Problems vs. Exercises

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mell14...@comcast.net

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Jul 22, 2010, 7:40:15 AM7/22/10
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In one of our previous classes our professor introduced us to the
concept of Problem Based Learning. The idea with this method was to
contruct tasks for the students that would require more that just a
simple answer. Problems were solved through a multi-step process.
The student needed to thoroughly understand the problem and then
devise a way to solve it. Tasks chosen in this fashion would be more
demanding and hence more rewarding for the students. One of the key
elements of this strategy is to make sure that the task is relevent
and engaging for the students. The hope is that tasks will match the
goals of the curriculum and that they will not exceed the student's
abilities. This approach is designed to mimic "real world" situations
and instill confidence in students who persevere through to the
ulimate solution. This is the really important stuff in high school
math because it clearly demonstrates the need for mathematical
solutions in life. The problem with a "Problem Based" approach is
that many times the tasks must be differentiated within the confines
of your particular class. Readiness levels can vary dramatically
within a single class. This demands a considerable amount of work on
the part of the teacher since care must be taken in the creation of
the tasks and much preparation is needed to ensure the effectiveness
of the method. That being said I believe that a "Problem Based"
approach must be a part of any successful plan for educating students.
The importance of exercises within the realm of a high school
math class cannot be understated. Without the discipline needed to
complete assignments no student can hope to move foward in his or her
educational pursuits. Exercises by definition are designed to
strengthen the skills needed to achieve success at a certain level.
Like problems they must be relevent to the material being covered in
the class but the crucial element in exercises is student discipline.
This is the nuts and bolts of math. If you have not paid your dues
you can't sing the blues. I firmly believe that the process of
learning mathematics is linear. Concepts build upon prior concepts.
Concrete ideas move toward abstract representations and skills must be
acquired along the way. The challenge of teaching a diverse
population of students who arrive in our classrooms with vastly
divergent levels of understanding is daunting. We must be armed with
the latest technology, the latest pedagogical strategies, and the
willingness to put them to use in our classrooms.
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