Transfer from structured to open-ended
problem solving in a computerized
metacognitive environment
指導教授: Ming-Puu Chen
報告者: Hui-Lan Juan
時間： 2008.03.29
Kapa, E. (2007). Transfer from structured to open-ended problem solving in a computerized
metacognitive environment. Learning and Instruction, 17, 688-707.
Introduction
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Problem-solving transfer occurs when a student is able to
use what s/he has learned in order to solve problems that
are different from those presented during instruction.
The present study explored these two notions specifically:
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What kind of metacognitive support mechanisms (MSMs)
should be provided to word problem(應用題) solvers in
order to increase their transfer from structured (near
transfer) to open-ended problems (far transfer)?
To what extent is the effect of the MSMs on transfer
behavior conditioned by the level of prior mathematical
knowledge (PMK)?
Theoretical background
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
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Transfer behavior in problem-solving situations is
strongly connected with metacognitive functions.
Metacognitive functions are mental operations that
direct an individual’s cognitive functions and support a
learning conceptualization
Montague (1992) specifies three metacognitive strategies
that support the above functions: (1) Self-instruction (2)
A self-question (3) Self-monitoring
The metacgonitive functions (meta-level) may affect
cognitive tasks (object-level) in each problem-solving
phase.
Students with high or low prior
mathematical knowledge (PMK)

High PMK students might behave differently from low
PMK students during the six problem-solving phases as
follows:
1.
2.
3.
4.
5.
6.
Identifying and defining the problem
Mental representation of the problem
Planning how to proceed
Executing the solution according to the plan
Evaluation of students’ performance
Students’ reactions to receiving feedback
Description of the aims of the software and
the transferable MSMs
The transferable computerized MSMs were developed
to enhance the acquisition of cognitive and
metacognitive functions and strategies for word
problem-solving transfer among students.

1.
2.
3.
4.
Teaching MSMs for the activation of monitoring and
controlling meta-processes in each-problem-solving phase by
means of metacognitive questions
empowering the awareness of the importance of prior
knowledge pointing out the differences and similarities between
a current problem and a previously solved example.
Impart a problem-mapping strategy while analyzing a
mathematics word problem.
Supply MSMs to intensify the self-feedback.
Research hypotheses
Differences among the participants who learn according
to different type of MSMs world be found on near and
far transfer.


The direction of the expected effect would be as follows: Group
A (phases and conclusion MSMs) > Group B (phases MSMs) >
Group C (conclusion MSMs) > Group D (no MSMs).
Differences would be found on near and far transfer
tasks among the students with high/low PMK.


The effect of the MSMs on near and far transfer would be found
among low PMK students more than among high PMK students.
Method

Participants
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A total of 231 eighth-grade students from four public junior
high schools
Design- 4x2 factorial design
 different types of MSMs
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Group A - phases and conclusion MSMs
Group B - phases MSMs
Group C - conclusion MSMs
Group D - no MSMs
student’s level of PMK
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high PMLK
low PMK
Experimental methods
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In each of the four MSM
groups, cognitive support was
available to the student at the
click of a button.

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Solved example
Problem mapping
Obtaining the right answer
after two incorrect trials.
Experimental methods
Method

Near and far transfer tasks were examined in twodimensions:

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the product - the final outcomes of students for each task
the process - for each phase of the problem-solving process
whether or not there were cognitive / metacognitive
statements.
Results-hypothesis1
the effect of the metacognitive support mechanisms
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Structured task
Pre-test scores
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各組Product 分數有顯著差異
Post-test scores
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各組Product and process 的分數都有顯著差異
Results-hypothesis1
the effect of the metacognitive support mechanisms
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Significant differences in the structured task were found by
post hoc comparisons between the MSM groups regarding the
product level (p < 0.0003). According to these results, the
groups were scaled as follows: Group A =Group B > Group C
=Group D
Regarding the process level, significant differences were found
between the MSM groups A and D, B and D(p < 0.0001), A and
C (p < 0.001), A and B, and B and C (p < 0.07), but not for the
pairs C and D, in which no significant differences were found.
According to these results, the groups were scaled as follows:
Group A >Group B > Group C =Group D
Results-hypothesis1
the effect of the metacognitive support mechanisms

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Significant differences in the open-ended task were found by
post hoc comparisons between the MSM groups regarding the
product level between groups A and D (p < 0.0001), C and D,
and B and D (p < 0.001), but not for the pairs C and B, and A
and C, in which no significant differences were found.
Regarding the process level, significant differences were found
between the MSM groups A and D, B and D (p < 0.0001), and C
and D (p < 0.01), but not for the pairs A and B, C and B, and A
and C.
According to these results, the groups were scaled as follows:
Group A= Group B =Group C > Group D for both product and
process.
There are great effects for the experimental groups, A, B, and C, versus a low effect
for the control group D, for both near and far transfer tasks.
The effect for the open-ended task show an interesting scaling among the MSM
groups for both product and process.
The scaling, Group A >Group B >Group C >Group D is in line with the first research
hypothesis.
Results-hypothesis2
the effect of prior mathematical knowledge (PMK)

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students with low or high PMK in each of Groups A, B
and C scored higher achievements in both the product
and process phases regarding both the structured task
and the open-ended task, as compared to the control
group.
Post hoc analyses
 Process level show statistical differences between
students with high or low PMK regarding both
structured and the open-ended tasks (p<0.03) in favor
of students with low PMK.
Discussion

The present research clearly indicates that computerized MSMs are
effective for the development of far transfer in both the product and
the process phases, as compared to the control group.
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Character of MSMs -directive question
Problem-solving habit of students
By the end of the experiment, student of both type who received
MSMs were able to solve an open-ended task that was not presented
in the intervention program.
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students with high PMK, as well as those with low PMK, demonstrated
far transfer ability when solving the open-ended task.
students with high PMK were able to maintain their high achievements
and even improve upon them, while students with low PMK significantly
improved their scores .