In this ever changing modern technology world, people should be empowered by great potentials and skills to meet its demand. Multi-tasking individuals are the great demands of more companies in different countries around the world. Moreover, everyone is expected to become more functional, more skillful and more productive whether at home, in school, in community and in work place to survive in this competitive world. Furthermore, acquiring a decent job and be employed is a tool for survival and existence.
Improving employability skill equates to possessing critical thinking, a mode of thinking - about any subject, content, or problem - in which the thinker improves the quality of his or her thinking by skillfully taking charge of the structures inherent in thinking and imposing intellectual standards upon them (Elder, 2008).
The development of critical thinking skills produces intellectuals and socially competent citizens who effectively cooperate with other people and challenge real world problems (CTGV, 1993; Glaser, 1985 in Glazer, 2001). Thus, developing the critical thinking should be integrated in the educational programs of all teaching institutions. With this, students will improve their skills and enhance their critical thinking to greatly achieve success in any field of work. Mathematics plays a vital role in developing the critical thinking of students. In 1938, Harold Fawcett (in Acharya, 2011) introduced the idea that students could learn mathematics through experiences of critical thinking. Students do calculations and estimations which serve as brain exercise to compute fluently. And through problem solving in mathematics that students develop and hasten their critical thinking. Thus, critical thinking and problem solving go hand in hand.
In order to learn mathematics through problem solving, the students must also learn how to think critically (Marcut, 2005). Students think critically by dissecting every detail of the problem and examining the problem at different angles. As the students understand the problem, which is the first process in solving it (Polya, 1957), they begin to create, formulate and investigate different solutions and explore different techniques that could result to a new method of solving a problem. Sometimes these solutions would be rational, irrational or imaginary depending on how the students perceived the given problem. Problem solving provides a variety of experiences. Students' experiences in problem solving exposed them to real life situations, thus, preparing them to face the challenge of the real world which is the primary focus of education. Furthermore, these experiences challenged their minds to function more and develop skill in thinking critically. Moreover, problem solving allows the student to experience a range of emotions associated with various stages in the solution process. Mathematicians who successfully solve problems say that the experience of having done so contributes to an appreciation of the inner beauty of mathematics.
The existence of critical thinking in problem solving is very much evident. Since 1980s, the National Council of Teachers of Mathematics recommended that problem solving be the focus of mathematics teaching because it encompasses skills and functions which stimulate critical thinking. Nowadays, employer hires fresh graduate students who are mathematically inclined because they assume that these newly graduates can think critically.
As a mathematics teacher, it is not enough to know the importance of critical thinking in problem solving and applying this in instruction. What important is how we assess and what we assess gives a clear indication of what we value and directs what and how students learn (Van de Watering et al, 2008). However, assessing critical thinking is difficult. When solving a problem, students must understand, represent and decide on relevant problem's facts, conditions and goals, and when a solution is reached, it must be judged by how well it fits the problem's facts, conditions and goals. And if little has been communicated to assess the students' thinking, assessing their critical thinking would be limited. In line with this, Ennis (2001) stated that critical thinking assessment although difficult to do well, is possible. According to him, the difficulties and possibilities vary with the purpose of critical thinking assessment and the format used, and there are numerous traps to unwary. Moreover, effective assessment of critical thinking depends heavily on how well we can facilitate the communication of evidence of students' understanding, critical thinking, and reasoning (Szetela, 1993).
To meet the challenge of assessment of critical thinking, the present study aimed to assess the critical thinking of students aided with enhanced formats of problem solving situations to promote critical thinking and improve students' abilities to communicate their thinking.
Critical thinking rooted from the teaching practice and vision of Socrates, 2500 years ago wherein his method of questioning was known as the "Socratic Questioning" which was the best known critical thinking teaching strategy. Over the years definitions of critical thinking varies and can be categorized to being philosophical, psychological and educational.
Philosophical definition of critical thinking focuses on ideal critical thinker, its qualities and characteristics. As what Scriven and Paul (1992) define critical thinking as the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. In its exemplary form, it is based on universal intellectual values that transcend subject matter divisions: clarity, accuracy, precision, consistency, relevance, sound evidence, good reasons, depth, breadth, and fairness. Also, Bailin (2002 in Lai, 2011) defines critical thinking as thinking of particular quality - essentially good thinking that meets specified criteria or standards of adequacy and accuracy. Moreover, critical thinking is self-guided, self-disciplined thinking which attempts to reason at the highest level of quality in a fair-minded way (Elder, 2007). Paul and Elder (2008) define critical thinking as that mode of thinking - about any subject, content, or problem - in which the thinker improves the quality of his or her thinking by skillfully taking charge of the structures inherent in thinking and imposing intellectual standards upon them.
Psychological definition of critical thinking focuses on how people actually think, the types of actions or behaviors critical thinker can do and the final outcome of thinking. Halpern (1998 in Lai, 2011) defines critical thinking as the use of those cognitive skills or strategies that increased the probability of a desirable outcome. Also, Ennis (2001) defines critical thinking as reasonable reflective thinking focused on deciding what to believe or do. According to him in reasonably and reflectively going about deciding what to believe or do, a person characteristically needs to do most of these things:
Judge the credibility of sources
Identify conclusions, reasons, and assumptions
Judge the quality of an argument, including the acceptability of its reasons, assumptions and evidences
Develop and defend a position on an issue
Ask appropriate clarifying questions
Plan experiments and judge experimental designs
Define terms in a way appropriate to the context
Try to be well-informed
Draw conclusions when warranted, but with cautions.
Furthermore, Willingham (2007 in Lai, 2011) defines critical thinking as seeing both sides of an issue, being open to new evidence that disconfirms your ideas, reasoning dispassionately, demanding that claims be backed by evidence, deducing and inferring conclusions from available facts, solving problems, and so forth.
Educational definition of critical thinking is based on years of classroom experience and observations of student learning. Bloom's Taxonomy (1956 in Krathwohl, 2002) which is hierarchical with knowledge at the bottom and evaluation at the top is one of the most cited sources when it comes to teaching and assessing higher-order thinking skills. The upper three levels of Bloom's taxonomy of educational objectives (analysis, synthesis and evaluation) are often offered as a definition of critical thinking (Ennis, 2001). Anderson and Krathwol (2000) revised the Bloom's taxonomy which they introduced the dimensions of knowledge wherein the fourth dimension, metacognitive knowledge, is an awareness of and knowledge of one's own thinking (Pickard, 2007) is where critical thinking exists. Also, Szetela (1993) discussed the aspects of critical thinking in problem solving: analyzing a problem situation, making decisions, monitoring progress, and evaluating the completed solution.
This study aimed to assess the critical thinking of students in problem solving using problems with enhanced formats based on the aspects of critical thinking in problem solving: analyzing a problem situation, making decisions, monitoring progress, and evaluating the completed solution, to improve students' abilities to communicate their thinking and to promote critical thinking.
The conceptual paradigm of this study is found in Figure 1. It can be seen from the figure the aspects of critical thinking in problem solving which are analyzing a problem situation, making decisions, monitoring progress, and evaluating the completed solution. In solving a problem, a student must identify first what is being asked in the problem, what are the given facts and what solution or mathematical process to be used. Then, decide on which of the given facts are relevant and understand how limiting the conditions and how clear the goals are. And when a student arrived at a solution, the solution should be judged by how well it fits the problem's facts, conditions and goals.
Statement of the Problem
The main purpose of this study was to assess the critical thinking in problem solving of third year high school students.
Specifically, this study sought answers to the following questions:
How can the critical thinking in problem solving of students be described in terms of
analyzing a problem situation
monitoring progress, and
evaluating the completed solution?
What is the students' performance in the Critical Thinking Test?
How do students critical thinking differ when they are grouped according to
mathematical ability, and
Scope and Delimitation of the Study
This study was limited to the assessment of critical thinking of students in problem solving which includes analyzing a problem situation, making decisions, monitoring progress, and evaluating the completed solution.
Specifically, the study was conducted at Philippine Institute of Quezon City (PIQC) during the first quarter of school year 2012-2013, on 15 students who were in third year high school undertaken the topics on Right Triangle Trigonometry.
Critical thinking was measured using the Critical Thinking Test developed and validated by the researcher. The Critical Thinking Test consists of 10-item enhanced problem solving questions designed to encourage communication of critical thinking as suggested by Szetela (1993). Also, the Scoring Rubrics that was adapted from Szetela (1993) was used to assess the critical thinking in the solutions of the students. Thus, this study was limited to the results gathered using these instruments.
Significance of the Study
This study is deemed significant to the following:
Teachers. The result of the study will help them examine and improve the strategies and interventions they utilize in the classroom. Also, this will guide the teachers to develop instructions that will greatly improve the critical thinking of students. In addition, teachers will be equipped in analyzing students' processes in problem solving and encourage them to communicate their thinking.
Students. This study may also encourage the students to know the aspect of their critical thinking in problem solving and work towards improving it. They may also appreciate the time they spent in assessing their critical thinking. Also, this will help the students reflect on their own abilities and potentials.
Educational Policy Makers. This study will be beneficial to them because the results will provide insights and baseline information on the situation and needs of both teachers and students. This will serve as a guide in assessing students' progress. Furthermore, the information gathered in this study will help them to make appropriate and rational decisions on assessment of students' development and achievement.
Curriculum Developers and Writers. The result of the study is a potential source of information that will help them in curriculum planning and improving academic programs and activities to empower the teachers in enhancing the critical thinking of students.
The results of this study are additional contributions to the researches made in mathematics education especially in assessing the critical thinking of the students. And the urgent need to enhance the critical thinking of students will motivate future researchers to conduct similar studies in other levels or areas.
Definition of Terms
In order to have a common point of reference, some terms in this study are conceptually or operationally defined
Assessment. This refers to an ongoing process aimed at understanding and improving student learning. It involves making our expectations explicit and public; setting appropriate criteria and high standards for learning quality; systematically gathering, analyzing, and interpreting evidence to determine how well performance matches those expectations and standards; and using the resulting information to document, explain, and improve performance. In this study, this refers to the process of analyzing and describing the solutions of the students using the adapted Scoring Rubrics.
Critical Thinker. This refers to those who use broad in-depth analysis of evidence to make decisions and communicate his/her beliefs clearly and accurately.
Critical Thinking. This refers to that mode of thinking about any subject, content, or problem in which the thinker improves the quality of his or her thinking by skillfully taking charge of the structures inherent in thinking and
imposing intellectual standards upon them (Elder, 2007). In this study, this was measured using the Critical Thinking Test.
Critical Thinking Test. The refers to the instrument that was developed and validated by the researcher which consists of 10-item enhanced problem solving questions designed to encourage communication of critical thinking as suggested by Szetela (1993).
Problem Solving. This refers to the process of confronting the novel situation, formulating connections between given facts, identifying the goal, and exploring possible strategies for reaching the goal (Szetela and Nicol, 1992). In this study, this refers to the process used by the students to answer the typical word problems with supplementary questions.
Rubrics. A description of the standards that will be used to judge a student's work on each of the criteria or important dimensions of learning. In this study, this refers to the adapted rubrics made by Szetela (1993).