit that the traditional way of teaching and learning mathematics is going out of fashion in the computer age.

Researchers could all take this time to wax philosophical about the teaching and learning of mathematics through technology. We could debate the merits of teaching math through lectures, we could argue about the efficacy of paper and pencil vs. computers for design and problem solving. However, time is running out for our teachers. They need a clear direction. If the direction is “let’s teach kids good mathematics with technology and engage them in modeling, deep thinking and imagination,” then our teachers need great technology-based math tasks and appropriate training to develop knowledge and skills for teaching mathematics with technology.

Mathematics and Technology (edited by Aldon, Hitt, Bazzini, and Gellert) does an impressive job of presenting mathematical tasks in which technology serves as an important tool to facilitate student learning and engage them in mathematics. The book is divided into five parts, and a collection of relevant papers in each part argues for and draws a concrete and convincing picture of students engaging in mathematics with technology. Part one lays the theoretical groundwork for the rest of the book; addressing the need to improve our current practice of teaching mathematics with the use of technology. Part two presents multiple studies in which students use technology and engage in meaningful mathematics such as proofs and constructions of physical shapes and abstract concepts. A commentary to this part uses the phrase “learning uses technology while technology uses learning” (p. 335) to describe an ideal yet complex relationship between technology and the learner through “the co-construction of humans and technologies”. Parts three and four focus on how technology can help students and teachers communicate not just mathematics but also values and beliefs and help create a new relationship between knowledge, problem solving, and engagement. Part five reflects on professional development for teachers to teach with technology and introduces important principles for the design of professional development. It also discusses teachers’ pedagogical realities along with beliefs and attitudes that may conflict with the policy of using educational technology in the classroom.

A commentary at the end of each section summarizes the chapters and provides new insights that are consistent with the spirit of the book. It may help to start with the commentaries and then select a chapter based on your interest for further reading. Going back to my fascination with the Wolfram brothers, I believe the authors of each chapter also speak for a paradigm change in mathematics education. Their stances are more sophisticated and nuanced, if not more radical, than the educational ambitions of the Wolfram brothers. Indeed, there is a lot more to learning mathematics than coding and building computer modeling to solve application problems.

This book tells us that there are knowledge and skills which should be acquired, but posits that we have technology available as a tool. Then there is an educational task to use the tool, engage in mathematics, and there is the need to build a community of mathematics educators dedicated to developing useful teaching materials and sharing effective teaching methods with technology. And more and more to reflect on. I believe this book offers a great deal of information and insight concerning the aforementioned needs for technology-based mathematics education. 

Woong Lim (woonglim@unm.edu) is an Assistant Professor of Mathematics Education at University of New Mexico. His research interests include mathematics teacher education; and discourse, language, and equity in the mathematics classroom.