76
JPAIR Multidisciplinary Research
Metacognitive Knowledge Predicts Success
in Problem Solving Transfer
BEVERLY T. REGIDOR
ORCID No. 0000-0003-1883-8154
beverlytabayregidor@gmail.com
University of the Immaculate Conception
Davao City, Philippines
ABSTRACT
Problem solving skills play a vital role in solving real life problems. This study
was conducted to determine the influence of metacognitive and motivational
aspects of problem solving skills to the students’ success in problem solving
transfer. Furthermore, it determined what aspect of the problem solving skills
predicts success in problem solving transfer. The descriptive correlation method
was used to determine the relationship of the metacognitive and motivational
aspects of the problem solving skills and the students’ success in problem solving
transfer. The respondents of the study are the fourth-year high school students
of Davao Central College, Philippines. There are three instruments used in the
study: 1) The Metacognitive Awareness Inventory which measures their awareness
in metacognitive skills such as knowledge and regulation, the 32-item Academic
Intrinsic Motivation (AIM) Inventory which measures motivational aspect of
the problem solving skills and lastly, the non-routinized test which measures
the success in problem solving transfer. The data gathered were summarized,
translated, and analyzed using the mean scores for both aspects of the problem
solving skills and problem solving transfer. At 0.05 level of significance, the
Pearson product moment r was used to test the significant correlation between
the aspects of the problem solving skills and the success of problem solving
transfer. Findings show that only the metacognitive knowledge predicts success in
problem solving transfer and this is the only problem solving skills is significantly
correlated to the success in problem solving transfer.
Vol. 17 · July 2014
Print ISSN 2012-3981 • Online ISSN 2244-0445
doi: http://dx.doi.org/10.7719/jpair.v17i1.283
Journal Impact: H Index = 3 from Publish or Perish
JPAIR Multidisciplinary Research is produced
by PAIR, an ISO 9001:2008 QMS certified
by AJA Registrars, Inc.
77
International Peer Reviewed Journal
Keywords - Mathematics Education, metacognitive knowledge, predicts
success, problem solving, descriptive- correlation design, Davao City, Philippines
INTRODUCTION
One of the greatest failures of Mathematics education is how the students deal
with worded problems. At this point, students tend to get bored, avoid, dislike
and unloved Mathematics as one of the disciplines taught in schools. Moreover,
students perform poorly on Mathematics achievement especially in terms
of problem solving. How can teachers and students learn ways in promoting
problem solving transfer? Dealing with real word problems, developing creative
thinking and acquiring the right attitude in Mathematics are great things the
world of Mathematics must ever face in this twenty-first century. As what has
been the mindset of every individual, Mathematics is always one of the difficult
subjects ever experienced by students because teachers give less emphasis on the
skills needed for the success of problem solving.
No Child Left Behind Act of 2001 (U.S. Department of Education, 2005)
emphasizes that teachers are having more pressure to teach to the test rather
than to work towards developing conceptual understanding on Mathematics.
Hence, many students would rather acquire the important formulas that would
only surpass the test requirement. However, when they encounter ill-structured
problems, the difficulty arises and exhibited misconception on the task given
(Mann, 2006).
These are the great dilemmas of Mathematics performance of the students
nowadays. They are able to retain such information taught by the teacher,
but cannot transfer it to real world problem (Mayer, 1998). These probably
motivate school heads to push through the problem solving as the center piece of
mathematics curriculum (Middleton et al., 2004).
The Trends in International Mathematics and Science Study (TIMSS)
conveyed that Asian countries are on top rank in the field of Mathematics. These
are the Singapore, Hong Kong, Chinese-Taipei, and Japan. Though Mathematics
achievement is very high, problem solving skills were still inadequate to perform
multi-step problem solving (TIMSS, 2007).
The result of National Achievement Test (NAT) here in Philippines for the
school year 2005 – 2006 reflected a declining education based on the performance
of the students in the country. The Grade 6 pupils average on overall achievement
rate of only 54.5% while fourth-year high school students were worse with only
78
JPAIR Multidisciplinary Research
44.3%. Fortunately, fourth-year students perform best in Mathematics. However,
only mastery of the skill was quite high and problem solving was not measured
in National achievement Test.
Based on the report of National Education Testing Research Center
(NETRC), Davao City ranked fourth (4th) from the bottom among 17 regions
in the Philippines during 2006 National Achievement Test for Fourth-Year High
School students. Hence, this cause an alarming situation that should seriously be
addressed by the educators of the region and the country, as a whole.
With this distressing situations, the researcher was encouraged to conduct a
study on the aspects that would probably give great contribution towards success
in problem solving.
FRAMEWORK
Regardless of success in understanding how to stimulate routine problem
solving using tried-and-true version of drill-and-practice method of instruction,
the discipline continues to endeavor with how to promote non-routine problem
solving.
This study is anchored on the idea that successful problem solving depends on
three components – skill, meta-skill, and will – and that each of these components
can be an influence by instruction, Mayer (1998). The meta-skill and will are the
components that being use in the study. Metacognitive aspect and motivational
aspect of Problem solving skill are the independent variable of the study. This is
also supported by the theory of Constructivism which states that learners are to
construct new ideas as an application on the concepts acquired by them. This is
in a way of showing deeper understanding on the ideas learned, (Bruner, 1996).
Constructivist learning improves students understanding into a different more
realistic application in actual life of where they can demonstrate the thinking
ability about the facts they have acquired.
Moreover, this is also supported by the Cognitive Flexibility Theory that
focuses on the nature of learning in complex and ill-structured domains. Cognitive
flexibility refers to the ability to restructure one’s knowledge spontaneously in
response to the increasing change in times. The theory is widely a concern with
the transfer of knowledge and skills beyond their level of understanding into
what field it may be. Another theory that supports the study is the humanistic
theory set forth by Carl Rogers (Huitt, 2009). It states that a motivation might
come from within an individual without any thought to an external reward. This
79
International Peer Reviewed Journal
theory exemplifies the intrinsic motivation, a cognitive approach to motivation
that necessitates students to think through the consequences of their actions
and base their decisions on the expected outcome of those decisions. Lastly, the
Behaviorist theory set forth by B.F Skinner (1963) which suggests as punishment
and reward system as a motivational tool that encourage students to perform well
in the task. In connection to the problem solving, students might work hard for
it in order to obtain positive feedback and reward on it.
With these theories as benchmark, it is conceptualized that the success in
problem solving transfer is dependent on the metacognitive and motivational
aspect of problem solving skills.
OBJECTIVES OF THE STUDY
The objective of the study is to determine the influence of the problem
solving skills such as metacognitive aspect containing knowledge and regulation
in particular and motivational aspects containing the intrinsic and extrinsic
motivation towards the success of the problem solving transfer. In particular
it aims to determine (1) the level of the problem solving skills of students in
terms of their metacognitive and motivational aspects, (2) the mean score of
the students in problem solving transfer, (3) the predictor of success in problem
solving transfer, (4) relationship of metacognitive aspect of the problem solving
skills and success in problem solving transfer, (5) relationship of motivational
aspect of problem solving skills and success in problem solving transfer.
METHODOLOGY
The study used the descriptive/quantitative correlational method. Correlations
were computed between problem solving skills and problem solving transfer.
The study was conducted at Davao Central College, Philippines of S.Y. 2011-
2012. The respondents of the study were the three sections such as Faith (90%),
Hope (88%) and Love (66%) of Fourth-year high school students.
The instrument used in this study are the 52-item Metacognitive Awareness
Inventory (Schraw & Dennison, 1994) of which the researcher has adopted.
The test is composed of two parts, namely; metacognitive knowledge and
metacognitive regulation. The Academic Intrinsic Motivation (AIM) was adopted
from the study of Shia (1998) on her study, Academic Intrinsic and Extrinsic
Motivation and Metacognition. This inventory is divided into two categories of
80
JPAIR Multidisciplinary Research
motivation; Intrinsic and Extrinsic motivation. These two adopted instruments
are modified by the researcher to which fits the students in mathematics. Both
instruments require respondents to rate each item on a 5-point scale ranging
from strongly disagree (1) to strongly agree (5). Another instrument used was
the 25-item “multiple choice” type of test from Nevara, 2009 in her textbook
entitled Advanced Algebra with Trigonometry and Statistics. This measures the
students’ success in problem solving transfer. This test instrument encompasses
the real life problems on selected topics in Fourth-Year Mathematics. This test
has a reliability α = 0.85. This means that the instrument passes the reliability
test.
The conduct of the study was done by seeking permission first to head offices
of the school before administering the instruments to the fourth-year students
and gathered it after done on the first session. The second session was allotted for
the conduct of the problem solving transfer test to the same students. Retrieval
of the test was done, and the results were treated through the use of appropriate
statistical tools.
RESULTS AND DISCUSSION
The problem solving skills in this study is measured through metacognitive
and motivational aspects. Under metacognition, there are to indicators and these
are metacognitive knowledge and metacognitive regulation. On the other hand,
the motivational aspect also has two indicators and these are intrinsic motivation
and extrinsic motivation.
The Level of the Problem Solving Skills in terms of the Metacognitive Aspect
Table 1. Level of the problem solving skills of students in terms of the
Metacognitive aspect
Metacognitive Aspect of Problem Solving Skills Mean Descriptive equivalent
1. Metacognitive Knowledge
2. Metacognitive regulation
Overall
3.78
3.74
3.76
High
High
High
Data shows that there is a high level of manifestation on the metacognitive
aspect both in knowledge (3.78) and regulation (3.74). This would mean that
metacognitive aspect of the problem solving skill is high (3.76) also. This implies
81
International Peer Reviewed Journal
that students are highly developed in the knowledge of cognition in determining
appropriate skills and strategies that work best for the learner and for knowing
how and when to use the chosen skills and strategies. On the other hand, the
respondents also developed high regulation of cognition in controlling one’s
thinking and learning that includes planning, monitoring comprehension and
evaluation. This is consistent with the idea that metacognitively aware students are
more strategic that perform better than unaware learners. The knowledge about
cognition and regulation are essential, and this knowledge allows individuals to
plan, sequence, and monitor their learning in a way that directly improves their
performance in non-routinize problems.
Level of Problem Solving Skills in terms of Motivational Aspect
Table 2. Level of problem solving skills of students in terms of Motivational
Aspects
Motivational aspect of Problem Solving
Skills
Mean Descriptive equivalent
1. Intrinsic Motivation
2. Extrinsic Motivation
Overall
3.68
3.53
3.61
High
High
High
The motivational aspect of problem solving skills is high (3.61) generated from
the intrinsic motivation as high (3.68) and extrinsic motivation as high (3.53) as
well. This result indicates that students manifest awareness on the motivational
aspect of problem solving skills towards mathematics. This would imply that
students who are intrinsically motivated developed mastery of goals and the need
for achievement. On the other hand, students who are extrinsically motivated
cultivated the factors such as authority expectations (family and teachers), peer
acceptance, power motivations and fear of failure. Motivation is a force within
the educational system to encourage students learning and understanding and
thus dictates the students’ behavior due to either external or internal factors.
82
JPAIR Multidisciplinary Research
The Summary on Problem Solving skills
Table 3. Summary on problem solving skills
Aspects of Problem solving Skills Mean Descriptive equivalent
1. Metacognitive
2. Motivation
Overall
3.76
3.61
3.67
High
High
High
Problem solving skills reflects 3.67 mean score or high manifestation. This
is due to the result obtained in its aspects namely; metacognition (3.76) and
motivation (3.61) of which both are high in awareness. This implies that students
are able to develop and explore the problem, extend solutions, process and develop
self-reflection. On the other hand, metacognition and motivation are two of
the aspects and skills necessary to a successful problem solver (Bruner, 1996).
Likewise, students are highly equipped with metacognition and motivation in
Mathematics. It emphasizes that organizing thoughts in such material, checking
comprehension regularly, analyzing the usefulness of strategies differentiating
learning strategies considering intellectual strengths and weaknesses and setting
and meeting goals are demonstrated by the students. Moreover, the respondents
are also motivated to set high goals for themselves. Students spend time for the
things that interest them, demonstrate abilities in the classroom, and prefer to
obtain good grades for the acceptance of others.
The Level of Success in Problem Solving Transfer
Table 4. Level of success in problem solving transfer
Problem Solving Transfer Mean
Descriptive
Equivalent
Interpretation/level
Fourth year Students 15.70 Very satisfactory Denoted a high level of success
The mean score of the success in problem solving transfer is 15.70 with a
descriptive equivalent of very satisfactory. This would mean that the students
have a high level of success in the problem solving transfer. This supports the
theory of Cognitive Flexibility (Spiro, Viltovitch and Coulson, 1990) that an
individual may transfer the mastered skill in an ill-structured type of domain if
83
International Peer Reviewed Journal
he is flexible in cognition. Thus, this implies that the students can construct new
version of understanding highly in solving real life problems.
The Prediction of Success in Problem Solving Transfer
Table 5. Model Summary: The Prediction of Success in Problem Solving Transfer
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
1
B Std. Error Beta
(Constant) 14.77 2.782 5.313 0.00
Metacognitive
Aspect 1.558 .767 .216 2.059 0.42
Academic
Motivation -1.370 .776 -.185 -1.764 .080
This shows that the metacognitive knowledge predicts the dependent variable
which in problem solving transfer as reflected in the model shown in table 4.
Academic motivation is not significant. The predicted success in problem solving
transfer (Y) is approximately equal to 14.779 plus 1.558 of the metacognitive
knowledge (X), that is:
Y = 14.779 +1.558X.
The aspect of problem solving skills that predicts the success in problem
solving transfer was the metacognitive awareness and metacognitive knowledge in
particular. The model emphasized that as the metacognitive knowledge increases,
problem solving transfer also increases. Furthermore, the unit and a half increase
of metacognitive knowledge correspond to the increase of success in problem
solving transfer.
The Relationship between the Aspects of Problem Solving Skills and Success
in Problem Solving Transfer
The computed r-value for the correlation between metacognitive aspect of
problem solving skills and problem solving transfer is 0.120 with its corresponding
indicators knowledge and regulation as .186 and .041 respectively.
84
JPAIR Multidisciplinary Research
Table 6. Relationship between problem solving skills and problem solving transfer
Aspects of Problem Solving Skills r - values P-value Decision on H
o
Knowledge .186* .040 Rejected
Note: Significant (Sig) if p<0.05
This means that the variance of success in problem solving transfer of the
students could not be explained by the variance of the metacognitive regulation
for its p-value 0.653 which is greater than the level of significance. However, only
the small variance of success in problem solving transfer could be influenced by
metacognitive knowledge in Mathematics contributes to the success in academic
learning domains for its p-value = .040 is less than the level of significance. Hence,
the null hypothesis that there is no significant relationship on the metacognitive
aspect of the problem solving skills and success in problem solving transfer is
not rejected. Therefore, there is no significant relationship on the metacognitive
aspect of the problem solving skills and success in problem solving transfer. The
result only implies that there is a need to consider how metacognitive abilities
are acquired and develop, how knowledge could be used to help improve the
performance with learning difficulties and how it relates to self-evaluation
processes (Reeve & Brown, 1985). Somehow, on the aspect of metacognitive
knowledge, students have acquired the skills and strategies that work best in the
and even how to use the content and skills in solving real life problems.
On the other hand, data also show that the correlation between the
motivational aspect of the problem solving skills and the success in problem solving
transfer was 0.120 or not significant, 0.033 or not significant between intrinsic
motivation and success in problem solving transfer, 0.073 or not significant
between extrinsic motivation and success in problem solving transfer. This means
that motivational aspect of the problem solving skills did not significantly relate
to a very satisfactory level of problem solving transfer for its p-values of .424
(motivational aspect), .187 (intrinsic motivation) and .717 (extrinsic motivation)
are greater than the level of significance. Thus, the null hypothesis that there is no
significant relationship between motivational aspect of the problem solving skills
and success in problem solving transfer was accepted. The findings of this study
are consistent with the idea that extrinsic motivation across grade level proved
negatively correlated with the academic outcomes (Lepper et al., 2005).Based on
the result, it is not always true that when students are intrinsically motivated with
85
International Peer Reviewed Journal
appreciation and enjoy the learning process on mathematics will tend to have
focus on learning such as the mastery needed on mathematical concepts.
Among all indicators of the problem solving skills, only the metacognitive
knowledge is significantly related to the success in problem solving transfer.
Metacognitive knowledge refers to the knowledge of cognitive processes and
product such as what a student knows about his cognition, how to use the
strategies and procedure, and why or when to use a particular strategy. Hence,
this implies that at the very start, knowledge of skills and strategies is significantly
correlated to their success in problem solving transfer. This is supported by the
predictability result of the study as mentioned earlier. Activities concerning control
of students’ thinking and learning as planning, monitoring comprehension and
evaluation were observed to be not significantly correlated with students’ success
in problem solving transfer. It was also on the variables excluded as the predictor
of the said success.
To sum it up, metacognitive skill acquisition is likely to accelerate students
comprehension, understanding, mastery and reasoning skill necessary for
problem solving transfer (Pesut &Herman, 1992), but, only to those who
consistently create rules, picture out the conceptual problem, identify and make
rules in describing the problem on it which is done simpler and easier without
taking complex ways on solving problems.
CONCLUSIONS
Based on the findings, the following conclusions were drawn. The level of
metacognition and motivation of students in the problem solving skills are high.
Students’ success in problem solving transfer was very satisfactory. Metacognitive
knowledge predicts success in problem solving transfer. The metacognitive aspect
of problem solving skills does not relate to the success in problem solving transfer.
The motivational aspect of problem solving skills does not relate to the problem
solving transfer.
LITERATURE CITED
Bruner, J. S. (1966). Toward a theory of instruction (Vol. 59). Harvard University
Press.
86
JPAIR Multidisciplinary Research
Mann, E. L. (2006). Mathematical creativity and school mathematics: Indicators of
mathematical creativity in middle school students (Doctoral dissertation, University
of Connecticut).
Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of
problem solving. Instructional science, 26(1-2), 49-63.
Huitt, W. (2009). Humanism and open education. Educational psychology
interactive.
Skinner, B. F. (1963). Operant behavior. American Psychologist, 18(8), 503.
Middleton, J. A., Heid, M. K., Reys, R., Gutstein, E., Dougherty, B., D’Ambrosio,
B. & Hala, M. (2004). An agenda for research action in mathematics education:
Beginning the discussion. Journal for Research in Mathematics Education, 74-80.
Pesut, D. J., & Herman, J. (1992). Metacognitive skills in diagnostic reasoning:
making the implicit explicit. International Journal of Nursing Terminologies and
Classifications, 3(4), 148-154.
Reeve, R. A., & Brown, A. L. (1985). Metacognition reconsidered: Implications
for intervention research. Journal of Abnormal Child Psychology, 13(3), 343-356.
Schraw, G., & Dennison, R. S. (1994). Assessing metacognitive awareness.
Contemporary educational psychology, 19(4), 460-475.
Shia, R. M. (2005). Academic Intrinsic and Extrinsic Motivation and
Metacognition. Assessing Academic Intrinsic Motivation: A look at Student
Goals and Personal Strategy. Wheeling Jesuit University. Retrieved on October
11, 2014 from http://www.cet.edu/pdf/motivation.pdf.
Trends in International Mathematics and Science Study (TIMSS) (2007). No
Child Left Behind. Retrieved on October 11, 2014 from http://timssandpirls.
bc.edu/isc/publications.html