The Effect of Problem-Based Blended Learning Models on the Mathematical Problem Solving Ability of Middle School Students

This study aims to analyze the effect of problem-based blended learning models on problem solving abilities. The sample of this study were 64 students who were grouped into two classes, namely class VIII A as BLBM class and class VIII B as Direct class. Data obtained through KAM tests, and tests of students' problem solving abilities. Data were analyzed using two-way ANAVA. Based on the results of the analysis using two-way ANAVA research results obtained problem solving abilities taught by problem-based blended learning models are better than direct learning. The significance value obtained from anava is 0.004 <significance level value of 5%. This shows that there are significant differences in problem solving skills in both learning, then obtained the significance value of the learning model and KAM of 0.607> a significance value of 5%. So there is no interaction between the learning model and KAM on the ability to solve problems. The research findings recommend a problem-based blended learning model to be one of the learning approaches used in secondary schools.

provides several definitions of blended learning, namely (1) a combination of traditional learning with a web-based learning approach, (2) a combination of media and tools in an e-learning environment, (3) a combination of several learning approaches, use of learning technology. Carman (2005: 2) explains that there are five keys to implementing learning with blended learning, namely: 1) Live Events, 2) Self-Paced Learning, 3) Collaboration, 4) Assessment (assessment), 5) Performance Support Materials. These five things are key components in the application of blended learning, which of course must exist in its implementation.
The syntax of the Blended learning model according to Grant Ramsay (2001): Phase 1: seeking of information, Finding information from various sources of information available on ICT (online), books, and delivery through face to face in class. Phase 2: acquisition of information, Interpreting and elaborating information personally and communally. Phase: synthesizing of knowledge, Reconstructing knowledge through the process of assimilation and accommodation based on the results of the analysis, discussion and formulation of conclusions from the information obtained.
Arends in Trianto (2009) states that Problem Based Learning not designed to help teachers convey large amounts of information to students, however Problem Based Learning designed prioritized to help students develop thinking skills, problem solving skills, and intellectual abilities, learn the process of maturity by experiencing it through various real situations or situations that are simulated and become independent and autonomous students.Problem-based learning can be applied by referring to the following steps: 1) Students' orientation to problems, 2) Organizing students to learn, 3) Guiding individual or group investigations, 4) Developing and Presenting Work, 5) Analyzing and evaluating problem solving processes (Trianto, 2009: 28

RESEARCH METHODS
This study uses a quasi-experimental method with a pretest-posttest control group to examine the effect of differences in problem solving abilities between two groups of students who are given Blended Learning Problem-based learning and Direct Learning.
This study uses two parallel classes by applying different learning. The first class is given the treatment of problem-based Blended Learning while the second class is not given treatment. The experimental design of this research can be seen in the table below: : Pretest students' problem solving abilities. Q2 : Postest student problem solving skills. X : Treatment of the problem based Blended Learning model. O.
: no treatment The population in this study were all grade VIII students of SMP N 4 Air Putih, Batu Bara Regency. There are 64 students. The study sample was selected in groups (cluster sampling). Considering the small population and study groups in the school for class VIII consisting of two classes, the researcher may not take students randomly to form a new class, because it will disrupt the learning process at school so the researcher takes the smallest sampling unit is the class. Two classes were selected, namely class VIIIA, VIIIB with 32 students in class VIIIA and 32 students in class VIIIB. Then from the two classes the selection is carried out so that class VIIIB is obtained by direct learning and class VIIIA with problem-based blended learning models.
This study uses test instruments in data collection. The test instruments take the form of pre-test and posttest mathematical problem-solving abilities. Each test consists of 5 items each containing four indicators of problem solving based on the steps of solving the problem polya.
This study uses inferential statistical analysis Analysis of variance of two paths or also called Anava more than one path. This inferential statistical analysis is used to test comparisons and regressions with two conditions fulfilling the requirements: the study sample is normally distributed and the sample research is homogeneous.
Journal of Education and Practice www.iiste.org ISSN 2222-1735 (Paper) ISSN 2222-288X (Online) Vol.11, No.18, 2020 Anava can be used to determine whether the average value of two or more samples is significantly different or not. And to produce an F value that significantly shows the researcher that the sample under study is from a different population. Anava is also a univariat that can be used to determine the influence and interaction of two factors with one dependent variable, namely the interval, type ratio and several independent variables which are nominal or ordinal types.

RESULTS AND DISCUSSION
The grouping of students based on KAM (Early Mathematics Ability) is divided into three groups namely high, medium and low. The number of students in the experimental class and control class is the same, 32 students. The division of students is based on KAM for each class (experiment and control), namely: 6 students have high KAM, 20 students have medium KAM and 6 students have low KAM. the average KAM score of students in the experimental class in the high category was 88.5 in the medium category at 69.15, and in the low category at 46.3.
Pretest will be given to students before being given the problem-based Blended Learning model treatment and direct learning. The pre test consists of 4 items, each question has a weight of 12. For the posttest also consists of 4 items problem solving and each item has a weight of 12. so the maximum value that students will get in the pre test or posttest is 12 x 4 = 48.The results of descriptive analysis of the problem solving skills of students in the two learning groups based on the grouping of students' initial mathematical ability (KAM) categories are presented in Table 3 below:   Table 5, the summary model above, it can be seen that the coefficient of determination R-Square is 0.532 (53.2%). This shows that 53.2% of the variation of the dependent variable (problem solving ability) can be explained by 2 independent variables (problem-based blended learning and direct learning), meaning that the influence of the independent variable on changes in the dependent variable is 53.2%, while the remaining 46.8% is influenced by other variables besides the independent variable.
Confirmation results using SPSS 20 are presented in Table 5 above. Based on the results of the two-way ANAVA test in Table 5, the information obtainedFcount value of 0.503 andthe significance value of the learning model and KAM 0,607 is greater than 0.05, which means Ha is rejected and H0 is accepted, it means that it can be concluded that there is no interaction between the learning model and KAM in influencing students' problem solving abilities. More details are presented in Figure 1. below:

Figure 1. Graph of Interaction between Learning Model and KAM Against Students' Problem Solving
Ability Problem solving in mathematics is a psychological activity to find solutions to mathematical problems faced by using integrally all the stock of mathematical knowledge that is already possessed. In this case, the proposed problem must be meaningful and beneficial to improve students' ability to find solutions to problems.
In solving problems, it must refer to the steps or stages of problem solving. according to Polya (1973), there are four stages in solving problems namely; (1) Understanding the problem (Understanding the problem), (2) Planning a solution (devising a plan), (3) Implementing the problem solving plan (carrying out the plan), (4) Rechecking the truth of the completion (looking back).
Based on the results of descriptive data analysis before being given treatment, students in both classes have the ability to solve problems that are not significantly different. This can be seen from the average KAM BLBM grade test scores and direct respectively are 68.34 and 61.56. After being treated, the problem-solving ability of students who learn with a problem-based blended learning model is higher than students who learn by direct learning. This is shown from the dataaverage normalized gain scores of students' problem solving abilities taught with learning blended learning problem based amounted to 0.4977 higher than the average normalized gain score of students' problem solving abilities taught by direct learning that is equal to 0.3199.
In line with this delivered by Sumartini (2016: 18) that increasing the mathematical problem solving ability of students who get problem based learning is better than students who get conventional learning.
A similar sentiment was conveyed by Ekawati (2018) the application of blended learning with the edmodo application based on the PDEODE learning strategy can improve student achievement in class VIII-F MTs N Magelang. This is evidenced by the percentage of students' mastery learning that is pre-cycle to cycle 1 an increase of 31%, an increase from cycle I to cycle II of 62%, and an increase from pre-cycle to cycle II of 93%.
The results showed no interaction between KAM and the model on the ability to solve mathematical problems. A similar sentiment was also conveyed by Setiawati, Syahputra and Rajjagukguk (2013: 12). There was no interaction between the learning approach used and students 'initial mathematical abilities (high, medium,  Vol.11, No.18, 2020