Higher Order Thinking Skills In Mathematics Research Articles

Development and validation of Mathematical Higher‐Order Thinking Scale for high school students

AbstractGlobally, significant attention is given to the cultivation and evaluation of Mathematical Higher‐Order Thinking Skills (MHOTS). This study aims to address the gap in developing and validating suitable MHOTS structures for high school students. In this study, 53 items were determined by experts in the field of mathematics education and scale development. The study group of this study consists of 654 students educated at the high school level. We decided to split the samples randomly in two by designating a random half as exploratory factor analysis (EFA) and the other half as confirmatory factor analysis (CFA). EFA was used to confirm a robust “four‐dimensional, nine‐factor” measurement structure, encompassing four key dimensions, namely mathematical critical thinking, mathematical creative thinking, mathematical problem‐solving, and mathematical metacognitive skills. The scale's quality was assessed through a retest using CFA and the structural validity was evaluated through CFA and correlation analysis. The criterion validity of the scale was also examined using math scores. The results from the double validity analysis showed that the scale had a reasonable and valid structure. The findings established the MHOTS for high school students as a reliable and valid instrument for measuring the level of MHOTS among high school students. This newly developed scale holds promise as an effective tool to assess and enhance mathematical higher‐order thinking in the student population.

Algebra essay questions: A validated instrument for evaluating the students' higher-order thinking skills

Indonesian pupils need help solving problems, particularly in mathematics, due to the need for practice questions with the higher-order thinking (HOT) type. This research aims to develop a reliable and valid tool for assessing students' higher-order thinking skills in mathematics. Developing a test involves gathering requirements, creating questions, assessing answers, running trials, analyzing data, making adjustments, and finally putting everything together. The instrument trial was conducted at SMAN at Majalengka, West Java. The total number of test subjects was 32 students. Research data were collected using a description test. The test instrument consists of 10 descriptions, but only 6 had good validity based on the value of V on the V-Aiken. In addition, the test package produces reliable questions based on Cronbach's Alpha scores. The test results of the instrument showed that the HOTS of mathematics for Grade X students was good. This step provides an overview to teachers in designing valid and relevant instruments.

Assessing Mathematical Higher-Order Thinking Skills: An Analysis of Turkish University Entrance Examinations

ABSTRACT Internationally, mathematics education reform has been directed toward characterizing educational goals that go beyond topic/content/skill descriptions and develop students’ problem solving. The Revised Bloom’s Taxonomy and MATH (Mathematical Assessment Task Hierarchy) Taxonomy characterize such goals. University entrance examinations have been seen as one way of accomplishing these goals and influence learning, teaching, and assessment in mathematics. The present study analyzed mathematics items (N = 1077) in Turkish university entrance examinations in 1998-2013 and objectives (N = 621) in mathematics curricula in 2005, 2011, and 2013 to determine the extent to which they represent the dimensions/categories of these taxonomies and the degree to which items are aligned with objectives in terms of reflecting the dimensions/categories of these taxonomies. The findings reveal that the items demand, to a large extent, automated computational skills; this is also evident in the relevant mathematics curricula. Implications for practice are discussed and could play a role in reforming assessment.

Development of Interactive Student’s Worksheets to Improve Mathematical HOTS of Tenth Grade Students in Trigonometry Topic

It is undeniable that Higher Oder Thinking Skills (HOTS) have become the center of attention and essential skills needed, especially in mathematics today, but there are so many research shows that the average thinking ability of Indonesian students is still low. One of the student's low thinking abilities cause is teaching materials that still dominated by questions in the Low Order Thinking Skills (LOTS) category. Therefore, this study aims to develop valid, practical, and effective interactive student worksheets to improve tenth-grade students' higher-order thinking skills. This research used Research and Development (R&D) designs and methods guided by the ADDIE development model with five steps: Analysis, Design, Development, Implementation, and Evaluation. The data obtained from this study is quantitative and qualitative data, which was obtained from the interview, validation test sheet, students and teacher response sheet and pretest-posttest result. The assessment from experts from both the material and media shows that the worksheet is valid with 4.30 and 3.97 average scores. Furthermore, based on the questionnaire responses of teachers and students with the "Excellent" score category, it shows that the developed interactive student worksheet is practical. The interactive student worksheet is also effective in improving mathematical HOTS of tenth-grade students since there is a significant increase in students' mathematical higher-order thinking skills based on student learning outcomes with 0.64 value of N-Gain. Besides the N-Gain, the students' response through the learning after using the interactive worksheet was also in the "Excellent" category, with an average score of 4.54 in the small trial and 4.27 in the field trial. Therefore, this study has produced a valid, practical, and effective interactive student worksheet to improve tenth-grade students' mathematical Higher Order Thinking Skills (HOTS).

PROFIL HIGHER ORDER THINKING SKILLS MATEMATIS PESERTA DIDIK KELAS VIII SMP

This study aims to describe the mathematical higher-order thinking skills of eighth-grade students in junior high school. This research is descriptive research with a qualitative approach. The research subjects were 2 students of class VIII SMP Negeri 1 Palu. Data collection techniques include tests and interviews. The results obtained indicate that at the level of analytical thinking, students only apply problem-solving procedures without analyzing (C4) the principles that are relevant to the given problem. At the level of evaluating thinking (C5), students can provide valid arguments in verifying the given problem. While at the creative thinking level (C6), students cannot find work ideas to solving the problems presented

Characteristics of problems for developing higher-order thinking skills in mathematics

A large number of studies in the literature have illuminated the issue of higher-order thinking skills with different perspectives. The purpose of the study was to establish a synthesis of the literature on the theoretical basis of higher-order thinking skills in mathematics learning. This study reviews and analyses all resources, including articles published in academic journals and books. Based on a content analysis of selected resources, this article formulates a definition of higher-order thinking skills and proposes ten substantial characteristics of problems for developing students’ higher-order thinking skills in mathematics learning. The present study makes several significant improvements to the field of mathematics education by providing a framework for test construction and an agenda for future research.

Two-Level Model of Attitudes and Beliefs Influencing Higher Order Thinking (HOT) Skills in Mathematics

Abstract This article focuses on a two-level model analysis of attitudes and beliefs affecting students’ higher order thinking (HOT) skills in mathematics in Aceh, Indonesia. The data used are nested within the hierarchical ordering of both student (level 1) and teacher (level 2). The variables used at level 1 in the study include liking mathematics, valuing mathematics, confidence in mathematics, and individual judgement of mathematics ability, as well as beliefs concerning mathematics related to lower order thinking (LOT) and higher order thinking (HOT). The variables at level 2 involve beliefs concerning mathematics teaching related to LOT and beliefs concerning mathematics teaching related to HOT. The analysis reveals that there are four variables at level 1 contributing to student HOT skills in mathematics: liking mathematics, individual judgement of mathematics ability, beliefs concerning mathematics related to LOT, and beliefs concerning mathematics related to HOT. At level 2, the one variable affecting student HOT skills in mathematics is teacher beliefs concerning mathematics related to HOT.

Influence Of 7 Sunnah Improves Higher Order Thinking Skills Of Indonesian Students In Mathematics

The quality of mathematics education in Indonesia is of great concern. This is proven based on the survey results conducted by international survey institutions such as PISA and TIMSS and national survey institutions such as ACTION. This conclusion is strengthened by the fact that the UN scores for junior high and high school levels have decreased. Improving the quality of mathematics education in Indonesia, especially among Muslims, research on the relationship of students' persistence in performing worship with their high-level thinking skills was conducted. The purpose of this research is to (1) Formulating the application of the 7 Sunnahs of the Prophet Muhammad S.A.W. in mathematics using Higher-Order Thinking Skills (HOTS). (2) Analyzing the effect of implementing the 7 Sunnahs of the Prophet Muhammad S.A.W. in improving students' higher-order thinking skills/HOTS. (3) Analyzing the practice of worship that is most influential in the implementation of the 7 Sunnahs that affect the higher-order thinking skill/HOTS.
 This study uses a quantitative approach with data collection techniques through in-depth interviews, surveys, questionnaires, and documentation. The data is processed and analyzed using a computer as a tool and using the SPSS 16 for Windows program to determine the correlation of existing data. The research resulted in (1) A model of implementing the 7 Sunnahs in mathematics learning. The lesson begins with reciting surah Al-Fatihah, praying to the prophet, praying before studying, reciting Asmaul Husna, and reciting short surah in the Quran and ends with the advice to motivate students to be persistent in carrying out worship. (2) The implementation of the 7 sunnah that has significant influences is tahajud pray while the achievement of the competition that has a significant influence are KMNR competition, OSN competition, and International competition (3) The implementation of the 7 Sunnah that has significant influences are congregational pray, Dhuha prays, almsgiving, reading the Qur'an, sunnah fasting and maintaining ablution. This study found that the spiritual activity approach influenced improving students' higher-order thinking skills in mathematics. This learning model can be used in various non-formal educational institutions with having the same vision. This learning model can also be applied in formal education after being adapted to the situation and conditions of the school.

THE ROLE OF CONSTRUCTIVISM-BASED LEARNING IN IMPROVING MATHEMATICAL HIGH ORDER THINKING SKILLS OF INDONESIAN STUDENTS

To make students actively involved in learning to grasp mathematical higher-order thinking skills (MHOTS) is not easy. Meanwhile, the ability is so important for students to master for it takes place when students continue their studies to a higher level or work within a variety of professions, especially in the era of industrial revolution such nowadays. Many factors affect students' thinking abilities, including learning factor. This study, which implemented constructivism-based learning, aims to investigate the role and contribution of constructivism-based learning approaches as well as mathematical prior knowledge (MPK) to the achievement of MHOTS of middle secondary school students. The data tested through Multivariate Analysis at the 0.05 significance level. In general, this study found that: (1) In the experimental class, learning approach plays an important role in the way it increased students' MHOTS significantly. (2) The average contribution of constructivism-based learning to MHOTS was at the range 18% to 57%. (3) Student activity in learning increased significantly. (4) In some cases, there is an effect of interaction between learning factors and MPK towards the achievement of MHOTS. The study recommended the teachers to have courageous to implement constructivism-based teaching learning in order to improve students’ MHOTS.

Learning Approach and Soft-skills Contribution toward Mathematical Higher Order Thinking Skill of Junior High School Students

Life skills such as social skill and emotional quotient recognized as soft-skills. Indonesian students soft-skills such as generous and helpful tends to decrease time to time which considered to threat nation character. Meanwhile, many researchers reported soft-skills is a dominant factor to determine one successfulness in life. Moreover, many hypothesize that it contributes much on mathematical higher-order thinking skills (MHOTS). Therefore, this research took place to help students keep and enhance their aspects of soft-skills. This quasi-experiment research applied constructivism-based learning at a public junior high school. Instruments used to collect data on soft-skills were questionnaire, interview, and observation. An essay test was administered to get data on students MHOTS. The data then analyzed using t-test and variance analysis. The findings showed that: (1) Learning approach contribute significantly toward student mathematical high order thinking skills as much as 57.4%. Constructivism learning approach gives more influence to the students student mathematical high order thinking skills than direct instruction, (2) Student soft-skills contributed only 29.9 % (categorize low) toward mathematical high order thinking skills. However, student soft-skills in the guided discovery classroom is better than its counterpart in the direct instruction classroom, (3) Learning approach and soft-skills simultaneously influence significantly toward student mathematical high order thinking skills. Therefore, it is recommended that teachers not only focus on the cognitive development of students but must care about the development of affective aspects as well.

Computer-based assessment of mathematics into the twenty-first century: pressures and tensions

In recent decades, technology has influenced various aspects of assessment in mathematics education: (1) supporting the assessment of higher-order thinking skills in mathematics, (2) representing authentic problems from the world around us to use and apply mathematical knowledge and skills, and (3) making the delivery of tests and the analysis of results through psychometric analysis more sophisticated. We argue that these developments are not pushing mathematics education in the same direction, however, which creates tensions. Mathematics education—so essential for educating young people to be creative and problem solving agents in the twenty-first century—is at risk of focusing too much on assessment of lower order goals, such as the reproduction of procedural, calculation based, knowledge and skills. While there is an availability of an increasing amount of sophisticated technology, the related advances in measurement, creation and delivery of automated assessments of mathematics are however being based on sequences of atomised test items. In this article several aspects of the use of technology in the assessment of mathematics education are exemplified and discussed, including in relation to the aforementioned tension. A way forward is suggested by the introduction of a framework for the categorisation of mathematical problem situations with an increasing sophistication of representing the problem situation using various aspects of technology. The framework could be used to reflect on and discuss mathematical assessment tasks, especially in relation to twenty-first century skills.

Analisis Peningkatan Kemampuan Representasi Matematis Siswa SMA Ditinjau dari Perbedaan Gender

Mathematical representation is one of the mathematical higher order thinking skills, as a tool or way of thinking in communicating mathematical ideas. Referring to a research about the inconsistency of a mathematical communication profile involving gender differences and the phenomenon of more female students than men right now, there appears to be an allegation that there is a connection between gender differences and students mathematical representation. The purpose of this study is to analyze the improvement of students' mathematical representation capability in terms of gender differences. Subjects in this research were students of class X of High School in Medan, Indonesia, consisting of 13 men and 19 women. The research instrument is a mathematical representation test consisting of 4 questions. Data analysis to find out how the category of improvement of students’ mathematical representation, using index of N-gain. The results of the research are: (1) the improvement of mathematical representation ability in the lower and middle categories of male students is higher than female students, (2) there is no male students have high category mathematical representation, but there are female students have high category mathematical representation abilities, and (3) the ability of representation to make mathematical models and explain the verbal language of male students is higher than female students. While the representational ability of making tables and drawing female students is higher than male students. The implication of the research is needs to do deeper research to see the relationship of mathematical representation ability with the students' mathematical ability profile.

Effectiveness of Non-Traditional Activities to Develop the Mathematical Higher Order Thinking Skills of Grade-Seven Students

Developing critical thinking and problem solving skills of students are some of the important goals that every school must set. This study determined the effectiveness of non-traditional activities to develop mathematical higher order thinking skills of grade seven students. This study employed the non-equivalent control group experimental design, which involved 83 grade 7 students of Sawata National High School. There were two sections used in this study, the control group which the researcher used the traditional lecture activity and the experimental group, were the students exposed to non-traditional activities: manipulative activities, computer-aided activities, and reflective writing activities. The specific subject matters covered were the second-grading mathematics seven topics which are measurement and measuring of length, measuring mass/weight and volume, and measuring angles, time and temperature. The data were gathered using the multiple choice teacher's made test in the pre-test and post-test. Prior to the study, the higher order thinking skills of the two groups had no significant difference. The result changed after the treatment was given. The study concludes that the used of non-traditional activities were effective over the traditional activity in the development of the higher order thinking skills of the students. The study recommends integration of non-traditional activities to develop the higher order thinking skills of the students.

Teachers’ Perceptions and Classroom Application of Mathematical Computer Software

Mathematics teachers from elementary and secondary school settings reported that the main advantage of instructional software pertained to enhancing students’ motivation and educational experiences, whereas the main disadvantage pertained to the poor content and sequencing of much of the available software. Teachers typically used software as a supplemental activity but wanted more programs that encouraged students’ cognitive reasoning, problem-solving and higher-order thinking skills in mathematics. These findings support the notion that although use of computer software has the potential to motivate, provide practice, and facilitate students’ learning and thinking in mathematics, students still require appropriate teacher-led instruction to enhance their mathematics knowledge as they interact with the software.