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In this study, I administered a series of six warm-up problems
to my students over the course of several weeks. Some of the problems
were specifically designed to be easy with a graphing calculator but very
difficult without one, others such that a graphing calculator would likely
lead to mistakes, and others that could be done with or without a calculator.
Two days after each warm-up, I gave a mini-lesson to the class about that
particular type of problem. Specifically, I discussed several possible ways
to approach the problem, and demonstrated why a calculator would or would not
be useful in solving it. At the end of the study, I gave the entire class a
post-quiz comprised of similar (but not identical) problems, to assess if
the students' skills had improved significantly.