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Problem solving approaches
Problems are everywhere and any approach in real life human has to approach, have to think
about the most efficient solution. Problem solving is a part of the critical thinking. Critical
thinking includes problem solving but not the opposite. Considering the Definition of problem
solving and critical thinking, there will be a slight difference; problem solving is a reasonable
logical method taken to solve a structured problem while the critical thinking suggest a
reasonable solution structure to an ill-structured problem. Students usually feel anxious about problem solving and critical thinking in general. They get
worried that their exam has any higher order thinking questions, challenging questions or any of
this. It takes more time for the students to learn how to solve problem solving than learning how
to solve applications. Keller and Concannon (1998) carried out a study which showed the obstacles students face when
they solve problems and suggested the strategies that instructors have to consider while teaching
problem solving. Their study identified teachers usually ignore students’ anxiety and worry as
obstacles while solving problem and the learning style differs from one student to another. Some
of the learning styles that students can achieve better are auditory, visual or aurally. The study indicated two strategies that can be used to overcome the obstacles in problem
solving; “pedagogical strategies” and “methodological strategies”. The pedagogical strategy
suggests that a teacher to open a discussion with the class to bring the chance for the students so
that they can be in a position of expressing their fears and worries about problem solving, encourage them to work on problem solving while expressing their thoughts in problem solving.
Opening discussions with students through various ways, like essays, can encourage students to
express their solutions and thoughts and this can lead them to learn from each other and solve the
problems in different ways. Such attempts make students to express themselves in the target
language helping them to improve on their speaking skills. Considering “methodological strategy” as a technique for (Keller and Concannon1998) problem
solving, a constructivist model in instruction, it was identified by Dewey first then by Polya who
considered problem is a setting that arise doubt to inquire. He considered that the problem to be
solved, it has to be adequate for the culture and related to the students. The problems are to be
from the experience carried by the students. The experience should contain two criteria,” content
and the process of knowing”. The teacher’s job at this stage is to clarify and clear out how to
think of the problem and how to follow the steps in solving a problem. The teacher assists in
showing how to investigate by collecting the best information out of the given, test and evaluate
to find conclusions. Students are not necessary to follow the investigation systematically; the
students have the freedom in creating their own technique that suits in solving the problem.
Dewey created steps in problem solving that the teacher can use in teaching how to solve the
problem. The steps are:
“1) becoming aware of a situation or even that is labeled as a “problem”,
2) Identifying the problem in exact terms,
3) Defining all terms,
4) Establishing all the limits of the problem, 5) Conducting a task analysis so that the problem may be subdivided into discrete elements for
investigation,
6) Collecting data that are relevant to each task,
7) Evaluation the data foe apparent biases or errors,
8) Synthesizing the data for meaningful relationships,
9) Making generalizations and suggesting alternatives to rectify the problem,
10) Publishing the results of the investigation.”
Cambridge handbook of thinking and reasoning (2005) defined thinking as follows: “A
systematic transformation of mental representation of knowledge to characterize actual or
possible states of the world, often in service of a goal.”
The process in constructing a course of action that can achieve a goal is represented as a problem
solving. The conceptual relation between a problem solving and an individual is relative. In other
words, each problem varies for each individual because it is either no blocking or no acceptance
of the goal that exists for an individual. Throughout history, solving a problem comes into many
categories depending on the situation the problem is set and the individual’s cognitive level. The
strategies differ according to the type of the problem thus creating different techniques or
strategies. According to Malouff J. ( n.d.), he listed the types as follows:
“ Types to help understand the problem, to simplify the task, to determine the cause of the
problem, involving the use of external aids to help you identify possible solutions, involving the
use of logic to help you identify possible solutions, using a possible solution as a starting point to
help you solve a problem, to determine which possible solution is best, using a geometry of
problem solving, to help you use your maximum capacity while solving a problem, and to help
you solve different problems.” To carry out the solution correctly and to simplify how to solve problem solving, different
models were unidentified yet, in 1957, Polya broke down the problem solving strategies into
stages mainly used in mathematics by experts (Reardon, 2001).
• Understand the problem,
• Devise a plan,
• Carry out the plan, and
• Look back (verifying)
Recently, the field of problem solving in education is becoming an interesting subject to
investigate due to its compatibility with the requirements of the information age; it requires
graduates with high complex thinking skills that can work under pressure and vague situations.
Problem solving is important element in teaching mathematics because it enhances the logical
thinking, contributes in increasing curiosity, organization, and analysis to interpret
communication of information. Research on mathematical problem solving explains the
importance of problem solving in improving the potential of the students in mathematics, it
improves reasoning over intuition, and in addition, it increases the students’ motivation and
enthusiasm in solving math problems. Problem solving and its effect on student achievement
A study done in Pakistan, 2010 on grade eight students from Girl’s public school investigated the
effect of using problem solving strategies in teaching mathematics on their achievement.
Seventy-six female students divided into two groups controlled and experimental participated in the research. The control group was of 38 female students where traditional teaching
methodology implemented and experimental group consisted of 38 female students instructed by
problem solving method. A pre-test, post-test and a self-developed test were used which was
reviewed by experts. The results of the students’ achievement showed there is significant
difference between the students who were taught problem solving method as compared to the
student who learned through traditional method. The research concluded that problem based
strategy enhances the students’ achievement who have same educational background (Ali et al,
2010).
Another research investigated on the effects of problem solving strategies on students’
achievement, attitude and motivation in physics. It was experimental research designed for two
groups control and experimental, constitute altogether of 46 students where 20 females and 26
males. Pretest and posttest used in this study and data was collected from five achievement tests.
The controlled group was instructed using the traditional teaching strategies while the
experimental group was instructing problem solving methods in cooperative groups. The results
showed that there was significant in students’ achievement, attitude and motivation but there was
no gender difference in the medium where problem solving strategies was applied in cooperative
group (Gok & Silay, 2010).
In presenting previous work, it is important to highlight some data reviewed as strengths and
weakness, compare and contrasts of their findings. First, both articles discuss the same issue but
are different in subject and culture. A quantitative critique research Table-1-(see Appendix D)
was done to compare and contrast the strengths and weaknesses of each research using ASRT
(American Society of Radiological Technologists) quantitative research manuscript checklist.
The checklist comparing it with the other another article that is a guide to critiquing research, “Part 1- critiquing quantitative and qualitative research” validates similar ideas. However, some
parts were omitted from ASRT checklist manuscript due to the fact of inappropriateness with the
research field.
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The table discusses what is valid and invalid in each research. In both researches, the title
indicated of the content of the topic. The abstract was brief, coherent to the reader where he can
know what sample is tested, under what method, for what purpose, and its findings. The main
purpose of writing a literature review in a research is to identify and construct a research
question. In both articles, the literature review illustrated conceptually in the introduction,
covering all the aspects of the research questions; the articles covered the importance of problem
solving, the problem solving strategies applied in each subject, and how does new teaching
strategies enhance the student achievement in problem solving. The introduction included two
things the literature review that gave enough points that were used as a guide to the study, giving
enough boundaries to the research. The research question was correlated to the literature review
and it clearly identified the problem that lead to the investigation of this research. In the method
and research design, it included the material, the data analysis and the procedure used illustrating
a brief description and clear comprehension of the investigation route. Though it differs in the
procedure, however, both articles went into comparing between two groups, controlled and
experimental. The sample taken in the first article was small to be supportive in generalizing the
results. The research designs in both articles were appropriate to the research questions and it
was adequate with the nature of the investigation. Due to the nature of the research as
experimental where two groups get different treatments, it requires to compare between two
groups to show significance thus pretest and posttests was being followed in those researches where they studied the mean, standard deviation, and the t-tests. The students were chosen
randomly and the analysis did not require any sophisticated program, but in the first article, the
sample size consisted of 25 students for the experimental group (12 female and 13 male), the
controlled group consisted of 21 students (8 females and 13 males). Relating the sample size of
the first article with the research question number three which was focusing on gender difference
in student achievement, it does not give equilibrium in the results. The sample size in general is
small and specifically the sample size of females in the controlled group. Thus, this might fall the
third question as a weak irrelevant question. The small size representation that might increase the
error, however, who and what
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criteria were used to exclude population was expressed clearly and its reason to the connected
concept. The first article (Gok & Silay, 2010) supported the sample size by sample error tests and
analysis to validate and assure its credibility. The 2nd article (Ali R. et al, 2010), had equal
sample size in each group (38 student), which support and reduces the sample error to test only
the validity of the instruments that will be used. The students were chosen at random in both
articles where the 2nd article the random students were chosen based on the pretest, thus this
shows that there is no randomness but under certain criteria that was not mentioned in the article.
This raises a question: what background do the students come from? Does this affect on the
students’ achievement?
In case of adopting instruments on a new population, the researcher should show reliability and
validity of the instruments to show it is accurate measure that studies the required goal. In case of
article one, since they adopted the instruments to apply on this small population, validity and
reliability test were taken showing the statistical tools. Instead, the 2nd article went into validity test and pilot test to ensure the change in the sampling strategy later and support the instrument
measures taken. Ensuring the authenticity of the procedure taken they have described
chronologically how the group work was done in the 1st article and the teaching strategy taken in
2nd article.
The findings in both articles were not conceptually different. In the first article, explaining the
data analysis shows the researcher using inferential statistics that can identify the difference
between variables and whether these variables are statistically significant. The results overall
hold all the significance of the literature review in addition to the research questions except the
significance of gender difference which was obtained by variance analysis. Of course, with
respect to the sample size it is not enough to show any difference. This sample size was a
weakness in the research because it generalized the connection of the students’ achievement of
problem solving in gender difference. An important point to mention is that the research could
have been investigating in achievement and attitude motivation. In spite, the research was
focusing on the students’ achievement academically and behaviorally the 3rd question research
was meaningless to give it an attention. Another aspect is that the investigators didn’t mention
future suggestions in the study; instead it was a summary of the findings. While in the 2nd
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article, the analysis of the results was done by the t-test. The conclusions were pointed out as the
final result correlated to the literature review, those three results mentioned could have been
structured under one idea. The article succeeded in giving recommendations but no limitations of
the study. Limitations in such research can be established regarding the period of the
investigation taken and the teaching procedure taken, what obstacles occurred during the
investigation so it can protect any further research from falling into same mistakes. There was no need to study gender difference due to the nature of the school; a high school for girls in
Pakistan. The references in 2nd article were more up to date than the first article.
Such results show that problem solving strategies can be implemented in schools for several
reasons. It organizes the student’s logical thinking; it enhances the behavior of the student.
Teaching problem solving strategies by either group work or problem solving based technique
enhances the students’ achievement in problem solving, their attitude and motivation. It helps
develop their mathematical ability, their intuitions and their reasoning. It develops the students’
motivation and enthusiasm with respect to mathematics. Both researches showed those results
above but in different samples one that is a small sample in Turkey and the other a sample in
Pakistan of same gender. Looking from the cultural perspective, the gap in the first articles is the
gender difference and in the other the contextual background of the students especially knowing
the students in this school are all girls. It raises the interest of the research in the gender
difference in achievement of problem solving, the cultural effect of problem solving in
mathematics, and the effect of cooperative learning of problem solving in mathematics The problem-based learning method has been described as a suitable method for constructivist
approach since it allows students to associate their previous knowledge with newly acquired
knowledge while working in cooperative groups to solve a daily life problem (Yenal, İra and
Oflas, 2003; Tarhan and Acar, 2007; Tseng, Chiang and Hsu, 2008). Problem-based learning was
developed in mid-1960s as an alternative method to the conventional approach and was first
applied to the McMaster Medical Faculty in Canada (Bowdish et al., 2003; Loyens, Magda and
Rikers, 2008). Problem-based learning has been employed since then in other fields including
business, education, law, nursing and engineering (Chen, 2008; Massa, 2008). Problem-based learning is a learning method that uses problems as a basis for students to improve their problemsolving skills and to obtain knowledge (Uden and Beaumont, 2005). In the problem-based
learning method, which highlights the use of real problems from daily life as a stimulus for
learning, students work on scenario-based problems in a small group of 5-12 individuals (Berkel
and Schmidt, 2000; Arts, Gijselaers and Segers, 2002). In problem-based learning environments,
students learn new information while in the process of solving problems about daily life (Atan,
Sulaiman and Idrus, 2005). For this reason, while conventional teaching uses problems to apply
related concepts and principles at the end of the subjects in a unit, problem-based learning
environments use problems as an instrument to improve students’ problem solving skills and to
teach them new concepts (Maudsley, 1999; Neville and Britt, 2007). In the conventional approach, students are seen as individuals who passively accept information;
whereas, in problem-based learning environments where learning takes place through problems,
students are regarded as individuals who can access information through research and who
question information. Therefore, in problem-based learning, students assume greater
responsibility for their own learning. Due to such transformation in students’ roles, teaching by
knowledge transfer from the teacher is much less frequent in problem-based learning than in the
conventional approach (Yip, 2002). That is why in problem-based learning environments,
teachers’ roles also differ from those in the conventional approach. In such learning
environments, teachers (guides) play a helper’s role by assisting students to learn by themselves.
The guide should not transfer his/her knowledge about a subject to the students so that the
student can acquire learning skills through self-management, but the teacher should try to reveal
his/her existing knowledge by encouraging students in cognitive activities (Dolmans et al., 2005). Thus, students will not rely on their teachers to learn; instead, they will become
independent learners throughout their lives (Sungur and Tekkaya, 2006).

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