There is, of course, nothing wrong with math. Math is wonderful. It’s the foundation of science and technology. It lets us describe and discover how the world works. However, there is something very wrong with the way math is taught, and that poses a serious problem.
An oft-stated goal is that students should develop a deep understanding of mathematics and be able to apply this knowledge across subject areas in the solving of non-routine problems. It’s an excellent goal, but one that today’s dominant instructional materials were not designed to achieve.
Most curricula present worked-out examples of routine problems, then have students reenact the steps on a few variations of those problems. These curricula are usually static, with no real-time feedback, giving students practically no opportunity to learn from mistakes and adjust their understanding.
Even computer-adaptive programs typically resort to giving students the answers after only a few incorrect attempts. This is not the way to build the depth of knowledge, the flexible problem-solving skills, and the perseverance needed to contribute to the advancement of science and technology.
We need to radically improve the instructional materials. At MIND Research Institute, we have been researching how to create learning environments where students understand math by doing math. Through well-designed interactive visual puzzles, we find that students experience first-hand how and why math works. They try things out, form and test hypotheses, and actually learn from their own mistakes.
Because games can provide real-time informative feedback, students get to see why an incorrect solution doesn’t work, and why a correct solution does work. As the game evolves, students are confronted with a wide range of non-routine problems, compelling them to continuously exercise genuine problem-solving skills as they develop a deep understanding of the mathematics. Furthermore, we find that periodic steep increases in difficulty are able to build perseverance and instill a joy of being challenged—a joy that breeds life-long learners.
I propose that by more explicitly matching the design of the instructional materials to the goal of the instruction, and using new technologies to engage with students directly, we have a far better shot at improving math education.
This post first appeared on District Administration, March 2011