Rigorous Mathematical Thinking Research Articles

Metacognitive Self-management in Developing Students' Rigorous Mathematical Thinking Skills

This study aims to describe the metacognitive self-management of students in developing rigorous mathematical thinking. This study uses a qualitative method with a case study approach. The participants were three students from the thirdlevel mathematics education department, who were selected and made a contract with for real analysis lectures. The first student experienced a significant change from the beginning of the meeting, resulting in the metacognitive self-management process being well-conditioned. He completed the task more confidently than the initial presentation, used several references and sources of information to complete the job, and represented each answer in the form of mathematical symbols. This studentscognitive function appears to be of level-1, with qualitative thinking. For the 2nd student, a change was observed in the learning process and the teacher’s motivation and guidance. The results of the interviews showed that the student applied strategies in completing assignments. He answered them systematically, based on experience, and mastered the prerequisite material. This student showed improved thinking skills related to mastery of concepts from new material, analyzing the problems given, being critical and focused when answering, and looking hard to get maximum evaluation results. This 2nd student entered the level of quantitative thinking with precision. Lastly, in the 3rd student, self-management seems stable, but was still lacking in adjusting the understanding of prerequisites with understanding concepts from new material. The development during the learning process shows that he can activate his mathematical knowledge, compose logical proofs of Real Analysis material problems, and build relationships between prerequisite concepts and new material. This type of student enters the level of abstract relational. The results of the study can be a reference for teachers to determine the learning model and the related instruments, so that they can grow the level of mathematical thinking before, during, and after the learning process. Keywords: Metacognitive, self-management, Mathematical thinking skill

PENGARUH RIGOROUS MATHEMATICAL THINKING TERHADAP KEMAMPUAN LITERASI MATEMATIKA SISWA KELAS VII SMP N 2 KOTA BENGKULU

This study aims to determine the effect of the Rigorous Mathematical Thinking learning on Students' Mathematical Literacy ability. This type of research uses the Quasi Experiment method. Data collection is done through tests. Data analysis used the Ancova test. The sample of this study were students of SMA Negeri 2 Bengkulu City in class VII I and VII K. The results showed that: (1) there was a linear covariate effect of initial ability on students' mathematical literacy abilities with an effect of 26,5%, (2) there was an effect of Rigorous Mathematical Thinking learning on students' mathematical literacy abilities with an effect of 62,6%, and (3) there was a higher mathematical literacy abilities achievement for class VII students of SMP Negeri 2 Bengkulu City who are taught using Rigorous Mathematical Thinking learning compared to classes taught with conventional learning

Developing Rigorous Mathematical Thinking Approach-Based Learning Materials for Sequences and Series Concept at High School Level in Tanjungpinang

Mathematics encourages logical reasoning and critical thinking. Rigorous thinking helps in analysing problems to decision-making and ensures that solutions are accurate and reliable. Prior research indicated students’ lack of those abilities when learning the concept of sequences and series. Therefore, this research aims to develop learning materials for the concept of sequences and series based on rigorous mathematical thinking (RMT) approach. The learning materials developed with the ADDIE model include mobile learning, student worksheets, and test instruments, which provide clear explanations, examples, problem-solving activities with RMT approach, and assessments enabling teachers to evaluate students’ understanding of mathematics concepts of the sequences and series. The learning materials were validated using a questionnaire by mathematics experts. The quantitative and qualitative data results show that the mobile learning, student worksheets, and test instruments are valid. Mobile learning that was developed and tested valid entails that the study can add to a new learning strategy that proposes technology and digital tools to engage students in the learning process and promote RMT.

Research on conical UAV formation position adjustment based on CTLS algorithm and pigeon flock behavior mechanism

UAVs should be kept as silent as possible during field operations and missions for concealment and to prevent electrostatic interference. In this paper, with rigorous mathematical argumentative thinking, the CTLS algorithm is referenced and optimized to give a solution model for the multi-error passive pure orientation cooperative position adjustment problem, and the results are reviewed in terms of polar coordinate groups. The self-adjustment problem of conical swarm is solved and the method is shown to be applicable to attitude correction of any ordered swarm where translation invariance of subsystems exists. The convergence results of the algorithm are reviewed in terms of polar coordinate groups and line graphs of iterative data, and the results are found to be good.

UAV planar passive pure orientation positioning under different conditions

UAVs should be kept as silent as possible during field operations and missions in order to conceal and prevent electrostatic interference. In this paper, with rigorous mathematical argumentative thinking, the planar passive pure orientation localization problem under error-free conditions is based on the triangulation localization model of basic analytic geometry. The triangulation model is solved by applying a combination of plane geometry and analytic geometry. The accurate planar triangulation model is obtained, and the target is located according to the determined observation points.

Electronic Student Worksheets Based on Rigorous Mathematical Thinking for Sequence and Series Materials in Senior High School

The rapid development of technology must be utilized as well as possible, especially in the world of education, because education is the basis for forming individuals who are strong and able to compete in facing the challenges of the times. The habit of students using existing formulas without knowing the concept of the material causes them to have difficulty solving the same problem but in a different form of problem. Therefore, the development of electronic student worksheets based on Rigorous Mathematical Thinking (RMT) on the material of rows and series becomes an electronic teaching material that contains the stages of the learning process to build an in-depth understanding of the concepts of students as well as being one of the changes from existing technological developments. This study aimed to assess the validity and practicality of electronic student worksheets based on RMT developed. The research method used is Research and Development (R&D) with the 4D development model. The validity and practicality assessment instrument is a student questionnaire sheet with a Likert scale. The data obtained were analyzed using the percentage of the assessment score. The validation results show that electronic student worksheets are categorized as valid, with an average percentage of material validation of 88.13%, an average percentage of media validation of 94.62%, and an average percentage of language validation 93.64%. The practicality test obtained an average percentage of 78.39% in the practical category.

Rigorous Mathematical Thinking: Conceptual Knowledge and Reasoning in the Case of Mathematical Proof

This study aims to analyze in-depth students' conceptual knowledge and reasoning when solving problems using mathematical proof as a rigorous mathematical thinking paradigm. The research uses a qualitative method with a case study approach that analyzes the mathematical proof ability of nine students who represent different cognitive functions from each level of rigorous mathematical thinking. The results showed that each level of rigorous mathematical thinking meant other indicators according to their ability to master conceptual knowledge and implement mathematical ideas through reasoning. This research has an impact on the treatment that the teacher must give in determining the learning model and evaluation instrument that can raise students' conceptual knowledge and reasoning.Penelitian ini bertujuan untuk menganalisis secara mendalam pengetahuan konseptual dan penalaran siswa ketika memecahkan masalah menggunakan pembuktian matematis sebagai paradigma berpikir matematis yang ketat. Penelitian ini menggunakan metode kualitatif dengan pendekatan studi kasus yang menganalisis kemampuan pembuktian matematis sembilan siswa yang mewakili fungsi kognitif yang berbeda dari setiap tingkat pemikiran matematis yang teliti. Hasil penelitian menunjukkan bahwa setiap tingkat berpikir matematis yang teliti berarti indikator lain sesuai dengan kemampuannya untuk menguasai pengetahuan konseptual dan mengimplementasikan ide-ide matematika melalui penalaran. Penelitian ini berdampak pada perlakuan yang harus diberikan guru dalam menentukan model pembelajaran dan instrumen evaluasi yang dapat meningkatkan pengetahuan konseptual dan penalaran siswa.

BERPIKIR MATEMATIS RIGOR: KONTRIBUSI PADA PENGEMBANGAN PENGETAHUAN METAKOGNITIF-SELF ASSESSMENT MAHASISWA

This study aims to analyze students' rigorous mathematical thinking from three levels of cognitive function structures associated with their contribution to self-assessment metacognitive knowledge in Real Number System lectures. This research is qualitative research with a type of case study. The research subjects were three students of the Mathematics Education Study Program who contracted the Real Number. System course selecting research subjects based on test results identifies students into three rigorous mathematical thinking cognitive function structure levels. This study's results indicate that rigorous mathematical thinking contributes to students' self-assessment metacognitive knowledge. The quality of review of students who have a rigorous mathematical thinking level can lead to thoroughness, intellectual perseverance, critical investigation, and truth-seeking in solving problems appropriately, structurally, and systematically into a direct experience in the learning process is described as metacognitive. Students at the level of abstract relational thinking can assess their own abilities very well, learn independently, and choose with certainty how to solve problems by placing the right method. Qualitative thinking level students focus more on symbols or symbols and represent their knowledge through visualization. He prefers that the type of evaluation problem solving is not in the form of long, detailed sentences but instead immediately transforms the sentences into clear mathematical symbols

Design of Learning Activities using Rigorous Mathematical Thinking (RMT) Approach in Application of Derivatives

Learning design is one of the factors that support the learning process in order to achieve learning objectives in all subjects including mathematics. Many approaches can be employed by a teacher in making learning design, one of which is rigorous mathematical thinking (RMT) approach. The RMT approach puts forward students actively in constructing their knowledge through the use of psychological tools and mediation. This article reports a set of learning activities designed through a developmental study using the RMT approach in the topic of application of derivatives. Participants of this research were twenty-six of 11th grade students from a private secondary school. Data were collected through written test and classroom observation. The research instruments were student worksheet and observation sheet. In the learning process, students use psychological tools to connect their previous knowledge to the material being studied. This makes students able to construct their own knowledge more thoroughly. On the other hand, with the mediation carried out by the teacher, students can focus more and understand each material well and bridge the conceptual errors. Based on the results of the study and some literature, Design of learning activities using Rigorous Mathematical Thinking (RMT) on application of derivative can be an alternative as effective learning.

The Influence of Rigorous Mathematical Thinking (RMT) Learning Pathway to Junior High School Students’Conceptual Understanding

The purpose of this study is to determine whether there is a significant influence of the Rigorous Mathematical Thinking (RMT) learning approach to the conceptual understanding of students of SMP Negeri 5 Kupang grade VIII on the concept of the Two Variable Linear Equation System. This is motivated by the difficulty of students in understanding the subject matter because it is considered difficult so that the resulting understanding of students' mathematical concepts is low. This type of research is quasi experimental research (quasi experiment). The research design used was a pretest-posttest non-equivalent control group design. The population in this study were all eighth grade students of SMP Negeri 5 Kupang, selecting samples using a purposive sampling technique. Retrieval of data using the instrument test item description and observation sheet. Samples are given a pre-test, the results are to test homogeneity. From the results, both have homogeneous variance. After the treatment of both samples were given a post-test, the results are to test the research hypothesis. Based on the prerequisite test, the sample is normally distributed and the variance is homogeneous. Based on the initial ability test, there was no difference in the average pre-test values of the two samples. The results of the study by using a hypothesis test that is a two-way ANOVA test showed a significance value of 0.784> 0.05 so it can be concluded that there was no difference in students' conceptual understanding based on the sex of students of SMP N 5 Kupang.

Implementation of lesson study with rigorous mathematical thinking based on student worksheet to enhance the students’ mathematical critical thinking

This article is an implementation of lesson study with an RMT-based student worksheet which aims to enhance students' mathematical critical thinking skills. The subjects of this study were 32 students of class VII A in MTsN 1 South Lampung, who represented: (1) different mathematical learning styles; and (2) different self-efficacy. Research begins with a plan, then begins to implement and reflect. The instruments of this study were students' worksheets based on RMT integer and fraction topics, Mathematical Learning Style (MLS) questionnaire, self-efficacy questionnaire, test instrument of critical thinking, and observation sheet. This study aims to improve students' critical thinking skills with the help of Student Worksheets based on RMT in terms of MLS and student self-efficacy. Based on the results of the study, students with Self-Expressive Learning (SL) and Mastery Learning (ML) learning styles experienced a high increase in critical thinking skills with N-gain scores of 0.73 and 0.71, respectively. While students with Understanding Learning (UL) and Interpersonal Learning (IL) learning styles have increased critical thinking skills in the medium category with N-Gain scores of 0.64 and 0.63. Students with high self-efficacy have increased high critical thinking skills. Students with intermediate self-efficacy experience an increase in mathematical critical thinking skills in the medium category.

Rigorous Mathematical Thinking: Why are Cognitive Levels Important in Three-Dimensional Learning for Pre-service teachers?

Learning material three dimensions is closely related to processing high-level abstract thinking skills. The ability in question is Rigorous Mathematical Thinking (RMT). Some research results do not focus on the relationship of RMT with cognitive levels. The cognitive relationship between RMT is essential because students must have abstraction skills to be able to teach according to the concept. The study aimed to determine the ability of RMT mathematics teacher pre-service based on cognitive levels in a three-dimensional material. The research method is qualitative descriptive because of the use of test sheets and interviews as instruments. The research sample consisted of three students, each with low, medium and high cognitive abilities. Research has resulted in the ability of prospective RMT mathematics teachers to have a close relationship with their cognitive level. High-level RMT students can link the three-dimensional concepts of the Pythagoras theorem, great line propositions, angular definitions, the definition of squared angles, and several trigonometric principles. Medium RMT, able to sort diagonal concepts until the trigonometric proposition is systematic. A low RMT can label a right triangle and cube side. The results of this study are the basis for giving appropriate treatment to students before carrying out teaching practices.

Pendekatan Rigorous Mathematical Thinking Untuk Meningkatkan Kemampuan Pemecahan Masalah Matematika Siswa

This research was conducted because of the students' low ability to solve mathematical problems. The aim of this research is commited to increase the mathematical problem solving abilities of VIII E students in second semester of SMP Negeri 2 Sewon academic year of 2018/2019 using the Rigorous Mathematical Thinking (RMT) learning approach. This type of research is Class Action Research (CAR). This research consists of two cycles where each cycle consists of three meetings. The subjects of this study were students of class VIII E, amounting to 30 students, consisting of  20 male students and 10 female students. The object of this research is students' mathematical problem solving abilities using the RMT approach. Data collection techniques used in the form of observation instruments, tests, interviews. Data analysis techniques were carried out by qualitative descriptive analysis. The results showed that learning with the RMT approach can improve students' mathematical problem solving abilities. The results of the analysis of cycle test assessment sheets in Cycle I percentage of students' ability to solve problems was 65.56% with sufficient categories. While the results of the analysis of cycle test assessment sheets in Cycle II the percentage of students' ability to solve problems was 79.72% with good categories. From these results there was an increase in students' ability to solve mathematical problems by 14.16%.

IMPLEMENTASI PENDEKATAN RIGOROUS MATHEMATICAL THINKING (RMT) UNTUK MENINGKATKAN KEMAMPUAN PEMECAHAN MASALAH SISWA

The purpose of this research is to improve students' problem solving skills using Rigorous Mathematical Thinking (RMT) approach.  Qualitative research method with the type of Classroom Action Research (CAR). This research was conducted in class VIII H of SMP N 2 Sewon, Bantul. As a data collection technique used consists of tests, observations, and interviews. This research data analysis technique uses an interactive analysis model according to Miles, Matthew B, Michael. Huberman (2014). The results showed that mathematics learning using rigorous mathematical thinking (RMT) approach could improve the problem solving abilities of class VIII H students of SMP N 2 Sewon.

Comparing the Effect of Explicit Mathematics Instruction with Rigorous Mathematical Thinking Approach and 5E’s Instructional Model on Students’ Mathematics Achievement

This study investigated the effect of explicit mathematics instruction with rigorous mathematical thinking (EMI-RMT) approach and 5E’s instructional model in mathematics achievement. It utilized the quasi-experimental pretest-posttest non-equivalent control group research design to gather the data. The researchers made use of the teacher-made test with a Cronbach alpha reliability coefficient of .74. Two intact classes of freshmen education students enrolled in the school year 2018-2019 at the University of Science and Technology of Southern Philippines, Cagayan de Oro City participated in this study. One section was taught using EMI-RMT approach in discussing the concept of the plane and spherical trigonometry while the other group was taught using the 5E’s instructional model. The analysis of covariance (ANCOVA) with posttest as the dependent variable and pretest as the covariate, yielded F(1,60)=.068, p=.796, which is not significant at .05 level. This implies that the achievement of students taught with EMI-RMT is comparable with the achievement of students taught with 5E’s instructional model. Since many studies showed that 5E’s instructional model is effective, the researchers recommend that mathematics teachers may also employ the EMI-RMT approach in their classes to improve their students’ achievement in mathematics.

PENGARUH PEMBELAJARAN RIGOROUS MATHEMATICAL THINKING (RMT) TERHADAP BEBAN KOGNITIF KONSTRUKTIF DAN KOMPETENSI STRATEGIS MATEMATIS SISWA DI PONDOK PESANTREN

Mathematical Strategic C ompetenc e (MSC) is one of the components of Mathematics Proficiency needed in learning mathematics. After learning of mathematics sometimes students haven't been able to have MSC . So it takes an intruction to learning strategic competence of mathematical students. One of the intruction s that can be used, namely the Rigorous Mathematical Thinking (RMT) intruction . RMT can also mediate the intruction makes it easy to process the received knowledge with the cognitive burden of providing the opportunity for constructive happens automatically to students. This study aims to know the effect RMT to MSC and M athematical G ermane C ognitive L oad. This study is the research of design experiment al with Treatment by Level 2x3 model Group Within Treatment (GWT). The subject is the class XI boarding schools Daar el-Qolam 1 (DQ1), DQ2 and DQ3 DQ4, who were randomized into 8 groups, namely: each one experimental class DQ1 , DQ2 , DQ3, DQ4 and control class one DQ 1, DQ 2, DQ 3 and DQ4. The analysis of the data using analysis of variance (An o va) two way model GWT. The study results obtained (1) the Learning intruction alone does not e ffect the MCS of students, (2) Early Mathematics Ability (EMA) alone does not e ffect the MCS students, (3) there is the influence of the interactions between the learning intruction and EMA e ffect the MCS students. It appears also that the Group has no e ffect the MCS students, ( 4) students who were given RMT intruction is lower than direct intruction to students with high EMA , (5) students who were given RMT intruction is higher than direct intruction to students with medium EMA, (6) students who were given RMT intruction is lower than direct intruction to students with low EMA , (7) Germane Cognitive Load does e ffect students RMT intruction . Keywords: Rigorous Mathematical Thinking, Mathematical Competence Strategic, Mathematical Germane Cognitive Load and Boarding Schools

Implementation of rigorous mathematical thinking approach to analyze the students’ ability of algebraic thinking and understanding concept and mathematical habits of mind

This study aims to analyze the students’ algebraic thinking skills and understanding of mathematical concept and Mathematical Habits of Mind (MHoM) students using Rigorous Mathematical Thinking (RMT) approach. To do so, we carried out three phases of a small-scale study. First, we analyzed three matrix problems, considered as tasks inviting the use of problem solving and algebraic ability and theoritically in the light of the RMT principles. Second, we tested problems to 54 students of mathematics education major of Indonesia University of Education in academic year 2016/2017. Finally we analyzed student written work, questionnaire of MHoM and compared these empirical to the theoritical results. We found that students who learn by using rigorous mathematical thinking have algebraic thinking skills and good conceptual understanding. In addition, students also have good mathematical habits of mind. We concluded that RMT approach fruitfull framework to increase students’ algebraic thinking skills and understanding of mathematical concept and MHoM students of Indonesia University of Education.

Rigorous mathematical thinking based on gender in the real analysis course

Real analysis is a course that is abstract and high difficulty level. Male students are weak in understanding basic concepts, while women are always follow on examples of answers from lecturers. Consequently, their abstraction abilities do not develop. To provide appropriate treatment, the lecturer should know the rigour mathematical ability of the students. Therefore, this study aims to identify students’ rigour mathematical abilities in Real Analysis courses. The research method is descriptive qualitative. The research instruments are test questions and interview sheets. The sample was six students. The researcher divides the students into three cognitive levels based on test results, i.e. two for low cognitive level, two for medium, and two for a high cognitive level. This study concludes that there is a difference of mathematical thinking of rigour of students based on gender-related to three levels of cognitive ability. Male students have a simple way of thinking impacting on a short answer pattern. The way of thinking of female students is systematic, and the pattern of the answer is long and sorted. The results of this study can be the basis of the treatment of students based on the level of cognitive ability and gender.

The development of teaching material: Rigorous mathematical thinking in a geometry classroom

This study aimed to develop a teaching material, a textbook, using a Rigorous Mathematical Thinking (RMT) approach. It was constructed by considering some activities involving problem-solving, problem posing, open-ended problem, connection problem, conjecture, creativity task, mini lab, and drawing skill. The subject in this study was the undergraduate mathematics students who enrolled in the geometry subject in the University of Wijaya Kusuma Surabaya. A textbook was developed because of the necessity. It was developed using the Mediated Learning Experience based on the Rigorous Mathematical Thinking. This study employed Plomp’s Research Design model consisting of three phases: the preliminary research, prototyping phase, and assessment phase. However, this paper focused only on the validation of the textbook involving five experts. Students have been mediated to construct their understanding by using mental operation. One important task about creative thinking including in the textbook dealing with the trapezium definition. Students were asked to create a new definition of trapezium which is different from the preceding definition they learned at school. The results showed that the development of student book using Rigorous Mathematical Thinking approach was valid.

The Development of Learning Tool Models on Triangle using Problem Solving Based of Rigorous Mathematical Thinking in Wijaya Kusuma Surabaya University

Geometry learning given to Mathematics education program, Faculty of Language and Science, Wijaya Kusuma SurabayaUniversity use various strategy and learning models even acquired maximum result. Students still have difficulties this to prove theorems, therefore concepts understanding is needed about triangle. One of the alternatives that can build up geometry concepts in students mains is by carrying out an approach of Rigorous Mathematical Thinking (RMT). The goals of this research are to describe processes and results of the development learning tools models of triangle using problem solving based on Rigorous Mathematical Thinking (RMT). This Research is a developmental one which carried out for the students of Mathematics education program, Faculty of Language and Science University of Wijaya Kusuma Surabaya academic year 2017-2018. The research object is learning triangle using problem solving approach. Two subjects are subject for validation and subject for limited try out. The learning instruments consist of validation sheets, observation of students activity sheets, students response sheets and test. The technique of data collection uses observation method, test, and questionnaire. Research yields teaching handbook, syllabus and student activity sheets.