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Unformatted text preview: nsfer is a key factor in learners’ ability to solve
problems both in and out of the classroom. 5
Transfer and Problem Solving
Problem solving involves taking the physical or mental actions necessary to
solve a problem. In order to make this definition meaningful we must define what a
problem is. Most psychologists identify three characteristics that are shared by all
problem situations (Mayer, 1992). First problems situations always include a goal or
objective. Second, problem situations have givens. Givens are defined as the information,
materials, and tools that are available when the problem is first perceived. Finally, a
problem situation has obstacles that prevent the problem solver from immediately
reaching the goal. Students’ problem solving will be affected by how they perceive or
understand the various components of a problem solving situation.
Perception and Problem Space
In the case of problem solving, the term problem space is applied to learners’
mental representations of a problem situation (Newell and Simon, 1972). The problem
space that learners create is based on their perceptions of the problem situation, and the
prior learning experiences that are applied or transferred to the problem situation will
influence how that problem situation is perceived. The problem space is critical because
it influences the problem solving activities of the learner. Consider how Sandra’s and
Billy’s previous experiences influence the way they approach the mathematics problem
presented in Figure 8.1 (appears at the end of the chapter).
⇒ Sandra is in 10th grade. “Okay, I need to figure out how tall the flagpole is.
Well, I remember from my earth science class that the rays of the sun are
parallel at the Earth’s surface. This means that the angle between the top of 6
the shadow and the top of an object will be the same for all objects at the same
time of day . . .. Oh this is a geometry problem!”
⇒ Billy is in 3rd grade. Billy notices the numbers in the problem statement and
thinks, “This must be an arithmetic problem. That means I’ll have add,
subtract, multiply, or divide some of these numbers to get the right answer.
Looking at the picture, Billy thinks, “ Hmmm, the flagpole has to taller than
the mailbox, so I’ll probably have to add or multiply.”
For both Sandra and Billy the goal of the problem situation seems to be the same,
find the height of the flagpole, but their perception of the givens is different. For Sandra,
important givens include the lengths of both shadows, the height of the mailbox, and that
the shadows occur at the same time of day. She recognizes that the relationships among
these elements are described by the angles they form. For Billy the important the givens
are the numbers. Recognizing that the relationships between objects and their shadows
are described by angles Sandra identified the problem as one requiring geometric
reasoning and operations. On the other hand Billy’s focus on numbers and his
understanding of word pro...
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 Spring '08
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