The Relationship between Higher Order Thinking Skills and Academic Performance of Student in Mathematics Instruction

Higher order thinking skills (HOTS) is one of important aspects in education. Students with high level of higher order thinking skills tend to be more successful. However, do this phenomenon also happen in the learning of Mathematics? To answer this question, this research aims to study the relationship between HOTS and students' academic performance in Mathematics instruction. The research is conducted by occupying correlation research method on 41 students of mathematics education in university of Papua who had already completed 120 credits. The instrument in a test format for HOTS measurement has two main indicators; the critical thinking skill and creative thinking skill. Students are selected as research subjects, and are asked to do 9 questions of HOTS test in 60 minutes. The holistic rubric is used to assess the higher order thinking skills of students. The results of research show that these two variables have a high value of correlation (r = 0.814) and the regression equation is grade point average = 2,105 + 0,017 HOTS. Both of statistics show that there is a significant relationship between HOTS and students' academic achievement.


Introduction
Human thinking skills can be classified into two major groups; low-order thinking skills (LOTS), and higher order thinking skills (HOTS).LOTS are the first three aspects of taxonomy bloom, which are remembering, understanding, and applying.HOTS are the last three aspects of taxonomy bloom namely analyzing, evaluating, and creating (Moore & Stanley, 2010).In other words, HOTS is the highest part in Bloom's taxonomy of cognitive domain.
HOTS are important aspects in teaching and learning.Thinking skills are fundamental in educational process.A person's thought can affect the ability, speed and effectiveness of learning.Therefore, thinking skills is associated with learning process.Students who are trained to think demonstrate a positive impact on the development of their education.Students with HOTS are able to learn, improve their performance and reduce their weaknesses (Yee, Othman, Yunos, Tee, Hasan, and Mohammad, 2011).
According to Kings, Goodson, and Rohani (2013), HOTS are the ability to think that not only requires the ability to remember, but also higher capabilities.HOTS are student's abilities that are activated when students encounter unfamiliar problems, uncertainties, questions, or dilemmas.Moreover Pogrow (2005) states that HOTS are valued because they are believed to prepare students better for the challenges both in advanced academic life and adult's work and responsibility in daily basis.Therefore, HOTS can be used to predict the success of a student.Students who have good level of HOTS are expected to succeed in their studies later.
Various efforts have been made by some researchers to improve HOTS students in some countries.Foong (2000) in Singapore conducted research on open-ended problems for higher order thinking in mathematics.In Georgia, Murray (2011) examines the implementation of higher order thinking in the middle school mathematics classrooms.The other research is conducted by Ghasempour, Kashefi, Bakar, and Miri (2012) in Malaysia on higher order thinking via mathematical problem posing tasks among engineering students, while Tajudin (2015) studies mathematical knowledge and higher order thinking skills for teaching algebraic problem solving in Turkey.
Furthermore, there are several other studies that investigate the relationship between HOTS and academic performance of students.Yee et al. (2011), concludes that there is a very low positive relationship between the level of Marzano HOTS with gender, academic achievement and socio economic status.Consequently, students should be assisted to acquire HOTS; either through the conventional teaching and learning environment or a selfinstructional, individualized manual.On the other hand, Ramos, Dolipas, and Vilamor (2013) examines the relationship between HOTS and academic performance in physics of college students, and concludes that HOTS level on analysis, comparison, and evaluation significantly influence the physics performance of male students, while the HOTS level on analysis, inference, and evaluation significantly influence the physics performance of female student.Yoshida (2015) concludes that task-specific coaching rubrics enhance learners' knowledge and understanding of curriculum development for higher-order thinking, and promotes learners' skills to develop a curriculum for higher-order thinking.
The problem arises is, is there is a relationship between HOTS and academic performance of students in mathematics instruction?How to measure HOTS of students who learn mathematics?What are the indicators of HOTS in mathematics instruction?Ramos et al. (2013), states that HOTS include skill such as creative and critical thinking, analysis, problem solving, and visualization.These skills involve categorizing items, comparing and contrasting ideas and theories, and being able to write about and solve problem.In the classroom, abilities and skills that include the use of HOTS are complex thinking that goes beyond basic recall of fact, such as evaluation and invention, enabling students to retain information and to apply problem-solving solution to real-world problems.Barak, David, and Uri (2007), stated that HOTS is composed of three components: critical, systems, and creative thinking, while according to Wang and Wang (2011), there are three main components in HOTS, i.e. critical thinking skills, thinking design and systems thinking.Based on these two statements, then the creative thinking skills proposed by Barak et al. (2007) similar to design thinking skills proposed by Wang and Wang (2011).Thus there are three components in HOTS, namely: (1) critical thinking skills, (2) creative thinking skills, and (3) systems thinking skills.Furthermore, Tanujaya (2014) in his analysis states that there are at least two indicators in HOTS, i.e. critical thinking and creative thinking skills.Moreover Tanujaya (2016) also asserts that there are nine factors that comprise HOTS in mathematics instruction; the use of mathematical concepts, the use of mathematical principles, impact predicting, problem solving, decision-making, working in the limits of competence, trying new things, divergent thinking, and imaginative thinking.Thus, there are at least nine items as test instruments used to measure HOTS.
Various test instruments have been developed by the experts to be used as a selection tool in order to get prospective students.One such instrument is an instrument to measure developed by Tanujaya (2016).Moreover, he said that the HOTS instruments can be used to measure HOTS of students in mathematics instruction, because the instrument has acceptable validity and reliability Therefore, some questions raised are: is there a relationship between HOTS and student performance in Mathematics?How strong is the relationship between HOTS and student performance?Is the relationship linear?To answer this question, it is necessary to investigate the relationship between HOTS and GPA in mathematics instruction.

Method
The study is conducted using correlation research method.Gall, Gall, and Borg (2007) claim that correlation research method is a specific type of non-experimental design used to describe the relationship between two or more variables.The study is a research to determine the relationship and the strength of relationship between two variables without manipulating the variables.Correlation research refers to studies in which the purpose is to discover relationships between variables through the use of correlational statistics.
Subjects for this research are 41 students of mathematics education from University of Papua, Manokwari West Papua Province, Indonesia.In this research, the subjects are mathematics education students who have completed 120 of 144 credits.In other words, they are most likely in their final year in Mathematics Education Department.The subject of research is selected using purposive sampling method.Purposive sampling, according to Etikan, Musa, and Alkassim (2016) is the deliberate choice of a participant due to the qualities the participant possesses.It is a non-random technique that does not need underlying theories or a set number of participants.Simply put, the researcher decides what needs to be known and sets out to find people who can and are willing to provide the information by virtue of knowledge or experience.
There are two variables used in this study; HOTS and GPA.HOTS are used as predictor variables, while the GPA as the criterion variable.Predictor variables according to Gall et al (2007) are measured before the criterion variable measured.The predictor variables are used to predict the criterion variables.
HOTS students are measured using test instruments, while the students' GPA obtained from mathematic education department, university of Papua.The instrument in a test format used in this study for HOTS measurement has two main indicators; the critical thinking skill and creative thinking skill.The instrument has 9 variables, consisted of 5 variables for critical thinking and 4 variables for creative thinking.Five variables used for measuring critical thinking skill are conceptual comprehension, principles comprehension, impact prediction, problem solving, and decision-making.Meanwhile, the other four variables for creative thinking skill are working in competence limit, coping with new challenges, having both divergence thinking pattern and lateral thinking pattern (imagination).
Students are selected as research subjects; they are asked to do 9 questions of the HOTS test during 60 minutes.The holistic rubric is used to assess the HOTS of students.The assessment is done based on the three major components; problem comprehension, procedure of problem solving, and the correct answers.
The data obtained from this study are students' test scores ranging from 0 to 111.This score is then converted into a value ranging from 0 to 100.The conversion is made because the range of scores commonly used is ranging from 0 to 100.Data resulted from the conversion was then statistically analyzed using correlation and regression analysis.Correlation is a statistical technique that measures direction and strength of the linear relationship between the two variables, while regression analysis is a statistical process for estimating the relationships among variables.The use of correlation and regression analysis in this research was to determine the relationship between HOTS and academic achievement of students in mathematics.Academic achievement used in this study is the GPA of Mathematics education students.
According to Moore, Notz, and Fligner (2013), the calculation of correlation coefficient (r) used the formula: while estimating equation regression is done by using the formula: (2) with slope: (3) and intercept:

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(4) Furthermore, Best and Kahn (1998) stated that there are a number of ways to interpret a correlation coefficient.The interpretation is depending on the research's purpose and the circumstances that may influence the correlation's strength.One method that was frequently presented crude criterion was presented on Table 1.In order to simplify the calculations, the data was analyzed using SPSS program package.SPSS is statistical package for social sciences.Therefore, the results of the data analysis presented in the form of SPSS modified output, and other results of the study were included in the following section. ies.ccsenet.

Descrip
Descriptiv statistics h form of so  Best and Kahn (1998), correlation coefficients is always a number between -1 and 1.Values of correlation coefficients near 0 indicate a very weak linear relationship.The strength of the linear relationship increases as r moves away from 0 toward either -1 or 1.Values of correlation coefficients are close to -1 or 1 indicates that the points in a scatter plot lie close to a straight line.Positive r indicates positive association between the variables, and negative r indicates negative association.The extreme values, where r = -1 and r = 1 occur only in the case of a perfect linear relationship, or when the points lie exactly along a straight line.
Table 3 shown that there is a strong positive relationship (r = 0.814) between the two variables, HOTS and GPA.Furthermore, on the test p-value, it shows a very strong evidence (p<0.001) to suggest that there is a linear correlation between the two variables, HOTS and GPA.Based on the correlation coefficient and the p value, it can be stated that the higher the HOTS, the higher the GPA will be.The higher the students' HOTS, the higher the GPA they will get.

Regression between HOTS and GPA
Regression analysis generates an equation to describe the statistical relationship between one or more explanatory variables and the response.Therefore, regression analysis is used to model the relationship between a response variable and one or more explanatory variables.In order to develop a regression equation, SPSS produces two types of coefficients, i.e. standardized coefficients and unstandardized coefficients as presented in the Table 4.The standardized coefficients are appropriate in multiple regressions when the explanatory variables were measured on different units.These coefficients are obtained from regression after the explanatory variables are all standardized.The idea is that the coefficients of explanatory variables can be more easily compared with each other as they are then on the same scale.In simple linear regression, they are of little concern.Therefore, the estimation of regression equation is done by using unstandardized coefficients (Best and Kahn, 1998).
Based on Table 4, the intercept is 2.105 and the slope is equal to 0.017.Thus, the regression equation that stated the relationship between GPA and HOTS are as follows: The model of regression analysis stated that for each increase of one unit in HOTS, the GPA value was expected to increase by 0.017 units.This statement implied that if two people have different HOTS value of 10, then they would have different GPA of 0.17.Based on the regression equation, it can also be predicted that a student who has a GPA of 70, his GPA is therefore equal to 3.295.
Furthermore, the standard errors on Table 4 are the estimation of the variability of the (unstandardized) coefficients and are used for significance tests for the coefficients.The t values and corresponding significance values are tests assessing the worth of the (unstandardized) coefficients.Based on Table 4 we can conclude that both test are highly significant (p<0.001),indicating that we have very strong evidence of need both the coefficients in regression model.Feasibility of the regression model also appears at the results of analysis of variance regression model as presented in Table 5.Table 5 shows model regression with a value of F is equal 76 633, and p value <0.001.The value of less than 0.05 implyes that there is sufficient evidence to reject the hypothesis (H 0 ).The null hypothesis tested in this study is two coefficients (slope and intercept) equal to zero.In other words, the coefficients do not equal to zero and can be used in the regression model.

Conclusion
Based on the results of research and discussion, we can conclude that there is a linear, positive and strong relationship between HOTS and the GPA of students.Students with high level of HOTS are expected to succeed in their next study in study program of mathematics education.Students who have high HOTS tend to get high GPA in mathematics instruction, whereas those with low HOTS tend to have low GPA.Therefore, the value of HOTS can be used as an indicator in the selection of new students.
In order to thrive in learning mathematics, mathematics education students should have high level of HOTS.One of the most important things that can be done to improve students' HOTS is by revising textbooks used in mathematics learning in primary and secondary schools.

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Table 1 .
Criteria for the relationship between the two variables using coefficient correlation

Table 3 .
Correlation between variables HOTS and GPA

Table 4 .
Coefficient of the estimated regression model of GPA and HOTS

Table 5 .
Analysis variance of Regression between HOTS and GPA The mathematics textbooks used in Indonesia should promote students' critical and creative thinking.Examples and practice tests provided should be able to train students to think critically and creatively by using open-ended test.The open-ended test is a test used as an instrument in this study to measure students' HOTS.