How and Why Math Machines Improve Learning

Discovery is an essential component of effective learning experiences. Textbooks, lectures and demonstrations can be valuable, but students must still discover for themselves how concepts and methods fit into their own minds. Ultimately, we must each construct our own understanding by selecting, adapting and assembling the ideas we encounter.

Motivation is crucial. Many students have already tuned out, either because they believe math and science are "useless" or--worse--because they believe they are too "stupid" to master difficult material. Most students will excel in math and science when they see that the material is relevant and when they believe that they can succeed. It certainly helps too if we can make the learning both challenging and fun.

Time on Task is critical. Students learn more if they spend more time working with and thinking about the key ideas. Some students may be very good at quickly memorizing answers for a test, but the kind of learning that will last a lifetime does require time and focused effort. Short, focused and fun tasks are a good way to keep students engaged with the material long enough to learn it thoroughly.

Positive social interactions are key. Both in school and on the job, people must work effectively as part of a group. Positive interactions and improved learning occur when students and teachers work together to achieve shared goals. If, for example, students work together to move a SAM robot through a maze, the tasks of measurement, calculation and planning become shared responsibilities. If teachers of math, science and technology work together to help students master difficult skills and concepts, everyone benefits.

Realistic Career Applications should be part of all learning in math, science and technology. Every student (even the exceptional few who go on to earn a Ph.D. in math or science) will eventually need to earn a living. School-based education must always look beyond the school environment. This does not mean, however, that we should focus on narrow technical training. Good, high-paying jobs demand that students be able to solve realistic semi-structured problems, to apply math and science to realistic problems, and to adapt to new and often challenging situations. Career education is not an extra topic for math and science teachers--it's a better way of teaching the fundamental concepts and skills.

Real Assessment is better than testing. We all need tests at some point, but eventually we must judge ourselves in terms of what we actually achieve. Real tasks allow students to find out for themselves what they can do and what they still need to learn. By guiding students as they master real tasks, we can help them understand for themselves the power of what they know and what they can do.



"Sometimes we have to go out on a limb, because that's where the fruit is."
Will Rodgers

"Technological innovation moves forward hand-in-glove with the fresh science and engineering knowledge that drives it. Discovery and innovation are the twin pillars of 21st century progress."
Dr. Joseph Bordogna, Deputy Director, NSF