AN ANALYSIS OF STUDENTS’ CREATIVE THINKING
5) communicating the result, while Krathwohl and Anderson in Bloom Taxonomy Revised (Mayer, 2002) synthesize the cognitive process domain of create are the process of generating, planning and producing. The creative thinking process described by Torrance and Bloom Taxonomy Revised are connected and related each other.
Table 1. Comparison between creative thinking process of Torrance and Bloom Taxonomy (revised)
Torrance’s Bloom Taxonomy
(Revised)
1.
Sensing difficulties, problems, gaps in Information, missing elementUnderstanding the problem
2.
Making guesses and formulating hypothesesTesting the hypoteses and evaluating
3.
Communicating the resultProblem
representation, in which student
attempts to
understand the task
and generate
possible solutions;
1.
(generating) solution planning, in which a studentexamines the
possibilities and devises a workable plan (planning) solution execution, in which a student successfully carries out the plan (producing)
Measuring creative thinking is necessary to do. Some people used creative thinking test such as TTCT (Torrence Test of Creative Thinking), CAMT (Creative Ability in Mathematical Test), Guilford Alternative Uses Task and others. Getzel and Jackson used task that has multiple answers or could be approached from multiple directions (Silver, 1997).
Open-ended problem is a problem that has multiple correct answer (Suherman, 2003).
Shimada et al described open-ended learning as a learning start with presenting a open-ended problem, then the lesson proceeds by using many correct answer to the given problem to provide experience in finding something new in the process (Takahashi, 2005).
Cooney (2002) made characteristics for open- ended question that should be involve significant mathematics, elicit a range responses, require communication, be clearly stated, and lend itself to a scoring rubric.
2. Research Method
The research approach is qualitative aiming to analyze student’s creative thinking process and ability. Some works we did are: 1) designing a learning activity through open-ended learning to familiarize students to open-ended questions; 2) giving the test of creative thinking ability using open-ended question; 3) determining subject for focus interview by categorizing the students as high, medium, or low creative ability; 4) doing the focus interview to generalize the model of creative thinking process include: identifying and understanding the problems, making guesses and formulating hypotheses, evaluating and testing the hypoteses, and communicating the result.
Data were collected through task-based interview of fifth grade of elementary school students. Snowball sampling was used to select two students of high ablity, two students of medium ability, and two students of low ability. The category is determined by the ability of students in giving response of the open-ended question based on fluency, flexibility, originality, and elaboration criterions. The first problem is as below.
A plane can be formed by other plane, for the example a rectangle can be formed by two acute isoceles triangle and two obtuse triangle which are congruent.
Figure 1. Rectangle formed by acute and obtuse triangle
Students’ task is make some planes and the plane formers as much as you can such as the example above. Students are is categorized as high creative thinking ability if they can give responses as much as they can in some categories and their response is relevant, elaborate and different with other students. The process will be analyzed start from how students understand the problem, how they will solve the problems and how they can think about alternative solution.
The second problem is given the area of a plane is 144cm2, but the plane is unknown. Students are asked to determine the plane as well as the measurement which area is 144cm2. Students are also given the example of paralellogram which has base length of 18 cm and the height is 8cm and a right triangle which has base length of 24 cm and the height is 12cm.
Obtuse triangle
Acute triangle
Figure 2. Parallelogram and triangle has area of 144 cm2
Students are classified as high ability if they can make more than three different planes with the measurement, prove that the area satisfies the condition (144cm2), and make a different and unique response. The creative thinking process will be recognized by giving the students question about what planes that has the area of 144cm2 and its measurement, how they prove that the area is 144cm2, and how they find alternatif solution.
The last problem is students are given figure as below and followed by two questions.
a. How many squares do you find in the figure above?
b. How many rectangles do you find in the figure above?
The highest level of students is achieved if they can recognize that 4 small squares can form a bigger squares, so that 9 squares and 16 squares, it is also prevailing for rectangular case.
3. Result
After the students given the task, the author analyze the answer of each students. By using rubric, 6 students are categorized as high, 10 students are medium, and 14 students are low ability of creative thinking. Two students taken as sample of high ability, EA and FR. VD and CH taken as representative of medium ability and CI, SA, and S taken as representative of low ability. the following result is as followed.
For the first problem, EA from high ability category made 11 kinds of combination planes that formed by other plane. Four of the eleven responses that he gave are original and the rests are the same answers with other students. He named each former plane correctly and completely. The average number of response that given by medium ability students is about 4 until 5 responses which has medium level in originality. Some of them named the plane former incompletely. The low ability students did many mistakes in named the plane former even many of them did not named at all (CI, SA, and S).
Further interview was carried out to analyze the students’ creative thinking process. At first, students of high ability category (EA and FR) were directly understanding the problem that presented.
They were intended to make some rectangles and parted the rectangles into other planes, then named the plane former. The work result of EA is shown in this following picture.
Figure 3. Figure EA’s work result in the first problem
The students of medium ability category (CH and VD) did not understand the problem in the beginning, but after reading the question several times they got the point. CI, SA, and S did not understand the problem in the beginning and still needed guidance of the teacher to understand the problem. Because of doing the task incompletely, they were asked the reason why they did not name the planes. All of them said that they run off time, but when the author asked them to mention the name of the plane in their answer sheet, they named wrongly. CI mention the isoceles trapezoid as triangle and obtuse triangle as acute triangle. S also named wrongly the planes she had made. SA only made 3 figures and when she asked wheather she could make another figure or not she was not sure.
In the second problem, EA made 4 planes and FR made 5 planes that have certain measurement which satisfy the condition (the area is 144 cm2).
EA made the measurement of rectangle, parallelogram, kite, and rhombus, while FR is richer in combining the formula and the number so that he could make the measurement of rectangle, parallelogram, trapezoid, rhombus, and triangle.
The only one answer that give the measurement of trapezoid correctly and complete with the prove is FR’s answer. After interviewing the student, author found out that FR first understand the problem by determining two numbers that has a product of 288 and he made a guess by selecting 4 as a number can be devided by 288. This is shown as the interview result below.
18 cm 8 cm
24 cm 12 cm
Interviewer : So, you guess that the height of the trapezoid is 4 and the two parallel side is 20 and 52?
FR : Yes, ma’am.
Interviewer : Okay, could you please tell me what you think first so that you can find the measurement of trapezoid?
FR : First, I remembered the formula of trapezoid area, that is . Then I chose a number that can be divide by 2.
Interviewer : Why did you choose a number that can be divide by 2?
FR : In order to omit the
Interviewer : Then, what number did you choose?
FR : 4.
Interviewer : After that? What step did you take?
FR : I divided 144 by 2 and obtain 72. I determine the parallel side of the trapezoid by choosing two numbers when added result 72, those are 20 and 52.
Interviewer : It is possible to choose other number exclude 20 and 52?
FR : yes ma’am, as long as the result is 72 if the height is 4.
VD and CH made measurement of three planes correctly complete with the procedure of proving that the area is 144 cm2. Actually CH tried to find the size of trapezoid, but he could not remember the formula of trapezoid area perfectly, then he determine the incorrect size. CI from low ability category tried to find four planes but she ended to give only two planes because of she failed in finding the measurement of the other two planes.
Figure 4. CI’s work in second problem The third problem needs more elaboration to obtain the answer. None of students answered completely. But many of them understood the problem well and chose the appropriate strategy.
EA and FR knew that the squares are not only as shown in the picture. They recognized that 4 squares, 9 squares and 16 squares as shown below also form squares.
Figure 5. Kind of squares as solution of third problem
They also found out that there were many rectangles can be formed. Some of them are shown below.
Figure 6. Kinds of rectangle as solution of third problem
Medium ability students could recognize 1 unit,4 unit, and 16 unit squares. They could not find the 9 unit squares. The low ability students could only recognize 1 unit and 16 unit squares, but most of them only found out 1 unit squares as shown in the picture.
Based on these data, the author considered the students’ creative thinking process and product for each category through open-ended as shown in this following table.
Table 2. Creative thinking process and product Category Creative
thinking process
Creative thinking product
High ability Students understand the problem and they can make some guesses,
try the
hypoteses and evaluate. They communicate the idea well.
The creative thinking product of high ability students are various in kind of responses, categories, and even some of the responses are different to others.
Medium ability
Students understand the problem and they can make some guesses,
try the
hypoteses as well as high ability, but
The creative thinking product
of medium
ability students are less various in
kind of
responses, categories, and some of the
when the find an obstacle they easier to give up and cancel the prosedure they have done.
responses are same to others.
Low ability Students are difficult to understand the problem, and make a guess.
When they
make a guess they can not evaluate wheather the guess is correct or not.
The creative thinking product of low ability students are less various in kind of responses, categories, and the responses are too common.
4. Conclusion and Discussion
Students’ skill is not something that we only need to score. It is also something that we have to study carefully and in depth. Siswono (2004) believed that creative thinking of students could not be described only by giving levels to responses to assigned problems without concern for other perspective. Creative thinking is an important skill for everyone, not only when they are in school but also when they face the workforce. In mathematics learning, as an educator or a researcher we can do many things about this skill. Developing a learning that involved divergent thinking can foster students’
creative thinking. Teachers can give opportunity to explore some methods or solution in solving problems by considering fluency, flexibility, originality, and elaboration. Educator or researcher also can compare, make a relationship, or involve other aspect such as gender, ethnicity, academic achievement, or other field. We also can explore and analyze the students’ creative thinking by using certain task or test.
This research is concerned in analyzing or identifying students’ creative thinking. Through open-ended learning, students are familiarized to solve problem with multiple answer or multiple method to approach. Students are given opportunity to find many solutions using their creative thinking ability. After having three tasks, the author analyze students’ answer and do the placement weather the students will be categorized as high, medium, or low ability of creative thinking. Then, some students are chosen as representative of their category to do the task-based interview.
5. Future Works
This research is one of method to analyze the creative thinking of student. This paper has only been able to show a few examples. It is necessary to elaborate the students’ creative thinking deeply and
refine the category not only for high, medium, and low ability. Open-ended problem solving can be used in other work but using other learning that support the creative thinking of students also possible to do.
ACKNOWLEDGMENT
I would like to thank Prof. Hardi Suyitno, Semarang State University for the guidance and giving some advices and support.
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