TEACHER STUDENT’S METACOGNITIVE FAILURE WHEN SOLVING SPHERE EQUATION QUESTION AND THEIR SCAFFOLDING

Problem solving is the core of mathematics. To determine one’s problem-solving performance, metacognition is frequently used. Instead of success, metacognition failure could occur and scaffolding is needed to achieve correct solution. Three selected participants are students of Mathematics Education Department of UIN Maulana Malik Ibrahim Malang, due to their low-level question-solving performance in Task 1. This qualitative research aims to describe these three participants’ metacognitive failure and their scaffolding. Task 1 answer-sheet and Task 1-based interview from each of the participants are triangulated as main data. The result of this research indicates metacognitive blindness, metacognitive mirage, and metacognitive vandalism occur variously from these participants. Based on metacognitive failure which occur, the proper scaffoldings are chosen. They are reviewing, restructuring, and making connection from the question given to help participants achieve correct solution. Task 2, equivalent with Task 1, is given to all three participants to observe whether these participants are making no metacognition failure or no need for more scaffolding. This research provides practical example in using combination from task answer sheet and task-based interview to assess students’ metacognition, particularly metacognitive failure. In conclusion, after students’ metacognitive failure is identified, proper scaffolding support may be applied and variously. Then, better mathematics learning quality can be achieved.


Kata kunci: Kegagalan metakognitif; metakognisi; perancah.
This is an open access article under the Creative Commons Attribution 4.0 International License

INTRODUCTION
Problem solving performance is one of the main competencies in 21 st century skill (Lin, Yu, Hsiao, Chang, & Chien, 2020;Yusoff, Ashaari, Wook, & Ali, 2020).To answer the problem or question will lead to the metacognitive process.Wilson & Clarke (cited in Kuzle, 2018) define metacognition as one's awareness, regulation, and evaluation of his/her thinking.The main feature of the metacognitive process is that problem solver can aware with appropriate strategies, mathematical notations, logical reasons (Güner & Erbay, 2021) and problem-solving performance (Zhao et al., 2019).In fact, assessing students' metacognition become rare activity to do.Further, giving scaffold into students' metacognition failure is needed to improve students' problem-solving performance (Matsuda, Weng, & Wall, 2020).
Scaffolding is defined as the process that assisting learner to solve problem, performing a task, or achieving a goal which would be beyond his unassisted efforts then remove it when learner can do it by himself (Bakker, Smit, & Wegerif, 2015).Different contexts of scaffolding are peer scaffolding (Haataja et al., 2019), whole-class setting (Abdu, Schwarz, & Mavrikis, 2015), and technological support (Albano & Dello Iacono, 2019).Proper scaffolding can be given after identifying metacognitive failure which occurs.
There are two kinds of method to assess one's metacognition when solving problem, online assessment or offline assessment (Muncer et al., 2022;Veenman & van Cleef, 2019).Online assessment is a method when a person conveys immediately what he/she think during problem solving but it is called offline assessment when a person conveys after problem solving.Further, both online and offline assessment has advantages and disadvantages (Kuzle, 2018).To deepen the analysis of one's metacognition, there are several problem-solving frameworks can be chosen.cognitive-metacognitive framework and combine it with taskbased interview situation.Secondly, multivariable calculus is known by student as difficult course.Thirdly, red flag metacognitive failure analysis is chosen in this research.These three aspects are chosen since mostly educators (lecturer and teacher) has no practical guide to improve their students' metacognition.
This research provides best practice for educators to assess their students' metacognition effectively and efficiently.By paying attention to how students think, educators can provide proper scaffolding so that later students can improve their performance with their own efforts (Cevikbas, Kaiser, & Schukajlow, 2022).As a result, better quality in mathematics learning is achieved.
supporting instruments were Task 1, Task 2, and task-based interview protocol which validated by researcher's colleague by three aspects, they are content, construct, and language aspect.The Task 1 and 2 can be seen in Figure 1 and 2. Task 1 and Task 2 (Figure 1 and Figure 2) were two equivalent tasks with the same topic, determining general sphere equation from two points given.Each task has two main steps, they are: 1) finding the sphere radius by using distance formula from two points given, and 2) substituting the radius in the first step into general sphere equation.Participants were asked to answer Task 2 to check whether scaffolding was successful.
To deepen the analysis of participants' metacognition, five-phase cognitive metacognitive framework by Yimer & Ellerton (cited in Muhali et al., 2019) was applied (see Table 1).By using this framework together with task-based interview, participants' metacognition failure can be identified.After gaining valid data with respect to participants' metacognitive failure, scaffolding is constructed by each participants' metacognitive failure.| 783 Based on Task-1 Answer Sheet (Figure 3   Based on Task-1 and interview, for S1, scaffolding type reviewing, restructuring, and making connection were chosen (Wulan, Subanji, & Muksar, 2021).In the reviewing interaction, it shows us that S1 is engaged with the question.S1 succeed in identifying the goal of question number 2 was to find spere equation that it's center in P 1 .In the restructuring interaction, it shows us that S1 can identify the goal and what unknown is missing to complete the sphere equation.S1 successfully managed to calculate the sphere radius.Making connection interaction is used when S1 need to apply the result (radius) into general sphere equation.S1 successfully found that the general sphere equation was (x+2)²-(y-0)²-(z-2)²=3².To check the effectiveness of the scaffolding, S1 is asked to do Task-2 (Figure 4).From S1's Task-2 Answer Sheet, it is concluded that no metacognition failure occurs.
Based on Task-1 and interview, for S2, scaffolding type reviewing, restructuring, and making connection were chosen (Wulan, Subanji, & Muksar, 2021).In the reviewing interaction, it shows us that S2 knows the goal of the question given.S2 successfully mention the goal of the question was seeking sphere equation.In the restructuring interaction, S2 can identify what is the unknown which is missing to complete the sphere equation.S2 could determine the radius of the spere.Making connection interaction is used when S2 need to apply the result (radius).S2 successfully implemented the radius into sphere equation.S2 answered the sphere equation correctly (x+2)²-(y-0)²-(z-2)²=3².
To check the effectiveness of the scaffolding, S2 is asked to do Task-2 (Figure 6).From S2 Task-2 Answer Sheet, even though S2's didn't provide good explanation, it is concluded that S2 has right path to the solution.Furthermore, no scaffolding is needed.Based on Task-1 and interview, for S3, scaffolding type reviewing, restructuring, and making connection were chosen (Wulan, Subanji, & Muksar, 2021).In the reviewing interaction, it shows us that S3 knows the goals of the question given.S2 could determine the aim of the question was to find general solution of sphere with certain center point (P 1 ) and through another point (P 2 ).In the restructuring interaction, it shows us that S3 can identify what unknown is missing to complete the sphere equation (radius).Making connection interaction is used when S3 need to remind the distance of P 2 P 1 is also become the sphere radius.
To check the effectiveness of the scaffolding, S3 is asked to do Task-2 (Figure 8).From S3's Task-2 Answer Sheet, we conclude that no metacognition failure occurs.

Figure
Figure 1.Task-1 instrument ) from S1 above, it can be observed that S1 has assessed the question difficulty [1C], tried to formulate a plan but has no global planning [2D], and tried to determine feasibility of the question [2E].S1 successfully initializing the formula to find radius.S1 feels that his performance doesn't suit his plan [3D].However, after achieve r 2 =9, S1 cannot continue any further and feel he didn't solve the question very well [4D].Hence, r 2 =9 become red flag because S1 committing no wrong calculation but doubtful to apply the result into next plan.This finding is described as metacognitive mirage situation (from S2, it can be observed that S2 has some difficulties.S2 tried to assess the feasibility of his plan [2E] and try to recall related knowledge.S2 assessing the plan with the conditions and requirements set by the problem [3B].S2 is not confident the model/representation he made [3D].S2 did not assess for reasonableness of his result.Further, general sphere equation become red flag since S2 can correctly recall general sphere equation but cannot identify what are the unknowns to carry on into planning phase.This finding is described as metacognitive mirage situation (Huda & Marsal, 2021; Rozak et al., 2018).Based on Task-1 Answer Sheet (Figure 5) from S3, it can be observed that S3 has done many cognitivemetacognitive activities.In orientation phase, S3 has successfully done in analyzing the information and conditions given [1B], assessing familiarity with the question given [1C]