The Influence of Problem Based Learning Models and Metacognition Knowledge on Students Mathematics Learning Outcomes

Abstract


INTRODUCTION
Problem-based learning (PBL) in the field of educational technology is included in the assessment/research area, namely problem analysis.Problem-based learning is learning that requires students' mental activity to understand a learning concept through situations and problems presented at the beginning of learning (Fadila, 2021;Sakir & Kim, 2020).The problems presented to students are problems of everyday life (contextual).This problem-based learning is designed with the aim of helping students develop thinking skills and develop problem-solving abilities, learning various adult roles through their involvement in experiences (Hoyi & Liza, 2021;Kolar & Hodnik, 2021).In required to set their own learning goals and determine appropriate learning strategies to achieve these goals.Learner responsibilities also include monitoring the learning process and changing learning strategies when necessary.
Metacognition as knowledge and awareness about cognitive processes.Metacognition is a process of generating interest because someone uses cognitive processes to reflect on their own cognitive processes.Metacognition is very important because knowledge about cognitive processes can guide students in developing and choosing strategies to improve positive performance (Stephanou et al., 2020).Thus metacognition relates to a person's knowledge about their own cognitive processes and the ability to use these processes.Students need to be aware of the strengths and weaknesses of their cognitive abilities and try to organize them to be applied appropriately in solving tasks or problems.
Metacognition refers to higher-level thinking that involves active control in the cognitive learning process.Activities such as planning how to approach a given learning task, monitoring understanding, and evaluating progress in completing tasks are metacognitive in nature (Stanton et al., 2021).Metacognition is the ability to think where the object of thinking is the thought process that occurs within oneself.In the learning context, students know how to learn, know their abilities and learning modalities, and know the best learning strategies for effective learning.Metacognition is a form of ability to look at oneself so that what one does can be controlled optimally.Students with metacognitive knowledge are aware of their strengths and limitations in learning (Ramadhanti & Yanda, 2021).This means that when students know their mistakes, they are aware of admitting that they were wrong, and trying to correct them.
Previous research found that the Problem Based Learning (PBL) model was effective on students' metacognitive skills in class X Science (Sari et al., 2022).This can be seen in, the characteristics of learning using the PBL model for students' metacognitive skills to support each other.Thus, learning stages that are easy to understand are very necessary in implementing learning so that students are not burdened with complicated steps, but can focus on the learning process so as to improve students' metacognitive skills.So as a form of novelty and generalization of previous research, this research was carried out, the difference is that this research was carried out at junior high school level in mathematics subjects.
Metacognition is a person's ability to regulate and control their thinking processes, which include problem solving, decision making, critical thinking, and creative thinking.It consists of two main components: metacognitive knowledge, which includes awareness of thinking and strategy selection, and metacognitive experience/metaregulation, which includes planning, evaluation, and monitoring.The components of metacognition include knowledge about cognition (declarative, procedural, conditional) and regulation of cognition (planning, information management strategies, monitoring understanding, debugging, evaluation).Learning outcomes are a process that involves behavior, talent, training, and experience, not just final achievement (Asim et al., 2021).In learning, it is important to understand what material will be taught and how to teach it to achieve learning objectives.
Learning needs to be adapted to environmental conditions and the existence of learning facilities available at the school or those that can be created by the teacher himself.The meaning of learning outcomes cannot be separated from what happens in teaching and learning activities, learning outcomes both in the classroom, at school and outside school.In the teaching and learning process, student learning outcomes are the grades obtained after completing the learning process and are carried out through tests at the end of each lesson.It is important for teachers to know student learning outcomes as a basis for creating more appropriate learning objectives.After the learning process is complete, student success is measured through the implementation of teaching objectives (instructional objectives).The aim of this research is to explore and identify the influence of using the Problem Based Learning (PBL) model on the mathematics learning outcomes of class VII students at Public Middle School 1 Tanjung Jabung Timur, as well as to understand the relationship between students' metacognitive knowledge and their learning outcomes in the context of using the PBL model.

Research Design
In this study, the research design followed a 2x2 factorial design with a pretest and posttest.Both groups of students; treatment and control, following learning with the same materials, objectives, learning resources and teachers.The implementation of learning differs in terms of the methods used.The first group as the treatment group carried out learning using the PBL method, while the second group or control group carried out conventional learning.Each group conducts learning in the same room and environmental conditions at Public Middle School 1 Tanjung Jabung Timur.
In line with the hypothesis to be tested, namely the effect of using the PBL model with the influence of high and low student metacognitive knowledge variables, as well as the influence of the interaction between these two variables on the dependent variable, namely mathematics learning outcomes, a 2x2 type factorial experimental design was used in this research.Table 1 below shows the factorial design (2x2) used in this research.

Research Target/Subject
The population in this study were students at Public Middle School 1 Tanjung Jabung Timur.The sampling technique in this research used simple random sampling.The sample obtained in this research was 50 students who were made into two class groups.Each group conducts learning in the same room and environmental conditions at Public Middle School 1 Tanjung Jabung Timur.Each group consists of 25 students.

Research Procedure
The experiment consisted of 4 meetings in a series of activities, namely the first was pre-learning preparation and group division and determining group leaders.Next, each group underwent a metacognition knowledge questionnaire test and a learning outcomes test (pretest).At the next meeting, each group was given treatment according to the planned learning plan.The treatment will be carried out over 4 meetings of 2 x 45 minutes each (2 class hours).The experiment ended by holding 1 meeting at the end to carry out a post-test, namely an essay test.

Instruments, and Data Collection Techniques
The instruments in this research used a metacognitive knowledge questionnaire and learning outcomes tests.The experiment ended by holding 1 meeting at the end to carry out a post-test, namely an essay test.

Data analysis technique
After the pretest average similarity test (one way ANOVA) was completed, namely t count <t table so that H 0 was rejected, meaning there was no difference in initial ability between the experimental class and the control class or both classes had the same initial ability.Then proceed with testing the research hypothesis, namely testing the difference between the independent variable and the dependent variable using posttest-pretest difference data (Prabawati et al., 2020).There are assumptions that must be met before carrying out the ANOVA test, namely that the data is normally distributed in each class and the variance is the same.Based on this, an assumption test was carried out first for each class (upper and lower in the experimental and control classes), including: 1) Lilliefors normality test; and 2) Barlett's Homogeneity Test, each of which was calculated manually using Microsoft Excel.

RESULTS AND DISCUSSION
The results of the table calculate the average mathematics learning outcomes from the pretestposttest scores for the four testing groups.Recap the data in the following table.The statistical test shows that the F count is 14.602 with a probability of 0.000.Because the probability <0.05 then H 0 is rejected.In other words, there is an influence of metacognitive knowledge on students' mathematics learning outcomes.3).For hypothesis 3, using the Tukey test, there is no value 0, so µ i = µ j , then µA 1 B 1 = µA 2 B 1 in other words, there is an influence of the PBL model on the mathematics learning outcomes of students in the group of students who have high metacognitive strategies.4).Hypothesis 4, the results of the Tukey value calculation, interpret that there is no value of 0, so µ i = µ j , then µA 1 B 1 = µA 2 B 1 so H 0 rejected, or in other words there is an influence of the PBL model on the mathematics learning outcomes of students in the group of students who have low metacognitive knowledge.5).Hypothesis 5: Looking at the interaction between PBL learning model variables and metacognitive knowledge: H 03 : A X B = 0 H 03 : A X B ≠ 0 The statistical test shows that the Fcount is 8.165 with a probability of 0.06.Because the probability is > 0.05 then H 0 rejected.In other words, there is an interaction between the PBL model and metacognitive knowledge on mathematics learning outcomes.Based on table 5, it is discussed that students with high metacognitive knowledge have a difference in scores that is not much different whether taught with a problem-based learning model or taught with a conventional model.In the sense that students who have high metacognitive knowledge have no problem being taught with any learning model because these students are able to control, monitor and control themselves in learning, these students are independent in learning.Meanwhile, students with low metacognitive knowledge are better taught using a conventional model, because if taught using a problem-based learning model, students with low metacognitive knowledge are not yet able to understand problems and solve problems, these students need teacher direction and guidance, students are not yet able to learn independently.
The learning process using conventional methods has weaknesses in improving learning outcomes, in this research it is metacognitive knowledge.The weaknesses include that students are less able to develop their minds (lazy to think), tend to be passive, have difficulty working together and are individual, and are less motivated in learning activities in class.Students' weaknesses in learning are thought to be from the habits carried out by teachers in the learning process which places more emphasis on teacher-centred where learning is teacher-centred, resulting in students' potential and thinking abilities not being "activated" to the maximum, students are only listeners during the learning process.This causes students to tend to be passive and less skilled at communicating in learning activities in the classroom.
Learning is a necessity to face the problems that occur in this world, so it is appropriate for students to be able to solve problems that occur, especially those related to mathematics.In response to this, the appropriate model is the PBL learning model.The PBL learning model is a learning model with a student approach to authentic problems (real problems), so that students are able to develop their own knowledge, develop higher skills and inquiry, make students independent and increase their selfconfidence, so that students learn, especially in mathematics lessons.one of the characteristics is that it is abstract and becomes real because it is connected to problems that occur in the student's environment (contextual).
PBL is built on the theory of constructivism, brought by researchers such as John Dewey, Lev Vygotsky, Jean Piaget, Jerome Bruner, who rely on the belief that all humans have the ability to build knowledge in their thinking through the process of discovery and problem solving.If discovery is the goal of learning, students must be able to develop their thinking abilities.To develop students' willingness to think, educators must first be able to develop a good perception of what is being learned.The teaching and learning process of mathematics subjects will run smoothly if students and teachers are both active in carrying out activities.Success in the teaching and learning process is one of the responsibilities of the teacher/instructor, while other elements function as supporters.Good metacognitive knowledge about mathematics will be able to encourage students' interest and motivation to take learning seriously.
Various efforts have been made to optimize mathematics learning outcomes.First, the mathematics learning material measured only consists of 3 basic competencies, so this research is only able to rely on basic competencies which are used as measuring tools in improving mathematics learning outcomes.Second, the implementation of the PBL model in this research is only limited to one subject for students at Public Middle School 1 Tanjung Jabung Timur class VII, even semester for the 2021/2022 academic year.Third, controlling for covariates, in this case students with high metacognitive knowledge will be enthusiastic about learning, while those with low metacognitive knowledge or lack of preparation before studying mathematics will be lazy to learn, let alone think about solving problems.
There are many ways to improve mathematics learning outcomes and metacognitive knowledge, one of which is by using the PBL model.The PBL model is proven to be superior both in terms of learning outcomes and other aspects such as attitudes and behavior.This is supported by the results of previous research that the problem-based learning model provides students with the opportunity to search for and understand the material presented through problem solving activities in order to provide a deeper understanding so that cognitive learning outcomes increase (Irmawati. H et al., 2023).The difference is that previous research was conducted on class VII students in the Sulawesi Region.
The results of this research have important implications in the context of developing more effective mathematics learning.The finding that students with high metacognitive knowledge do not show significant differences in scores, whether taught with a problem-based learning model or a conventional model, shows that these students have the ability to learn independently.However, for students with low metacognitive knowledge, it is better to be taught using the conventional model because they still need teacher guidance and direction in understanding and solving problems.This highlights the importance of developing metacognitive knowledge in improving mathematics learning outcomes.
In addition, these findings also show that the use of the PBL model has the potential to improve mathematics learning outcomes and students' overall metacognitive knowledge, especially through authentic approaches to problems and increasing student involvement in the learning process.Therefore, this research provides a strong foundation for developing more innovative and inclusive mathematics learning strategies, with an emphasis on using the PBL model to improve students' thinking skills as well as their metacognitive knowledge.The limitations of this research include a limited sample of class VII students, only considering the influence of the PBL model and metacognitive knowledge on mathematics learning outcomes, and limited time and resources.

CONCLUSION
Based on research on the use of the PBL model in class VII students at Public Middle School 1 Tanjung Jabung Timur, it can be concluded that the PBL model has a positive effect on students' mathematics learning outcomes, with a higher level of achievement compared to the conventional approach.In addition, metacognitive knowledge also influences mathematics learning outcomes, where students with high metacognitive knowledge show statistically significant differences compared to students who have low metacognitive knowledge.The interaction between the use of the PBL model and metacognitive knowledge has also been proven to influence students' mathematics learning outcomes, indicating that the superiority of the PBL model in mathematics learning can be influenced by the variable of students' metacognitive knowledge.Recommendations for further research are to further explore the mechanisms of how the PBL (Problem-Based Learning) model and metacognitive knowledge interact to influence students' mathematics learning outcomes.

Table 2 .
Recapitulation of Average Values for Mathematics Learning Results

Table 3 .
Comparison of the calculated F value with the Two Way Anova F table