Finding pattern of physics problem solving
strategies from metacognitive perspective
Marlina Ali, Corrienna Abdul Talib, Hafizah Harun, Nor Hasniza Ibrahim, Abdul Halim Abdullah & Johari Surif
Department of Educational Science, Mathematics and Creative Multimedia,
Faculty of Education, Universiti Teknologi Malaysia
Skudai, Malaysia
[email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
Abstract—The purpose of this paper is to discuss how this
study identifies the pattern of physics problem solving strategies
from metacognitive skills between “more successful” and “less
successful” problem solvers. This study consisted of 21 local
students and no international students involved. All students
undergone similar education system. Respondents solved four
physics problems while talking aloud. However, for the purpose
of this paper, only results from lift problem were discussed. Each
of the respondents were videotaped. Interviews were conducted
right after the test. Written answers from the physics task were
marked according to the schema. The thinking aloud were
transcribed verbatim from the videotapes as well as interviews.
Transcripts were coded and examined looking for both
similarities and differences. As a conclusion, there were
differences between “more successful” and “less successful”
problem solvers in solving physics problems. The pattern of
physics problem solving in this paper presents two comparisons;
one pattern was identified by comparison between two students;
one from the “more successful” group and one from the “less
successful” group. Two students, one called Emma who was a
more successful (MS) problem solver and Sophia who was a less
successful (LS) problem solver, were selected as a benchmark
based on overall perception that they differed in their level of
metacognition. The second pattern was identified by comparison
between the two groups of more and less successful problem
solvers where both groups consisted of five students. However,
for the purpose of this paper, only patterns from lift problem
were discussed.
Keywords—more successful vs less successful; problem solving;
pattern; metacognition; thinking aloud
I.
INTRODUCTION
Numerous physics problem solving models have been
proposed [1-3]. The steps that were proposed by Adamovic
and Hedden [1] are only successful when students are dealing
with easy and straightforward questions. In fact, Adamovic
and Hedden [1] admitted this, where the proposed model was
successful only when students were dealing with traditional
physics problems. In all these models, it is expected that
students’ actions can be oriented to the direction of finding the
right or best solution to a problem. Examples of steps that are
taught to find the right solution are given in Table I.
Metacognitive skills can help solve physics problem solving
successfully [4, 5]. For example: Larkin [6] discovered that
physics experts differ from novices where the experts perform
an initial qualitative analysis of the problems before using
Sponsors: Ministry of Higher Education (MOHE), Malaysia and
Universiti Teknologi Malaysia (UTM)
appropriate equations for the quantitative solution to the
problems. Malone [5] demonstrated that students who
received Modelling Instruction pedagogy are actively
monitoring and regulating their cognitive processes while
solving problems. In addition, they routinely made more
metacognitive statements compared to students that learnt
using
conventional
instruction
especially
in
evaluating/checking as follows: approach taken; information
used; appropriateness of the equations; and answer as well.
Chi et al., [7] analyzed self-explanation of good and poor
problem solvers in physics as they studied and worked out
examples. This study shows that actively and accurately
monitoring their comprehension of the examples helps good
problem solvers produced more self-explanations compared to
poor problem solvers. Ferguson-Hessler and de Jong [8] also
discovered when studying a physics text, monitoring of their
comprehension helps good problem solvers produce more selfexplanations and become better at detecting comprehension
failures.
TABLE I.
Activities/
Author(s)
Reif,
Larkin &
Brackett [9]
Heller,
Keith &
Anderson
[10]
Adamovic
& Hedden
[1]
PHYSICS PROBLEM SOLVING STRATEGY
1
2
3
4
5
-
Description
Planning
Impleme
ntation
Checking
Focus
the
problem
Describe
the physics
Plan the
solution
Execute
the plan
Evaluate
the
answer
Read the
problem
Write down
what you
know,
Write down
what you
don’t
know-what
is the
problem
asking for?
-
Find the
correct
equations
to use,
and write
it down,
Rewrite
the
equations
with
correct
numbers
in it and
solve it
Write the
answer
down with
the correct
units
A. Research Objectives
The purpose of this study is to identify the pattern of
physics problem solving between more successful and less
successful problem solvers in solving physics problem.
B. Research Questions
What are the patterns of physics problem solving between
more successful and less successful problem solvers in solving
physics problem?
II.
BACKGROUND OF THE PROBLEM
The following sections discuss relevant issues why this
study is important. The literatures for the following problems
have been extracted from many areas particularly in physics
and mathematics because it seems these areas possess many
similarities. There are four problems that have been identified
as follows:
A) Absence or lack of metacognitive skills in Physics and
Mathematics
There have been several studies that show that
metacognition is either lacking or absent in situations where:
students do not solve the problem successfully -that there is an
absence of consistent monitoring and regulating of the
problem solving processes [11]; without metacognitive
monitoring, students are less likely to take one of the many
paths available to them and are almost certainly less likely to
arrive at an elegant mathematical solution [12]; the absence or
lack of metacognition causes students to fail to solve the
problem succesfully [13-15].
In contrast, a study by Sternberg [16] showed how the
presence of metacognition in problem solving lead experts to
resolve geometry problems successfully. Experts manage to
solve problems even though novices knew more about
geometry. The reason experts arrived at successful solutions
was because they utilised self-monitoring and self-regulation
consistently when dealing with the problem [16]. From
research, metacognition has been demonstrated as a factor that
can enhance problem solving performance [4, 13, 17]. The
importance of metacognition in problem solving has been
claimed by Heller [18] to help students: manage time and
direction, determine next steps, monitor understanding, ask
skeptical questions, and reflect on their own learning
processes. In addition, Davidson, Deuser, and Sternberg [19]
also claim that metacognition helps the problem solver to see
that there is a problem to be solved, work out what exactly the
problem is, and understand how to reach the solution.
Moreover, Fernandez, Hadaway, and Wilson [20], claim that
metacognitive skills like planning, monitoring and evaluating
are important to manage problem solving strategies. A number
of these studies were in mathematics [11] not physics. While
one would expect that many of the aspects of metacognition
that are useful in math would also be useful in physics, one
would also expect some differences. Therefore, the researcher
intends to study the roles of metacognition in problem solving
processes in physics.
B) Traditional problems do not reinforce problem solving
Learning by solving problems is an essential component in
the development of skills in physics. However, according to
Phang [4], traditional problems or textbook problems are
genuine problems only for novices but easy for experts. Foong
[14] reported, there was little or no evidence of metacognition
if the students dealt with easy and routine problems. The more
complex the problem, the more likely it seems that reflection
will be used in problem solving by successful problem solvers
[14]. According to Heller [18], traditional problems can often
be solved by manipulating equations, they need little
visualization, few decisions are necessary, they are
disconnected from students’ reality and can often be solved
without knowing physics. There is a considerable amount of
research, particularly in physics problem solving, employing
traditional or textbook problems e.g., Gaigher, Rogan, and
Braun [21]; Charles and Hedden [22]; Larkin [23].
The use of context rich problems positively influences
students’ attitude towards problem solving. As demonstrated
by Heller, Keith, and Anderson [10] the use of context rich
problems can:
• change students’ behavior and reduce their problem
solving strategies of searching for equations that have the
same variables as the knowns and unknowns;
• increase students’ descriptions of more expansive
strategies within their reflections. In particular, there is a
large increase in describing the use of diagrams, and
thinking about concepts first.
The advantage of using context rich problems was also
demonstrated by Ogilvie [24] who showed that context rich
problems required students to engage in analysis and planning
stages. Therefore, in this proposed study, the researcher
intends to use context rich problems as tasks in problem
solving.
C) Fewer studies about problem solving from metacognitive
perspective have been done at university level
According to Veenman and Spaans [25], metacognitive
skills emerge at the age of 8 to 10 years and expand during the
years thereafter. Also, certain metacognitive skills, such as
monitoring and evaluation, appear to mature later. A
considerable number of studies have been carried out on
problem solving and metacognition among students at primary
and secondary level, for example, Yeap [26] - grade 7
mathematics; Siemon [27] - children/mathematics; Mohamed
and Nai [28] - form 4 mathematics; Stillman and Galbraith
[29] - senior secondary students for mathematics, Wilson and
Clarke [30] - grade six mathematics, Galbraith, Goos, and
Renshaw [31] - senior secondary school mathematics; Goos
and Galbraith [32] - high school mathematics, Phang [4] - 1416 year olds and physics; Finegold and Mass [33] - grade
twelve physics; and Malone [5] - first and second year
physics. However little research has been done on students at
university level. Chi et al. [7] studied physics university
students. Biryukov [15] investigated second year university
students doing mathematics and not physics, and Foong [14]
studied pre service teachers at university level, but again
mathematics not physics. For this reason, this study intends to
investigate physics problem solving and metacognition among
students at university level.
D) Fewer studies to differentiate physics problem solving
between successful problem solvers and less successful
problem solvers from a metacognitive perspective
Most physics problem solving studies reported in section
focus on the differences between experts and novices in
behavior and knowledge organisation. Consequently, these
studies select expert participants among professors in Physics
and novices among undergraduate physics students [34-43].
There are also some studies focusing on the comparison
between “more successful” and “less successful”, for example,
Chi et al [7], Finegold and Mass [33].
The earliest physics problem solving study that focused
on metacognition was Simon and Simon [41]. This study
found that experts made fewer metastatements than novices,
for examples “wait a while”; is that right?”. However, Malone
[44] claimed that the problems given were very simple for the
experts such that they probably had to do little planning,
monitoring or evaluating of the problem solving processes. A
recent study by Rosengrant, Van Heuvelen, and Etkina [45]
demonstrated that experts employed metacognitive skills when
solving electrical circuit problems. For example, experts
would constantly turn their attention back and forth between
their work on the circuit in the questions and on the circuit that
they redrew. In constrast, novices were less likely to do this.
Moreover, when experts finished their work, they would look
over their entire work to check whereas the novices did not.
There are also comparative studies between the so called
“more successful” and “less successful”. Two studies in
physics have compared “more successful” and “less
successful” students [7, 33]. According to Chi et l. (1989)
more successful students defined as those who achieved good
rank at the top four and less successful those who achieve rank
at bottom four. Finegold and Mass [33] referred the students
as Good Problem Solver (GPS) and Poor Problem Solver
(PPS). GPS were defined as students who excelled in problem
solving and whose final graduating grades in Physics at least
90%. PPS were defined as students who experienced
difficulties in solving problems and whose final graduating
grades were above 60%. Finegold and Mass [33] found
statistically significant differences between “more successful”
and “less successful” in planning their solutions more fully
and in detail before carrying them out. Further, significant
differences were found that “more successful” students spent
more time on translation and planning than “less successful”
students [33]. The “more successful” students accurately
monitored their comprehension failure compared to the “less
successful” students [7], “more successful” students generated
self-explanations more frequently than “less successful”
students [7].
From all the studies above, it seems that comparisons are
mostly made between experts and novices rather than between
the so called “more successful” and “less successful” students.
For this reason, the proposed study intends to compare
problem solving between “more successful” and “less
successful” students in physics. Studies of differences between
“more successful” and “less successful” students are important
because identification of such differences will make it possible
to improve strategies employed by “less successful” students.
According to Finegold and Mass [33], by comparing “more
successful” and “less successful” students, studies can gain a
better understanding of the scientific problem solving
processes. In addition, the results from the differences can be
used for developing instruction to enhance students’ problem
solving skills [33]. The proposed study is different from that
of Finegold and Mass [33] as a different approach to data
gathering; while Finegold and Mass [33] used a quantitative
approach, a qualitative approach was used in the present study.
The importance of the proposed study is that it will be able to
analyse the data in more depth than Finegold and Mass [33].
III.
METHODOLOGY
This study employed a qualitative research design and think
aloud method was chosen to collect and analyse the data.
Think aloud method was the most appropriate for this study
because the method avoids interpretation by the subject and
only assumes a very simple verbalization process. Secondly,
the think aloud method treats the verbal protocols, that are
accessible to anyone, as data thus creating an objective
method [46].
This study consisted of 21 students, which all had a physics
background at the university level. 10 students were involved
in the first fieldwork and 11 in the second fieldwork. The
purpose of the first fieldwork was to check the difficulty of the
physics task (Physics Problem Solving Achievement Test) and
to refine the coding schemes called Coding Metacognitive in
the Thinking Aloud Protocol (CMBTAP). All of the
respondents solved four physics problems in a physics pencil
and paper test while talking aloud. The physics task is named
Physics Problem Solving Achievement Test (PPSAT). The
problems were given one by one to the respondents. The
respondents were instructed to provide full solutions to each
problem on the test paper. No time limitation were given for
the respondents to answer the problems, however if the
respondents show impasse in their work, it was suggested that
they move to the next question. In the meantime, each of the
respondents were videotaped. Interviews were conducted right
after the test. During the interview, the respondents’ written
answer to each of the problems were shown and the
respondents were asked to discuss their recollection of their
thinking when solving that problem.
There are 5 levels of proficiency, excellent, good medium,
weak and very weak (see table II). In any performance test on
Malaysian examination usually, those who achieved less than
40% are considered weak and very weak (Table II).
TABLE II.
RANGE OF SCORES FOR DETERMINE THE LEVEL OF
ACHIEVEMENT IN MALAYSIA EXAMINATION
Range of Scores (%)
80-100
60-79
40-59
20-39
0-19
CLASSIFICATION OF MORE SUCCESSFUL AND LESS
SUCCESSFUL STUDENTS
No.
Name
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
Adam
Emma
Ruby
Isabelle
Thalia
Student a
Student b
Student c
Student d
Student e
Student f
Student g
Student h
James
Student i
Sophia
Student j
Georgia
Jack
Student k
Olivia
Fieldwork
2
1
1
2
1
1
1
1
2
2
2
2
1
1
2
1
2
2
1
2
2
Scores
(%)
75.7
62.2
59.5
48.6
48.6
48.6
43.2
43.2
37.8
35.1
29.7
27.0
24.3
24.3
24.3
21.6
21.6
18.9
13.5
13.5
13.5
FINDINGS AND DISCUSSION
Level of achievement
Excellent
Good
Moderate
Weak
Very Weak
Based on this preferences, 40% was chosen as the cut-off for
differentiating between “more” and “less” successful [47].
Participants were then labelled accordingly. It was anticipated
that not all participants will fall neatly into one of these two
groups. Respectively, eight participants were classified as
“more successful (MS)” and 13 participants categorised as
“less successful (LS)”. The 10 students selected were assigned
pseudonyms as Emma, Ruby, Adam, Isabelle, Thalia, James,
Olivia, Georgia, Sophia and Jack while their real identities
were kept anonymous. As shown in Table III, Ruby, Emma
and Isabelle were chosen from first fieldwork. They were
classified as top rank participants from the scores of the first
fieldwork. Adam and Thalia were chosen from fieldwork 2 and
were classified as top rank participants as well from the scores
of the second fieldwork. When the score of the participants
from both fieldworks were merged together, Adam, Ruby,
Emma, Isabelle, and Thalia emerged as the top five.
On the other hand, for “less successful” participants,
James, Sophia and Jack were chosen from the first fieldwork.
They were classified as the bottom participants from their
score of the first fieldwork. Georgia and Olivia were chosen
later and they were classified as the bottom rank participants
as well as from the score of the second fieldwork. The criteria
for selecting the students also looked at respondent’s
cooperation during thinking aloud. Students who shows lacked
of cooperation such as not trying to solve the problems and
simply withdraw in answering the question also become
criteria in selecting the students especially for less successful.
TABLE III.
IV.
Age
Gender
20
23
23
23
23
23
23
23
23
21
23
23
23
25
20
23
20
24
20
20
23
M
F
F
F
F
M
F
F
M
F
F
F
F
M
F
F
F
F
M
F
F
Rating
MS
MS
MS
MS
MS
MS
MS
MS
LS
LS
LS
LS
LS
LS
LS
LS
LS
LS
LS
LS
LS
Fig. 1. Diagram of comparison between Emma (MS) and
Sophia (LS) (First pattern)
To identify the pattern, comparison were made between two
persons, each one from the more successful (MS) and less
successful (LS) group for the “lift” problem. Two students,
one called Emma who was a more successful (MS) problem
solver and Sophia who was a less successful (LS) problem
solver, were selected as a benchmark based on overall
perception that they differed in their level of metacognition.
Then, the differences identified between the two persons is
determined as the benchmark to compare between the two
groups of “more successful” and “less successful” problem
solvers for the “lift” problem. Then, comparison between the
two groups in the “lift” problem is identified as the benchmark
to determine the pattern for “car on the hill” problem and the
process of comparison continues until all four problems is
done. However, for the purpose of this paper, only patterns
from the lift problem will be discussed.
Emma and Sopia are the two persons compared in the first
stage of the analysis. They are the benchmark for the
comparison of the “more successful” and “less successful”
problem solvers group in the lift problem. The differences
between Emma (MS) and Sophia (LS) can be summarised as
follows (Refer diagram in Figure 1):
1) In the early phase, Emma (MS) and Sophia (LS) showed
similarity in terms of planning the problem.
a. Sophia (LS) reread more than Emma (MS).
b. Emma (MS) qualitatively analysed the problem and
Sophia (LS) leapt to an equation.
c. Emma (MS) figured out the goal of the problem
much faster than Sophia (LS).
d. Emma (MS) used “physics representation” while
Sophia used “naïve representation”.
e. Emma (MS) worked forward, while Sophia (LS)
worked backward.
f. Both of them drew a diagram; however, Sophia’s
diagram lacked understanding of the problem.
2) In the middle stage, Emma (MS) did lots of monitoring,
qualitative analysis and evaluating. Sophia (LS) also
showed that she sometimes monitored her thinking.
3) At the end stage, Emma (MS) evaluated her answer while
Sophia (LS) did not evaluate her answer.
Pattern 2 was developed after differentiating between “more
successful” and “less successful” groups in solving the “lift”
problem using the benchmark formed by differentiating
between Emma and Sophia.
TABLE V.
COMPARISON BETWEEN MORE AND LESS SUCCESSFUL IN
MONITORING AND QUALITATIVE ANALYSIS
More successful
Adam
Emma
Isabelle
Tahlia
Ruby
1
6
1
1
4
Monitoring
Qualitative Analysis
Mark for “lift”
Fig. 2 Diagram of comparison between more successful (MS)
problem solvers and less successful (LS) problem solver from
“lift” problem (2nd pattern)
As might be expected, the difference in the pattern are not
neat, however taken as a whole, the more successful problem
solvers engaged more often in actions that can be labelled as
metacognitive than the less successful group.
In the early stage of problem solving, there were five
differences between groups. Firstly, “more successful”
problem solvers planned more often than “less successful”.
Secondly, “less successful” problem solvers re-read more
often than “more successful” problem solvers. Thirdly,
drawing diagram is common among groups and both groups of
solvers drew the free body diagram except Isabelle. Fourthly,
the “more successful” qualitatively analyzed the problem more
often than “more successful” problem solvers. Thirdly,
drawing diagram is common among groups and both groups of
solvers drew the free body diagram except Isabelle. Fourthly,
the “more successful” qualitatively analyzed the problem more
often than the “less successful” problem solvers. And fifthly,
the “more successful” used “abstract concepts” more often
than the “less successful” while the “less successful” used
more “naive concepts” than the “more successful”.
In the middle stage of problem solving, two differences
between groups were identified. Firstly, two problem solvers
from the “more successful” group were planning in the middle
stages. The reason they planned for a second time was because
they could not find a suitable solution and were also
unconfident about the answer. Secondly, members of both
groups demonstrated aspects of monitoring in solving “lift”
problem, but there were differences between the groups.
Based on table IV, the “less successful” group shows
greater number of monitoring compared to the “more
successful” group. On the other hand, the “more successful”
group shows greater number in the qualitative analysis of the
problem compared to the “less successful” group. Monitoring
and qualitative analysis are basically interrelated. Based on
this study, the “less successful” group demonstrated higher
monitoring, but without qualitative analysis, it does not help
the solver to solve the problem successfully. This finding also
supports the study by Chi, et al. [7] where similar result was
found.
TABLE IV.
13
19
Qualitative Analysis
14
11
0
0
6/6
3/6
Sophia
Olivia
Georgia
Jack
Monitoring
Qualitative
Analysis
6
2
4
3
4
0
1
10
0
0
Mark for “lift”
1/6
1/6
2/6
1/6
2/6
V.
James
CONCLUSIONS
As a conclusion, there were differences between “more
successful” and “less successful” groups in solving physics
problems. As might be expected, the difference in the pattern
are not neat, however taken as a whole, the more successful
problem solvers engaged more often in actions that can be
labelled as metacognitive than the less successful group.
ACKNOWLEDGMENT
The authors would like to thank the Ministry of Education
(MOE), Malaysia and Universiti Teknologi Malaysia (UTM)
for their financial funding through FRGS Grant Vote No
R.J130000.7831.4F427.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
Monitoring
1
6/6
Based on table V, almost every student shows monitoring
during problem solving. However, lack of qualitative analysis
among the “less successful” group caused them to fail to solve
the “lift” problem [48].
At the end stage of the problem solving process, only one
difference between groups was identified. The “more
successful” group evaluated their answer while none of the
“less successful” evaluated their answer.
LESS SUCCESSFUL GROUPS
Less successful
12
6/6
Less successful
MONITORING AND QUALITATIVE ANALYSIS BY MORE AND
More successful
1
3/6
[7]
C. Adamovic and C. J. Hedden, "Problem-solving skills," The
Science Teacher, vol. 64, pp. 20-23, 1997.
P. Heller and H. Mark, "Teaching problem solving through
cooperative grouping. Part 2: Designing problems and structuring
groups," American Journal of Physics, vol. 60, pp. 637-644,
1992a.
F. Reif, "Teaching problem solving-A scientific approach," The
Physics Teacher, vol. 19, pp. 310-316, 1981.
F. A. Phang, "The pattern of physics problem-solving from the
perspective of metacognition," PhD Thesis, University of
Cambridge, 2009.
K. L. Malone, "A comparative study of the cognitive and
metacognitive differences between modeling and non-modeling
high school physics students," Doctor of Philosophy, Department
of Psychology Center for Innovation in Learning, Carnegie Mellon
University, Pittsburgh, PA, 2006.
J. H. Larkin, "Processing information for effective problem
solving," Engineering Education, vol. 70, pp. 285-288, 1979.
M. T. H. Chi, M. Bassok, M. W. Lewis, P. Reimann, and R.
Glaser, "Self-Explanations: How Students Study and Use
Examples in Learning to Solve Problems," Cognitive Science, vol.
13, pp. 145-182, 1989.
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
M. G. M. Ferguson-Hessler and T. de Jong, "Studying Physics
Texts: Differences in Study Processes Between Good and Poor
Performers " Cognition and Instruction, vol. 7, pp. 41-54, 1990.
F. Reif, J. H. Larkin, and G. C. Brackett, "Teaching general
learning and problem-solving skills," American Journal of Physics,
vol. 44, pp. 212-217, 1976.
P. Heller, R. Keith, and S. Anderson, "Teaching problem solving
through cooperative grouping. Part 1: Group versus individual
problem solving," American Journal of Physics, vol. 60, pp. 627636, 1992b.
A. F. Artzt and E. Armour-Thomas, "Development of a cognitivemetacognitive framework for protocol analysis of mathematical
problem solving in small groups," Cognition and Instruction, vol.
9, pp. 137-175, 1992.
A. Yimer and N. F. Ellerton, "Cognitive and Metacognitive
Aspects of Mathematical Problem Solving: An Emerging Model.,"
in MERGA 2006, Wahroonga, 2006.
B. Kramarski, Z. R. Mevarech, and M. Arami, "The Effects of
Metacognitive Instruction on Solving Mathematical Authentic
Tasks," Educational Studies in Mathematics, vol. 49, pp. 225-250,
2002.
P. Y. Foong, "A metacognitive-heuristic approach to mathematical
problem solving," PhD Thesis, Faculty of Education, Monash
University, 1990.
P. Biryukov, "Metacognitive aspects of solving combinatoric
problems," International Journal for Mathematics Teaching and
Learning, pp. 1-19, 2004.
R. J. Sternberg, "Metacognition, abilities, and developing
expertise: What makes an expert student?," Instructional Science,
vol. 26, pp. 127-140, 1998.
G. Özsoy and A. Ataman, "The effect of metacognitive strategy
training in mathematical problem solving achievement,"
International Electronic Journal of Elementary Education, vol. 1,
pp. 67-82, 2009.
K. Heller, "Teaching Introductory Physics Through Problem
Solving," University of Minnesota, Workshop at National Summer
Conference , Integrating Science and Mathematics Education
Research into Teaching, The University of Maine (Orono,
Maine)June 23 to 25 2002 2002.
J. E. Davidson, R. Deuser, and R. J. Sternberg, "The role of
metacognition in problem solving," in Metacognition : knowing
about knowing, J. Metcalfe and A. P. Shimamura, Eds., ed
Cambridge, Mass.: MIT Press, 1994, pp. 207-226.
M. L. Fernandez, N. Hadaway, and J. W. Wilson, "Problem
solving: managing it all," The Mathematics Teacher, vol. 87, pp.
195-199, 1994.
P. K. Tao, "Peer Collaboration in Solving Qualitative Physics
Problems: The Role of Collaborative Talk," Research in Science
Education, vol. 29, pp. 365-383, 1999.
E. Gaigher, J. M. Rogan, and M. W. H. Braun, "Exploring the
Development of Conceptual Understanding through Structured
Problem-solving in Physics," International Journal of Science
Education, vol. 29, pp. 1089 - 1110, 2007.
R. Charles, F. Lester, and P. O'Daffer, How to evaluate progress in
problem solving. Reston, Virginia: National Council of Teachers of
Mathematics, 1987.
C. A. Ogilvie, "Impact of Context-Rich, Multifaceted Problems on
Students' Attitudes Towards Problem-Solving," 2008.
M. V. J. Veenman and M. A. Spaans, "Relation between
intellectual and metacognitive skills: Age and task differences,"
Learning and Individual Differences, vol. 15, pp. 159-176, 2005b.
B.-H. Yeap, "Metacognition in Mathematical Problem Solving "
presented at the Australian Association for Research In Education,
Adelaide, 1998.
D. E. Siemon, "The role of metacognition in children's
mathematical problem solving: An exploratory study," PhD PhD
Thesis, Faculty of Education, Monash university, 1993.
M. Mohamed and T. T. Nai, "The use of metacognitive process in
learning mathematics.," presented at the The Mathematics
Education into the 21st Century Project Universiti Teknologi
Malaysia, Johor Bahru, Malaysia, 2005.
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
G. A. Stillman and P. L. Galbraith, "Applying Mathematics with
Real World Connections: Metacognitive Characteristics of
Secondary Students," Educational Studies in Mathematics, vol. 36,
pp. 157-195, 1998.
J. Wilson and D. Clarke, "Towards the modelling of mathematical
metacognition," Mathematics Education Research Journal, vol.
16, pp. 25-48, October 2004 2004.
P. Galbraith, M. Goos, and P. Renshaw, "A money problem: A
source of insight into problem solving action," International
Journal for Mathematics Teaching and Learning, April 13th 2000.
M. Goos and P. Galbraith, "Do it this way! Metacognitive
strategies in collaborative mathematical problem solving,"
Educational Studies in Mathematics, vol. 30, pp. 229-260, 1996.
M. Finegold and R. Mass, "Differences in the Processes of Solving
Physics Problems Between Good Physics Problem Solvers and
Poor Physics Problem Solvers," Res. Sci. & Technol. Educ., vol. 3,
pp. 59-67, January 1, 1985 1985.
R. Stavy and et al., Students' Problem-Solving in Mechanics:
Preference of a Process Based Model: Report: ED350151. 8pp.
1991, 1991.
J. Discenna, "A study of knowledge structure in physics," 143
Reports: Research; 150 Speeches/Meeting Papers1998.
M. T. H. Chi, P. J. Feltovich, and R. Glaser, "Categorization and
representation of physics problems by experts and novices,"
Cognitive Science: A Multidisciplinary Journal, vol. 5, pp. 121 152, 1981.
T. de Jong and M. G. M. Ferguson-Hessler, "Cognitive structures
of good and poor novice problem solvers in physics," Journal of
Educational Psychology, vol. 78, pp. 279-288, 1986.
R. J. Dufresne, "Problem solving: learning from experts and
novices," Instructional Science, vol. Volume 26, pp. 1-140, March
1998 1988.
P. T. Hardiman and et al., "The Relation between Problem
Categorization and Problem Solving among Novices and Experts,"
National Science Foundation, Washington, DC., 143 Reports:
Research1988.
P. B. Kohl and N. D. Finkelstein, "Patterns of multiple
representation use by experts and novices during physics problem
solving," Physical Review Special Topics - Physics Education
Research, vol. 4, pp. 1-13, 2008.
D. P. Simon and H. A. Simon, "Individual Differences in Solving
Physics Problems," in Children's thinking : what develops?, R. S.
Siegler, Ed., ed Hillsdale, N.J. New York: L. Erlbaum Associates ;,
1978, pp. 325-348.
J. L. Snyder, "An investigation of the knowledge structures of
experts, intermediates and novices in physics," International
Journal of Science Education, vol. 22, pp. 979 - 992, 2000.
H. L. Swanson, J. E. O’Connor, and J. B. Cooney, "An
Information Processing Analysis of Expert and Novice Teachers’
Problem Solving," American Educational Research Journal, vol.
27, pp. 533-556, 1990.
K. Malone, "The convergence of knowledge organization, problem
solving behaviour, and metacognition research with the modelling
method of physics instruction-part II," Journal of Physics Teacher
Education Online, vol. 4, pp. 3-15, 2007.
D. Rosengrant, A. Van Heuvelen, and E. Etkina, "Do students use
and understand free-body diagrams?," Physical Review Special
Topics - Physics Education Research, vol. 5, p. 010108, 2009.
M. W. Van Someren, Y. F. Barnard, and J. A. C. Sanberg, The
think aloud method A Practical Guide to Modelling Cognitive
Processes. London: Academic Press, 1994.
A. Marlina, I. Nor Hasniza, A. Abdul Halim, S. Johari, and S.
Nurshamela, "Physics problem solving: Selecting more successful
and less successful problems solvers," International Conference of
Teaching, Assessment and Learning (TALE), pp. 186-191, 2014.
A. Marlina, A. Abdul Halim, and S. Nurshamela, "The importance
of metacognition in physics problem solving: Monitoring skills,"
presented at the International Conference on Educational Studies,
Pulai Spring Resort, Johor Bahru, 2015.