Abstract

This study aims to determine the effect of problem solving models on the ability of mathematical connections and self-efficacy. This type of research is a quasi-experimental study. The instrument used consisted of tests of mathematical connection ability, self-efficacy questionnaires, student activity sheets, and mathematical initial abilities. The population of this study was students in grades VII-1 and VII-2 in SMP Negeri 5 Tebing Tinggi. The instrument of this research was in the form of a mathematical connection ability test of 4 items in the description and self-efficacy questionnaire in students of 23 statements with 4 alternative answers. It can be seen that the Fcount value is 51.76 and the significance value α = 0.000. So the level of significance value <0.050 (sig. <0.050) then H_n is rejected and H₁ is accepted. However, if the significance> 0.050 (sig.> 0.050) then H_n is accepted and H₁ is rejected. Problem solving model is smaller than α = 0.05 then H_n is rejected and Ha is accepted. So that there is an influence of problem solving models on students' mathematical connection abilities accepted. obtained a value of F_n (B) of 19.81, if the value of F_n (B) is confirmed to the value of F table at α = 5%, then F_n (B) is greater than F table (19.81> 4.006). It was concluded that enough evidence to reject H_n. This means that there is an influence of the learning approach on students' mathematical self-efficacy. Furthermore, a F_n (A) value of 11,798 is obtained, if this F_n (A) value is confirmed to the value of Ftable at α = 5%, then F_n (A) is greater than Ftable (11,798> 4,006). It was concluded that enough evidence to reject H_n. This means that there is an influence of KAM on students' mathematical self-efficacy. Based on the calculation results obtained that the significance value of KAM * Learning towards students' mathematical connection ability is equal to 0.4280, greater than the predetermined significance level, that is, 0.05 (0.4280> 0.05), which means that is accept H_n. In other words there is no significant interaction between the learning model and the initial mathematical ability of students' mathematical connection abilities. Likewise with student self-efficacy, the results of data analysis obtained for the KAM significance value * Learning towards students' self-efficacy is 0.4801, greater than 0.05 (0, 4801> 0.05), so H_n is accepted which it means that there is no significant interaction between learning models and mathematical initial abilities of students' self-efficacy.

1. Introduction

The National Council of Teachers of Mathematics NCTM states that there are five standard processes in learning mathematics, namely (1) problem solving, (2) reasoning and proof, (3) communication (communication), (representation). Connection (connection) and problem solving (problem solving) there are (4) connection (connection), and (5) representation. Connection (connection) and problem solving (problem solving) are in the five standards of the mathematics learning process that has links to each other ¹. Mathematical connection ability according to Rohendi, is a person's ability to present internal and external mathematical relationships, which include relationships between mathematical topics, connections with other disciplines, and connections in everyday life ². According to Fariha the problem solving model aims to train the ability to think through the stages of understanding the problem until it can make conclusions ³. One aspect that shows a deep understanding of mathematics is the connections made between different mathematical ideas Mhlolo ⁴. Problem solving learning model is a way of teaching that is done by training students to deal with various problems to be solved alone or together Alipandie ⁵. Meanwhile according to Gulo 2002 states that problem solving is a method that teaches problem solving by emphasizing the reasoning of a problem solved ⁶. According to Polya in Hudojo mentioned four steps in solving problems, namely: (1) understanding the problem; (2) planning problems, (3) planning solutions; (3) doing calculations; (4) recheck ⁷. Bruner in Siregar and Surya states that there is no concept or operation in mathematics that is not connected with other concepts or operations in a system, because of the fact that the essence of mathematics is something that is always associated with something else ⁸. Making connections is a way of creating understanding and conversely understanding something means making connections. The perception that mathematical concepts are interrelated concepts must be pervasive in the learning of mathematics in schools. If this perception is the basis of the teacher in the learning of mathematics then each review the material always associate with other material from daily life. According to Anonymous in Atun, who argues, that the problem solving model in groups has the advantage, among others, (1) problem solving strategies that are arranged more powerful and complex ⁹. According to Shadiq revealed that the central issue related to the basic psychology of learning mathematics today is constructivism ¹⁰. According to Hendriana, argues that mathematical connections are one of the abilities that need to be owned and developed by high school students ¹¹. In addition, according to Bandura in Feist also defines self-efficacy as "one's belief in his ability to exercise some form of control over the functioning of the person himself and events in the environment" ¹². According to Russefendi states "this conventional learning with classical teaching, not only that ordinary learning is more pressing on the teacher demonstrating the material, and students are considered successful when completing exercises with appropriate steps taught by the teacher" ¹³. Meanwhile, according to Kardi in Trianto it can take the form of lectures, demonstrations, training or practice, and group work. Learning is usually used to convey lessons that are transformed directly by the teacher to students. In addition, ordinary learning can also be in the form of expository ¹⁴. The results of Capper's research Suherman show that previous student experience, cognitive development, and interest in mathematics are factors that greatly influence success in problem solving models ¹⁵.

2. Reasearch Method

This type of research used is quasi-experimental research because in quasi-experimental (quasi-experimental) a treatment subject that we will see the influence has formed. The treatment in this study was mathematics learning with Problem Solving models while the observed variables were students' mathematical connection skills and Self-Efficacy. The sample is a part of the population chosen at random and is considered representative, meaning that the characteristics of the population are reflected in the sample taken (Sudjana: 2013).

The sample in this study were students of class VII-1 and class VII-2 of SMP Negeri 5 Tebing Tinggi, each of which had 32 students. Sampling in this study was random (cluster random sampling) because based on the ability of students in each class evenly heterogeneous seen from the diagnostic results conducted by researchers before conducting research. From these results, researchers conducted one way to choose a sample representing the population is a simple random method. Learning using the Problem Solving Model is class VII-1 SMP Negeri 5 Tebing Tinggi junior high school, while class VII-2 uses the Conventional Model. To obtain data about students 'initial mathematical abilities, a scoring is performed on the students' answers for each item. Based on these scores students will be grouped into 3 groups (low, medium and high).

ANAVA is also a univariate one that can be used to determine the effect and interaction of two factors with one dependent variable that is interval or ratio type and several independent variables that are nominal or ordinal type.

3. Result and Discussion

Data analysis consisted of analysis of mathematical problem solving ability, and analysis of mathematical connection ability.

Based on Table 1 above, it can be seen that the significance values are 0.229 for experiment I and 0.023 for experiment II, respectively. The significance value of the two classes is greater than the significance level of 0.05. This shows that the experimental class I and experimental class II came from populations that were normally distributed.

The results of the post test homogeneity spatial test calculation are shown in the following Table 2:

From Table 2 it can be seen that the significance value of 0.749 is greater than the significance level of 0.05 so H0 which states there is no difference in variance between groups of data can be accepted.

The following Table 3 presents the results of the normality of the post test data on student self-eficacy.

Based on Table 3 above, it can be seen that the significance values are 0.130 for experiment I and 0.219 for experiment II, respectively. The significance value of the two classes is greater than the significance level of 0.05, then H0 which states that the data are normally distributed for the experimental class I and the experimental class II can be accepted.

The results of the post test homogeneity test calculation of student Self-Efficacy Questionnaire Test Results are shown in the following Table 4:

From Table 4 it can be seen that the significance value of 0.879 is greater than the significance level of 0.05 so H0 which states there is no difference in variance between groups of data can be accepted.

The first and third hypothesis test results with the two-way ANAVA test using the SPSS 21.0 Program are described in the following Table 5.

Based on Table 5, above, a value of F0 (B) of 19.80 is obtained, if the value of F0 (B) is confirmed to the value of Ftable at α = 5%, then F0 (B) is greater than Ftable (19.80> 4.006). It was concluded that enough evidence to reject H0. This means that there is an effect of learning on student self-efficacy. Furthermore, a F0 (A) value of 11,798 is obtained, if the value of F0 (A) is confirmed to the value of Ftable at α = 5%, then F0 (A) is greater than Ftable (11,798> 4,006). It was concluded that enough evidence to reject H0. This means that there is an influence of KAM on students' self-efficacy.

From Table 5 obtained information that the calculated F value is 0.618 and the significance value (sig.) for the KAM category that is 0.543 is greater than α = 0.05 which means that H0 is accepted and rejects H1, meaning there is no interaction between learning and students' initial mathematical abilities in influencing ability students' mathematical connections can be accepted. So, there is a joint effect that is given by learning and KAM on the ability of students' mathematical connections are rejected. This means that the difference between the average score of students' mathematical connection ability in the KAM category is low, medium and high respectively between those taught and the conventional problem solving and learning models are not significantly different. More clearly, there is no interaction between student learning and KAM on students' mathematical connection abilities.

This can also be described in the following graph 1:

From Table 6 above obtained information that the calculated F value is 2020 At the significance for the kam * model line of 0.142 (sig.> 0.05), thus H0 is accepted and Ha is rejected. can be explained by 2 independent variables (problem solving learning model and conventional learning), meaning that the influence of independent variables on the change in the dependent variable is 42%, while the remaining 58% is influenced by other variables besides the independent variables.

The second and fourth hypothesis test results with the two-way ANAVA test using the SPSS Program are described in the from Table 6. This can also be described in the from Figure 2:

From Figure 2 above shows that the difference between the average score of students' self-efficacy in the KAM category successively low, medium and high between those taught with the influence of conventional problem solving and learning models is not significantly different. More clearly, there is no interaction between student learning and KAM on student self-efficacy.

4. Conclusion

Based on the results of the analysis, the findings and discussion that have been presented in the previous chapter conclusions are obtained which are answers to the questions in the formulation of the problem. The conclusion is as follows:

1. There is a significant influence of the problem solving learning model on students' mathematical connection abilities.

2. There is an influence of the problem solving learning model on students' self-efficacy.

3. There is no significant interaction between the learning model and the initial mathematical ability (low, medium, high) of students' mathematical connection abilities.

4. There is no significant interaction between learning models and mathematical initial abilities (low, medium, high) on students' self-efficacy.

5. Suggestion

Based on the results of the research and the conclusions above, it is suggested that a number of things are as follows.

Mathematics learning with problem solving models can be expanded to use, not only in splsv material but also in other mathematics subject matter. It is suggested to the teacher to create a learning atmosphere that gives students the opportunity to express mathematical ideas in their own language and ways, so students become bold in their arguments, confident and creative.

The problem solving model by emphasizing the ability of students 'mathematical connections and self-efficacy is still very foreign to both teachers and students, therefore it is necessary to be socialized by schools or institutions concerned with the hope of increasing students' mathematical connection and self-efficacy abilities.

For further research this research should be able to include a variety of different factors, such as factors of students 'attitudes and learning interests, students' economic backgrounds, and so on. So that research on students' mathematical connection abilities and self-efficacy is not only influenced by the learning model.

References