Students in
classrooms where mathematical thinking is encouraged from a very young age
learn how to estimate and predict. (“How many pencils do you think there are
in the whole school? Is there a way we could know for sure without
counting?”) They acquire basic skills in the process of solving meaningful
problems -- often with their peers. They may use calculators, as adults
often do, so that they can tackle more challenging and engaging problems than
would be possible if they had to direct their energy to computation. In
contrast to a classroom whose main activities are listening to the teacher
and filling out worksheets, such a learning environment is distinguished by
students “sitting in groups, discussing ideas, doing experiments, making
diagrams, using concrete objects to test their conjectures, following blind
alleys, and now and then experiencing the satisfaction of discovering
something they did not know before.”[17]
Contents contributed and discussions participated by kwassink
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