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Should Students Discover Their Own Math Lessons?

Student-centered instruction is difficult jargon for lay people like myself to get their heads around, especially for a subject like mathematics. The idea, as I understand it, is to present students with questions, puzzles and scenarios and let them try to figure out the procedures for solving them, by themselves. A traditional teacher might simply explain, for example, how to graph a line, step-by-step, using y-intercept and slope. And a good traditional teacher can explain things in many ways and give students a tool box of procedures to tackle any problem. A student-centered teacher might turn the classroom floor into a giant graph-paper grid and ask the students to become data points and walk to where they should be plotted.