The book that influenced my approach to teaching mathematics to children is Mindstorms by Seymour Papert. Subtitled Children, Computers, and Powerful Ideas, this book provided a glimpse into a world of which I knew little but eagerly wished to learn more. As promised, powerful ideas emerged quickly and continued to be revealed at every turn. The most compelling idea for me, the one that figuratively jumped off the page, was the author's concept of Mathland. Papert envisioned a learning environment designed to make the development of mathematical concepts a more natural process. This novel vision captured my imagination and laid the groundwork for what would later become our after school math center.
So many questions arose. Could math achievement be improved by weekly trips to an authentic Mathland? What would such an environment look like? What did we want students to learn and how would they learn it? After a few false starts, we eventually succeeded in making our version of Mathland a reality. Each week students were transported to a world of numbers, mathematical ideas, and meaningful challenges. Gear Math was a hands-on, problem solving program designed to teach multiplication, division, ratio, and proportion to upper elementary students. Students programmed robots to traverse number lines and coordinate systems and designed containers based on volume and surface area restrictions. Most importantly, the residents did very well in school math despite the fact that curriculum objectives rarely overlapped.
How was that possible? Students learned to think and act and approach problem solving much like a mathematician would. This was accomplished by immersing students in credible learning environments and by providing challenges that were not only engaging but also demanded intellectual investment. Getting the right answer was important but it wasn’t the only goal. Making sense of those answers was critical. Explanations were reworked and refined. Multiple representations were encouraged. Our students developed a familiarity with math that all the practice sets and timed drills in the world could never accomplish. And, most importantly, it laid the foundation for future success in math. As our students moved from elementary to middle school, high school, and beyond, they always carried a piece of Mathland with them.