Literature Review And Conceptual Framework On The Effect Of Problem Solving Strategies On Students’ Achievement
Research on developing an effective general instruction for physics problem solving started at least 50 years ago and changed after the late 1970s with the works of researchers. Most of the researchers examined on general and specific problem solving strategies. The most notably general strategies are Polya’s and Dewey’s problem solving strategy steps. Dewey cited for his four steps (problem’s location and definition, suggestion of possible solution, development by reasoning the bearings of the solution, and further observation and experiment leadings to its acceptance or rejection) problem solving strategy.
Polya cited for his four steps problem solving strategy. The first step is Description, by identifying the unknown, the data, and the condition, and then drawing a figure and introducing suitable notation. The second step is Planning, in which the solver seeks a connection between the data and the unknown. If an immediate connection is not found, the solver considers related problems or problems that have already been solved, and uses this information to devise a plan to reach the unknown. In the third step, Implementation, the steps outlined in part two are carried out, and each step is checked for correctness. In the final step Checking, the problem solution is examined, and arguments are checked.
Recently, Loucks introduced a method for solving university physics problems, particularly when algebra is involved, which is similar to Savage and Williams’ problem solving. For Loucks, the most important factor is to set up the problem, so that the solver can determine which equations are suitable. Once it is set up, the problem becomes simply a mathematical problem. Loucks recommended five steps to effectively solve physics problems with algebra; a) identify the type of problem (for example, concept, keyword, feature), b) sort by interval and/or object (e.g., list everything, draw diagram), c) find the equation and unknowns, try to relate the intervals, d) outline solution or make a chain of reaction, e) do the mathematics.
Actually there are still a lots of problem solving strategies had develop by other researchers. However, Polya Theory will be choosen to apply with the cooperative teaching method in this study. This is because most of the problem solving strategy theories are developed from Polya Theory, which mean Polya Theory is the most basic of the problem solving strategy. Besides that, the steps cited by Polya is quite clearly and easy for students to apply in their eduction.
- Sample Procedure
The experimental procedures of the research were carried out on high school in Turkey. After according to pretest performed on 10th grade students, two classes, equivalent to one another in terms of knowledge, were chosen. One of them was named as experimental group; the other one as control group. The experimental group consisted of 25 students (12 female and 13 male). The control group consisted of 21 students (8 female and 13 male). High school education is three years in Turkey. After students graduated to high school, for higher education students take National University Entrance Exam done every year. 11th grade students must prepare to take the exam. Because of this, in this research 10th grade students were selected. Besides, the chosen reason of “Kinematics and Dynamics” subjects was connected with concepts.
- Problem Solving Strategy Scale (PSSS)
This survey was developed by Heller & Heller, 1995; Polya, 1945; Reif at al., 1976. This Problem Solving Strategy Scale (PSSS) consisted of 26 affirmative and four negative statements as indicated in Table 1. Respondents rated each item on a five point Likert scale, with the following scale anchors: 1= Very Often, 2= Often, 3= Sometimes, 4= Rarely, 5= Never.
- Mathematics Motivation Scale (MMS)
The items for the mathematics motivation scale were developed by both creating new items and adapting items from MSLQ. The items adapting from MSLQ were translated into Chinese by the authors with the supervision of two experts in English language. And then, the items, factors, design, and rating points of this scale were examined by three testing experts. According to these suggestions, the needed correction was made by the authors. Originally, there were three factors (value, expectancy, and affect) in mathematics motivation scale, and 36 items were included in this scale. The component of value could be divided into three elements: Intrinsic goal orientation (6 items), extrinsic goal orientation (6 items), and task value (6 items). The component of expectancy could be divided into two elements: Control beliefs for learning (6items) and self-efficacy (5 items). The component of affect only included one element: Test anxiety (7 items) (Table 2).
- Problem Solving Attitude Survey (PSAS)
This survey was developed to assess student’s attitude toward problem solving. This survey consists of 28 items, and all the responses inside the questionnaire will be kept confidential by Professors Dewar and Bennett. For Likert type scale survey, students read a statement and decided on the degree of important using 5 point scale. The scores for each item ranged from always to never. This survey included items is mainly to find out about student’s problem solving attitudes.
- Problem Solving Worksheets
Problem solving worksheets had been prepared to determine the problem solving strategies used by students while solving a mathematic word problem. The problems were being arranged at difficulty level to 3 set for students included in control and experimental group to solve them. Firstly problems will be solved in individually then a common solution of the group was to be written in the experimental group. Evaluation of the problem solved by group was made by the researcher. Common strategies of the students were determined while students were solving mathematic problems according to achievement and behaviors.
The study was performed during the spring semester in High School Physics II course covering “Kinematics and Dynamics” concepts. For this research two classes were selected as mentioned method. The same instructional material was used for both classes. Courses were taught by the same instructor using the same schedule with different instructional methods. The details of this research were given as follows.
First of all, the pre assessments were given on the day before the implementation session during the regular mathematic course hours. Before teaching of planned chapters, the students included in the experimental group were informed on teaching of problem solving strategy steps and cooperative learning method. Besides, the students included in the control group were told only on teaching of problem solving strategy steps. The information period was completed in 1 week.
During the experimental procedures, problem solving strategy steps were applied with the cooperative learning method to the experimental group and with the conventional teaching method to the control group. Problems were solved by using the same problem solving strategies on both groups. Besides that, Class structure of the experimental group was changed in each application according to cooperative groups. Students included in the experimental group were distributed as mixed groups according to achievement and strategy level. Each group consisted of three students. There were eight mixed groups in the experimental group. Students included in the experimental group were given various tasks during research. These tasks were changed in the group and among groups to provide changing dynamics of the groups at certain times.
The activities of both groups were performed by the math teacher and same problems were solved in the classes. In the experimental process, students in both groups studied on the problem solving worksheets prepared by researcher. Mathematic achievements of students during solve the problem worksheets will be evaluated by the math teacher. Students weren’t expected to submit practice problems or assignments. Besides that, students also didn’t take routine examinations. At last, the post assessments were given on the same day immediately after the implementation session.
The responses of the research questions were examined. The pre and post test’ arithmetic means and standard deviations of PAT, PSSS, PSAS, and AMS were calculated, and then t-tests for independent samples were applied to check whether the difference between the averages of the groups is meaningful. Results were shown in Table V.
Table V presented the mean scores and standard deviations of the pre and post assessments for the control and experimental groups. There were no significant differences on the pre assessments; it was assumed that the two groups started out with equivalent means. T-tests for independent samples were carried out to tests whether the experimental and control groups differed significantly on the post assessment on PAT (t=10.93, p<0.05), PSSS (t=9.97, p<0.05), PSAS (t=5.06, p<0.05), and AMS (t=5.28, p<0.05). Results in Table V showed that the scores of the experimental group were consistently higher than those of the control group while the standard deviations were consistently lower.
Table VI presented the mean scores and standard deviations of the pre and post assessment for the control and experiment groups according to subscales. There were no significant differences on the pre assessment. T-tests for independent samples were carried out for subscales whether the experimental and control groups differed significantly on the post assessment PSSS, PSAS, and AMS. Results in Table VI showed that the scores of the experimental group were consistently higher than those of the control group while the standard deviations were consistently lower. Also, Cohen’s d values support this outcome by large effect size.
Further, the variances analysis was applied to check the meaningful difference between strategy averages of the groups. For examining the effects of gender on strategy use, students included in groups were separated into four groups according to gender: “EG-F, EG-M, CG-F, CG-M”. The variance analysis related to each subscales was applied to check the meaningful difference between averages of the female and male students. Data related to pre and post assessment were given in Table IX.
According to obtained from results for PSSS, the strategy average of female students included in the experimental group was higher than the strategy average of male students, and strategy average of females and males included in the control group was almost equal, it can be observed from the results in Table IX. When standard deviations were compared, the standard deviation of the control group was found to be remarkably higher than the standard deviation of the experimental group. This result showed that the experimental group had more heterogeneous and the control group had more homogeneous structure.
- Contribution to Teaching and Learning
Through this study, teacher can try a new teaching method to enhance the achievement motivation of students in learning physic. To investigate the situation of student’s learning mathematic in Malaysia, many interviews had done with local primary school teachers. The result showed that there were many primary school teachers always face the problem that students showed bad attitude and less motivation in class mathematic, such like listless compliance, passive resistance, and rebelliousness under the conventional teaching. Less motivation and bad attitude in class will straightforward effect their achievement in physic. Skemp also noted the dilemma faced by teachers wishing to teach children with understanding when all they want to learn is ‘how’ rather than ‘why’. Likewise children who want to know ‘why’ are frustrated when only taught ‘how’. This is because conventional teaching is more to teacher center, teacher had less communication with students and students lack of participant in the lesson. With the combining problem solving strategies and cooperative learning method, which can help students to enhance their achievement in physic.
Besides that, with combining the problem solving strategy and cooperative learning method, physic class will be seem more interesting and attractive for students. If students starting think that physic is interesting, at the same they starting fall in love with physic. Normally, in cooperative learning method students will being giving a worksheet or problem, then they need to form a group and find out the solution together. From here, students are learning to be responsible and eager to learn a new knowledge because the reward is for group success. In addition to being accountable for their own learning and achievement, group members are rewarded for the success of the group as whole (Johnson & Johnson 1987; Slavin, 1983). The role of teacher now also is changing from main resources to monitor and guidance. Students need to find out and learn knowledge with automatically without order by the teacher.
Last, students are learning the ability of self evaluation. Once a group has accomplished its goal, it looks analytically and critically (often with the assistance of teacher) at the ways in which it has functioned effectively and the ways in which it needs to improve (Johnson & Johnson 1987). With the ability of self evaluation, students will find out their strengths and weaknesses. If any weaknesses were discovery, they will try to faced and solve it. Through the process of improvement, they will be more confidence to the value of themselves.