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VES Mathematics PLCSession 2: We’ve Got Problems11/13/12
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Speaking of Problems. . .
How do we know a good problem?
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A Good Problem... Involves a question that cannot be
immediately answered Is challenging to the learner Holds the learner’s interest Might have more than one answer Might have only one answer, but many
different approaches to the solution Is often connected to real life
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If it can be solved using a procedure or algorithm it is
not a “problem” it is an exercise.
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What is a problem at one time to one person may be
an exercise to another.
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Student Behaviors
The Problem
Teacher Behaviors
Problem Solving
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Classroom Environment Risk taking Provide enough time Respect for each other’s thinking Opportunity to discuss and challenge
solutions Values perseverance
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The Role of the Teacher is crucial...
in choosing the problem in determining how to present the
problem in determining how students will work in order to assess what the students
have learned for facilitating student communication
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Where do you find problems?
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Intermediate Problem
The John Hancock Building in Chicago is 1,127 feet tall. Another skyscraper in Chicago, the Amoco Building, is 1,136 feet tall. Which building is taller?
Primary Problem
There are 18 students in Mrs. Smith’s class. She wants to put them into pairs. How many pairs are there?
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What challenges did you face as you rewrote the problem?
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There is no other decision that teachers make that has a greater impact on
students’ opportunity to learn and on their perceptions about what mathematics is
than the selection of the tasks (or problems) with which the teacher engages
the students in studying mathematics.Lappan and Briars, 1995
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There are 25 sheep and 5 dogs in a flock. How old is the Shepherd?
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How many rectangles are there on a standard 8 X 8 checkerboard? Count only those rectangles (including squares) whose sides lie on grid lines. For example, there are nine rectangles on a 2 X 2 board.
1 2
3 4
5
697 8
Problem Solving: Sample
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Problem Solving: Sample
The Value of this problem• Deciding what determines a rectangle• Examining a simpler problem• Adding sequence of consecutive integers• Problem lends itself to discovering mathematical
applications based on number concepts• Multiple correct solution strategies can be
applied to arrive at a solution• Variety of solutions
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There are 9 cows in the barn. How many eyes are there?
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Sergi’s basketball team is traveling for a tournament. There are 13 kids on the team. If each car holds 3 kids, how many cars are needed for the team to get to the tournament?
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