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, they must each construct their own understanding by selecting, adapting and assembling the ideas that they 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 robot, the tasks of measurement, calculation and planning become shared responsibilities. If teachers of math, science and technology work together to help student 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.
