THE EFFECTIVENESS OF CONTEXTUAL APPROACH IN THE DEVELOPING OF MATHEMATICS CONNECTION SKILLS OF PRIMARY SCHOOL TEACHERS IN PREPARATION

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1 Global and Stochastic Analysis Vol. 3, No. 3 (2016) THE EFFECTIVENESS OF CONTEXTUAL APPROACH IN THE DEVELOPING OF MATHEMATICS CONNECTION SKILLS OF PRIMARY SCHOOL TEACHERS IN PREPARATION ERNA SUWANGSIH, HAFIZIANI EKA PUTRI AND SUPRIH WIDODO Abstract: Mathematical skills need to be developed because they may improve the quality of learning achievement and foster the mindset of the student, hence facilitate better preparation of students to face world challenges. One of the mathematical thinking skills required for development is the mathematical connection skill. This skill is important because it helps the students to develop their perspectives, to see mathematics as an integrated part of a whole rather than as a set of topics, and to recognize the relevance and application of mathematics, both in the classroom and outside the classroom. The primary school teacher candidates (the students who are currently learning in universities to be primary school teachers) are required to possess the skills they will teach to the students, as well as the skills needed to deliver the lessons. Without such skills, teachers will not be able to provide meaningful learning to students. In mathematics, it means that the students will not be able to understand the purpose or benefits of a mathematical concept, and will not be able to comprehend the relationship between each mathematical concept. In the PGSD (Primary School Teacher Education) institutions, the contextual teaching and learning approach can be implemented in mathematics learning. It is possible because a lot of topics in mathematics can be directly connected students daily life experiences. This study attempts to examine the mathematical connections in learning mathematics through a contextual approach for PGSD students, using the quasi experiment approach. 1. Introduction The importance of mastering mathematics skill for students is explicitly stated in the goals of the 2006 School Based Curriculum. Since students need to acquire mathematics skills, the pre-service teachers (students who are currently studying in colleges to become teachers) has to possess the same skills. The Committee in the Undergraduate Program in Mathematics (CUPM, 2014) proposes six fundamental recommendations for the department, study program, and subject of mathematics in universities. One of the recommendations is that the subject of mathematics should be designed as activities that facilitates students to build and develop their analytical thinking, critical reasoning, problem solving, and communication. CUPM also recommends the institutions that educates future mathematics teachers to prepare their students to possess the mathematics skills. NCTM (2003) describes several mathematics skills the students are expected to master, including the mathematics connection skill. This particular skill is important to master because it plays great role in developing students perspectives and mindset as a manifestation of the Keyword. Mathematical connections, contextual approach.

2 120 ERNA SUWANGSIH, HAFIZIANI EKA PUTRI AND SUPRIH WIDODO learning process. The Higher Education of Teacher Institutions of PGSD (Primary School Teacher Education Institutions) are responsible to produce primary school teacher candidates who will teach, among others, mathematics. Therefore, these institutions are responsible to prepare their students to develop and improve their mathematics connection skill. In other words, the lecturers play significant role in developing students (future teachers ) mathematics connection. NCTM (2000) notes that mathematical connections help students to develop their perspective, to see mathematics as an integrated part of the whole rather than a set of topics, and to recognize the relevance and application of mathematics both inside and outside the classroom. It is undeniable that mathematics is closely related with real life. Mathematics is used to solve various problems in life, from simple trading, transportation, to population growth. Besides the issues related with the improvement of students cognitive aspects; the students affective aspects are also focused on in the researches of education. The affective aspects of learning are part of the learning objective, as stated in the 2006 School-Based Curriculum. In this curriculum, the students are expected to possess the attitudes of respecting mathematics in life; i.e. by showing curiosity, attention, and interest in learning mathematics, and by being confident in solving problems. This way, students will be individuals with great cognitive skills, as well as be social creatures with high confidence, stable emotions, and good ideas. Therefore, the mathematics connection skill is important for students to master. However, the findings in the field concerning this skill indicates that the achievement is still below the expected requirement of the curriculum. It means that students communication and connection skills in mathematics need to be developed. The teachers and lecturers have to deliver their lessons using learning and teaching approach that can give students opportunities and motivation to develop their mathematical communication and connection skills. There are various approaches we can use to develop students connection skill. One of them is the contextual approach, or commonly known as Contextual Teaching and Learning (CTL) approach. Through CTL, students are expected to comprehend more about the mathematical concepts delivered in the lesson, and their functions. Berns and Erickson (Rusgianto, 2002: 2) states that: Contextual Teaching and Learning is a conception of teaching and learning that helps teachers relate subject matter content to real world situation; and motivates students to make connections between knowledge and its applications to their lives as family members, citizen, workers and engage in the hard work that learning requires. In other words, connection can be defined as interrelationship between various concepts of mathematics internally; in the mathematics itself, and externally; between mathematics with other disciplines and with real life. Bruner (Ruseffendi, 1988: 152) notes that, in mathematics, every concept is connected to other concepts. This is also true for other aspects, for example, between principles, theories, topics, and branches of mathematics (algebra and geometry).

3 THE EFFECTIVENESS OF CONTEXTUAL APPROACH IN THE DEVELOPING OF Therefore, to ensure that students succeed in learning mathematics, they should be provided opportunities to recognize these connections. In addition, Suherman et al. (2000: 65) states that: Mathematical learning and teaching follows a spiral method. It means that an introduction of new concepts or topics needs to consider the previously learned concepts or topics. New topics should always be connected to previous topics. This suggests that connections are important in the process of mathematics learning development and improvement. There are two common types of mathematics connections, according to NCTM (1989: 146); i.e. the modeling connections and the mathematical connections. Modeling connections are the relationship between a problematic situation in real life or in other discipline and their mathematical representatives. Mathematical connections are the relationship between two equivalent representatives, and between the processes of solving each representative. The objectives of mathematical connections are: Students are able to see mathematics as an integrated part of a whole; to explore problems and draw the results of their exploration in graphs, numeric, physical form, algebra, and verbal mathematics or representation; to use mathematical ideas to improve their comprehension of other mathematical ideas; to apply mathematical thinking and mathematical modeling in solving problems of other discipline, such as art, music, psychology, science, and business; and to respect the role of mathematics in our culture and society (NCTM, 1989: 84). In short, the standard aims to help students to widen their perspectives and develop their mindset, to see mathematics as an integrated part of a whole rather than as a set of topics; and to introduce the connections and uses of mathematics inside and outside of the classroom. NCTM (2003) further adds that the connection standards for the first to seventh grades (of primary school) is to focus the mathematics teaching on the following skills of the students : (a) Recognizing and using connections between mathematical ideas. (b) Recognizing and applying mathematics in other contexts. (c) To draw a picture of how mathematical ideas connect with each other and support each other to produce a comprehensive logical structure. In line with NCTM, Sumarmo (2012) states that the indicators of mathematics connection skill includes the ability to find the connection between various representation of concepts and procedures; to comprehend and use the connection between mathematical topics and the topics of other subjects or disciplines; to find the connection of one procedure to other procedures in an equivalent representative; to use mathematics in other disciplines/in real life; and to understand the equivalent representatives of a concept.

4 122 ERNA SUWANGSIH, HAFIZIANI EKA PUTRI AND SUPRIH WIDODO Table 1. Scoring Manual for Mathematics Connection Questions Students Responses to the Questions No answer/answering, but unrelated with the question/no correct response (answer). 0 Only some aspects of the questions are answered correctly. 1 Almost all aspects of the questions are answered correctly. 2 All aspects of the questions are answered thoroughly and correctly. 3 Score Contextual Teaching and Learning (CTL) is a learning model that focuses on meaningful learning; in which the learning is contextualized into students situation or experiences. Berns and Erickson (Rusgianto, 2002: 2) state that Contextual Teaching and Learning is a conception of teaching and learning that helps teachers relate subject matter content to real world situation; and motivates students to make connections between knowledge and its applications to their lives as family members, citizen, workers and engage in the hard work that learning requires. 2. Research Method Considering the problems formulated, and the objectives of the study, the researcher designs this study using the quasi-experiment method with pre- and post-test of the control group. After the population is determined using purposive sampling, the sample of this study is selected using cluster random sampling. The number of students in each sample (the experiment and the control classes) is 40. To obtain the data, this study implemented the instruments of academic achievement test, self-efficacy scale, observation sheets, and students journal. In this study, the data is analyzed based on the average score (value), not in a generalization level. 3. Findings and Discussion The pre-test data is obtained by delivering mathematics connection skill test to the students in the experiment and the control classes. This test aims to discover the preliminary skills the students possess. In this stage, the students are learning based on the lecturer s instructions. The descriptive calculation of the pre-test data of the two classes provides the results of the lowest score (X min ), the highest score (X max ), mean score, variance, and standard deviation for each class. The results of descriptive calculation of the pre-test data of the experiment and the control classes are as follow: Table 2. Descriptive Statistics of the Mathematics Connection Skill Pre-test Class N Minimum Maximum Sum Mean Std. Deviation Variance Experiment Control Valid N (listwise) 35 The Shapiro-Wilk normality test with significance level of 5% indicates that the two samples of the population are not distributed normally. Since it is so,

5 THE EFFECTIVENESS OF CONTEXTUAL APPROACH IN THE DEVELOPING OF a non-parametric test is needed. The Levene s test is implemented to test the homogeneity of the two classes. The result of this test indicates that the Sig (p value) is 0.184, which is higher than It means that the variances of both classes are homogeneous. The Mann Whitney (U Test) finds U value of and W value of These values, if converted to Z value, equal The Sig value or P Value is 0.971; which is higher than 0.01, indicating that there is no significant differences between the two groups. After delivering the treatment in the experimental class, a post-test is administered. The analysis of the post-test results is as follow: Based on the pre-test data analysis, it is found that the students preliminary mathematics communication skills in the experimental and the control classes are relatively similar. To know whether an improvement occurs in the students mathematics connection skill, the post-test data is analyzed. The post-test data is obtained from the result of students final test; i.e. the mathematics connection skill test in the experimental and in the control classes. The descriptive analysis result of the post-test data in both classes is displayed in the following Table 3: Table 3. Descriptive Statistics of Post-Test Mathematics Connection Skill Descriptive Statistics N Minimum Maximum Sum Mean Std. Deviation Variance Experimental Class Control Class Valid N (listwise) 35 The table shows that the mean score of post-test in the experimental class is 15.37, while the post-test mean score in the control class is The variance for the experimental class is with a standard deviation of The variance for the control class is with the same standard deviation of These results indicates that the post-test mean score of the experimental class is higher than that of the control class. Based on the findings and the analysis, the students mathematics connection skills, both in the control and in the experimental classes, is not distributed normally; indicating the need for Levene s test. The findings also indicate that both data are homogeneous. It means that the researcher conducted a study on two relatively similar groups. After the treatment of contextual approach implementation in the experimental class, the data obtained indicates that the post-test results of both groups are not distributed normally; which means a non-parametric test is needed. This test reveals that, with a significance level of 99%, there is a difference of connection skills between the experimental class and the control class. To determine the degree of improvement, a normalized gain test is conducted.

6 124 ERNA SUWANGSIH, HAFIZIANI EKA PUTRI AND SUPRIH WIDODO The result of the normalized gain is as follows: Output of Descriptive Statistics Gain N Minimum Maximum Mean Std. Deviation Variance N-Gain Experimental N-Gain Control Valid N (listwise) 35 The NG test shows that the mean N-Gain of the experimental class is with a standard deviation of The mean N-Gain of the control class is with a standard deviation of These results indicate that there is a difference of N-Gain between the experimental and the control classes. In other words, there is significant difference of improvement in the experimental class and in the control class. Normality Tests. The criteria to determine the result of normality test are: 1. If the significance value of the shapiro-wilk test is lower than 0.01, the H 0 is rejected. 2. If the significance value of shapiro-wilk test equals or is higher than 0.01, the H 0 is accepted. The result of the test is displayed in the following table. Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig. N-Gain Experiment,239 35,000,877 35,001 N-Gain Control,254 35,000,875 35,001 a. Lilliefors Significance Correction From the table, it can be seen that the significance values of the experiment and the control classes are the same, Since the significance values are lower than 0.01, the H 0 is rejected. In other words, the two samples of the population is not distributed normally. Since the samples are not distributed normally, it needs further analysis to determine their homogeneity. This is conducted using Levene s test. A. Homogeneity test (Levene s Test). The hypotheses in this test are: H 0 : Data sample has homogeneous population H 1 : Data sample has non-homogeneous (heterogeneous) population The determination criteria for the homogeneity test are: 1. If the significance value is lower than 0.01, H 0 is rejected. 2. If the significance value equals or is higher than 0.01, H 0 is accepted.

7 THE EFFECTIVENESS OF CONTEXTUAL APPROACH IN THE DEVELOPING OF The result of the homogeneity test is as follow: N-Gain Experiment Test of Homogeneity of Variances Levene Statistic df1 df2 Sig The value of Levene s Test is indicated on the based on mean value column; i.e. the Sig. (p value). In the table, the Sig. (p value) is 0.188, which is higher than It means that the variances of the two classes are homogeneous. Then, the analysis is continued with Pearson correlation test to discover the difference in N gain of the experiment and control classes, using Mann Whitney test (U-Test). B. Mann Whitney Test (U-Test). The hypotheses tested are: H 0 : There is no difference in the students average preliminary mathematics connection skill between the experimental class and the control class. H 1 : There is difference between the students average preliminary mathematics connection skill in the experiment class and that in the control class. The criteria of determining the result are: 1. If the significance value (sig value) is lower than α = 0.01, H 0 is rejected. 2. If the significance value (sig value) equals or is higher than α = 0.01, H 0 is accepted. The result of pre-test average scores comparison is displayed in the following table. Test Statistics a N Gain Mann-Whitney U 178,000 Wilcoxon W 808,000 Z -5,056 Asymp. Sig. (2-tailed),000 a. Grouping Variable: N Gain Test The Table shows U value of and W value of These values, if converted to Z value, equal The Sig value or P Value is Since the P value is below the critical limit of 0.01, it is indicates that there is significant difference between the two groups; in other words, H 1 is accepted. Thus, it can be concluded that there is differences between the gain (improvement) of mathematics connection skills in contextual learning and that in conventional learning. 4. Conclusion Based on the result of data analysis and the discussion of the findings, it can be concluded that students mathematics connection is influenced by the implementation of contextual approach. The data also indicates that selecting contextual approach to deliver a lesson will allow lecturer to improve students connection ability, because

8 126 ERNA SUWANGSIH, HAFIZIANI EKA PUTRI AND SUPRIH WIDODO the approach relates the lesson with students daily life. In addition, lecturers of mathematics subject need to work harder to improve students mathematic connection skill because the students achievement and completion of the learning objectives is still far from the expected result. REFERENCES 1. Committee in the Undergraduate Program in Mathematics (CUPM). [online]. Tersedia: cupm/cupm2004.pdf. [23 Maret 2012]. 2. Depdiknas.(2006). Kurikulum Tingkat Satuan Pelajaran. Jakarta: Depdiknas. 3. Ferreira dan Presmeg. (2001). Clasroom Questioning, Listening, And Responding: The Teacher Modes. Tersedia: cerme4/ papers %20/ 12/ ferreira.pdf. [7 april 2005]. 4. NCTM. (1989). Curriculum and Evaluation Standard for School Mathematics. Reston. VA: NCTM. 5. NCTM. (2000). Principles and Standards for School Mathematics. Reston. VA : NCTM. 6. NCTM.(2003). Program for Initial Preperation of Mathematics Specialists. Tersedia: ncate.org/programstandars/nctm/nctmelemstandars.pdf [28 April 2006]. 7. Pajares, F. (2002). Self-Efficacy Beliefs and Mathematical Problems-Solvings of Gifted Students. [online] Risnanosanti.(2010). Kemampuan Berpikir Kreatif Matematis dan Self Efficacy Terhadap Matematika Siswa Sekolah Menengah Atas (SMA) dalam Pembelajaran Inkuiri. Bandung: Disertasi SPS UPI. Tidak diterbitkan. 9. Ruseffendi, E.T. (1988). Pengantar kepada Membantu Guru Mengembangkan Kompetensinya dalam Pengajaran Matematika untuk Menigkatkan CBSA. Bandung: Tarsito. 10. Rusgianto, H.S. (2002). Contextual Teaching and Learning. Makalah pada Seminar Pendidikan Matematika 3 November 2002 UNY, Yogyakarta. Universitas Pendidikan Indonesia, Kampus Purwakarta