Analysis of student’s mathematical thinking in solving HOTs problems viewed from mathematics anxiety

can be useful in assessing how students' mathematical thinking processes solve problems. Mathematical


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Trying to solve a similar problem by changing the facts and what to ask Anderson and Krathwohl (2001) suggest that the dimensions of cognitive processes are divided into 6 levels based on the Taxonomy Bloom Revision book, namely remembering, understanding, applying, analyzing, evaluating, and creating.Brookhart in (Dwi & Jasilin, 2020) categorizes the last three of them as HOTS namely analyzing, evaluating, and creating.According to Anderson and Krathwohl, the higher order thinking approach is divided into learning to remember and learning to transfer.HOTS includes critical, logical, reflective, metacognitive and creative thinking that is activated when individuals are faced with unknown problems, uncertainties, questions or dilemmas.According to the National Council of Teachers of Mathematics HOTS requires non-routine problem solving.According to Anderson and Krathwohl in (Sa'dijah et al., 2021) HOTS is a process of analyzing, evaluating, and creating.HOTS thinking occurs when a person takes in new information and relates to, rearranges, and expands on their information to achieve a goal or find possible answers in a confusing situation.So, it can be concluded that HOTS thinking is thinking that refers to the 3 highest cognitive levels of the revised Bloom's Taxonomy, which includes analyzing (C4), evaluating (C5), and creating (C6).Where analyzing is breaking information into several parts to explore understanding and relationships, compare, organize, deconstruct, interrogate, and find.Evaluating is justifying a decision or action, checking, hypothesizing, criticizing, experimenting, and assessing.Creating or making is generating new ideas, products, or ways of seeing things, designing, building, planning, producing, and creating.
The results of the 2018 PISA survey on mathematics achievement show that Indonesia is ranked 7th from the bottom.This proves that the quality of mathematics education in Indonesia is still relatively low, which means that students' mathematical thinking skills are also low.One that affects mathematical thinking is math anxiety.Anxiety is a feeling of worry, tension, and fear when facing something.According to most people anxiety is something normal, especially in learning activities.According to Peplau, the anxiety experienced by each individual has four levels, namely mild anxiety, moderate anxiety, severe anxiety, and panic (Lisma, 2019).First, mild anxiety is anxiety related to the tension experienced in everyday life.In mild anxiety, individuals are still relatively aware of their perceptions and are still open, usually indicated by closing their eyes.Second, moderate anxiety, in this phase of anxiety, the individual is focused only on the thoughts that are of concern to him, there is a narrowing of the field of perception.Third, severe anxiety, that is, the individual's field of perception is very narrow, focuses his attention on small (specific) details and he can't think of anything else.Fourth, panic is when the individual loses self-control and attention to detail because he loses control, unable to do anything even with orders.Mathematical anxiety is associated with students' feelings of tension or anxiety in working on numbers or solving problems in mathematics (Guita & Tan, 2018).Math anxiety refers to feelings of tension, confusion, and helplessness that students experience when asked to solve complex math problems, carry out math assignments in front of their classmates, and make mistakes in math (Da Zhou et al., 2022).From these definitions,This means that students who experience anxiety in mathematics do not necessarily experience anxiety in other subjects.Anxiety in Maths is easy to explain.This can be manifested through feelings of discomfort and distraction that some individuals may face when experiencing problems in learning mathematics.
According to Cavanagh and Sparrow, math anxiety is divided into three dimensions: attitudinal aspects, cognitive aspects, and somatic aspects (Dinawati & Siswono, 2020).The attitude aspect describes math anxiety based on a person's perspective or attitude towards mathematics, such as a lack of confidence to carry out activities related to mathematics.The cognitive aspect defines anxiety as a change in one's cognitive processes or knowledge of mathematics, such as confusion when faced with mathematical problems and the inability to think clearly when faced with mathematics.While the somatic aspect describes the anxiety that occurs in a person's cognitive processes or knowledge when interacting with mathematics, which is indicated by the emergence of feelings of tension, sweating in the hands and body.Students' anxiety about mathematics can trigger various cognitive, affective, and physical reactions (Nida et al., 2020).Cognitive reactions are shown in the form of negative self-talk, blank thoughts, and avoidance of mathematics.Affective reactions are shown in the form of lack of confidence, fear of looking stupid and losing identity.Physical reactions include sweating, impulses in the heartbeat, tension, and nausea.Based on the description above, this study aims to analyze the mathematical thinking processes of students of Tadris Mathematics at State Islamic University Kiai Haji Achmad Siddiq Jember in solving Higher Order Thinking Skills (HOTS) questions based on mathematical anxiety.

RESEARCH METHOD
This study is a descriptive qualitative research with the aim of knowing students' inquiry thinking processes when solving Higher Order Thinking Skill (HOTS) questions which require qualitative data in expressing oral and written mathematical evidence.Qualitative research method is a research method in which the researcher acts as an instrument, purposive sampling and snowball, data analysis is qualitative/inductive, collection techniques are triangulation (combined), and the results of qualitative research emphasize meaning rather than generalization.Qualitative research is based on the philosophy of postpositivism and is used to study natural object conditions (Sugiyono, 2016).This study was conducted at Kiai Haji Achmad Siddiq State Islamic University Jember.The research subjects were 6th semester students majoring in Tadris Mathematics.The subject determination technique used was purposive sampling in which the researcher took samples according to the research objectives.Purposive sampling is a sampling technique for data sources with certain considerations (Sugiyono, 2016).The researcher took one class of subjects who were students of class 1 mathematics, given a math anxiety test instrument to measure student anxiety levels which were then categorized based on the test result classification guidelines (Hakim & Alpha, 2021).Data collection in this study was carried out by looking at students' mathematical thinking processes with test questions, documentation, and interviews.Data validity in this qualitative research was carried out through triangulation.The instrument used in this research is questionsHigher Order Thinking Skill(HOTS)from research (Annizar, et. al., 2020) which has been modified.Data analysis was carried out by looking at the results of the subject's work and interview transcripts.The process of data analysis uses the Miles and Huberman model, namely data reduction, data presentation, and drawing conclusions (Suhiyono, 2006).Analysis of mathematical thinking processes using Mason's mathematical thinking indicators.The study procedure in this study includes 4 stages, namely preparation, implementation, analysis, and preparation of reports (in Mawardi et al., 2020).In the preparatory stage, the researcher prepared math questions and Higher Order Thinking Skill (HOTS) questions that would be given to the subject.Implementation stage, (1)the researcher gave a math anxiety instrument which was given to math tadris students in math class 1 to find out the level of student math anxiety, (2) the researcher took five subjects who hadmath anxiety level is very high, high, medium, low, and very low,(3)the researcher gave Higer Order Thinking Skill (HOTS) questions to the subjects to do in writing and orally (think aloud or talk while working).In the analysis phase, the researcher analyzed the mathematical thinking processes of each subject.And in the fourth stage, the researcher compiled a research report.

RESULTS AND DISCUSSION
To find out the mathematical thinking processes of students who have very high, high, medium, low, and very low math anxiety in solving HOTS questions, the researchers gave HOTS-based test questions adapted from research (Annizar et. al., 2020) and modified.Then, the data obtained from the work of the 5 subjects (very high, high, medium, low, and very low anxiety levels), think aloud, and interview results (which were used as a complement) were processed and analyzed.The test instrument used is as follows!

How many bacteria after 6 hours?
How long does it take for the bacteria reach 1.064.960?Then it will be explained how to develop the mathematical thinking process used by the subject to observe, investigate, find patterns from objects presented in the problem, how to use strategies and how to find results from strategies applied in solving problems.According to Meidawati in (Annizar et. al., 2020), students are emphasized to seek and find answers to a problem through their thinking processes.The 5 subjects' mathematical thinking processes in solving HOTS questions are as follows: The first phase of the mathematical thinking process is Entry.At the entry stage, the indicators measured include I know, I want, introduce.When the S1 is given the HOTS question instrument, the first thing the S1 does is read and understand the questions carefully then the S1 finds things related to the questions, namely they are known and asked.
Even though what is known and asked is not written down in full, when working on the S1 it is stated that the information is in the problem.Then to be able to solve the problem, S1 groups information from bacterial patterns and time including arithmetic or geometric sequences.S1 then writes down what is known in each pattern, such as ratios.
In the second phase is attack.In this phase the indicators that are measured are try, maybe, and why.At this stage, the first thing S1 did was determine the guess by looking for a value n, the way S1 divides 6 hours by 0.75 produces 8. Then S1 tries to guess what the value is n = 8 those who have been searched can solve the first problem, namely determining the number of bacteria after 6 hours.S1 can determine the number of bacteria ie 16.460.Even though in the first question, S1 was able to answer the questions correctly, the steps used were not quite right.Not only that, the general formula Un for the geometric sequence that S1 wrote wrong, it should be . However the answer is correct because it is in specifying the value n, S1 directly divides 6 hour with 0,75 (the difference) that produces 8. Should n = 9 because Un was at minute 0 and Un used by S1 is , so the answer is correct because of the value n in the formula used S1 is not reduced by one.In question 2, the first step used by S1 is correct, namely looking for a value n.But formula Un which is used incorrectly so the value n generated is wrong.S1 answered value n = 14 should be right n = 15 by formula Then job S1 stops until the value n course, and replied that the time needed is 14 hours.It should still continue to determine the time needed, namely by formula because when it satisfies the conditions of an arithmetic sequence.In this case S1 does not understand the geometric sequence formula.The 3rd phase is a review which includes check, reflect, and extern.S1 does not meet the indicators in this phase because S1 does not check the accuracy of the suitability of the completion steps with the questions and does not look for other solutions.

Figure 2. Masters Work Result
In the first phase of entry, S2 did not understand the questions carefully.S2 is able to determine what is known and asked.This is proven by, S2 is able to write r = 2, n = 6 and a = 65.However, S2 assumes that the ratio between time and bacteria is the same, namely 2. Conjecture in the first problem n = 6 wrong.This is of course wrong, because of the value 6 here is not a value n but value Un.In the attack phase, after making assumptions about the first problem, because at time it satisfies the conditions for an arithmetic sequence so that the answer is correct 10,5 o'clock.In this case S2 does not understand the geometric sequence formula.In phase 3 of the review, S2 did not meet the check, reflect, and extend indicators, because S2 did not check the accuracy of the suitability of the completion steps with the questions and did not look for other solutions.

Figure 3. S3 Work Results
S3 in the first phase, namely Entry, S3 does not understand the problem carefully.S3 is able to determine what it knows and asks.This is proven by, S3 is able to write r = 2 and a = 65.However, S3 does not write down b (different) from time.S3 said that the ratio between time and bacteria was the same, namely 2. This was said when S3 was working.
Then in phase 2 for the first alignment, S3 made a guess at the solution regarding the number of bacteria after 2 o'clock.S3 suspects that what was asked in the first question is U6.This is of course wrong because of value 6 here is not a value n but value Un.Then S3 tries the conjecture that has been made to solve the problem using the formula with value n = 6, a = 65, and r = 2.The formula used by S3 is correct for the first problem, namely finding the number of bacteria, but S3 is not careful in reading what is known so that he thinks6 as value n, should be value n can be determined by the formula with Un = 6, a = 0, and b = 0, 74 then value n = 9.For the second question, in the S3 entry phase write down what is asked is the value n.This is of course wrong because in the second question asked is Un time, that is how long it takes for the bacteria to x reach 1.064.960.For the first step in the second problem solving stage, S3 answered correctly, namely looking for a value first before searching Un with n = 15.
However, S3 stops here, not continuing to look for values .This is because S3 did not understand what was asked in the second question.In phase 3, S3 did not fulfill the check, reflect, and extend indicators, because S3 did not check the accuracy of the suitability of the completion steps with the questions and did not look for other solutions.In the first phase of entry, S4 did not understand the questions, especially on sequences (geometry and arithmetic) and was not careful in finding things that were known and asked.This can be seen when S4 writes the ratio of bacteria, S4 writes b = 65, for the difference U1 to U2 65 right, but henceforth wrong.This is because S4 does not identify from what is known (bacteria and time) included in an arithmetic or geometric sequence.The ratio in bacteria should be because the bacterial sequence is a geometric sequence.In the second phase of the attack in solving the first problem, S4 does not use geometric sequence formulas or arithmetic sequences but uses a known pattern.However, S4's answer regarding the bacterial count after 6 hours is 1299, this is of course wrong.This happens because when S4 determines the guess, S4 is wrong, namely the guess about b = 65 when it should be r = 2 because of the geometric sequence.
In solving the second problem, S4 has written down what it knows, namely bacteria Un = 1.064.960.However, the formula used by S4 is wrong, because S4 uses a formula should use the geometric sequence formula .Not only that the S4 suspects on the second issue it asks is value n even though what is asked is the value Un (arithmetic sequence because the time series pattern is an arithmetic sequence), with answers n = 16,384.Should n = 15 find the geometric sequence formula.In this case S4 is not careful in identifying geometric sequences and arithmetic sequences.In addition, S4 did not understand what to look for in the questions.In phase 3, S4 did not fulfill the check, reflect and extend indicators, because S4 did not check the accuracy of the suitability of the completion steps with the questions and did not look for other solutions.

CONCLUSION
Based on the results of the research and discussion, it shows that students with very high math anxiety fulfill the entry phase with the I know, I want, and Introduced rubik.Fulfilling the attack phase which includes try, may be, why.However, it does not meet the review phase which includes check, reflect, and extend.This is evidenced by S1 correctly answering the first question and incorrectly answering the second question.This is because S1 wrote the wrong formula, besides that S1 also did not continue the work to determine the time needed for the bacteria to form x reach 1. 064.960.As shown in Figure 1, the S1 job stops until the value n just.The second subject (S2) with a high level of math anxiety.In the entry phase, S2 fulfills the I know and I want rubik, but does not meet the introduce rubik, the proof is that S2 assumes that the ratio between bacteria and time is the same.In the attack phase, S2 fulfills the try, may be, and why rubik.However, S2's answer to the first and second questions is wrong, this is because S2 wrongly guessed that n = 6 and the formula used is wrong.S2 in the review phase does not meet the check, reflect, and external phases.
The third subject (S3) with a moderate level of anxiety.In the entry phase, S3 fulfills the I know and I want rubik.But on rubik I know S3 doesn't understand the problem well.However, S3 does not fulfill the Rubik's introduce, the proof is that S3 assumes that the ratio between bacteria and time is the same.In the attack phase, S3 fulfills the try, maybe, and why rubik.However, S3's answer to the first question is incorrect due to grades nwrongly used.But S3's answer to the second question is correct in the initial step of determining values n.But S3 does not proceed to the next step to find the required time.This is because S3 doesn't quite understand the question.So in this case S3 does not meet the review phase.Fourth subject (S4) with a low level of anxiety.In the entry phase, S4 fulfills the I know and I want rubik even though it is only in the activity of understanding the questions, but S4 does not fulfill the introduce rubik.It can be seen that S4 did not write down clearly what was known in the problem.In the attack phase, S4 fulfills the try, may be, and why rubik, even though the answers to the second and third questions are wrong.In the review phase, S4 does not meet the check, reflect, external indicators.
The fifth subject (S5) has a very low level of math anxiety.In the entry phase, S5 fulfilled the I know, I want, and introduce indicators, even though S4 did not clearly write down what was asked and what was known.In the attack phase, S5 fulfills the try, may be, and way indicators.This is proven by S5 being able to solve the first and second questions.In the review phase S5 fulfills the Rubik's check with evidence that S5's answers are correct, but S5 does not fulfill the Reflect and Extern Rubik.This is proven by S5 not writing down the general form or the general formula for geometric and arithmetic sequences.
Skor ≤ M +1,5 S Currently M-0,5 S< Skor ≤ M +0,5 S Low M-1,5 S< Skor ≤ M -0,5 S Very low Skor ≤ M -1,5 S S2 uses these assumptions to solve the first problem by substituting what S2 has written into the formula Un for geometric sequences.The formula written by S2 is , this should be wrong .In question 2, the first step used by S2 is correct, namely finding the value .But formula which is used incorrectly so the value generated is wrong.S2 answers value n = 14 should be rightn = 15 by formula .Then job S2 stops until the value n course, and replied that the time needed is 14 hours.It should still continue to determine the time needed, namely by formula

Figure 5 .
Figure 5. S5 Work ResultIn the first phase of entry, S5 was able to understand the questions thoroughly and was able to find out what was known and what was being asked.S2 wrote down r = 2 for bacteria and write down the difference in time ie 0,75.In this case S5 is able to answer the first and second problems correctly.For the first problem, namely the number of bacteria after 6 hours, S2 answered 16.640 and for the second problem which is the time it takes for the bacteria to reach 1.064.960,S2 replied 10,5 It's just that in solving the problem, S2 does not use geometric and arithmetic sequence formulas.

Table 1 .
Masonic frame of mind Checking the suitability of the reasons for the settlement steps Check whether the completion steps used and questions are appropriate Reflect Thinking about the ideas that happened, what is the most difficult part of what can be learned from the solutions done and realizing the need for systematic calculations Reflect on provisional conjectures or use further specialization to check conjectures