Mathematical Higher Order Thinking Research Articles

Dakota/Lakota Math Connections: an epistemological framework for teaching and learning mathematics with Indigenous communities and students

Tribal colleges/universities have and continue to seek out connections between the local heritage and culture and the mainstream education content. In math, calls for culture to be more integrated into the classroom have been met with epistemological challenges as well as a dearth of math and local culture resources. The Dakota/Lakota Math Connections research project addresses both of these challenges. This article will specifically share the collaborative development, pilot, evaluation, and confirmation of an epistemological framework for curriculum development in both the math and language classrooms at Sitting Bull College. Following an Indigenous research paradigm focusing on relationality and relational accountability, the co-authors gathered a group of tribal college math instructors, Lakota language immersion teachers, and fluent elders. Altogether they experienced, evaluated, and confirmed the Dakota/Lakota Math Connections framework as a path for teaching and learning mathematics with Indigenous communities and students. Using an Indigenous research paradigm led to circular, reciprocal research questions for this article: In what ways, if any, did the framework impact the participants? In what ways, if any, did the participants influence the framework? The framework includes four major components (Western Math, Dakota/Lakota Math, the English language, and the Dakota/Lakota language) and the intersections among each component. The framework builds from the assumptions that language is intimately tied with culture and identity and that higher order mathematical thinking is embedded within Dakota/Lakota language and culture. This is based on the assumption that all cultures “do” math. The framework asserts that math fluency and Dakota/Lakota language fluency can grow together. The Dakota/Lakota Math Connections framework lays an epistemological pathway for Dakota/Lakota students to see their culture, identity, and language in the math curriculum as well as for math instructors to honor the call to connect the math classroom with the local heritage and culture.

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.

Investigating the presence of mathematics and the levels of cognitively demanding mathematical tasks in integrated STEM units

Effective K-12 integrated STEM education should reflect an intentional effort to adequately represent and facilitate each of its component disciplines in a meaningful way. However, most research in this space has been conducted within the context of science classrooms, ignoring mathematics. Also missing from the literature is research that examines the level of cognitive demand required from mathematical tasks present within integrated STEM lessons. In order to seek insight pertaining to this gap in the literature, we sought to better understand how science teachers use mathematics within K-12 integrated STEM instruction. We used an explanatory sequential mixed methods research design to explore the enactment of mathematics in integrated STEM lessons that focus on physical, earth, and life science content. We first examined 2030 sets of video-recorded classroom observation scores generated from the 10-item STEM Observation Protocol (STEM-OP) designed for observing integrated STEM education in K-12 classrooms. We compared the STEM-OP scores of classroom observations that included mathematics with those that did not. This quantitative analysis was followed by a closer, more in-depth qualitative examination of how mathematics was employed, focusing on the degree of cognitive demand. To do this, we coded and analyzed transcripts from video-recorded classroom observations in which mathematical content was present. Our study yielded two main findings about mathematics in integrated STEM lessons: (1) the presence of mathematical content resulted in higher STEM-OP scores on nearly all items, and (2) mathematical tasks within these lessons were categorized as requiring mainly low levels of cognitive demand from students. This study highlights the need for the increased inclusion of mathematical tasks in integrated STEM teaching. Implications for including higher-order mathematical thinking within integrated STEM teaching are discussed.

The Implementation Of Feedback In Means-Ends Analysis Of Student's High-Level Mathematic Thinking Ability

This research goals is to apply learning by using the Means-Ends Analysis model with direct corrective feedback to hope that higher-order thinking skills and students' self-efficacy can increase. Researcher used mixed method with sequential designs. Result of this research obtained means-ends analysis with a quality direct corrective feedback on achievement of learners’ higher order mathematical thinking skill. This research population was class VIII MTs Ma'arif 20 Kalidadi in the first Semesters for the 2020/2021 Academic Year. Sampling using cluster random sampling technique, which is randomly selected two classes from the population. Higher order thinking ability with high self-efficacy category shows that subject 1 has shown that answer has reached indicators of analyzing then evaluating but has not seen achievement of indicator of creativity.High-order thinking skills with moderate self-efficacy category indicate that subject 2 has shown that the answer had reached the indicators of analyzing and evaluating but has not seen achievement of indicators of creativity; Higher order thinking skills with high self-efficacy category indicate that subject 3 does not show the answer, has reached the indicators of analyzing, evaluating then creating and at evaluation stage there is no correct answer to complete answer to the end. This can also be seen in the interview stage which shows that subject 3 cannot give the right reason.

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

KETERAMPILAN BERPIKIR MATEMATIS TINGKAT TINGGI SISWA MADRASAH ALIYAH DITINJAU DARI GENDER DAN STATUS SEKOLAH

This study examines higher order mathematical thinking skills in terms of differences in school status (public and private) and gender differences (male and female). All madrasah aliyah students in the city of Yogyakarta became the subject of this research population. The sample subjects of this study were 83 students from one public school and four private schools which were selected using a stratified sampling technique. The Higher Order Mathematical Thinking Skills Test became the instrument in this study. Two-way analysis of variance is the technical data analysis used in this study. This study concludes that students' high order mathematical thinking skills are still low. This study also concluded that there was no difference between the higher order mathematical thinking skills of public madrasah aliyah students and private madrasah aliyah students and there was no difference between the higher order mathematical thinking skills of female and male students. Another conclusion is that there is no interaction between school status and student gender on higher order mathematical thinking skills .

Problem-based learning: Its effect on higher-order mathematical thinking skills in terms of student's initial abilities and mathematical beliefs

The higher-order thinking ability of students in Indonesia is still in the low category. This research aims to see the effect of the application of a problem-based learning model on higher-order mathematical thinking skills in terms of student's initial abilities and mathematical beliefs. This research uses a quasi-experimental design with a Non-Equivalent Control Group Design. Data on students' higher-order mathematical thinking skills were taken using a test instrument. This research was conducted at SMP Negeri 27 Jakarta with a total of 165 students obtained from cluster random sampling. Based on the analysis of the three-way ANOVA test, it was found that the problem-based learning model had a positive effect on students' higher-order thinking skills. Problem-based learning model gives better results than conventional learning models. This also applies to students with the initial ability and mathematical beliefs in the high category. Problem-based learning can be an alternative for teachers to improve students' higher-order mathematical thinking skills.

Exploring Students’ Learning Strategies and Self-Regulated Learning in Solving Mathematical Higher-Order Thinking Problems

<p style="text-align:justify">Considering the low achievement of Indonesian students in international studies (PISA), which measures Higher-Order Thinking Skill (HOTS) in solving the problem, improving the quality of mathematics learning in Indonesia is very important. The purpose of this research was conducted to explore the variations in students’ learning strategies and students’ Self–Regulated Learning (SRL) in solving mathematical HOT problems. The study employed a mixed-method, namely quantitative and qualitative methods were applied through five tests and seven interviews for over eight weeks. Two types of instruments were employed in this study, and they include tests and interviews. At the initial stage, we randomly selected 30 students from all those in grade 10 (Senior High School ), after which 12 were chosen purposively after the pre-test for an interview, having satisfied all complete group, middle group, and lower group. All of them were treated using metacognitive questions. Data analysis techniques used were percentage, data reduction, presentation, and conclusion. The quantitative results showed the students could generally use orientation, organization, and elaboration learning strategies as observed with 68.3%, 60%, and 56.7% for complete, middle, and lower groups. Moreover, the students were also observed to have conducted three cognitive processes in selecting the rules for solving the mathematical HOT problem, namely using models and drawing, written texts, and combining both. Furthermore, their final solution failures were affected by their misconceptions and errors in creating the mathematical model. The interview results on designing the learning procedures, monitoring the progress, and evaluating the outcomes, show that the students’ SRL level is good for complete (89.3%), middle (75%), and lower groups (60.7%).</p>

Improving students’ higher order mathematical thinking skills in accelerated classes through purdue learning model

The acceleration program is a positive alternative for intellectually gifted students to obtain relevant education with their potential to develop optimally. The purpose of this study was to improve higher order mathematical thinking skills (HOMTS) in accelerated class students through the Purdue learning model. The research was conducted at one of the state junior high schools in Tangerang Selatanfor the 2016/2017 academic year. The research method was Classroom Action Research (CAR) in two cycles. Data were collected using observation sheets, daily journals, and tests. The results revealed that the application of the Purdue learning model could increase the average HOMTS of 63.75 in the first cycle to 74.25 in the second cycle. The improvement of HOMTS includes aspects of analyzing, evaluating, and creating. Student activities including visual, oral, writing, drawing, motor, mental and emotional also increased in the very good category. In addition, the results of the study also revealed that most students gave positive responses to the Purdue learning model. The conclusion of this study is that the application of the Purdue model in mathematics learning can improve HOMTS, activities, and students’ positive responses.

Distribusi Kemampuan Berpikir Matematik Tingkat Tinggi pada Siswa Sekolah Menengah Atas Kota Tasikmalaya Tahun Pelajaran 2018/2019

ABSTRACT This study aims to determine the distribution of higher-order mathematical thinking skills of students of state senior high schools in Tasikmalaya City in the academic year 2018/2019, to find out whether there is a relationship between mathematical critical thinking abilities with students' mathematical creative thinking skills High School in Tasikmalaya City 2018/2019 academic year. This research is a type of descriptive research using quantitative descriptive methods. The population in this study were all students of Tasikmalaya City Senior High School in class X, class XI, and class XII, ranging in age from 16-18 years. The sampling technique in this study uses a probability sampling technique that is Proportionate Stratified Random Sampling, by taking 2 classes each school. The research instrument used in this study was a matter of high-level mathematical thinking ability tests which are slices of the cognitive dimension of Bloom's Taxonomy with the 2013 Curriculum Dimension dimension consisting of questions of critical and creative thinking skills. The results showed that the distribution of mathematical thinking ability levels in high school students in the City of Tasikmalaya academic year 2018/2019 as follows: a) mathematical HOTS ability with a very good category was obtained by 2 Schools or 20% of all High School Schools in Tasikmalaya City, the ability Mathematical HOTS with the good category is obtained by 7 Schools or 70% of all High Schools in Tasikmalaya City, Mathematical HOTS ability with a pretty good category is obtained by 1 School, namely SMAN J or 10% of all Public High Schools in Tasikmalaya City. There is a significant relationship between students' mathematical critical thinking skills with the mathematical creative thinking abilities of high school students in the City of Tasikmalaya 2018/2019 academic year. with the degree of correlation obtained a correlation coefficient of 0.283 or are in a low category. Keywords: Higher Order Mathematical Thinking Skills, mathematical critical thinking skills, mathematical creative thinking skills.

Capability Estimation of Student's Higher Order Thinking in Mathematics by Using Polytomous

One of the alternative approaches in the scoring of items that can be used is the Latent Trait Theory Approach for polytomous scoring with a Generalized Partial Credit Model (GPCM). This study aimed at estimating the test taker’s capability to think critically (higher order thinking) in maths in the form of essay questions with items scoring in GPCM by considering the level of difficulty in each of the steps that must be taken to obtain the correct answer. The instrument used in this study was essay question developed. The data analysis used in this study was SPSS version number 22 and Parscale from Ssi. SPSS version number 22 was used to detect the sufficiency requirements of the number of samples used and prerequisite analysis of scoring using the GPCM method. Parscale was used to estimate the capability of respondents. The estimation of capability was presented in Phase 3 on a scale (-4, +4) in which, then, it can be transformed with a linear transformation to the equation x = 12,5θ + 50, x is the estimation of capability in the range of [0,100]. The result of capability estimation was in the range of [0,100] so that it was obtained the minimum capability estimation 49.36 and maximum 100.

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.

Professional Learning Interventionn in Mathematics: A Case of Developing Portfolio Assessment

: This paper reports findings from a Fijian study that engaged secondary mathematics teachers in a two-day professional development workshop on the use of portfolios as an alternative means of assessing student learning in mathematics. Utilising an action research approach with a view to involve teachers as key stakeholders in mathematics education, the professional development prompted a small group of secondary mathematics teachers to think about the mathematics content and processes which could not be assessed using written tests, and to develop assessments that would reflect higher-order thinking in mathematics. While the majority of the teachers came up with ideas that were well suited for portfolio assessment, some participants faced minor difficulties in relating to real-world experiences and developing higher-order tasks. Teachers were able to come up with teaching and learning activities that could be used for portfolio assessment. At the end of the workshop ten of the 12 teachers were interviewed to gain an insight into their experiences. All of them stated explicitly that they had found the workshop very useful and rewarding because portfolios could provide an alternative way to assess student learning, and could possibly influence the way they taught mathematics.

Sdrawkcab scitamehtam: The case for understanding mathematics backwards

Despite the widespread acknowledgement of the need for graduates with quantitative problem-solving skills, many students enter university having relied heavily on pattern recognition techniques for high school mathematics. While these can often lead students to obtaining correct solutions for problems similar to those which they have practised, they do not lead to a deeper understanding of the material and, critically, may not develop more widely-applicable skills. Even when correct solutions are obtained, students can sometimes not understand or explain why their solution is indeed correct. Here, I present an argument in favour of avoiding predictability in question structures and, in particular, asking questions ``backwards'' to how they might traditionally be asked. Some mathematical topics readily lend themselves to such approaches --- the Fundamental Theorem of Calculus tells us that an integral problem is inherently linked to an antiderivative problem --- whereas other require much more care and subtlety to avoid routine or predictable assessments. I will discuss some preliminary results from a first year probability subject at the University of Technology Sydney (UTS) which suggest that student understanding of material can be increased when they feel that prioritising pattern recognition over problem solving is unlikely to be rewarded with high marks. References Khan academy. expected value. URL: https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/e/expected_value . Mark Asiala, Anne Brown, David J. Devries, Ed Dubinsky, David Mathews, and Karen Thomas. A framework for research and curriculum development in undergraduate mathematics education. Maa Notes, pages 37–54, 1997. I. 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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.

Developing Learning Model Based on Local Culture and Instrument for Mathematical Higher Order Thinking Ability

This research aims to develop a student-centered learning model based on local culture and instrument of mathematical higher order thinking of junior high school students in the frame of the 2013-Curriculum in North Sumatra, Indonesia. The subjects of the research are seventh graders which are taken proportionally random consisted of three public junior high schools with 86 students and two private schools with 40 students. As a Developmental Research, the work is done within three stages. The results obtained in the second stage, both learning tools (books of students, teachers, and students’ activities sheet) and research instruments are valid with minor revisions, and the results of the trial showed that the reliability scores of the tests comprising of Comparison (MAT-1), Social Arithmetic (MAT-2), Triangle (MAT-3), Quadrilateral (MAT-4), and Transformation (MAT-5) respectively 0.835, 0.588, 0.438, 0.833, and 0.908. The findings showed that the student-centered learning based on local culture model and the instrument for higher order mathematical thinking ability are valid and effective to use in teaching mathematics for junior high school.

Curriculum Interventions for Area Measurement Instruction to Enhance Children’s Conceptual Understanding

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children’s ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional geometry. Participants were 131 fourth graders, recruited from a city in northern Taiwan, and 1 instructor. The results confirmed the effectiveness of an enriched curriculum integrating knowledge of 2-dimensional geometry in enhancing children’s conceptual understanding of area measurement. The group that received the enriched curriculum outperformed the other groups that received the curricula stressing only 2-dimensional geometry or numerical calculations for area measurement in solving the area problems requiring mathematical judgments and explanations. The curriculum also facilitated children’s reasoning in distinguishing between the perimeter and area of a rectangle, which required higher-order mathematical thinking. Interview data revealed that approximately all children from the 3 intervention groups could identify the mathematical subject-matter components highlighted in the curricula. Interviewees tended to consider the use of formulae to solve area measurement problems to be important, despite some differences in learning gains among the 3 groups. In interviews, the participating instructor revealed a change of perspective regarding the importance of offering students opportunities for manipulation and geometric operations when teaching area measurement, prompted by curriculum enactment.

Design of learning objects for concept learning: effects of multimedia learning principles and an instructional approach

Literature suggests using multimedia learning principles in the design of instructional material. However, these principles may not be sufficient for the design of learning objects for concept learning in mathematics. This paper reports on an experimental study that investigated the effects of an instructional approach, which includes two teaching techniques – (a) variation theory and (b) representations of subject matter – on the design of learning objects for secondary school algebra concept learning. The results of this study showed that the experimental group performed significantly better than the control group on algebra learning achievement. The results also showed that only the experimental design with the addition of the instructional approach resulted in higher-order mathematical thinking skills and improved procedural skills of the students. Further analysis reveals that concept learning was simplified when multimedia learning principles were applied and the information was presented by the instructional approach.