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Students' Mental Acts of Anticipating
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Many students have acquired the habit of spontaneouslyapplying algorithms and formulas to solve mathematics problemswithout analyzing the problems. On the other hand, there are alsostudents who analyze the problem situation and think ahead beforethey embark on a course of actions. The act of thinking ahead, oranticipating, is valuable in problem solving. In this book, twotypes of anticipating acts--foreseeing and predicting--are used tocharacterize the ways students solve problems. The research thatled to the categorization of different ways of thinking associatedwith the act of foreseeing/predicting is reported in this book.These ways of thinking allow educators to communicate the way astudent approaches a problem, such as whether the student hastilyapplies a procedure (impulsive anticipation), is fixated on aparticular idea (tenacious anticipation), explores different ideas(explorative anticipation), analyzes the problem situation andidentifies a goal (analytic anticipation), or spontaneously applieswell-established ways of understanding (interiorizedanticipation).
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