Express Students' Problem Solving Skills from Metacognitive Skills Perspective on Effective Mathematics Learning

Measuring the standard of success in mathematics learning is whether students can apply mathematical concepts and solve mathematics problems completely. However, the ability of students in solving mathematics problems is sometimes limited to routine problems and when faced with non-routine and in the form of HOTs applications problems, there is complicatedness and difficulty in determining the solution. Therefore, this study aims to review systematically, which metacognitive skills are applied and practiced when students solve mathematics problems and also to clarify the effect of metacognitive skills on student's learning performance. Studies around 2006 and up to date have been explored based on approaches, methods, and practices of metacognitive skills implemented. A total of 12 articles were selected for analysis. This review shows that metacognitive skills are implied and practiced when students solve mathematics problems, but the metacognitive regulation subcomponents are more likely to affect the completeness of the solution than the metacognitive knowledge aspects. Metacognitive skills also have a positive impact on student learning. So, delivering effective learning is very reasonable and timely, and metacognitive skills are applied based on platforms for metacognitive learning strategy.


Introduction
Mathematical competencies are the ability of students to co-ordinate their cognition of mathematical concepts, knowledge, and skills in problem-solving [1][2][3] and can be transformed into a wider context [3][4][5]. The challenge to ensure that the goals are met is the weakness and the level of students' ability to solve mathematical problems, whether routine or non-routine questions [6,7]. Problem-solving skills are the student's ability to regulate and manage cognitive aspects [8]. This ability is based on the stimuli of the internal factor of self and external factors. According to Adnan & Arsad Bahri [9], Menz & Cindy Xin [10] and Stephanou & Mpiontini [10] internal factors are related to existing cognitive settings, experience, and knowledge. If students are accustomed and trained to solve mathematical problems independently (minds-on), then the experience can influence the success [12,13]. The impact of positive experiences and current expertise improved by cognitive coordination will enhance the success of mathematics problem-solving [14,15]. The external factor refers to external stimuli that can induce students' activeness and willingness to solve problems [3,16]. The interests of the issues and problems discussed in the task and the situation delivered of the assignment are also influencing problem-solving skills as an external factor. According to Tzohar-Rozen & Kramarski [17] and Smith & Mancy [8], the appropriateness and attractiveness of the delivery or the solution of problem-solving activities are also factors affecting the problem-solving skills of the students.
To bridge the gap between the internal and external factors discussed, some analyses have shown that metacognitive skills are very significant and can meet the needs of reducing the problem of the low level of mathematics problem-solving skills [3,4,11]. According to Schraw & Moshman [14] and Tzohar-Rozen & Kramarski [17], metacognitive skills are a reference and act like an engine that can leverage student learning. Metacognitive skills are the mastery and implementation of metacognitive components that are metacognitive knowledge and metacognitive regulation [18,19]. Metacognitive knowledge includes subcomponents which are declarative, procedural and conditional, while metacognitive regulation includes planning, monitoring, and evaluation. According to Schraw & Moshman [14], Tarricone [18] and Du Toit & Du Toit [5] these two components influence learning but will give an impact separately and can move in or follow the order [20,21] and according to Tarricone [18], these metacognitive skills will form taxonomy to metacognition and thinking chronology during the learning process. Metacognitive knowledge will stimulate emotional, motivational and previous knowledge of students to form problem-solving orientation [2]. This knowledge will create awareness of the good habit of learning, the necessary solution strategies and knowledge about the source of information to solve the problem [22]. The introduction of the activity and the presentation of the task will form an external stimulus which in turn will affect emotion and self-determination. This effect is an adaptation of metacognitive knowledge. Furthermore, to form behaviours and actions to solve the problem is the effect of metacognitive regulation on thinking procedure (process) and determine of solutions by managing, planning, monitoring and evaluating [4,13,14,16]. Just now, it is the metacognitive regulation acting on the internal factor of the learning. Students' skills in planning solutions, setting goals for solving, selecting strategies, acting on strategies, monitoring accuracy and reflecting findings will lead to perfection and accuracy in solving mathematical problems [2,9]. Therefore, simply by developing the student's metacognitive skills, mathematical problem-solving skills can be improved. However, specific research on how exactly this metacognitive skill affects the mathematical problem-solving skills and the details of the metacognitive components and subcomponents is a need. According to Stephanou & Mpiontini [11], Tony Karnain et.al [12], Menz & Cindy Xin [10], Smith & Mancy [8] and Cera, Mancini & Antonietti [23] metacognitive studies need to be continued to ensure metacognitive skills and strategies learning that applying metacognitive skills can contribute knowledge and ideas to generate intervention to learning, especially in scope of mathematical problem-solving. Tarricone [18] has outlined the metacognitive hierarchy and its existence based on one's thinking ability. However, in-depth studies of metacognitive skills as students solve mathematical problems are lacking. The discussion and relevance of mathematical problem solving and metacognitive skills also need to be clarified and proven by pieces of evidence [20].  [15], but do not in detail focus on how these metacognitive skills work and act during mathematical problem-solving steps.

Methodology
This review is to determine which metacognitive skills are applied and practiced when students solve mathematics problems and to study the effect of metacognitive skills on student's mathematical learning performance. To achieve the objectives, the research questions were created as follows: 1. What are metacognitive skills that students applied during the mathematical problems solving task 2. What is the effect of metacognitive skills on the student's learning performance The procedures and designs of this study are in the form of surveys by conducting systematic review based on the implementation of Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) proposed by Moher et al [25], on studies that deal with the effectiveness and influences of metacognitive on mathematical problems or mathematics learning in general. The journal or article must meet the requirements of this study to be selected which must show statistically evidenced and implied metacognitive inventory that has been recognized. Articles are selected after going through the steps such as Identification, Screening, Eligibility and Included.
Search through databases such as Google Scholar, Researchgate, ERIC, SpringerLink, Elsevier, and some other databases, begins with keywords such as mathematical problem-solving skills and metacognitive skills separately and then they are combined into metacognitive skills in mathematical problem solving to prevent journals and non-focused articles from being displayed. However, the journals and articles found are quite limited and the keywords subsequently changed to be more general by using metacognitive in mathematical learning. 'Snowballing' methods are also applied to increase the number of journals and articles funding [2], but the main requirements remain. 12 qualified and selected articles will be analyzed. The following table shows an analysis of the application of metacognitive skills and their effect on students' learning.

Finding and Discussion
Twelve qualifying studies have been reviewed and the findings will be discussed based on the research questions.

What Are Metacognitive Skills That Students
Applied during the Mathematical Problem-Solving Task?
Based on the findings of the study, it is found that the aspects of metacognitive skills are applied and always practiced while solving mathematical problems. However, there are more aspects of metacognitive skills practiced. The following is an interpretation of findings according to the basic steps in solving mathematical problems.
Based on the results of Table 2, it can be concluded that, while solving mathematical problems, students will practice metacognitive skills according to appropriate chronology. However, this study can explain that the practice of metacognitive skills is specific, that the metacognitive knowledge aspect is applied at the initial stage of problem-solving and so metacognitive regulation aspects will take over the entire process and subsequent actions. This coincides with the fact by Tariccone [18] who explains that metacognitive regulation is a secondary cluster in the thinking taxonomy and is an intermittent act of thinking. This is illustrated by Schraw & Moshman [14], Shaw [28] and Desoete & Roeyers [24]who said that knowledge and regulations can move together but will have different effects. Researchers such as Hasbullah [4], Phi [3], Shaw [28], Nongtodu & Bhutia [26], Desoete & Roeyers [24] and Su, Ricci & Mnatsakanian [27] discussed that regulation aspects play a role in and influence the student's mathematical competence. According to Moos & Ringdals [20], metacognitive regulation begins once the mathematical task is given. It begins with understanding the problem, which involves metacognitive knowledge. For the next, metacognitive regulation will continue the cognitive process by setting goals, designing, selecting strategies, using strategies and concluding by reflecting on such actions [3,26]. To understand that needs to ensure that accuracy and completeness in solving mathematical problems require the ability of students to plan, monitor and evaluate their thinking and learning activities.

What Is the Effect of Metacognitive Skills on the Student's Learning Performance?
Furthermore, the findings show that students who can practice and develop metacognitive skills will ensure that they can master the learning. The effect of metacognitive skills can be seen from two points of view which is the mastery of student concepts and the students' mathematical competencies. The following researchers report that metacognitive skills have a significant relationship with the mastery of the students, especially in solving mathematical problems. The studies conducted by Phi [3], Nongtodu & Bhutia [26], Desoete & Roeyers [24] and Tzohar-Rozen & Kramaski [17] show that there is a positive relationship between metacognitive skills, grades and achievements through the strategies implemented. This is because according to Schraw & Moshman [14] and Du Toit & Du Toit [5], metacognitive knowledge and regulations drive students to set the learning goals, plan, select strategies, monitor learning processes, and evaluate their learning outcomes. Through this metacognitive skill, thinking efficiency will increase and thus this skill will affect the students' understanding of the concept in parallel with studies of Du Toit & Kotze [22], Smith [16] and Warner & Kaur [1].
As reported by Kazemi [12] students who are given enough metacognitive skills training will always understand the relationships among the facts in a problem, allocate resources before learning, check themselves for accuracy, visualize the thinking processes such as self-concept of knowledge, self-intelligence, self-memory, attention, make adjustments if something goes wrong and so on. Thus, this result clearly shows that the student's mathematical competency has increased. Metacognitive knowledge opens up students' interest and emotional spaces towards looking at more specific problem orientation [17], while metacognitive regulation moves the hands-on and mind-on aspect of students to drive and build new knowledge when success in problem-solving achieved [3]. Metacognitive skills play a lot of roles in ensuring students can master mathematics and have better mathematical problem-solving skills.

Conclusions and Recommendation
To implement effective mathematical learning, metacognitive skills need to be provided with training and applied to improve students' performance and thinking skills which in turn lead to the mastery of mathematical concepts. Therefore, teachers and responsible parties need to provide a learning medium that can create a conducive learning environment that provides opportunities for students to develop metacognitive skills. This is because metacognitive skills can be affected and influence the mastery of the mathematical concept of the students. As a suggestion, the stakeholders or researchers will come up with an approach that implements metacognitive skills to transform conventional teaching practices into active learning practices that provide more opportunities for students to manage their learning naturally and on their own needs for examples, through knowledge, experience, and metacognitive regulation.
Through the literature discussed, some researchers suggest the need for an approach that implements knowledge of metacognitive skills to be in line with the technological developments and the transformation of the current curriculum. In fact, it generates learning kits, modules, models and applications to ensure students get real compatibility. It can be concluded that metacognitive skills are not only important to influence mathematical mastery, but also can affect the formation of students' attitudes and behavior towards mathematical subjects. This study should also have a continuing study on the impact of metacognitive skills and how to produce metacognitive learning strategies.