Effect of use of metacognitive instructional strategies in promoting mathematical problem solving competence amongst undergraduate students in facing competitive examination

Abstract Metacognition-related studies often focus on the knowledge, regulation, and experience components but little on the instructional strategies used. In particular and especially within the Indian context, not much focus is given regard to a clear and coherent academic framework that reinforces the use of metacognitive instructional strategies in mathematical problem solving amongst undergraduate students. Using a quasi-experimental method, the purpose of this study is to look closely into the use of metacognitive instructional strategies by undergraduate students. Eighty-four students participated and initial data were collected using the prepared mathematical problem-solving test based on competitive examinations. Single group pre-test and post-test focus group design and the test comparison method were used to analyze the data collected. Findings revealed undergraduate students in the focus group do differ significantly in their mathematical problem solving competence and use of metacognitive instructional strategies between the pre-test and the post-test. The findings shed some light on the distinct role of metacognitive instructional strategy and some ensuing factors during mathematical problem solving in competitive examinations.


Abstract:
Metacognition-related studies often focus on the knowledge, regulation, and experience components but little on the instructional strategies used. In particular and especially within the Indian context, not much focus is given regard to a clear and coherent academic framework that reinforces the use of metacognitive instructional strategies in mathematical problem solving amongst undergraduate students. Using a quasi-experimental method, the purpose of this study is to look closely into the use of metacognitive instructional strategies by undergraduate students. Eighty-four students participated and initial data were collected using the prepared mathematical problem-solving test based on competitive examinations. Single group pre-test and post-test focus group design and the test comparison method were used to analyze the data collected. Findings revealed undergraduate students in the focus group do differ significantly in their mathematical problem solving competence and use of metacognitive instructional strategies between the pre-test and the post-test. The findings shed some light on the distinct role of Rajkumar Rajadurai ABOUT THE AUTHORS Rajkumar Rajadurai is currently pursuing his Doctoral Degree in the Department of Education at Periyar University, Salem, Tamil Nadu, India. He has been working on doctoral research in the field of technology in mathematics education and Metacognition in Education. Hema Ganapathy is currently working as an Assistant Professor in the Department of Education at Periyar University, Salem, Tamil Nadu, India. She has got rich teaching experience of 20 years, as a teacher, Lecturer, and Principal in reputed institutions of schools and colleges of Teacher Education. She has published 2 books and contributed more than 50 articles in National and International Journals and papers presented in seminars/conferences from the international level to the regional level. She is an active reviewer of the

PUBLIC INTEREST STATEMENT
The purpose of the study was to investigate the effect of the use of metacognitive instructional strategies in promoting mathematical problem solving competence among undergraduate students facing competitive examinations. The study found that metacognitive instructional strategies are contributing to the mathematical problem solving competence of undergraduate students in facing competitive examinations, and also we have observed that there is a meaningful relation exists in the students in terms of the problem solving achievement level. This study highly recommended that in the future, teachers need to consider the design of mathematical problem solving activities to ensure they promote the use of metacognitive strategy knowledge among all levels of students.

Introduction
Numbers, mathematical content, and arithmetic is the main focus of the mathematics curriculum in the early years of elementary education, and appropriate learning experiences in these grades improve students' chances for later success (National Research Council & Mathematics Learning Study Committee, 2001). Recent reform efforts in mathematics education attempt to create space for students to use problem-solving strategies efficiently, creatively, and flexibly (National Council of Teachers of Mathematics, 1989;(2000); National Governors Association (NGA; 2010)); Peters et al. (2013); Sahin et al., 2020).
Metacognition has important significance for learning and instruction in educational research and practice (Jiang et al., 2016). In educational contexts, metacognition is continually used to explain the process by which students/teachers learn to understand their thinking, with the notion that if they can regulate their thinking effectively, they will be better learners (Perfect & Schwartz, 2002). In the last decade, there is a growing consensus that metacognition is of important in successful learning (McCormick, 2003) and efficient teaching (Ben-David & Orion, 2013;Fathima et al., 2014). Based on the theory suggested by Flavell and his colleagues (Flavell et al., 2002), also drawing lessons from Zohar and Barzilai's research (Zohar & Barzilai, 2013), we adopt the notion that integrated metacognition should comprise metacognitive knowledge, metacognitive regulation and metacognitive planning. Metacognitive knowledge consists of personal variables, task variables and strategy variables. Personal variable refers to self-knowledge including knowledge of one's strengths and weaknesses. Task variable includes knowledge about the range and demands of tasks, as well as knowledge about the conditions and factors that influence the tasks. Strategy variable refers to knowledge about specific and general cognitive strategies along with an awareness of the potential use for approaching and fulfilling certain tasks. The metacognitive aspect of such knowledge lies in knowing where it can be used and in knowing when and how to apply it. Metacognitive evaluation and reflection incorporate feelings, judgments, and online task-specific experience. Metacognitive instructional strategies comprise deliberate activities and the use of strategies for effort/time allocation, planning, monitoring and regulating cognitive processing, as well as evaluating the outcomes. Students with metacognitive skills ensure that they can plan, monitor, control, assess mathematical performances, and automatically reflect problem-solving actions while working on a mathematical issue (Jiang et al., 2016).
In the point of previous studies, metacognitive instructional strategies are the main component in solving mathematical problem solving. Rahman (2010) studied the relationship between the use of metacognitive strategies and achievement in English. The primary finding of this study is that the most often employed technique is rehearsal, and that the use of metacognitive methods varies amongst English language learners with and without proficiency. Kazemi (2012) investigated a comparison between two methods of measurement of meta-cognitive awareness in mathematical problem solving of university students. The results revealed a moderate and significant correlation between students' metacognitive awareness which was obtained via meta-cognitive inventory and protocol analysis. Consequently, this study suggests that the use of multiple methods for measuring meta-cognition provides a more reliable picture of the phenomena under investigation. Vula et al. (2017) findings showed a difference between the pre-test and the post-test results was statistically significant solely with the fifth-grade experimental classes, yet an improved performance was observed in third-grade experimental learners' classes compared to control classes. Related studies in the literature focused on the naming and categorizing of metacognitive instructional strategies to propose appropriate frameworks. Although such approaches can help develop an understanding in metacognition, and uncover potential associations between cognition and metacognition, they fail to provide a research base to facilitate students to improve metacognitive instructional strategy during mathematical problem solving activities. Such a research base is mainly vital for undergraduate students who need to be trained to develop problem-centered approaches in their teaching. This is to facilitate the development of metacognitive instructional strategies in their future students. This study focused on understanding the metacognitive instructional strategy employed by a sample of undergraduate students as they engaged in mathematical problem solving competence for competitive examination.
The present study was guided by the following research questions.
1. What metacognitive instructional strategies do undergraduate students use to solve mathematical problem solving competence for competitive examinations?
2. To what extent are the metacognitive instructional strategies used by undergraduate students associated with their mathematical problem solving competence?

Objectives
To identify the undergraduate students in the focus group do differ significantly in their mathematical problem solving competence and use of metacognitive instructional strategies between the pre-test and the post-test.
Examining the mathematical problem solving competence of undergraduate students in the focus group is associated with different dimensions of the use of metacognitive instructional strategies in the post-test.

Research method
Pre-test and post-test quasi-experimental design was used in this study. Participants in this study were eighty-four college students from two colleges are affiliated with Periyar University in Salem. The focus groups have both males and female aged from 19 to 22 years old.

Instruments
The Questionnaire on Metacognitive instructional strategies (QMIS) used in this study was developed based on mathematical problem solving. The questionnaire on metacognitive instructional strategies was developed by the researchers and the scale consisted of five subscales, including metacognitive task analysis, metacognitive Instructional objective, metacognition on the preparation of Instructional materials, metacognitive Evaluation, and metacognitive reflection. The scale was tested through a series of tests, including an expert validity test and construct validity test before it was used in the formal test. QMIS contains a 5-point Likert scale with 25 items divided into five dimensions: metacognitive task analysis, metacognitive Instructional objective, metacognition on the preparation of Instructional materials, metacognitive Evaluation, and metacognitive reflection. Undergraduate students thoroughly understand the given statements of mathematical problem solving. Think about a mathematical concept that might solve in the competitive examination with special reference to the following: What do you do before you solve a mathematical concept? What do you do while you solve a mathematical concept?, and What do you do after you solved a mathematical concept?. The reliability value (Cronbach's alpha) of QMIS was 0.872.
Mathematical Problem Solving Competence Test (MPSCT) is a self-made tool used in the study to measure mathematical problem solving competence. MPSCT consists of 60 items, each of which has four options. The reliability value (Cronbach's alpha) of MPSCT was 0.872. To minimize the effect of differences in mathematical knowledge among undergraduate students taking the test, the test questions used were based on competitive examinations conducted by the state government of Tamil Nadu and central government of India.

Procedure
The 40-hour metacognitive instructional strategy and a mathematical problem-solving test for undergraduate students have been given to the researchers to conduct the activities. During this instruction process, the treatment group's students were informed about metacognition, metacognitive instruction aims of the present study, the study process, problem solving activities used in the content and their roles during the study. The implementation of pre-tests, an instruction process called 'metacognitive instructional strategy using problem solving activities' has been carried out to develop the mathematical problem solving of students in the focus group. The purpose of instruction of metacognitive instructional strategy through problem solving activities is to develop students' metacognitive skills practically during problem solving activities. The researchers planned all the activities carried out in the treatment group. While the students are busy with the problems in worksheets during problem solving activities, the teacher monitored them and asked questions when necessary, such as "What do you think when you first read the problem?", can you read the problem thoroughly and do you understand it?', "Do you think that you have understood the problem?", and "Tell me what goes on your mind?". "What will you do now?", "Will this helps to arrive solution?", "Do you think you can solve this problem?" to trigger and encourage a greater range of metacognitive thinking in the students who were part of the focus group. The reasons behind these questions are addressed to arouse the students' opinions about themselves and the process is mainly to encourage students to ask questions themselves. The students have been asked to answer 30-word problems over a nine week/day period. Each time, their results were recorded in a systematic way.

Findings
H 0 1: Undergraduate students in the focus group do differ significantly in their mathematical problem solving competence and use of metacognitive instructional strategies between the pre-test and the post-test.
The results of the paired-sample t-test showed that the focus group's post-test scores were significantly higher than the pre-test scores in mathematical problem solving competence (t = 36.709, p < .001), and metacognitive instructional strategies (t = 8.064, p < .001).
From Table 1 the 't-test analysis indicates that students of the focus group (N = 84) differ significantly in their mathematical problem solving competence from the pre-test and the posttest at a 0.01 level of significance. The mean score of the post-test (M = 49.70) is greater than that of the pre-test (M = 18.98). It is noted that the focus method could enhance mathematical problem solving competence to a high extent as the respondents are undergraduate students. Further students of the focus group differ significantly between the pre-test and post-test in their use of metacognitive instructional strategies at 0.01 level of significance. These results also indicate that a significant difference exists between the pre-test and the post-test in the use of metacognitive instructional strategies.
H 0 2: Mathematical problem solving competence of undergraduate students in the focus group is associated with different dimensions of the use of metacognitive instructional strategies in the post-test.  Table 2 that the combinations of the dimensions of Metacognitive Instructional strategies significantly predict the mathematical problem solving competence of undergraduate students of the focus group in the post-test, as the value of the significance is 0.045 which is significant at 0.05 level. It can be inferred from the table of dimensions that all the five dimensions of metacognitive instructional strategies such as task analysis, instructional objective, preparation of instructional material, metacognitive evaluation and metacognitive reflection are contributing to the mathematical problem solving competence of undergraduate students of the focus group in the post-test. This shows that undergraduate students in the focus group tend to use metacognitive instructional strategies during their developmental process of mathematical problem solving competence. Hence it is clearly understood that the orientation of the mathematical problem solving competence model seems to be more effective.

Discussion
In the various reviewed studies that students are challenged when solving mathematical problems with metacognitive instructional strategies, this study examined metacognitive instructional strategy training as well as different ways of fostering strategy use in a realistic college setting. All the students studied a metacognitive instructional message related to the study and were tested on the contents immediately in a further week. Even though differences in the use of the metacognitive instructed strategies were found at least early in learning, some differences existed in the focus group were found in learning outcomes. Differences in learning metacognitive strategy use were only observed early in learning. While in the beginning, the focus groups used the instructed strategies more often than the end of the group, at a later stage these differences were highly found. These results might be the result of three different things. Undergraduate students first focused only on using metacognitive instructional strategies to solve problems. If they practice strategies regularly, then students remember how to apply all the steps to solve a mathematical problem. However, this idea that stimulates presented during mathematical problem solving and implementation intentions serves as permanent reminder. Second, undergraduate students might have made an effort to use the metacognitive instructional strategies but stopped at some point because adequate use is time-consuming and uses up cognitive resources. One might assume that cognitive resources become infrequent the longer the problem solving takes, which might be why undergraduate students stopped using the metacognitive instructional strategies towards the end of learning. Measuring cognitive load at several time points could give more insight into how students' allocation of cognitive resources develops over time. Yet, it is important to keep in mind that our strategy measure tapped only into overt metacognitive instructional strategy use. Thirdly, it's possible that students still used the metacognitive skills they were taught, but only in confidence. This concept could be more clearly explained through metacognitive reflection and assessment.
In conclusion, future studies should consider using metacognitive measures to get more insight into the mathematical problem solving process and a better understanding of how the metacognitive instructional strategies are used, how the frequency of use changes over time, and to identify possible reasons for such a change. In terms of learning outcomes, there were very effects of the use of metacognitive instructional strategy training.

Recommendations
For improvement in achieving desired academic goals, we recommend the following 1. Keeping in view that the metacognitive strategies need to be included in the syllabus and exclusively as practices.
2. Teachers may also be trained for enabling the students how to undertake self-questioning, self-assessment, self-regulation and thinking aloud during learning activities. If it is discovered that the teaching faculty currently has gaps in their current understanding of how to use metacognition learning to enhance students' experience and their memory, then training needs to be arranged for all tutors.
3. Our data exhibited that the students tend to apply metacognitive strategies primarily to learn by rote instead of conceptual learning and comprehension. The faculty members and counselling experts must focus on realizing to the students that understanding the information is primary to memorizing, otherwise, it might lead them to be conceptually weak in the subject and unable to further learning. 4. Furthermore, the researchers need to evaluate the impact of the application of metacognitive strategies in various subjects excluding mathematics. 5. Teachers design mathematical problem solving activities that promote metacognitive strategy knowledge or metacognition in general among students and may set a classroom environment that promotes the development of metacognitive instructional strategy or metacognition through using this study as a frame of reference.

Contribution and practical relevance
The findings contribute to the understanding that metacognitive instructional strategy use is rather challenging meaning that instructional support is indeed needed. However, the strategy training used in the present study, as well as its combination with further instructional support, was effective to enhance learning mathematical problem solving content for competitive examinations for undergraduate students. Thus, further effort needs to be invested in identifying more effective strategy support interventions. At the same time, this also implies ensuring the use of well-designed instructional materials in mathematics education, where strategy support is embedded into the materials, as an effective to enhance strategy use via training.