The Effect Of Application-Based Problem Learning Models For The Ability Of Problem Solving And Mathematical Communication

The Effect Of Application-Based Problem Learning Models For The Ability Of Problem Solving And Mathematical Communication

 

Hendra Darmawan¹ , M. Ikhsan² , Zainal Abidin³

¹The master program of students of Mathematics Education, University of Syiah Kuala

^{2 3}Lecturer Master of Mathematics Education program, University of Syiah Kuala

Email: hendradarmawan89@gmail.com

 

Attachment : The ability to solve problems and mathematical communication become important things that must be owned by students. One learning model that has the potential to make students able to develop problem solving skills and mathematical communication skills is problem-based learning. This is a problem solving abilities and students' mathematical communication skills after being taught with problem-based learning models. To achieve this goal, this study used a quantitative approach with a pretest-postest groups design experimental research design. The population in this study were all grade IX students of Bandar Baru Middle School 1, Pidie Jaya Regency. The sampling technique used was a random sampling technique. The sample in this study was class VIII-1 and class VIII-2 respectively as the experimental class and the control class. Data processing results from this study were carried out with t-statistics. The problem solving abilities and mathematical communication are conventionally taught.

 

Keywords: Problem Based Learning, Problem Solving Ability, Mathematical Communication

 

 

 

 

 

 

 

 

 

 

 

 

 

Preliminary

              School mathematics is a part of mathematics whose elements are chosen to support the educational and developmental interests of science and technology. This explains that school mathematics is based on its presentation, mindset, limitations and its level of literature is not the same as mathematics in general (Soedjadi, 2000: 37). Innovations in learning mathematics in schools are expected to be able to improve and improve the quality of Human Resources (HR).

The purpose of teaching mathematics in schools, among others: so that students have the ability; (1) understanding mathematical concepts, explaining the relationship between concepts and applying concepts or algorithms, flexibly, accurately, efficiently and precisely in problem solving; (2) Using reasoning on patterns and traits, making mathematical manipulations in making generalizations, compiling evidence, or explaining mathematical ideas and statements; (3) Solve problems that include the ability to understand problems, design mathematical models, complete models and interpret solutions obtained;(4) Communicate ideas with symbols, tables, diagrams, or other media to clarify the situation or problem; (5) Having an attitude of appreciating the usefulness of mathematics in life, namely having curiosity, attention, and interest in learning mathematics, as well as being resilient and confident in solving problems (BSNP, 2006: 148). Meanwhile, the National Council of Teachers of Mathematics or NCTM (2000) states that school mathematics standards must include standard content and process standards. The standard process includes problem solving, reasoning and proof, connection (connection), communication, and representation.

From the description above it can be concluded that the problem solving abilities and mathematical communication skills are two essential mathematical abilities that must be possessed by students.Somakim ( 2000 ) explains that problem solving abilities and mathematical communication skills are referred to as mathematical power ( mathematicalpower ) or mathematical skills ( doingmath ).

One mathematical skill that is closely related to mathematical characteristics is problem solving ability. Problem solving is very important so that it becomes the main goal of teaching mathematics even as the heart of mathematics (Sumarmo, 1994) .

The importance of having mathematical problem solving skills for students as stated by NCTM (2000) problem solving is the process of applying the knowledge previously obtained to new and different situations. In addition, the NCTM also revealed the purpose of teaching problem solving in general is to (1) build new mathematical knowledge, (2) solve problems that arise in mathematics and in other contexts, (3) apply and adapt various strategies that are appropriate for solve problems and (4) monitor and reflect on the process of solving mathematical problems.

Furthermore, NCTM (2000) states that problem solving ability is part of the high order of thinking that enables students to develop intellectual and non-intellectual aspects. Therefore, problem solving skills need to be targeted in mathematics learning. Even NCTM (2000) recommends that problem solving must be raised since children learn mathematics in elementary school onwards. This explains that every student in all levels of mathematical abilities and levels of education needs to be trained in problem solving skills. Polya (1973: 5-6) explains that there are 4 stages in problem solving, namely: (1) Understanding the problem; (2) Prepare a problem solving plan; (3) Carry out problem solving plans; and (4) Re-checking problem solving.

In addition to mathematical problem solving abilities, students must also have mathematical communication skills, as revealed by Baroody (1993: 107), there are at least two important reasons, why communication in learning mathematics needs to be developed among students. First, mathematics as language , meaning that mathematics is not just a tool to aid thinking , a tool for finding patterns, solving problems or drawing conclusions, but also mathematics "an invaluable tool for communicating a variety of ideas clearly, precisely, and succinctly , second , mathematics learning as social activity : meaning, as a social activity in mathematics learning, as a vehicle for interaction between students, as well as a communication tool between teachers and students.

The above situation explains that, the teacher no longer acts as a giver of information ( transfer of knowledge ), but as a driver of student learning ( stimulation of learning ) in order to construct their own knowledge through various activities including aspects of communication. This is reinforced by Baroody (1993: 107), that learning must be able to help students communicate mathematical ideas through five aspects of communication namely representing, listening, reading, discussing and writing . Thus, mathematical communication skills as one of social activities ( talking) and as a writing toolrecommended by experts so that it continues to be developed among students.

Given the level of student understanding in learning mathematics material is strongly influenced by communication skills and mathematical problem solving, it requires a learning innovation that can spur students 'enthusiasm to actively get involved in their learning experiences, so that students' communication skills and mathematical problem solving can be developed. One of them is by using innovative learning models in the learning process.

One innovative learning model that has the potential to make students able to develop their ability to solve problems and mathematical communication skills and find their own knowledge ( reinvention) is problem-based learning (PBL abbreviated). Through the PBL model the ability to solve problems and mathematical communication can be achieved because in PBL students are encouraged to engage actively in small groups discussing each other in solving real-life problems that are challenging, complicated, cannot be solved with just one step, and are open-ended .

Problem-based learning provides opportunities and experiences for students to see and work on problem solving in various ways and various types of problems. Problem-based learning is the main vehicle for building high-level thinking skills ( high order thinking skills (HOTS). Assessment in PBL is on going . Trianto (2007: 68) explains that the problem-based learning model also refers to other learning models, including: (1) Project Learning ( Project Based Learning ), (2) Experience Based Education ( Experience Based Education ), (3) Learning Authentic ( Autentic Learning ), and (4) Meaningful Learning ( Anchored Instruction ).

Based on the background above, the researcher is interested in conducting research with the title "Effect of Problem-Based Learning Model Implementation on Problem Solving Ability and Mathematical Communication Ability" . The formulation of the problem in this study is whether there is an effect of the application of a problem-based learning model to students' problem solving abilities and mathematical communication skills .

 Method

This study aims to determine the problem solving abilities and mathematical communication skills of students with the application of problem-based learning models and compared with problem solving abilities and mathematical communication skills of students with the application of conventional learning models and to determine the relationship between problem solving and mathematical communication. Data from this study are in the form of numbers obtained from the test ( pretest-posttest ). Thus, this type of research is experimental research with a quantitative approach. The design of the experimental research is in the form of pretest-postestgroups design .

The population in this study were all IX grade students of SMP Negeri 1 Bandar Baru, Pidie Jaya Regency. The sampling technique in this study used a random sampling technique because of the different level of student achievement by Karen, the researcher took random sampling consisting of students who were high, medium and low level of intelligence. According to Kerlinger (2006: 188), simple random sampling is a method of withdrawal from a population or universe in a certain way so that each member of the population or universe has the same opportunity to be selected or taken.

Data collection in this study was carried out by tests. The test in this study consisted of pretest and posttest . Pretest aims to collect data on students' initial abilities. The initial data collection aims to determine whether the two groups of students have relatively similar initial abilities so that the two groups can be compared . The posttest aims to find out the test results data after being taught with problem-based learning.

To get validity, reliability, power difference, and level of difficulty, then the question must be tested on other students in the school at the same level. Before statistical validation is carried out, the test questions are validated first by a validator consisting of two expert lecturers , after being validated by an expert validator, then the test is validated by statistical tests using validity, validity is a measure thatindicates the level of validity or validity an instrument. According to Arikunto (1998), an instrument is said to be valid if it is able to measure what is desired. To test the validity of the measuring instrument is done by using the Correlation Person Correlation formula , namely:

 

Information:

r _xy      : correlation coefficient between variables X and Y

X        : score item items

Y        : number of total scores for each question

n       : number of respondents

 

The interpretation of the magnitude of the correlation coefficient of the score of each item with the total score is done by comparing the value of r _count with _critical r . Furthermore, with the reliability, reliabilitas a test instrument is a consistency of the instrument. A test that is reliable when given to the same subject even though in different people and at different times, it will give relatively the same results.This is in line with what was revealed by Sundayana (2010) is "a tool that provides results that remain the same or consistent. The tool tests reliability using the Cronbach Alpha (α) formula (Sundayana: 20), namely:

Information:

r           : reliability coefficient

n          : many test items

               : number of variance items

S _t        : total variance

Then the level of difficulty, the level of difficulty is the existence of an item about being difficult, moderate, or easy to do (Sundayana, 2010: 77). To find the difficulty level of a test instrument using the formula:

Information:

SA               : number of top group scores

SB               : number of lower group scores

HE               : number of ideal scores for the lower group

IB               : number of ideal scores for the lower group

Data obtained from the results of this study in the form of data on the results of problem solving abilities and mathematical communication of students in the experimental and control classes. Then the data is done data analysis with t-test assisted by SPSS 22 software for data comparison of problem solving abilities and mathematical communication skills . While processing data interactions between learning models with students' initial ability to problem solving abilities and interactions between learning models with students' initial ability to students' mathematical communication skills performed with ANAVA assisted by SPSS 22 software .

The hypothesis that will be tested is:

H₀:  ( Students 'mathematical communication skills taught with problem-based learning models are no better than students' mathematical abilities taught with conventional learning )

H₁ :  ( Students 'mathematical communication skills taught with problem-based learning models are better than students' mathematical abilities taught with conventional learning )

 

 

 

 Research result

This research was conducted in 8 meetings, with 4 meetings in the experimental class, namely classes taught with problem-based learning models and 4 meetings in the control class namely classes taught with conventional learning models. Before the implementation of the learning process in each class with a learning model that has been done, the pretest is given first and at the end of the learning implementation schedule the posttest was given for each class.

1. Student Problem Solving Ability

The description of the results of frequency distribution from the data on problem solving abilities of students from both classes is presented in Table 4.2 the following.

Table 4.2 Data description of problem solving ability of experimental class students and control class

Class	N	Max score	Min Score
Experiment	2 2	5,14	1 , 00	4 , 02	0, 87	0, 75
Control	2 0	5,14	1.00	3.27	0.98	0.9 5

 

Data Table 4.2 above shows that the experimental class has an average of 4.02 with a standard deviation of 0, 8 7. While the control class has an average of 3, 27 with a standard deviation of 0.98. This shows that there are differences in the average posttest results of students' problem solving abilities of 0 , 75 . But both classes have a calcium score and the same minimum score . For need statistical analysis on hypothesis testing, a normality test is performed on the student's problem solving ability score. In addition, statistical analysis on hypothesis testing also considers the homogeneity of the variance of the two classes. For more details, the prerequisite test of the statistical hypothesis testing is presented below .

1. Normality test

Based on the processing of normality test data, the description of the results of the normality test of the data on the problem solving abilities of the experimental and control classes is presented in Table 4. 3 the following.

Table 4. 3 . The results of the posttest score normality test were problem solving abilities

            experimental class and control class

Data source	Class			Decision
Pretest	Experiment	8.8323	11,591	Normal
	Control	7.0115	10,117	Normal

              Source: Results of research data processing

Based on Table 4. 3 the results of the data processing from the normality test of the posttest score to the data on the problem solving ability of the experimental and control classes in the Conference   thus it can be concluded that the data on problem solving ability of the experimental class and control is normally distributed.

2. Homogeneity Test

Based on the results of the frequency distribution it is known that If =0,75 and   =0,95 . Therefore   so the hypothesis testing criteria is to reject H ₀ if   and accept H ₀ for other kedaaan. The results of the description of the test data processing homogeneity of problem solving abilities from the experimental and control classes are presented in Table 4. 4 below.

Table 4. 4 Test results for posttest score homogeneity solving ability

problem of experimental class and control class

Data source			Decision
Postest	1.27	2.16	Homogeneous

 

Based on Table 4. 4 above is known   =1,26<2,16 =  so that the data on problem solving ability of the experimental and control classes is data originating from a homogeneous population.

3. Hypothesis testing

The data were normally distributed problem-solving ability and homogeneous, then the pen g test hypotheses about the problem solving ability of students performed using t-test. T-test is intended todetermine the ratio of two average scores of students problem-solving between the experimental class and classroom s kontrol.Hasil description of hypothesis testing using t-test can be seen in Table 4.5below.

Table 4. 5 The results of testing the posttest score hypothesis solving ability

            problem of experimental class and control class

Data source			Decision
Postest	2,568	1,645	H 0 is rejected

 

From Table 4. 5 above it is obtained that the value of t _arithmetic = 2.568 while t _table = 1.645, so _count > t _table. Thus H _{0 is} rejected.

 

4. Analysis of the Hypothesis of Students' Problem Solving Abilities

The first problem formulation in this research is: "a pakah problem solving ability of students taught with problem-based learning model is better than problem solving skills are taught by conventional teaching? "The hypothesis to be proved is:" k Capacity of solving the problem of students being taught dangan problem based learning model is better than being taught by conventional teaching ".

Based on the formulation of the problem and the research hypothesis, the formulation of the research hypothesis to be tested in this analysis are:

H ₀ :  There were no differences in problem solving ability of students taught with problem based learning with problem solving ability of students taught by conventional teaching.

H ₁ :  The ability of problem solving ability of students taught with problem-based learning model is better than problem solving ability of students taught by learning konvensiona l.

The statistical hypothesis formulation of the research hypothesis is:

              H₀:     =

            H₁:       >            

            =  average problem-solving ability of students taught with problem-based learning model.

 =  the average problem solving ability of students taught by conventional learning l.

Hypothesis testing uses t-statistics (Test -t) . Where data from the experimental class and the control class are normally distributed and both data also originate in a homogeneous population. This is proven by the prerequisite test that has been done. Based on the results of testing the hypothesis obtained the value of t _arithmetic = 2.568 while t _table = 1.645. Thus t _count > t _table . This situation causes H _{0 to be}rejected _. Premises n Thus, we can conclude that there are differences between the problem solving ability of students taught with problem based learning with conventional learning in matter of statistics.

This explains that students 'problem solving abilities taught with problem-based learning models are better than students' problem solving abilities taught with conventional learning.

2. Analysis of the Hypothesis of Student Problem Solving

The description of the frequency distribution results from the problem solving ability data of students from both classes is presented in Table 4.6 below.

Table 4.6 Description of data on mathematical communication skills of class students experiment and control class

Class	N	Max score	Min Score		s
Experiment	2 2	4.19	1 , 00	3.11	0, 92	0, 84
Control	2 0	4 , 1 9	1.00	2.86	0.94	0, 89

            Data Table 4.6 above shows that the experimental class has an average of 3.11 with a standard deviation of 0, 92 . While the control class has an average of 2.86 with a standard deviation of 0.9 4 .This shows that there is an average difference in the results of students' mathematical communication skills of 0 , 25 . But both classes have the maximum score and the same minimum score .

For the purposes of statistical analysis on hypothesis testing, a normality test is performed on the student's problem solving ability score. In addition, statistical analysis on hypothesis testing also considers the homogeneity of the variance of the two classes. For more details, the prerequisite test of the statistical hypothesis testing is presented below .

1. Normality test

Normality test is one of the requirements to test hypotheses by using t-statistics (t-test). This is done to determine whether or not a normal distribution data of class k ontrol and the experimental class for data communication students' mathematical abilities. The normality test for the two classes is done using the chi-square statistic at a significant level of 5% with the free degree is  . . The decision criteria are to reject H ₀ if   and accept for other circumstances.

The formulation of the statistical hypothesis is:

H ₀ : Data is normally distributed

H ₁ : Data is not normally distributed

Based on the processing of normality test data, the description of the results of the normality test of the problem solving ability of the experimental and control classes is presented in Table 4. 7 below.

 

Table 4. 7 The results of the normality test post-communication score test results

Mathematical sis class experiment and control class

Data source	Class			Decision
Pretest	Experiment	9.517	11,591	Normal
	Control	7,188	10,117	Normal

              Source: Results of research data processing

Based on Table 4. 7 the results of the data processing from the normality test of the posttest score to the data on mathematical communication skills of the experimental class and control students in the Conference   thus it can be concluded that the data of mathematical communication skills of experimental class students and controls are normally distributed. 

 

2. Homogeneity Test

Based on the results of the frequency distribution it is known that If   =0,84 and   =0,8989 . Therefore   so the hypothesis testing criteria is to reject H ₀ if   and accept H ₀ for other kedaaan.

Processing homogeneity test data, the description of the homogeneity test results of problem solving abilities from the experimental and control classes are presented in Table 4. 8 below.

Table 4. 8 Test results for posttest score homogeneity solving ability problem of experimental class and control class

Data source			Decision
Postest	0.94	2.16	Homogeneous

 

Based on Table 4. 8 above is known   =0,94< 2,16 = =  so that the data of mathematical communication skills of the experimental class and control students are data originating from a homogeneous population.

3. Hypothesis testing

Data communication skills of students mathematical normal distribution and homogeneous, then the pen g test hypotheses about students' mathematical communication capability data is doneby t-test.T-test is intended to determine the ratio of two average score students' mathematicalability data communication between the experimental class andclassroom s kontrol.Hasil description of hypothesis testingusing t-test can be seen in Table 4.9 below.

Table 4. 9 The results of hypothesis testing posttest scores on communication skills

        k students' mathematical experimentation and k e elas elas k ontrol

Data source			Decision
Postest	0.939	1,645	H 0 accepted

 

From Table 4. 9 above, it is obtained that the value of t _arithmetic = 0.939 while t _table = 1.645, so that t _count <t _table . Thus, H ₀ accepted.

4. Analysis of Student Mathematical Communication Ability Hypotheses

The formulation of the problem in this research is: "a pakah mathematical communication ability of students taught by problem-based learning model is better than the mathematical ability of students taught by conventional teaching? "The hypothesis to be proved is:" k Capacity of students taught mathematical communication dangan problem based learning model is better than being taught by conventional teaching ".

Based on the formulation of the problem and the research hypothesis, the formulation of the research hypothesis to be tested in this analysis are:

H 0 :  No difference k Capacity of mathematical  ommunication ability of students taughtwith problem based learning model with k Capacity of mathematical communication students taughtby conventional teaching.

H 1 : K Capacity of students taught mathematical communication with problem-based learning model is better than k Capacity of mathematical communication students taught by learning konvensional

              The statistical hypothesis formulation of the research hypothesis is:

H0:      μ_1=μ_2

            H1:      μ_1>μ_2              

= average k Capacity of students taught mathematical communication with problem-based learning model.

 =average k Capacity of mathematical communication students taught by learning konvensiona l.

Testing the hypothesis using t-statistics . Where data from the experimental class and the control class are normally distributed and both data also originate in a homogeneous population. It proved berdas a Refresh prerequisite test that has been done. Based on the results of testing the hypothesis obtained the value of t _arithmetic = 0.939 with t _table = 1.645. Thus t _count <t _table . This situation causes H ₀ to beaccepted _. Premises n Thus, it can be concluded that there is no difference in students' mathematical communication skills that are taught with problem based learning model with mathematical communication ability of students taught by conventional teaching.

This explains that students 'mathematical communication skills taught with problem-based learning models are no better than students' problem solving abilities taught with conventional learning.

 Discussion

The results of this study are expected to provide an explanation of the results of the application of problem-based learning models to students' problem solving abilities and mathematical communication skills .

1. Problem solving skill

The problem solving abilities of students taught with problem-based learning models are better than those taught with conventional learning . The study concluded that k Capacity of solving the problem of students being taught dangan problem based learning model is better than being taught by conventional teaching .This is according to the results of research Sumartini (2016) which states that the increase in problem-solving ability of students to get a better problem-based learning than students who get conventional learning. This is because problem-based learning benefits directly to students as explained by Gick and Holyoak (in Krismiati : 2008 ), namely:

1. Motivation, where students feel given the opportunity to respond and get results from investigations,
2. Relations and contents, there is a clear answer to the questions posed,
3. High-level thinking, problem-based learning evokes creative thinking and is critical of students,
4. Learning how to learn, by developing regular self-metacognition and learning where students produce in their own way in solving problems, and
5. Authenticity, study the information and apply it to the situation in the future through the demonstration and understanding.

2. Mathematical Communication Ability

The ability of students' mathematical communication taught with problem-based learning models is better than those taught with conventional learning. The results of the study concluded that there was no difference in the ability of students' mathematical communication taught with problem-based learning models taught with conventional learning. This is because most students are still many who have not been careful in using algebraic symbols and seem not to carry out a careful examination of the answers that have been done. Although in the learning process researchers have reminded and tried to directstudents to re-examine the use of symbols and several other things.

This is in accordance with Choridah (2013) research that to reach the level of creative thinking students must be encouraged in mathematical communication both alone and in groups. Meanwhile Sumartini (2016) explains that students' mistakes in working on problems are often due to the ignorance done by students and mistakes in understanding the questions.

 Conclusion

Based on the results of data analysis that has been stated in the previous chapter, it can be concluded several things as follows.

1. The problem solving skills taught with problem-based learning models are better than students' problem solving abilities taught by conventional learning
2. Students 'mathematical communication skills taught with problem-based learning models are better than students' mathematical communication skills taught with conventional learning .

The suggestions are useful suggestions in order to improve the quality of learning mathematics, especially in SMP Negeri 1 Bandar Baru. The suggestions are as follows.

1. Learning with a problem-based learning model can be used as an alternative to mathematics learning, especially to improve students' problem solving abilities.
2. It is expected that the teacher in carrying out learning in the classroom so as to provide opportunities for students to build themselves about understanding the concept.
3. It is expected that teachers can add knowledge about the selection of strategies and learning models that are appropriate and effective in optimizing student activities and improving student learning outcomes.
4. For further research, it is expected to examine other mathematical abilities that have not been reached by researchers.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Bibliography

Baroody. AJ 1993. Problem Solving, Reasoning, and Communicating. New York: Macmillan Publishing.

BSNP. 2006. Content Standards for Primary and Secondary Education Units . Jakarta.

NCTM. 2000. Curriculum and Evaluation of Standards for School Mathematics.   Reston, VA: Authur .

Soedjadi, R. 2000. Tips on Mathematics Education in Indonesia . Jakarta: Directorate. General of Higher Education .

Somakim. 2010, Developing Student Self-Efficacy through Learning. Mathematics. Journal of Mathematics Education PARADICM , 3 (1): 31-36.

SUMARMO, U. 1994. A Teaching Alternative to Improve Mathematical Problem Solving Abilities in Middle School Teachers and Students . Bandung: FPMIPA Mathematics Education Bandung .

Trianto. 2007 Constructivistic Oriented Innovative Learning Models . Jakarta: Learning Achievement.