KEMAMPUAN PENALARAN MATEMATIS SISWA DALAM MENYELESAIKAN SOAL PADA MATERI RELASI DAN FUNGSI KELAS VIII SMP

The aims of this study is to describe students' mathematical reasoning skills in solving problems on relationship materials and functions. Research method is used descriptive qualitative. The research subjects consisted of six students of grade VIII SMP Negeri 51 Palembang with two students with high ability, two medium students and two students with low ability. Data collection is carried out by providing 5 points about tests, interviews, and documentation. This study, using 5 indicators of reasoning, namely analysis, synthesis, generalization, problem solving is not routine, and justification / proof. The results showed that students who have high ability are mostly able to fulfill all aspects of mathematical reasoning ability. As for students who have moderate ability is able to meet two to three aspects of the students' mathematical reasoning ability only. Then for students who have low ability is only able to meet one to two aspects of the student's mathematical reasoning ability.

Describing students' mathematical power: Do cognitive styles make any difference?

Mathematical competence refers to the skills of students in reasoning, connection, communication, representation, and problem-solving. Various researchers have massively discussed on how to foster mathematical competence. However, it is just a few of them comprehensively explain from the cognitive styles perspective. This research aims to measure the junior high school students’ mathematical competence based on their cognitive style.This research used a descriptive qualitative approach. There were 35 students took part in the mapping of cognitive styles using the Matching Familiar Figure Test and were then selected representative from the reflective and the impulsive cognitive style to have a further assessment of the mathematical competence using the mathematical competence test. The data analysis used the model of Milles and Huberman. The results showed that there was a difference mathematical competence between the subject having impulsive cognitive style and the one having reflective cognitive style. The percentage of mathematical competence of reflective subject was 69% while the impulsive subject was 56.89%. From all aspects of mathematical competence, the reflective subject tends better ability; for instance, the reflective subject has better ability than the impulsive subject on mathematical connection, mathematical reasoning, mathematical representation, and problem-solving

Analysis of the mathematical literacy skills of high school students in solving PISA questions content change and relationship viewed from self-esteem

Mathematical literacy is a person's ability to use mathematical science that includes aspects of understanding, application, reasoning, and communication in everyday life. This study aims to analyze and describe students' mathematical literacy in solving questions about changes in PISA content and the relationship that students' self-esteem checks. This research uses qualitative descriptive research methods. The subjects of the study consisted of three Class IX.2 students at Negeri 3 Secondary School Surakarta. Data collection techniques consisted of PISA self-esteem improvement, content change and relationship tests, and interviews. Data analysis techniques consist of data presentation, data reduction, and conclusions. The results of the study show that students with high self-esteem can meet the six indicators of mathematical literacy in both subjects

Profil Penalaran Proporsional Siswa SMP dalam Memecahkan Masalah Matematika Ditinjau dari Gaya Berpikir Sekuensial Konkret dan Acak abstrak

Abstrak Penalaran merupakan salah satu poin yang terdapat dalam standart isi kurikulum 2013. Terdapat beberapa jenis penalaran matematis, salah satunya yang berperan penting dalam pembelajaran matematika yaitu penalaran proporsional. Untuk meningkatkan kemampuan penalaran proporsional salah satu caranya yaitu melalui pemecahan masalah matematika, dengan diberikan masalah matematika, siswa dapat memecahkan masalah dengan mengaplikasikan pengetahuan mereka sehingga kemampuan penalaran proporsional dapat berkembang dan meningkat. Didalam proses pembelajaran tidak dapat dipungkiri bahwa setiap siswa memiliki karakteristik yang berbeda-beda sehingga menjadikan cara mereka untuk memperoleh informasi juga berbeda. Oleh sebab itu, cara berpikir atau gaya berpikir siswa pun akan berbeda. Salah satu faktor yang mempengaruhi yaitu gaya berpikir. Jenis penelitian ini adalah penelitian deskriptif kualitatif yang bertujuan untuk mendeskripsikan profil penalaran proporsional siswa SMP dalam memecahkan masalah matematika ditinjau dari gaya berpikir sekuensial konkret dan acak abstrak. Teknik pengumpulan data dengan TGB, TPMM, dan wawancara. Subjek penelitian yaitu dua siswa dengan gaya berpikir sekuensial konkret dan acak abstrak kelas VII-I dan VII-H SMPN 3 Gresik tahun ajaran 2018/2019. Hasil penelitian ini menunjukkan bahwa penalaran proporsional siswa dengan gaya berpikir sekuensial konkret dalam memecahkan masalah matematika terkait dengan memahami kovarian memunculkan semua aspek yang diamati, mengenali situasi proporsional dan nonproporsional memunculkan semua aspek yang diamati, menggunakan strategi multiplikatif memunculkan 2 dari 3 aspek yang diamati, sehingga dapat disimpulkan bahwa siswa dengan gaya berpikir sekuensial konkret menggunakan penalaran proporsionalnya pada saat memecahkan masalah matematika tetapi siswa hanya menggunakan satu strategi multiplikatif yaitu strategi perkalian silang. Penalaran proporsional siswa dengan gaya berpikir acak abstrak dalam memecahkan masalah matematika terkait dengan memahami kovarian memunculkan 4 dari 5 aspek yang diamati, mengenali situasi proporsional dan nonproporsional memunculkan 2 dari 4 aspek yang diamati, menggunakan strategi multiplikatif memunculkan 1 dari 3 aspek yang diamati, sehingga dapat disimpulkan siswa dengan gaya berpikir acak abstrak tidak menggunakan penalaran proporsionalnya pada saat memecahkan masalah, hal tersebut dapat dilihat dari hasil analisis data bahwa siswa tidak melibatkan hubungan multiplikatif dalam menentukan nilai kuantatis yang belum diketahui, tidak menggunakan strategi multiplikatif dan pada saat menyimpulkan kurang tepat. Kata Kunci: Penalaran proporsional, Gaya Berpikir Sekuensial Konkret, Gaya Berpikir Acak Abstrak. Abstract Reasoning is one of the points contained in the standard curriculum contents of 2013. There are several types of mathematical reasoning, one of which plays an important role in mathematics learning, namely proportional reasoning. To improve proportional reasoning ability one way is through solving mathematical problems, by being given mathematical problems, students can solve problems by applying their knowledge so that proportional reasoning abilities can develop and increase. In the learning process it cannot be denied that each student has different characteristics so that their way of obtaining information is also different. Therefore, students thinking or thinking styles will be different. One of the factors that influence is the style of thinking. This type of research is descriptive qualitative research that aims to describe the proportional reasoning profile of junior high school students in solving mathematical problems in terms of concrete and random abstract sequential thinking styles. Data collection techniques with TGB, TPMM, and interviews. The research subjects were two students with concrete sequential thinking styles and random abstracts in classes VII-I and VII-H Gresik 3 Junior High School in the academic year 2018/2019. The results of this study indicate that students proportional reasoning with concrete sequential thinking styles in solving mathematical problems related to understanding covariance raises all observed aspects, recognizes proportional and non-proportional situations, raises all observed aspects, using multiplicative strategies raises 2 of the 3 observed aspects, so that It can be concluded that students with concrete sequential thinking style use proportional reasoning when solving mathematical problems but students only use one multiplicative strategy, namely cross-multiplication strategies. Proportional reasoning of students with abstract random thinking styles in solving mathematical problems related to understanding covariance raises 4 of the 5 aspects observed, recognizing proportional and non-proportional situations raises 2 of the 4 aspects observed, using multiplicative strategies raises 1 of 3 observed aspects, so that they can It was concluded that students with abstract random thinking style did not use proportional reasoning when solving problems, it can be seen from the results of data analysis that students do not involve multiplicative relationships in determining unknown quantative values, do not use multiplicative strategies and when concluding incorrectly. Keywords: Proportional Reasoning, Concrete Sequential Thinking Style, Abstract Random Thinking Style

ANALISIS KEMAMPUAN PENALARAN DALAM MEMECAHKAN MASALAH MATEMATIKA DENGAN METODE POLYA PADA SOAL CERITA KELAS VI SDN BEJIREJO

This research was carried out because of the importance of reasoning in learning activities in elementary schools. So this research discusses how students' reasoning abilities are in solving mathematical problems using the polya method in story problems for class VI students at SDN Bejirejo. The aim of this research is to describe students' reasoning abilities in solving mathematics problems for class VI SDN Bejirejo. This research uses a descriptive approach with qualitative research methods. Data collection techniques include interviews, observations, questionnaires and reasoning ability test questions. The research results showed that learning activities in mathematics learning were included in the very good criteria and obtained a percentage of 79.46%. Meanwhile, the data on the classification of students' reasoning abilities which were reviewed based on ten aspects of reasoning showed that the aspect of understanding understanding obtained a percentage of 83.91%, the aspect of logical thinking obtained a percentage of 80.87%, the aspect of understanding negative examples obtained a percentage of 78.70%, the aspect of deductive thinking obtained a percentage of percentage 72.61%, aspect of systematic thinking gets a percentage of 70.00%, aspect of consistent thinking gets a percentage of 83.91%, aspect of drawing conclusions gets a percentage of 89.57%, aspect of determining methods gets a percentage of 81.30%, aspect of making reasons gets a percentage the percentage was 70.87%, and the aspect of determining strategy obtained a percentage of 85.22%. The overall average of students' reasoning aspects is a percentage of 79.70% with very high reasoning criteria

Analogical Reasoning in Mathematical Theorems

Analogical reasoning is one of the most powerful tools of mathematical thinking. For example, to prove a theorem it is necessary to see similarities with the previous theorem. This study aims to classify analogies in mathematics courses and examples. This classification is based on research results. The research was conducted use qualitative research. The research subjects are 12 lecturers who teach mathematics courses and study program managers. Analogical reasoning instruments are unstructured interview guidelines and observation sheets. Interview guides and observation sheets were made to be able to reveal mathematics analogical reasoning in the Mathematics Education Study Program course. The results of the research show that there are 3 types of analogy classifications in mathematics courses, namely definition analogy, theorem-defining analogy, and theorem analogy. First, the definition of similarity in the same or different courses. Second, the similarities between definitions and theorems in the same or different courses. Third, the theorem similarities in the same or different subjects. Our classification is related to theorems and analogical properties in several courses in the curriculum of the Mathematics Education Study Program. The analogy can be applied to certain mathematical topics related to real life. Meanwhile, to analyze other aspects of reasoning through analogy needs to be studied further

Supporting Spatial Reasoning: Identifying Aspects of Length, Area, and Volume in Textbook Definitions

Length, area, and volume share structural similarities enabling flexibility in reasoning for real-world applications. Deep understanding of structures can help teachers connect these concepts to support their students’ mathematical reasoning and practices involving real-world situations. In mathematics textbooks designed for future teachers, definitions of length, area, and volume vary from procedural (e.g., use a ruler to measure side lengths, use formulas to calculate measures) to conceptual (e.g., construct appropriate n-dimensional units that tessellate the n-dimensional space) to formal (e.g., construct a function mapping qualitative size to a quantity of appropriate units). Most textbooks describe length, area, and volume as quantitative measurements and provide examples of standard units. Definitional aspects such as describing size as an attribute or measurement, identifying dimensionality of a space, or constructing appropriate nonstandard units are inconsistently acknowledged across textbooks. Attending to definitional aspects of spatial attributes and their quantification can open conversations about the structure and essential meanings of length, area, and volume

Modal and Relevance Logics for Qualitative Spatial Reasoning

Qualitative Spatial Reasoning (QSR) is an alternative technique to represent spatial relations without using numbers. Regions and their relationships are used as qualitative terms. Mostly peer qualitative spatial reasonings has two aspect: (a) the first aspect is based on inclusion and it focuses on the ”part-of” relationship. This aspect is mathematically covered by mereology. (b) the second aspect focuses on topological nature, i.e., whether they are in ”contact” without having a common part. Mereotopology is a mathematical theory that covers these two aspects. The theoretical aspect of this thesis is to use classical propositional logic with non-classical relevance logic to obtain a logic capable of reasoning about Boolean algebras i.e., the mereological aspect of QSR. Then, we extended the logic further by adding modal logic operators in order to reason about topological contact i.e., the topological aspect of QSR. Thus, we name this logic Modal Relevance Logic (MRL). We have provided a natural deduction system for this logic by defining inference rules for the operators and constants used in our (MRL) logic and shown that our system is correct. Furthermore, we have used the functional programming language and interactive theorem prover Coq to implement the definitions and natural deduction rules in order to provide an interactive system for reasoning in the logic

Transitioning from "It Looks Like" to "It Has To Be" in Geometrical Workspaces: affect and near-to-me attention

Within a practitioner researcher framework, this paper draws on a particular mathematics education theory and aspects of neuroscience to show that, from a learner’s perspective, moving to a deductive reasoning style appropriate to basic Euclidean geometry, can be facilitated, or impeded, by emotion and/or directed attention. This shows that the issue of a person’s deductive reasoning is not a merely cognitive one, but can involve affective aspects related to perception – particularly perception of nearby sense data – and emotion. The mathematics education theory that has been used is that of the Espace de Travail Mathématique, the English translation of which is known as Mathematical Working Spaces (MWS). The aspects of neuroscience that have been used pertain to the distinct processing streams known as top-down and bottom-up attention. The practitioner research perspective is aligned with Mason’s teaching-practice-based ‘noticing’; qualitative data analysed in this report include individual interviews with school teachers on in-service courses and reflective notes from teaching. Basic Euclidean geometry is used as the medium for investigating transition from ‘it looks like’ to a reasoned ‘it has to be’