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kwassink

From The Schools Our Children Deserve - 0 views

www.alfiekohn.org/...math.htm

math education

shared by kwassink on 06 Nov 13 - Cached
  • 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]
  • When traditionalists insist that it’s most important for kids to “know their math facts,” we might respond not only by challenging those priorities but by asking what is meant by know.  The key question is whether understanding is passively absorbed or actively constructed.  In the latter case, math actually becomes a creative activity.
  • By thinking through the possibilities, students come up with their own ways of finding solutions.  They have to invent their own procedures.  What that means in practice is as straightforward as it is counterintuitive:  teachers generally refrain from showing their classes how to do problems.
  • ...8 more annotations...
  • figure out what works and why.
  • Recall that, from a constructivist point of view, one of the most important aspects of a teacher’s job is to know as much as possible about each student’s thinking.
  • A teacher (or parent) for whom the right answer means everything is one who will naturally want to tell the child the most efficient way of getting that right answer.  This creates mindlessness. 
  • The overall conclusion reached by the TIMSS researchers – which somehow didn’t make it into the headlines, or even into the news stories, when the test results were released – was that traditional forms of teaching, and an emphasis on the basics, contributed significantly to the low standing of older American students. 
  • Recall that these conclusions precisely mirror those of the National Assessment of Educational Progress (NAEP), the major US assessment of student achievement, in terms of math instruction.
  • The research conducted on such programs has been concentrated in the primary grades, and it points to a result that can be summarized in six words:  better reasoning without sacrificing computational skills – an interesting echo of what we’ve just seen about a nontraditional approach to teaching reading (namely, better comprehension without sacrificing decoding skills).
  • They reported that visitors “invariably remarked about the excitement for mathematics displayed by the children as they solved the activities.  Children frequently jumped up and down, hugged each other, and rushed off to tell the teacher when they solved a particularly challenging problem.”  Moreover, they persisted at difficult problems to an unusual degree and took pleasure in one another’s successes.[50]
  • But the tasks must be sufficiently engaging and open-ended so that success is potentially delightful – something far less likely to happen when children are just expected to go through the approved steps to get the correct answers on a worksheet.
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