Metacognition Knowledge of High School Students in Solving Limit of Functions Problems Viewed from Mathematical Ability

. The involvement of metacognition in the problem-solving process is paramount. This study aims to obtain a description of the metacognition knowledge of high school students in solving limit of functions problems. This type of research is qualitative descriptive research. The subjects of this study were two students who had high and low mathematical abilities. Data from the results of written assignments and in-depth interviews. The results showed that students with high mathematical abilities in solving limit of functions problems involved the metacognition knowledge they had at each stage of Polya, starting from their declarative, procedural, and conditional knowledge. The subjects with low mathematics at the stage of understanding the problem involved only their declarative knowledge. The step of making a plan involves the declarative knowledge their memory and their procedural knowledge, although incomplete in compiling the ideas. The step of carrying out the plan involves all three knowledge of metacognition that he possesses, while the stage of re-examining involves only his declarative knowledge and his conditional. The results of this research can be a reference in designing limits learning in high school .


Introduction
Logical, systematic, critical, and creative thinking of students can be developed with the help of mathematics.Based on Permendikbud Nomor 22 Tahun 2016, the objectives of learning mathematics include solving mathematical problems, which include the ability to understand problems, develop mathematical solving models, solve mathematical models, and provide appropriate solutions.The ability to solve mathematical problems greatly benefits students who can further develop important skills such as applying rules to non-routine problems, finding patterns, generalizing, and communicating mathematically (Indriana & Maryati, 2021).Based on the objectives of learning mathematics and the benefits of problem-solving, it can be said that the ability to solve a problem is the most important part of learning, especially mathematics.As stated by Telaumbanua et al. (2017), "problem-solving plays an important role in learning mathematics." Problem-solving is accepting problems as challenges (Pathuddin & Bennu, 2021).
Problem-solving helps students know what they know and how to apply it.In the field of pedagogy, this is called metacognition.(Flavell, 1979;Ramadhanti & Yanda, 2021;Erdoğan & Şengül, 2017) interpret metacognition as a person's awareness of his thought process and his ability to control the process.In addition, Livingstone (1997) and Kristanto and Pradana (2022) explain metacognition as "Thinking about thinking." Gartmann and Freiberg (1995) also describe a process of analyzing and organizing students' thinking called metacognition.This is in accordance with the statement of Rofii et al. (2018) that metacognition has an important role in regulating and controlling a person's cognitive processes in learning and thinking.Furthermore, Veenman et al. (2006) and Jaleel et al. (2016) explained metacognition is divided into metacognition knowledge and metacognition regulation.
Knowledge of metacognition refers to awareness of how a person learns (Sudjana & Wijayanti 2018).According to Rao (2020), metacognition knowledge is knowledge about cognition in general as well as awareness and knowledge of cognition itself.Metacognition knowledge includes declarative, procedural, and conditional knowledge (Desoete 2001).Furthermore, Antika (2018) also explains the components of metacognition knowledge, including declarative, procedural, and conditional.Metacognitive knowledge is important in helping students learn well, especially in solving problems.Bahri & Corebima (2015) and Astriani et al. (2020) stated that students solve problems better using metacognitive knowledge.This is as stated by Polya (Anggo et al., 2019), who considers thinking about the process the main thing about successful problem-solving.Students who have developed and used metacognitive knowledge well will succeed academically (Stephanou & Mpiontini, 2017).
Metacognition knowledge is closely related to the problem-solving process because, with problem-solving, we can know students' metacognitive knowledge.Problem-solving in the process requires a proper plan so that students can solve the problem well.However, the plans used in solving math problems between students can differ depending on differences in their math skills.There is a relationship between mathematical ability and problem-solving.According to the results of research from (Supriati et al., 2021), students with high mathematical abilities can understand problems well, make problem-solving plans, carry out problem-solving plans according to what has been planned before, and re-examine the answers obtained.Meanwhile, students with medium and low math skills cannot develop problem-solving plans as done by students with high mathematical abilities.
Mathematical ability also has an influence on students' metacognition knowledge during the problem-solving process by the results of research (Rohim & Maulana, 2021), which states that students with high and moderate abilities in solving problems have good metacognition knowledge, while students with low abilities in solving problems have poor metacognition knowledge.Differences in mathematical ability indicate differences in students' metacognition knowledge when solving mathematical problems, but not all students involve metacognition knowledge in their problem-solving activities.So, the metacognition knowledge of each student will differ according to their abilities; from the researchers' interviews with high school math teachers, it can be seen that some students have difficulty solving function limit problems.
Students have difficulty in factoring and rationalizing the shape of the roots.When working on the problem, there are still students who are less able to use the concept of limit function in solving function limit problems, such as problems that do not need to be factored in, just solved by direct substitution, so that students do not get the results of solving the problem.Conversely, for problems whose solution requires factoring, students answer with direct substitutions so that the answer is in the form of 0 0 .However, some students can solve function limit problems correctly.
The different student solution plans are because students at these schools have different problemsolving abilities.Some students have high mathematics abilities, some have moderate mathematics, and some have low mathematics abilities.Furthermore, it turns out that up to now, at the high school level, there has been no research on the description of students' metacognitive knowledge in solving function limit problems regarding students' mathematical abilities.In contrast, information regarding students' metacognitive knowledge in solving function limit problems is important because teachers can know to what extent Students involve their metacognitive knowledge in solving problems which can then be used as a basis for planning learning students who have developed and used their metacognitive knowledge well will excel academically (Stephanou & Mpiontini, 2017).
Apart from that, the material on function limits is a prerequisite material for derivatives and integrals, meaning that someone cannot master derivatives or integrals if their understanding of limits is not good.The application of functional limits material is also closely related to problems in everyday life.Kulsum (2020) argued that the concept of limits is widely used in engineering, natural sciences, economics, and business to account for measurement deviations.Seeing the importance of functional limit material and metacognitive knowledge possessed by students in solving mathematical problems, the researcher considers it necessary to know the metacognitive knowledge possessed by students in solving limit problems in terms of their mathematical abilities.
Research on metacognitive knowledge in solving mathematical problems, including students' metacognitive knowledge based on their learning style, has been widely carried out.The research results show that students with visual, auditory, and kinesthetic learning styles in solving mathematical problem-solving questions fulfill the three indicators of metacognitive knowledge, namely declarative knowledge, procedural knowledge, and conditional knowledge at each stage of Polya problem-solving (Rahmawati et al., 2017).Other research analyzes students' metacognition in solving sequence and series problems based on their mathematical abilities.The research results show that subjects with high mathematical abilities have good metacognition, namely declarative knowledge, procedural knowledge, and conditional knowledge, and can also use good planning skills, monitoring skills, and evaluation skills.Subjects with moderate mathematical abilities have fairly good metacognition, and those with low metacognition have poor metacognition (Rohim & Maulana, 2021).Research on the Metacognition Process of Middle School Students in Solving Comparative Value and Reverse Value Problems has also been carried out by Setyaningrum and Mampouw (2020).The results of the research show that the metacognitive process of the three subjects is being able to use prior knowledge that can help them solve problems.Subjects with high and moderate mathematical abilities can plan and rethink the steps that will be used to solve problems, which does not appear in subjects with low mathematical abilities.Subjects with high mathematical ability can have other ways of solving; subjects with moderate mathematical ability can solve problems and revise some mistakes, while subjects with low mathematical ability do not experience this process and are not aware of their mistakes in solving inverse value comparison problems.
Based on the search for various literature, there are several differences in terms of the focus of the research that will be carried out, namely metacognition based on students' learning styles (Rahmawati et al., 2017), middle school students' metacognition based on mathematical abilities in comparison of value and reverse value material (Setyaningrum & Mampouw, 2020) and analysis of students' metacognition in solving sequences and series problems (Rohim & Maulana, 2021), while this research focuses more on describing students' metacognitive knowledge profiles based on mathematical abilities in solving function limit problems.

Method
This research employed a qualitative descriptive approach, describing the metacognitive knowledge of high school students in solving function limit problems.This research was conducted at a high school in Palu City, Indonesia.The subjects of this research were students with high, medium, and low mathematics abilities, based on the groupings proposed by Arikunto (2019).The subject grouping uses final semester examination mathematics scores for the even semester of the 2021/2022 academic year.The criteria for students with high mathematical abilities is if the student's score is ≥ average (̅ ) + , standard deviation.Medium mathematics ability if (̅ − ) ≤ student's score is < (̅ + ), and for students with low mathematics ability if student's score is < (̅ − ).The calculation results show: SD = 3.47; Mean (̅ ) = 83.56.
Based on these calculations, a list of students who meet the categories is obtained in Table 1.
After obtaining the calculation results, ND was selected as a subject with high mathematical abilities and SN as a subject with low mathematical abilities.The selection of these subjects was based on recommendations from mathematics teachers, considering that the students could communicate well to make it easier for researchers to dig up information during interviews, were willing to collaborate, and could follow the research series to completion.The data in this research is provided in a written assignment sheet: A heated metal plate will expand with an increase in area as a function of time f (t) = 0,36t 2 + 0,6t (cm 2 ).The speed of change in the area of the metal plate is formulated by  =  (Pathuddin, 2016;Pathuddin et al., 2018;Trisnani & Winarso, 2019).
Data analysis techniques in this study use qualitative data analysis, according to Miles, Huberman, and Saldana (2014), namely data condensation, data display, and conclusion drawing/verification.The credibility of the data in this study used extended observations and member checks.Extended observations can increase the credibility of the data when researchers return to the field, double-checking whether the data that has been provided is correct.Member check is carried out to determine how far the data obtained is by what students provide so that the information obtained by researchers and used in research is by the intended data source or student.
After mutual agreement, students are asked to sign to be more authentic.In addition, it is also evidence that the researcher has conducted a member check.The research design can be seen in Figure 1.

Results and Discussion
The results obtained in this study are descriptions of metacognition knowledge of students with high (ND) and low (SN) mathematical abilities in solving function limit problems based on indicators of student metacognition knowledge according to Polya problem-solving stages.

ND in understanding the problem
The results of condensation on ND interview data in making a problem-solving plan are presented as follows.

P
: Can you reveal the problems contained in the problem?ND : (pause for a long time while focusing on the problem), The problem is that the value of ( 1 ) is not yet known, so the speed of change in the area of the metal plate cannot be determined.In this case, the limit value for the value of ( 1 ) must be found first, and then the method used to determine the limit is also unknown.P : Why is the problem like that?ND : (while looking back at the problem by frowning) yes, because the value of ( 1 ) is not yet known, it must be searched first to determine the limit and the method used to determine the limit.I also have to first analyze the concepts used so that I can solve the problem according to the question at hand.
Metacognition knowledge of subjects with a high mathematical ability to understand problems, ND subjects think by expressing all the information in the problem as it is known the increase in the area of the metal plate as a function of time () = 0,36 2 + 0,6 cm 2 , the rate of change in the area of the metal plate is formulated by  = lim was not yet known so she could not immediately determine the limit value, then the method used to determine the limit was also unknown, the ND subject was aware in using his initial knowledge of concepts that could help to solve the given problem, namely determines the limit value of the function at one point where it is visible when she thinks.This is in accordance with the research findings of Setyaningrum and Mampouw (2020), stating that subjects with high ability are aware of exploring previous knowledge, namely stating the knowledge/information used to solve problems and knowing the reasons why they use the information.When understanding the problem, the ND subject is aware of relating his procedural knowledge; namely, in order to better understand the problem, the ND subject carries out a strategy of reading the question repeatedly and knowing the information contained in the problem.This is by Maswar's (2019) statement that repetitive reading is part of a strategy to absorb new information and associate the new information with students' initial knowledge.ND subjects are aware of their conditional knowledge when expressing the reasons for using strategies to better understand the problem.The steps taken by ND subjects are in accordance with the indicators of metacognitive knowledge in the early stages of Polya problemsolving (Pathuddin, 2016;Pathuddin et al., 2018;Trisnani & Winarso, 2019).

ND in making a problem-solving plan
The condensation results on ND interview data in making a problem-solving plan are presented as follows., (pause for a long time) then after entering the value, distribute the function 0,36 2 + 0,6 -12 and then factor the function 0,6 2 +  -20 P : That's it?ND : hmmm the last step is to determine the limit value by substitution P : Why did you choose this step as a plan to solve the problem?ND : (while holding the head with a serious face) because for the first one, the problem is that the value of ( 1 ) on the limit I substitute first the value of  1 = 5 at () = 0,36 2 + 0,6, after obtaining the value of ( 1 ) the substitution and to find the result for this limit I also have to Enter the values () and (5) in the limit.P : Then why the plan you chose is distribution and factoring?ND : (pause while calculating mentally) and it turns out that after entering the value of (), (5) on the limit, I get the result of the indeterminate value 0 0 ; because I get the result of this indeterminate value then I think of another way to solve the problem by distributing on the function 0,36 2 + 0,6 -12, after that factor the function 0,6 2 +  -20, Continue for the last step, I can determine the limit value with substitutions because I no longer get an indeterminate value.
In making a problem-solving plan, the ND subject is aware of recalling declarative information by mentioning the concepts of substitution, distribution, and factoring in making the plan.This is in accordance with the research findings of Maswar (2019) that students with high mathematical ability remember concepts stored in their memory at the step of planning problemsolving.ND subjects are aware of procedural knowledge, that is, how to formulate solution plan ideas that will be used in the problem-solving process.The ability to link existing concepts with the information on the problem makes it easier to formulate a solution plan that will be carried out further (Holm & Steenholdt, 2014).
The idea expressed regarding the ND subject's knowledge of the steps of the function limit problem solving plan and the formula to be used, the ND subject substituted  1 = 5 at () = 0,36 2 + 0,6, then the ND subject substituted  1 = 5 at lim after entering the value, then the ND subject uses his knowledge to perform a distribution on the function 0,36 2 + 0,6 and factors the function 0,6 2 +  -20, then determines the limit value by substitution, the ND subject thinks by expressing his reason, using the steps of the plan she made for the first the value of ( 1 ) is not yet known, so to find the value of ( 1 ) at the limit she substitutes first the value of  1 = 5 at () = 0,36 2 + 0,6, after obtaining the value of ( 1 ) substitution  1 = 5 at lim → 1  ()−( 1 ) − 1 then in order to find the result for this limit, the subject ND also includes the values of () and (5) at the limit, the ND subject thinks by mentally calculating the ND subject gets an indeterminate result of 0 0 so she thinks of another way using his knowledge namely distribution and factoring.The ND subject is aware of his conditional knowledge when the ND subject mentions his reason for using the chosen concept of distribution and factoring into the solution plan is because it gets an indeterminate result of 0 0 .This conditional knowledge relates to the situation and conditions of when and why a particular strategy, in this case, the concept of distribution and factoring, is used to solve a problem correctly (Swanson, H & Fung, 2016).

ND in carrying out the problem-solving plan
The results of the written assignment subject ND in carrying out the plan are presented in Figure 2. The results of the condensation of ND interview data in carrying out the problem-solving plan are presented as follows.

P
: (pointing to the answer sheet) here why do you distribute 0,36 2 +0,6 -12 to 0,6 × (0,6 2 +  -20) ND : (while holding my head) yes, as at the stage of making the fourth step completion plan that I made earlier after entering the value of (), (5), I do the distribution on the function 0,36 2 + 0,6 -12 because if I don't do the distribution I will get an indeterminate value when making direct substitutions at first, Then the result of the distribution of 0,6 2 +  -20 we factor it so that it becomes (0,6 + 4) ( − 5) P : After you distribute it, you factor it in; why is his previous knowledge as his declarative knowledge; that is, he writes down and mentions the concepts of distribution and factoring to help solve the problem.This is by the statement (Fitria et al., 2019) that declarative knowledge trains students' thinking skills in organizing their knowledge.The ND subject is aware of his procedural knowledge that he realizes that he can solve the problem because the steps of the solution plan have been explained before; the ND subject is aware of how to carry out the solving steps to find the speed of change in the area of the metal plate or the limit value of the function, how to make the limit value not an indeterminate value.The ND subject is aware of his conditional knowledge.It is aware of his reasoning by establishing a concept in solving the limit to not produce an indeterminate value, using the concept of factoring.In this stage, highly capable subjects can plan the implementation of ideas (factoring concepts) productively and smoothly and do not have significant difficulties (Rican et al., 2022).

ND, in re-examining the answer
The results of condensation of ND interview data in re-examining the answer are presented as follows.

P
: Is the solution obtained to meet the requirements asked in the question?ND : (while holding the head long enough) hmmm, yes, the solution obtained meets the requirements asked, namely, the speed of change in the area of the metal plate at the time  = 5 minutes is 4,2 cm 2 /min P : Did it cross your mind about what strategy you would take to check your answers?ND : (while shaking my head) Yes, it occurred to check it by counting back to being done again from the beginning, as in the step of implementing the plan and checking whether the results are the same or not with the results of solving the problem as I have done before.
At the stage of re-examining the answer, the ND subject is aware of his declarative knowledge, that is, by using his knowledge in choosing to do a strategy to re-examine the answer, namely by counting again from the beginning as in the step of carrying out the solution, the ND subject realizes the solution she gets meets the requirements specified in the problem.Students with high mathematical ability know their procedural knowledge, namely writing and expressing how the ND subject can ensure the correct solution.The procedural knowledge possessed by ND is general pedagogic knowledge, namely the knowledge needed to create and optimize the learning process (Voss et al., 2011).The ND subject is aware of his conditional knowledge, that is, of his reasoning, using a means to ascertain the correctness of the answer.In this case, ND is able to involve cognitive skills and dispositions, namely creativity, to critically evaluate intellectual products (Lai, 2011).

SN in understanding the problem
The results of SN interview data condensation in understanding the function limit problem are presented as follows.

P
: Can the younger brother express the problems contained in the problem?SN : (paused for a long time while holding the head) the problem is that the value of ( 1 ) is not yet known, so you must first find the value of ( 1 ) to be able to determine what is asked, namely the speed of change in the area of the metal plate formulated by  =  requires the value of ( 1 ) P : Furthermore, did you think of a concept to help solve the problem?If so, please mention it.SN : (pause) yes, there is using the concept of limit function P : Oh, that's it.Why do you think of using the concept of limit function?SN : (while holding the head) it is because the formula used to determine the speed of change in the area of a metal plate using the limit is  =  → 1  ()−( 1 ) − 1 P : Are there strategies you can use to better understand the problem?SN : Umm, I just read the problem until I understood, and it took me a long time to understand the problem P : That's it?Why do you use that strategy?SN : Yes, because that's all I can do.
In the metacognitive knowledge of subjects with low mathematical abilities in the step of understanding the problem, SN subjects are aware of remembering information in their memory in the form of declarative knowledge, where students with low mathematical abilities are aware of the problems contained in the problem, can access their declarative knowledge about mathematical concepts related to limits (Pathuddin et al., 2018).The SN subject is aware of using his initial knowledge of mathematical concepts, especially regarding limits, which can help solve problems even though they are incomplete.This can help SN subjects find out more about concepts that are still poorly understood and develop their understanding of these concepts.The subject requires sufficient practice using their metacognitive knowledge to develop declarative knowledge (Saks et al., 2021).

SN in making a problem-solving plan
The condensation results on SN interview data in making a problem-solving plan are presented as follows.

P
: Try to explain what plan you have to do to solve this problem.SN : (while moving your head) hmm, on the question of unknown value of ( 1 ) so find ( 1 ) first (pause) hmm by substituting the value of  1 = 5 at () =0,36 2 + 0,6 P : Ooh, that's the next step?SN : After that, find the value of  → 1  ()−( 1 ) − 1 , then we just enter the value of (), (5) in the limit.After that we calculate the limit value P : Why did you choose this step as a plan to solve the problem?SN : (holding my head) I chose the first step, substituting the value of  1 at () = 0,36 2 + 0,6, because the problem is that the value of ( 1 ) is not yet known (holding my head) I chose the first step, substituting the value of t_1 at f(t) = 0.36t 2 + 0.6t because the problem is that the value of f(t_1) is not yet known, so it must be found first to determine the speed of change in the area of the metal plate at the time  = 5 minutes, in this case,  → 1  ()−( 1 ) − 1

P
: after that, the value of ( 1 ) and () is entered in the limit?SN : (frowning) yes, after that, just calculate the limit value.
When making a problem-solving plan, the SN subject is aware of recalling declarative information by mentioning the concept of substitution in planning the solution.In this case, the subject can remember that substitution is a mathematical strategy that involves replacing the value of a variable with a known value to determine the value of another variable, especially in limit problems (Alam, 2020).This aligns with research findings (Maswar 2019) that at the step of planning problem-solving, subjects with low mathematical ability recall knowledge stored in their memory in the form of concepts that have been processed and stored in their brains.SN subjects know their procedural knowledge, namely how to compile ideas or steps for a resolution plan that will be used in the problem-solving process even though it is incomplete.The SN subject is aware of his conditional knowledge when expressing his reasons for choosing the concept of substitution as a completion plan.By using metacognitive knowledge, which includes declarative, procedural, and conditional knowledge, subjects with low mathematical abilities can make effective and accurate problem-solving plans using substitution strategies (Anif et al., 2019;Egodawatte & Stoilescu, 2015).

SN in carrying out the problem-solving plan
The results of the written assignment subject SN in carrying out the problem-solving plan are presented in Figure 3 it is equal to 1 as taught by Mr. Tajudin (math teacher), so only  →5 0 , 6 × (0,6 + 4)

P
: means that  -5 can be crossed out yes and produce 1? SN : Yes, I can, but I forgot to cross it out.P : What is the next limit?SN : I direct substitution, enter the value of  into 5 to produce 0,6 × (0,6 × 5 + 4) P : Why did you directly substitute it?SN : (pause for a moment while holding the head) because according to the concept of limit can be substituted directly if the result is not uncertain, so I calculate it into a result of 4,2 At the stage of carrying out the problem-solving plan, the SN subject consciously rethinks previous knowledge as his declarative knowledge, namely by writing down and mentioning factoring concepts that can help resolve limit problems so as not to produce indeterminate values.
SN subjects are aware of their procedural knowledge; that is, they are aware of how to carry out the stages of completion in determining the speed of change in the area of a metal plate, in this case, the limit value of a function, how to make the limit value not produce an indeterminate value.SN subjects are aware of their conditional knowledge; that is, they realize the reason by establishing a concept of factoring in solving the limit so that the result is not an indeterminate value of 0 0 even though they had difficulty in factoring and tried again to remember the way of factoring.By mentioning and writing down the concept of factoring and how to factor it, you can clarify your understanding of the technique and remember the steps to solve limit problems (Gurbuz et al., 2018).This can help subjects with low math skills perform calculations more effectively and avoid mistakes in the problem-solving process.This shows that subjects with low mathematical abilities cannot plan properly according to Polya's problem-solving stages (Yayuk and Husamah, 2020;Pathuddin, 2016).When re-examining the answers, the SN subject is aware of his declarative knowledge, and she realizes the solution she obtained meets the requirements specified for the problem.Subjects with low mathematical ability are aware of their procedural knowledge, namely writing down and expressing how SN ensures that the solution obtained is correct, which is to be reworked and reworked from scratch.By re-calculating from the beginning, the subject can re-check each calculation step that was carried out and ensure that there are no errors or mistakes in the calculation process.In addition, it can also help subjects with low mathematical abilities to correct errors that may occur in calculations and increase their understanding of mathematical concepts related to the problem being solved (Salido and Dasari, 2019).Thus, these subjects can learn from their mistakes and improve their math skills for further problem-solving.
The results of the research show that subjects with high mathematical abilities, namely ND, in solving function limit problems involve their metacognitive knowledge, including declarative knowledge, procedural knowledge, and conditional knowledge at each stage of Polya starting from the stage of understanding the problem, making a problem-solving plan, implementing the problem-solving plan, and check the answers again (Salido & Dasari, 2019;Yayuk & Husamah, 2020).Meanwhile, SN subjects (with low mathematical ability) in solving function limit problems involve their metacognitive knowledge; at the stage of understanding the problem, they only involve their declarative knowledge; at the stage of making a plan to solve the problem, they involve their declarative knowledge, their procedural knowledge even though it is incomplete in formulating plan ideas.completion, and involves conditional knowledge; at the stage of carrying out the problem-solving plan, the SN subject involves declarative, procedural, and conditional knowledge, while at the stage of checking the answer again, the SN subject only involves declarative knowledge and procedural knowledge (Pathuddin & Bennu, 2021;Rohim & Maulana, 2021).

Conclusion
Based on the description of the results and discussion, it is concluded that subjects with high mathematical abilities in solving function-limit problems involve their metacognitive knowledge.At each stage, Polya begins to understand the problem, which involves declarative knowledge, procedural knowledge, and conditional knowledge; in the step of making a problemsolving plan, then implementing the problem-solving plan, and in the stage of checking the answer again, it also involves the three metacognitive knowledge that he has.Subjects with low mathematical abilities in solving limit function problems involve their metacognitive knowledge.
At the stage of understanding, the problem only involves declarative knowledge; at the stage of making a plan, it involves declarative knowledge in memory and procedural knowledge, even though it is not yet complete in developing ideas for a solution plan and involves conditional knowledge.At the implementation stage, subjects with low mathematical ability involve all three metacognitive knowledge, while at the re-examination stage, subjects with low mathematical ability only involve their declarative knowledge and conditional knowledge.Based on the findings and conclusions above, the suggestions that can be given in this research are for teachers and prospective teachers to be more effective in learning, especially in mastering students' metacognitive knowledge, which includes declarative knowledge, procedural knowledge, and conditional knowledge.If students have metacognitive knowledge, it will be very useful in helping them overcome difficulties in the problem-solving process and useful in building students' awareness of their knowledge during the problem-solving process.
=  1 minute,  in cm 2 / minute.Determine the change rate in the metal plate's area at time t = 5 minutes.The problem is designed to be solved using the Polya stages, which consist of understanding the problem, planning to solve the problem, implementing the problem-solving plan, and checking again.In addition, it can also explore students' metacognitive knowledge, including declarative knowledge, procedural knowledge, and conditional knowledge.Next, indepth interviews were conducted to obtain data describing students' metacognitive knowledge in solving function limit problems.The interviews carried out were direct meetings between researchers and research subjects to search for or complete data that had previously been obtained from the results of written assignments.Audio recordings were made during interviews so researchers could review the data obtained repeatedly.The assignment is expected to explore metacognitive knowledge (declarative, procedural, and conditional knowledge).Before being used, the assignment was first validated by a lecturer in the mathematics education study program at the Faculty of Teacher Training and Education, Tadulako University.The indicators of students' metacognitive knowledge used in this research correspond to Polya's problem-solving stages, as presented in Table2 =  1 minutes  in cm 2 /minutes,  1 = 5 minutes, and asked about the speed of change in the area of the metal plate at the time  = 5 minutes, the ND subject thought with a frown, she realized the problem contained in the problem, namely the value of ( 1 )

P:
Try to explain what plan you have to do to solve this problem.ND : (while shaking my head) hmmm, the solution plan I thought of for the problemgiven first, I substituted  1 = 5 at () = 0,36 2 + 0,6 (paused) yes substitution first P : Then?ND : (while holding the head) the second, after substituting the time function () = 0,36 2 + 0,6 (cm 2 ), substituting  1 = 5 in

0 P:
Figure 2. Results written assignment subject ND At the step of carrying out the problem-solving plan, the ND subject consciously rethinks

P:
Why is the problem like that?SN : (while moving my head) because what I understand from such a problem is that the value of ( 1 ) is not yet known, while to determine  =  → 1  ()−( 1 ) − 1 , and the results of condensation of SN interview data in carrying out the problem-solving plan are presented as follows:P: Next, how do you implement the settlement plan?SN : (while moving my head) I substitute the value of  1 = 5 in  the value of () = 0,36 2 + 0,6 and (5) at the limit so that calculating mentally) I calculated the limit value with direct substitution and it turned out that I produced an indeterminate value of 0 0 , because indeterminate value is not allowed, so I think of ways that I can use so that the results are no longer uncertain.P: So what way do you use?SN : (while holding my head for a long time) hmm I used the factoring method, which I previously distributed first, namely  , but I had difficulty in factoring then I tried to remember how to factor this so that I could produce

Figure 3 .
Figure 3. Results written assignment subject 4. SN in re-examining the answer The results of the condensation of SN interview data in re-examining the answer are presented as follows:

Table 1 .
Data on grouping students' mathematical ability levels

Table 2 .
Indicators of Students' metacognitive knowledge in problem-solving Hmm, yes there is, that is, to determine the limit value of the function at one point, P : Well, then, did it cross your mind about the concept that can help solve the problem?If there is, please mention it.ND : P : Why use that concept?ND : (while holding the head and frowning) yes, because to determine the change in the area of a metal plate where the formula is  =  → 1  ()−( 1 ) − 1 I use the concept of limit function at one point.P : Are there strategies you can use to better understand the problem?ND : (while moving my head), the strategy I use in understanding the given problem is to read the question repeatedly, (pause) yes, read the question repeatedly after that, knowing what is known and what is asked in the problem, then analyze what concepts can be used in solving this problem.P : Why use a strategy of repeatedly reading questions?Keep knowing what is known and what is asked and analyzed concepts?ND : (pause for a moment and eyes focus on the question and read it) yes, because by reading the question repeatedly, I can understand it well and know what is known and what is asked in the problem; if I don't know it, I can't solve it well.
Furthermore, does the solution meet the requirements asked in the question?SN : (while holding my head) Yes, the solution I got met the requirements asked, namely, determine the speed of change in the area of the metal plate, where the results I get by finding the speed of change in area are 4,2 cm 2 /minute P : Did it cross your mind what strategy you would take to check your answers? P: