Inquiry Co-operation Model for Enhancing Junior High School Students' Mathematical Problem Solving Ability PDF

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Inquiry Co-operation Model for Enhancing Junior High School Students' Mathematical Problem Solving Ability Heni Pujiastuti1, Yaya Sukjaya Kusumah2, Utari Sumarmo2, Jarnawi Afgani Dahlan2 1 Universitas Sultan Ageng Tirtayasa 2 Universitas Pendidikan Indonesia To cite this article: Pujiastuti, H.,...

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Inquiry Co-operation Model for Enhancing Junior High School Students' Mathematical Problem Solving Ability Heni Pujiastuti1, Yaya Sukjaya Kusumah2, Utari Sumarmo2, Jarnawi Afgani Dahlan2 1 2

Universitas Sultan Ageng Tirtayasa Universitas Pendidikan Indonesia

To cite this article: Pujiastuti, H., Kusumah, Y. S., Sumarmo, U., & Dahlan, J. A. (2014). Inquiry co-operation model for enhancing junior high school students' mathematical problem solving ability. International Journal of Contemporary Educational Research, 1(1), 51-60.

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Authors alone are responsible for the contents of their articles. The journal owns the copyright of the articles. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of the research material.

International Journal of Contemporary Educational Research Volume 1, Number 1, January 2014, Page 51-60

Inquiry Co-operation Model for Enhancing Junior High School Students' Mathematical Problem Solving Ability Heni Pujiastuti1*, Yaya Sukjaya Kusumah2, Utari Sumarmo2, Jarnawi Afgani Dahlan2 1 Universitas Sultan Ageng Tirtayasa 2 Universitas Pendidikan Indonesia

Abstract This research aims to describe the enhancement and achievement of students' mathematical problem solving ability (MPSA) as a result of Inquiry Co-operation Model (ICM) and Conventional Learning (CL) implementation. This research used experimental method with pretest-posttest control group design. Population of the research is Junior High School students in Serang City, Banten Province, Indonesia. The sample is eighth grade students from two school levels classified as high and medium levels. Two classes are randomly selected from each school, one class as the experimental group who received ICM and the other class as a control group who received CL. The instrument used consists of MPSA test and observation sheets. The results of data analysis using t-test and two-way ANOVA concluded that: (1) the enhancement and achievement of students' MPSA who received ICM are better than those of students who received CL; (2) school level factors has significantly affect toward enhancement of students' MPSA, but does not has significantly affect toward achievement of students' MPSA; and (3) there are no interaction between learning model and school levels toward achievement and enhancement of students' MPSA. Key words: Inquiry co-operation model, Mathematical problem solving ability

Introduction Problem solving is important ability to mastered by students. It is argued that students who are skillfull in solving problems will also be skillfull in identifying a problem, selecting relevant information, composing, analyzing, evaluating, and reflecting on the results. According to Nasution (2000), those skills will lead to students’ intellectual satisfaction, enhance their intellectual potential, and encourage them to investigate throughly a discovery activity. National Council of Teachers of Mathematics (NCTM, 2003) stated that problem solving has been an integral part of all mathematics learning so that it should not be an isolated part of mathematics program. Anderson (2009) also asserted that problem solving is recognised as an important life skill involving a range of processes including analysing, interpreting, reasoning, predicting, evaluating and reflecting. It is either an overarching goal or a fundamental component of the school mathematics curriculum in many countries. However, some results of the study found that students' MPSA is low, as mentioned by Kadir (2010) that the MPSA of junior high school students is still low. This can be seen from the mean scores of MPSA test of students who obtained a score of only 2.7 of maximal ideal score 10. Preliminary studies involving 38 junior high school students (Pujiastuti, 2012) reported that the mean score of MPSA test of students is only 6.5 and the highest score obtained by the students only reached 12, while the maximal ideal score is 28. This result shows that the percentage of students' mean score was only 23.21% of the maximal ideal score. In general, the results of the study concluded that junior high school students' MPSA is still low. The results of the studies described above illustrate that in general mathematics learning process so far only develop the ability to think in such a low level which is very procedural in nature. In other words, the learning *

Corresponding Author: Heni Pujiastuti, [email protected]

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processes that occur have not been able to develop students' mathematical thinking skills to a higher level. As stated by Kesumawati (2010), the emphasis of teaching mathematic today is emphasized more on math formulas, sample questions, and regular exercises. In this case, students only do exercises directly by using formulas and algorithms that have been given. Through this way, the students are only trained to memorize things they have learned before. As a result, the learning process creates mostly passive students with limited knowledge to what is transferred by teachers. These conditions lead to students' inability to solve various problems in which they are only able to resolve the problem in accordance to the examples given by teachers. Schoenfeld (Even & Tirosh, 2003) in his study revealed that students who have all the knowledge needed to solve a problem are often not able to use that knowledge to solve problems that are not familiar to them. These findings indicate that the students have not been able to apply important concepts in solving the problems being faced. To overcome the students' inability in using the knowledge in solving problems, an effort that does not just develop mathematical ability of a procedural nature is needed. The efforts should allow to train and develop students' MPSA optimally. Therefore, it is indeed a need for a supportive learning and training aspects of the capabilities in the learning process to be included. Aspects of students' MPSA can be trained through learning Inquiry Co-operation Model (ICM). ICM is a process of learning that emphasizes inquiry, discovery of a concept (knowledge), and problem resolution. The principles of ICM is that the knowledge students gain is the result of investigations (findings) of the students themselves. Alr∅ and Skovsmose (2002) explain that ICM consists of eight components of learning process, namely: (1) getting in contact, (2) locating, (3) identifying, (4) advocating, (5) thinking aloud, (6) reformulating, (7) challenging, and (8) evaluating. The eight components are integrated each other and engage students to be more active in their learning. Students' involvement in ICM can be seen from the processes that occur at each components. In the component getting in contact, a teacher presents a situation or mathematical problems related to the material being studied. Then in locating component, each student learns how to express and write down their perspective (ideas or opinions) to a given problems. This is followed by identifying the things that are necessary and are known from the given problems (identifying). Advocating component may arise when students are discussing and critiquing each other, giving advice and when providing an alternative way to other students. Furthermore, each student is guided to be able to solve the problem based on the identification result and the way they had planned (thinking aloud). In reformulating component, students are guided to solve the problem in a different way or to make a conclusion with their language. Once they understand simple problems, they are given a challenge (challenging) through the provision of more complex problems. In the final stage, teacher does evaluation (evaluating) in order to determine the quality of students' understanding in the concepts that have been studied. Furthermore, ICM encourages students to engage actively in the process of investigation, to construct a concept, and to resolve the problems through the guidance and direction of teachers. However, this does not necessarily mean that the teachers provide students with information or answers of the problems they face. In this context, the teachers only assist students when they really need it. In this way, the students have an opportunity to express broader perspectives (ideas or opinions), to construct concepts, and to solve problems. In this situation, it is possible that the teacher finds a different solution shared by the students.

Method This study used experimental method with pretest-posttest control group design, as described below (Fraenkel, 1993). R O X O R O O Notes: R = Random sampling X = ICM O = Pretest of MPSA = Posttest of MPSA (test of mathematical problem solving ability)

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Population and Sample The population of the research is Junior High School students in Serang City, Banten Province, Indonesia. The sample is eighth grade students from two school levels classified as high and medium levels. Two classes are randomly selected from each school, one class as the experimental group who received ICM and another class as a control group who received CL. School category has been determined based on school accreditation level which is valid until the year 2013. High and medium-level school, respectively, are schools that have accreditation A and B. In this research, one school was randomly selected from both the high and medium-level school. Furthermore, two classes were randomly selected from all of the eighth grade students in the high-level school (SMP A) and medium-level school (SMP B). One class was treated as experimental group and the other class as a control group. Students in the experimental group received ICM while students in the control group received CL.

Instruments The research instrument used is in the form of MPSA test and observation sheets. MPSA tests are given prior to the learning activity (pretest) and after the learning activity (posttest). MPSA test used in this research is analytical test that is intended to find out the students' ways of thinking in solving problem in order to make it more clearly defined. This is in accordance to the opinion of Ruseffendi (1991) saying that one of the advantages of analytical test is that we can see clearly the thinking process of the students through their answers of the given problem. MPSA test consists of 6 test items with a maximal ideal score of 38. The material of MPSA test was adjusted to the subject matter of Mathematics in the second semester of 2012/2013 which refers to the curriculum. The preparation of the test begins with a first lattice covering subject matter which measured the ability aspects, indicators of MPSA, and the number of test items. Then, continued by preparing the MPSA test in accordance to their respective indicators to measure along with the answer key and the scoring guidelines. The achievement of students' MPSA is obtained by posttest scores of MPSA test. Criteria for achievement of students' MPSA can be seen in Table 1. Table 1. Category of achievement Posttest score (X) Category High Medium X % Low % The magnitude of the enhancement of students' MPSA is calculated using the formula of normalized gain developed by Meltzer (2002), as follows:

The results of the calculation of the gain were interpreted by using the classification gain of Hake (1999) and can be seen in Table 2. Table 2. Category of gain (g) g Category g  0.7 High 0.3  g < 0.7 Medium g < 0.3 Low

Results Description of the data

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Pujiastuti, Kusumah, Sumarmo, & Dahlan

The mean scores of students' MPSA is obtained based on the pretest and posttest. Recapitulation of students' MPSA test result can be seen in Table 3. Table 3. Recapitulation of students' MPSA test result Means Group N Pretest Posttest ICM 40 8.13 24.63 CL 41 8.29 19.61 Medium ICM 34 8.35 23.18 CL 37 8.22 17.03 Total ICM 74 8.23 23.96 CL 78 8.26 18.38 School Levels High

g 0.56 0.39 0.52 0.31 0.53 0.34

From Table 3 above it is known that the enhancement of students' MPSA from experimental group is greater than the control group. Overall, the enhancement of experimental group students' MPSA is 0.53, while the control group is only 0.34. In a high level schools, the enhancement of experimental group students' MPSA is 0.56, while the control group students' MPSA is only 0.39. In a medium level schools, the enhancement of experimental group students' MPSA is 0.52, while the control group students' MPSA is only 0.31. The achievement percentage of students' MPSA can be determined based on posttest scores. The achievement percentage of students' MPSA can be seen in Figure 1 below.

Figure 1. The achievement of students' MPSA From Figure 1, it is known that the achievement of students' MPSA from experimental group is greater than the control group, both in terms of overall and every school level. In terms of overall, the achievement of experimental group students' MPSA is 63.05% of the maximal ideal score, while the control group is only 48.37% of the maximal ideal score. In a high-level school, the achievement of experimental group students' MPSA is 64.82% of the maximal ideal score, while the control group is only 51.61% of the maximal ideal score. In a medium-level school, the achievement of ICM students' MPSA is 61% of the maximal ideal score, while the CL students' is only 44.82% of the maximal ideal score.

Data Analysis To determine whether the enhancement and the achievement of students' MPSA who received ICM is better than those of students who received CL, further testing through statistical mean difference test is conducted. Before doing the mean difference test, test of normality of distribution and homogeneity of data variance were firstly conducted. The test of normality of distribution data using the Kolmogorov-Smirnov Z (KS Z) and homogeneity of data variance using Levene's test.

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The statistical test results of enhancement and achievement data of experimental and control groups students' MPSA, both known to have a normal distribution data and homogeneous variance. Thus, the mean difference test used is t-test. The summary of mean difference test results of MPSA enhancement data can be seen in Table 4. Table 4. The summary of mean difference test results of MPSA enhancement School Levels Group g t Sig. (5%) H0 High ICM 0.56 3.869 0.000 rejected CL 0.39 Medium ICM 0.52 4.202 0.000 rejected CL 0.31 Total ICM 0.53 5.688 0.000 rejected CL 0.34 From the summary of mean difference test results of the enhancement of students' MPSA data in Table 4, it is known that the probability value (significance), both in terms of overall and every school levels are smaller than the significance level  = 0.05, so that the null hypothesis is rejected. Thus, it can be concluded that the enhancement of MPSA of ICM students better than those of CL students, both in terms of overall and every school level categories (high and medium-level). The summary of mean difference test results of MPSA achievement data can be seen in Table 5. Table 5. The summary of mean difference test results of MPSA achievement School Levels Group posttest t Sig. (5%) H0 High ICM 24.63 0.0005 rejected 3.338 CL 19.61 Medium ICM 23.18 0.000 rejected 3.663 CL 17.03 Total ICM 23.96 0.000 rejected 4.950 CL 18.38 The mean difference test results of the achievement of students' MPSA data in Table 5 shows that the probability value (significance), both in terms of overall and every school level is smaller than the significance level  = 0.05, so the null hypothesis is rejected. Thus, it can be concluded that the achievement of MPSA students who received ICM better than those of students who received CL, both in terms of overall and every school level categories.

Interaction between Learning Model and School Levels toward Enhancement of Students' MPSA The two-way ANOVA was used to determine the interactions between learning model and school levels toward enhancement of students' MPSA. Before performing two-way ANOVA, the data was assured to have normally distributed and has homogeneous variance. The summary of two-way ANOVA results are presented in Table 6. Table 6. The summary of two-way ANOVA of MPSA enhancement Type III Sum of Source df Mean Square F Squares Corrected Model 1.523a 3 0.508 12.580 Intercept 29.726 1 29.726 736.640 Learning Model 1.329 1 1.329 32.944 School Level 0.173 1 0.173 4.277 Learning Model * 0.017 1 0.017 0.431 School Level Error 5.972 148 0.040 Total 37.329 152 a. R Squared = 0.203 (Adjusted R Squared = 0.187)

Sig. 0.000 0.000 0.000 0.040 0.513

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Pujiastuti, Kusumah, Sumarmo, & Dahlan

From Table 6 it can be seen that the learning model has a significant effect on the enhancement of students' MPSA. This is indicated by the value of the probability (significance  = 0.00) that is smaller than 0.05. Similarly, school level factors have a significant effect on the enhancement of students' MPSA. This is indicated by the value of the probability (significance  = 0.040) is smaller than 0.05. Based on the enhancement of students' MPSA, student in higher school level obtained higher enhancement of MPSA. The results of statistical tests and the enhancement mean of students' MPSA, it can be concluded that the enhancement of students' MPSA in high-level school are better than those of students in medium-level school. In Table 6 above, it can also be seen that the probability value (significance) for the interaction between the learning model and school levels is 0.513. The significance value is greater than 0.05, so the null hypothesis is accepted. It can be concluded that there is no interaction between learning model (ICM and CL) and school levels (high and medium) toward enhancement of students' MPSA. Graphically, the interaction between learning model and school levels toward enhancement of students' MPSA can be seen in Figure 2.

Figure 2. Interaction between learning model and school levels toward enhancement of students' MPSA Figure 2 shows that enhancement of MPSA in high and medium-level school students who received ICM is higher than students who received CL. In ICM, the order of the enhancement mean of students' MPSA from the largest to the smallest are high-level school students followed the medium-level school students. The same sequence happened with the enhancement mean of students' MPSA who received CL. The similarity sequence suggests that there is no interaction between learning model and school levels toward enhancement of students' MPSA. The lack of interaction between learning model and school levels toward enhancement of students'MPSA also can be seen from the difference in the enhancement mean. The difference in enhancement mean of students' MPSA who received ICM and students who received CL in the high-level school are relatively the same as the mediumlevel school.

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