THE DIFFERENCE DF STUDENT’S MATHEMATICAL CRITICAL THINKING ABILITC TAUGHT BC PRDBLEM BASED LEARNING
MDDEL AND CDDPERATIVE LEARNING MDDEL THINK- PAIR-SHARE (TPS) TCPE IN SMPN 2 LIMA PULUH
by : Asifa Nur IDN. 4113111008
Mathematics Education Study Program
Thesis
Submitted in fulfillment of the requirements for the degree of Sarjana Pendidikan
DEPARTMENT DF MATHEMATICS
FACULTC DF MATHEMATICS AND NATURAL SCIENCE STATE UNIVERSITC DF MEDAN
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THE DIFFERENCE DF STUDENT’S MATHEMATICAL CRITICAL THINKING ABILITC TAUGHT BC PRDBLEM BASED LEARNING MDDEL AND CDDPERATIVE LEARNING MDDEL
THINK-PAIR-SHARE (TPS) TCPE IN SMPN 2 LIMA PULUH
Asifa Nur
ID. Number 4113111008
ABSTRACT
This research was conducted at SMPN 2 Lima Puluh academic year 2014/2015. It intended to know whether student’s mathematical critical thinking ability in Problem Based Learning classroom is better than student’s mathematical critical thinking ability in cooperative learning model Think-Pair-Share (TPS) type classroom at SMPN 2 Lima Puluh.
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1.2 Problem Identification 6
1.3 Problem Formulation 6
1.4 Problem Limitation 7
1.5 The Objective of Research 7
1.6 The Benefits of Research 7
1.7 Operational Definition 8
CHAPTER II LITERATURE REVIEW 10
2.1 Mathematics and Learning Mathematics 10 2.2 Mathematical Critical Thinking Ability 12
2.3 Problem Based Learning 18
2.3.1 The characteristics of problem-based learning 24 2.3.2 Advantages of problem-based learning 25
2.4 Cooperative Learning 26
2.4.1 Elements of Cooperative Learning 27
2.5 Think-Pair-Share 28
2.6 Learning Theory Support of Geometry The Van Hiele Levels
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2.7 Learning Material 33
2.7.1 The Net Cube and Cuboid 34
2.7.2 Surface Area of Cuboidand Cube 35
2.7.3 Volume of Cube and Cuboid 35
2.8 Sample Implementation of Problem Based Learning Model in
Teaching Cube and Cuboid Matter 36
2.9 Sample Implementation of Cooperative Learning Model
Think-Pair-Share Type in Teaching Cube and Cuboid Matter 37
2.10 Relevant Research 38
2.11 Conceptual Framework 38
2.12 Hypothesis 40
CHAPTER III RESEARCH METODOLOGY 41
3.1 Place and Time of Research 41
3.2 Population and Sample 41
3.3 Variable and Instrument of Research 42
3.3.1 Variable of Research 42
3.3.2 The Instrument 42
3.3.2.1 Mathematical Critical Thinking Ability Test 42
3.3.2.2 Instrument Trial 55
3.4 Design of Research 59
3.5 Technique of Collecting Data 60
3.6 Technique of Data Analysis 62
3.6.1 Descriptive Analysis 62
3.6.2 Analyzed Assumption Test 62
3.6.2.1 Normality Test 62
3.6.2.2 Homogeneity Test 62
3.6.2.3 Hypotheses Test 62
CHAPTER IV RESULTS AND DISCUSSIONS 66
4.1 Research Result Description 66
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4.1.2. The Description of Mathematical Critical Thinking Ability
Test 68
4.2 Analysis of Research Data 69
4.2.1. Normality Test 69
4.2.2. Homogeneity Test 70
4.2.3. Hypothesis Test 71
4.3 Research Discussion 73
CHAPTER V CONCLUSION AND SUGGESTION 76
5.1 Conclusion 76
5.2 Suggestion 76
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TABLE LIST
Page Table 2.1 Indicators of Critical Thinking Ability 16 Table 3.1 Blue Print of Mathematical Critical Thinking Ability Test 43
Table 3.2 Scoring Guideline of Mathematical Critical Thinking Test 47 Table 3.3 Classification of Validity Interpretation 56
Table 3.4 Result of Validity Test 57
Table 3.5 Classification of Reliability Interpretation 58 Table 4.1 Data of Mathematical Critical Thinking Ability Test in Both
Of Experimental Classes 67
Table 4.2 Mean Percentage of PBL Class and TPS Class 69 Table 4.3 One-sample Kolmogorov-Smirnov test 70
Table 4.4 Homogeneity Variance Test 71
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FIGURE LIST
Page Figure 1.1 Student’s answer for the First Question 2 Figure 1.2 Student’s answer for the Second Question 3 Figure 2.1 Structures, action and products f small group learning 23
Figure 2.2 Cube 33
Figure 2.3 Cuboid 33
Figure 2.4 Cuboid Nets 34
Figure 2.5 Cube Nets 34
Figure 3.1 Procedure of Research 61
Figure 4.1 Histogram of Mathematical Critical Thinking Ability Test
in Both of Experimental Classes 68
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APPENDIX LISTS
Page
Appendix 1. Lesson Plan 1 (PBL Class) 81
Appendix 2. Lesson Plan 2 (PBL Class) 87
Appendix 3. Lesson Plan 3 (PBL Class) 93
Appendix 4. Lesson Plan 1 (TPS Class) 99
Appendix 5. Lesson Plan 2 (TPS Class) 105
Appendix 6. Lesson Plan 3 (TPS Class) 111
Appendix 7. Student Activity Sheet 1 116
Appendix 8. Student Activity Sheet 2 120
Appendix 9. Student Activity Sheet 3 124
Appendix 10. Syllabus of PBL Class 127
Appendix 11. Syllabus of TPS Class 140
Appendix 12. Observation Sheet of PBL Class 152
Appendix 13. Observation Sheet of TPS Class 155
Appendix 14. Student’s Mathematical Critical Thinking Ability Test
Before Doing Validity 158
Appendix 15. Validity Test of Mathematical Critical Thinking Test 161
Appendix 16. Reliability Test Mathematical Critical Thinking Test 165
Appendix 17. Student’s Mathematical Critical Thinking Ability Test 167
Appendix 18. Blue print of Mathematical Critical Thinking Ability Test 169 Appendix 19. Scoring Guideline of Mathematical Critical Thinking
Ability Test 171
Appendix 20. Posttest Score of PBL Class and TPS Class 175
Appendix 21. One-Sample Kolmogorov-Smirnov Test 176
Appendix 22. Test of Homogeneity of Variance 177
Appendix 23. Independent Sample Test 178
Appendix 24. r-Table Value of Product Moment 179
Appendix 25. t-Table value of t-Distribution 180
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CHAPTER I INTRODECTION
1.1 Problem Background
Thinking is a natural part of a human being’s interaction with the world. The way of thinking will influence the daily actions. One of the thinking skill is critical thinking. The thinking skills will be learned by students in school through the content of material on mathematics.
Mathematics is not only a subject but a way of thinking. Baykul (in Biber, 2013 : 110) stresses that mathematics courses should aim to improve such skill as reasoning, critical thinking and problem solving in order to prepare students for life and further education.
Critical thinking is required to navigate the ever-complex environment in which they live. Critical thinking is defined as thinking that evaluates reasons and brings thought and actions in line with evaluations. If they do not invest any time in evaluating the information they use, their efforts often result in a low-quality product. Worse, failure to evaluate may result in unfavorable outcomes when teamed with bad decision-making based on flawed information.
Fisher (2011 : 11) defines that critical thinking is skilled and active interpretation and evaluation of observation and communications, information and argumentation. Indicator of critical thinking are : (1) The ability to identify the focus (
the issue, question, or conclusion), (2) The ability to deduce and judge deductions,
(3) The ability to consider and reason from premises, reasons, assumptions, positions,
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reasons, assumptions, positions, and other propositions with which one disagrees or about which one is in doubt without letting the disagreement or doubt interface with one’s thinking (“suppositional thinking”)
In fact, based on researcher’s preliminary study of students in grade VIII at SMPN 2 Lima Puluh, the students are not able to fulfill the indicator of mathematical critical thinking ability from the problem given. It can be seen from student’s answer sheet when the students have the test about student’s mathematical critical thinking ability. For example, the problem number one is : if known the function
28 ) 5 ( 4
) 3 ( , )
(x axb f and f
f , then determine the value of a and b!
Figure 1.1. Student’s answer for The First Poblem
From the above figure 1.1 can be seen that they can not identify the focus, where the important information is what known and asked. They can not deduce and judge deductions it seems by they do not giving reason and deduction. It means the student’s mathematical critical thinking ability is low.
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Figure 1.2. Student’s answer for The Second Problem
From the figure 1.2 can be seen that they can not consider and reason from the question. It means student’s ability is low.
From preliminary study, it can be conclude that the student’s mathematical critical thinking ability is still low and unsatisfactory. This happens because the learning habbit of the students is passive learning, so they can not use their thinking ability to solve the problem.
In the process of learning, mathematical critical thinking skills are not yet fully developed expressly. It proved by the interview result with mathematics teacher in SMPN 2 Lima Puluh Mrs. Ningsih, she said that in the classroom, too most students is a passive activity because students only listening and will not build their own knowledge. So that the teacher do not want to take any other learning model but just direct method.
The importance of teaching and develop critical thinking skills should be viewed as something that is urgent and can not be ignored anymore. Mastery of critical thinking skills are not quite used as educational purposes only, but also as a fundamental process that allows students to cope with future uncertainties, Cabera (in Fachrurazi, 2011 : 77). It is very naive when critical thinking skills are ignored by teachers.
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says in order to maximize the learning process and outcomes of learning mathematics, teachers should encourage students to engage actively in discussions, ask and answer questions, think critically, explain any answers given and give reasons for any proposed answer.
The mathematics classrooms are encouraged to be a place where discussion and collaboration are valued in building a climate of intellectual challenge. Such reform oriented classrooms are described as communities of mathematical inquiry where students learn to speak and act mathematically by participation in mathematical discussion and solving new or unfamiliar problems.
The difficulties involved in teaching critical thinking, led down a path that resounds with common sense, namely if teachers can agree that critical thinking arises from the need to solve a complex problem by observing and forcing perspectives of the problem from many angles then it should follow that being presented enough unique problems, forcing repetition of unique problem solving then students can become a critical thinker.
The learning models that are considered can be used to improve critical thinking skills are models of Problem Based Learning (PBL). The following are some research based reasons for the importance of PBL that processing infomation at higher levels, such as with problem solving, critical thinking, inquiry strategies, and reflection on practice, leads to deeper understanding (Perkins in Barell, 2007 : 4).
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According to Arends (2011 : 411), the syntax of Problem Based Learning are orient students to the problem, organize students for study, assist independent group investigation, develop and present artifacts and exhibits, analyze and evaluate the problem-solving process.
Other learning model is cooperative learning model Think-Pair-Share (TPS) type. Think-pair-share is a cooperative learning technique which involves presenting students with a task or question and giving them time to think by individually. Then in pairs, they report their individual findings, discuss their own thoughts and then refine their individual work if they see fit in order to come up with a consensus on the question or task. Then after pairs have had time to discuss, the class reconvenes and members of the different pairs share their thoughts with the class. Think-pair share encourages student participation in discussing and promotes forming and critiquing arguments both in small and large groups (Sampsel, 2013 : 3).
Think-Pair-Share is a cooperative learning strategy that can promote and support higher-level thinking. The teacher asks students to think about a specific topic, then pair with another student to discuss their thinking and, after that, share their ideas with the group. Benefits of Think-Pair-Share (Lyman, 1987 : 2) :
1. When students have appropriate “think time”, the quality of their responses
improves.
2. Students are actively engaged in thinking.
3. Thinking becomes more focused when it is discussed with a partner.
4. More critical thinking is retained after a lesson in which students have had an
opportunity to discuss and reflect on the topic.
5. Many students find it easier or safer to enter into a discussion with another
classmate, rather than with a large group.
6. No specific materials are needed for this strategy, so it can be easily
incorporated into lessons.
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Lyman (in Fisher and Frey, 2007 : 30) and colleagues, there are three stages of student action, think, pair, and share.
Exposure above shows that Problem Based Learning and Think-Pair-Share have the potential to develop student’s mathematical critical thinking ability. From these two model, researcher want to know whether student’s mathematical critical thinking ability in Problem Based Learning classroom is better than student’s mathematical critical thinking ability in cooperative learning model Think-Pair-Share (TPS) type classroom because of steps of PBL it seems can more enrich mathematical critical thinking ability. Then the researcher intends to do research with the title “The Difference of Student’s Mathematical Critical Thinking Ability taught by Problem Based Learning Model and Cooperative Learning Model Think-Pair-Share (TPS) Type in SMPN 2 Lima Puluh.”
1.2 Problem Identification
Based on the background above, some problems can be identified as :
1. Consciousness about the important of student’s mathematical critical
thinking ability is still low
2. Learning habbit of the students is passive learning
3. Learning model which used by teacher has not been proper with the
student’s mathematical critical thinking ability.
1.3 Problem formulation
Problem formulation in this research is :
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1.4 Problem Limitation
This research needs to bound the problem to get precise target of expectation. The limitation of this research are :
1. The model used were Problem Based Learning (PBL) model and
Cooperative Learning model Think-Pair-Share (TPS) type.
2. The student’s mathematical critical thinking ability in this research is
bounded in the student’s mathematical critical thinking ability at determine the surface area of cube and cuboid matter in grade VIII semester II.
3. This research is conducted at SMP Negeri 2 Lima Puluh.
1.5 The Objective of Research The objective in this research is :
To know whether student’s mathematical critical thinking ability in Problem Based Learning classroom is better than student’s mathematical critical thinking ability in cooperative learning model Think-Pair-Share (TPS) type classroom at SMPN 2 Lima Puluh.
1.6 The Benefit of Research
1. For teacher, especially mathematics teacher, this can be as consideration in
selecting one of alternative model or approach in mathematics learning to improve mathematical critical thinking ability at school.
2. For the candidate of teacher, this can be as proper consideration for handle
problem which often appears at school so can be the next professional teacher.
3. For the student, this can makes students have enthusiasm to improve
mathematical critical thinking ability.
4. For the research, to enrich the research’s knowlege about problems which occur
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5. For the school, this can be consideration and suggestion to improve the quality of
teacher and learning system at class.
1.7 Operational Definition
Operational definition emphasize to things which will be standard or indicator of variable. So, operational definition in this research are :
1. The indicator of student’s mathematical critical thinking ability which will be
measured are :
a. The ability to identify the focus ( the issue, question, or conclusion)
b. The ability to deduce and judge deductions
c.
The ability to consider and reason from premises, reasons, assumptions,positions, and other propositions with which one disagrees or about which one is in doubt without letting the disagreement or doubt interface with one’s thinking (“suppositional thinking”)
2. The syntaxes of PBL like the following :
a. Phase 1 : Orient students to the problem.
Teacher go over the objectives of the lesson, describes important logistical requirements, and motivates students to engange in self-selected problem-solving activity.
b. Phase 2 : Organize students for study
Teacher help students defined and organize study tasks related to the problem.
c. Phase 3 : Assist independent group investigation
Teacher encourage students to gather appropriate information, conduct experiments, and search for explanations and solutions.
d. Develop and present artifacts and exhibits
Teacher assist student in planning and preparing appropriate artifacts such as areports, videos, and models and helps them share their work with others.
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Teacher helps students to reflect on their investigations and the processes they used.
3. The syntaxes of TPS like the following :
a. Think. The teacher enganges students; thinking with a question, prompt,
reading, visual, or observation. The students should take a few minutes (not seconds) just to think about the question.
b. Pair. Using designed partners, students pair up to discuss their respective
responses. They compare their thoughts and identify the responses they think are the best, most intriguing, most convincing, or most unique.
c. Share. After students talk in pairs for a few moments, the teacher asks pairs to
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CHAPTER V
CONCLUSION AND SUGGESTION
5.1Conclusion
Based on the result of research obtained can be concluded that students’ mathematical critical thinking ability taught by Problem Based Learning (PBL) model in experimental class I is better than students’ mathematical critical thinking ability taught by cooperative learning Model Think-Pair-Share type in experimental class II on subtopic cube and cuboid at SMP Negeri 2 Lima Puluh.
5.2Suggestion
Based on the conclusion above, so as a follow-up of this study is suggested several things which are:
1. Problem Based Learning (PBL) model can be as consideration to teachers
in enhancing junior high school student’s mathematical critical thinking ability.
2. Learning process of mathematics by using PBL model needs longer time
since in the learning, students need more time in finding, constructing, and discussing the material to their group so that it is needed preparation of teacher and students in its implementation.
3. When form the pair in Think-Pair-Share make sure that the students in
pair is heterogen.
4. For further researcher, result and instrument of this research can be used
as consideration to implement PBL model and Cooperative Model TPS type in different class level and topic.
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