Identifikasi Penalaran Kreatif Siswa Madrasah Ibtidaiyah dalam Memecahkan Masalah Bangun Ruang

Reasoning in mathematical proof is a thinking process to draw conclusions based on logical ideas by rebuilding previous knowledge and connecting it with current knowledge in order to demonstrate the truth of a mathematical statement supported by logical arguments. To be able to know students' reasoning in mathematical proving is associated with problem solving because problem solving and reasoning have a close relationship. Differences in students' mathematical abilities allow for differences related to reasoning in mathematical proof. The purpose of this study is to describe the reasoning of high school students with high, medium and low mathematical abilities in proving mathematics on trigonometry material.
 This study used a qualitative approach with a descriptive research type. The research subjects consisted of 3 students from class X, namely students with high, medium and low mathematical abilities. The research data were obtained from the results of mathematical ability tests, mathematical proving tests, and interviews. Mathematical ability tests were used for the selection of research subjects, mathematical proof tests were used to find out how students reasoned in proving mathematics on trigonometry material and interviews were conducted to find out more clearly about the explanation of the reasoning process written by the subjects on the mathematical proof test.
 The results showed that the three students understood the problem by identifying information that was known and that was not known to students with high mathematical ability and logical reasons, but students with moderate and low mathematical ability, there were statements that were not accompanied by logical reasons. In planning the completion, students with high mathematical ability are accompanied by logical reasons but students with moderate and low mathematical ability have statements that are not accompanied by logical reasons. In carrying out the completion plan students with high mathematical ability can solve problems according to plan accompanied by logical reasons, for students with moderate mathematical ability can solve problems according to plan, even though there are statements that are not accompanied by logical reasons, but students with low mathematical ability they cannot solve problems and did not succeed in carrying out according to the plan because they were confused about proceeding with problem solving. In re-examining the process and results, students with high ability get conclusions from their completion and examine the process from the start, starting from reading the problem, planning, implementing plans and conclusions with logical reasons, for students with moderate mathematical ability getting conclusions from their completion and checking their calculations with logical reasons. However, students with low mathematical ability did not get a conclusion from the solution because they could not solve the problem and did not re-examine the process.

The research is a combination of quantitative-qualitative (mixed method). The design of mixed method used is Concurrent Triangulation Design aims to describe be communication ability and mathematics logic thinking of students in generative learning and to discover the improvement of communication ability and mathematics logic thinking of students in generative learning of class XI students Majoring in Health Analys at SMK Kesehatan Mega Rezky in Makassar. The population of the research were all of the students in class XI at SMK Kesehatan Mega Rezky in Makassar. The sample consisted of one class, namely class XI Majoring in Helath Analys as the experiment class taught by using generative learning model chosen by using random sampling technique. The subjects of the research were three students consisted of one student with high mathematics ability, one student with medium mathematics ability, and one student with low mathematics abilitiy. The data of research consisted of mathematics communication data and mathematics logic thinking ability data. The instruments used in collecting the data were mathematics communication ability test, mathematics logic thinking ability test, learning implementation observation sheet, and interview guidance. The data of mathematics communication ability and mathematics logic thinking were analyzed by using descriptive and inferensial analysis and analyzed qualitatitvely. The results of the research reveal that : (1) the implementation of generative learning model in Circumference nd Area of Two Dimensional Figure material is well implemented, (2) the improvement of students’ communication abilities after being taught by implementing generative learning model with average 0.63 is in medium classification, (3) the improvement of students’ mathematics logic thinking abilities after being taught by implementing generative learning model with average 0.59 is in medium classification, (4) mathematics communication ability in generative learning such as the subject who have high, medium, and low mathematics abilities have ability to state mathematics ideas in writing and drawing it, although the picture/sketch made by the subjects with high and low mathematics ability are still not correct. Then, the subject who have high, medium, and low mathematics abilities have ability to interpret and evaluate mathematics ideas in writing although the subject who have high, medium, and low mathematics ability can only write most of the reason/proof which are correct. Moreover, the subjects who have high, medium, and low mathematics abilities also have in using terms, mathematics notations, and its structures to model mathematics situation or problem, although the subjects who have medium and low mathematics abilities can only write most of terms, notations, and mathematics structure correctly, (5) mathematics logic thinking ability in generative learning such as the subjects who have high, medium, and low mathematics ability have ability in thinking orderly, namely the subject with high, medium and low mathematics abilities write the acknoledged information and are questioned in question items completely and correctly, and write correct formulation to solve the problems. Then, the subjects who have high, medium, and low mathematics abilities have argument ability, namely student can write reason/proof in deciding solving stages which can be used to answer questions, although the subjects with medium and low mathematics abilities write the reason which still is not correct but the subjects can solve the questions correctly. Then, the subject with high, medium, and low mathematics abilities have ability to write formulation of conclusion by using their own languages based on the purpose of the question and answer correctly.

This study aims to obtain a problem-solving profile of a two-variable linear equation system for grade VIII students of SMP Negeri 21 Palu reviewed from the student’s mathematical abilities based on Polya steps. This study uses a qualitative method with a qualitative descriptive approach based on the problem-solving steps proposed by Polya. The results of the study showed that the subjects used in this study were three students, namely students with high mathematical ability (ZN), students with moderate mathematical ability (LT), and students with low mathematical ability (KB). The results of the study showed that subjects who had high, medium and low mathematical abilities in solving SPLDV mathematical problems were as follows: (1) in understanding problems, subjects with high mathematical abilities and were reading problems repeatedly, as well as their knowledge of "statement" sentences and "question" sentences. In contrast to subjects with low mathematical skills, they can identify the information available with their knowledge of "statement" sentences and "question" sentences, but subjects with low ability cannot understand every information in the problem even though they have read the problem repeatedly, (2) in planning problem solving, subjects with high mathematical ability and have a solution plan that The same is by using a combined method between elimination and substitution. In contrast to subjects with low mathematical ability who do not have a single mathematical solution plan at all, (3) in carrying out the problem-solving plan, subjects with high and medium mathematical ability can apply problem-solving strategies according to what has been previously planned, in contrast to subjects with low mathematical ability who do not solve problems because they cannot plan problem solving, (4) In re-examining the results of problem solving, the subject with high mathematical ability re-examines the results of his work by re-examining the results step by step of each process to find the answer. Furthermore, subjects with medium and low mathematical abilities do not re-examine their work because the subject cannot solve the given problem.

Problem solving is one of several important abilities a student must have. Problem solving is a planned process that mustbe done in order to get a certain solution of a problem that is not obtained immediately. One type of problem studentsmust solve is an open-ended problem. Open-ended problem solving for every student is certainly different from oneanother. The level of mathematical ability of students is one of the factors that influence these differences. This type ofresearch is a qualitative descriptive with the purpose to describe the profile of open-ended problem solving based onPolya’s steps viewed from mathematical ability level of junior high school students. Three students from grade VII arethe subjects in this research (one student having high mathematical ability, one student having moderate mathematicalability, and one student having low mathematical ability). This research uses instruments mathematical ability test, openended problem solving test, and interview guidelines. The results showed there were differences in the open-endedproblem solving profile on students with high, moderate, and low mathematical ability. Student with high mathematicalability can carry out all the steps of Polya’s problem solving. Student with moderate mathematical ability are able to carryout the step of understanding the problem, devising a plan, carrying out the plan, however there are indicators that are notfulfilled at looking back’s step they are using the other way to solve the problem and make conclusion. Student with lowmathematical ability can not show the adequacy of the data at understanding the problem’s step and can not carry out thesteps of devising a plan, carrying out the plan and looking back.

The purpose of this study is to describe the intuition characteristics of junior high school students in solving mathematical problems viewed from mathematical abilities. This research based on qualitative descriptive study. The subjects of this study were taken from Lab School UNESA Junior High School, which consisted of three students from class VIII A, namely one student with high, moderate, and low mathematical ability. The method that used to collect data consists of the mathematical ability test, problem solving test and so of the interview method. Data analysis uses the intuitive characteristic indicators at each stage of the problem solving. The conclusion of this study indicate that student with high mathematical ability at the stage of understanding the problem using affirmatory intuition with the characteristics of extrapolativeness, intrinsic certainty and perseverance, at the stage of making plans using anticipatory intuition with the characteristics of global ideas, and at the stage of carrying out plans and checking again not using intuition. Student with moderate mathematical ability at the stage of understanding the problem using affirmatory intuition with the characteristics of extrapolativeness, intrinsic certainty and perseverance, at the stage of making plans using anticipatory intuition with the characteristics of global ideas, and at the stage of carrying out plans and checking again not using intuition. Student with low mathematical ability at the stage of understanding the problem using affirmatory intuition with the characteristics of perseverance and coerciveness, at the stage of making plans using anticipatory intuition with the characteristics of global ideas, and at the stage of carrying out plans and checking again not using intuition. Keywords: Intuition, Problem solving , Mathematics ability

Abstract: Numeracy is the ability to locate, use, interpret, evaluate, and communicate mathematical information and ideas in the real context. This research purpose to describe the numeracy of eighth grade students in solving AKM-like problems in equations and inequalities subdomain based on high, moderate, and low mathematical abilities. The research subjects were eighth grade students consisting of one student with high mathematical ability, one student with moderate mathematical ability, and one student with low mathematical ability. The research method used in this research is qualitative descriptive research. Data were obtained by numeracy test. Students with high mathematical abilities present the information obtained in the form of equations and inequalities, use mathematical rules and procedures on equations and inequalities, interpret the results in the context of the problem, evaluate the results of problem solving through supposed, and communicate the results of their interpretation to others both orally and writing appropriately. Students with moderate mathematical abilities present the information obtained in the form and use procedures and rules of equations and inequalities in solving problems appropriately. However, students with moderate mathematical abilities interprets the results inaccurately so that in communicating the results of the interpretation is also inaccurate and evaluate the results only by correcting or recalculating. Students with low mathematical abilities do not present information in the form of equations and inequalities, nor do they use procedures and rules of equations and inequalities in solving problems. The interpretation of students with low mathematical abilities is also incorrect so that communicating the results of interpretations is not correct. In addition, students with low mathematical abilities do not evaluate the results of problem solving, either through supposed or correcting and recalculating.

Mathematical abilities need to be possessed on the grounds of being able to equip life in solving problems regularly. The RME course bridges students to study mathematics in everyday life. The research was conducted to determine the mathematical thinking abilities of PGSD students in the RME course on number types. The type of research carried out was descriptive qualitative with the use of random sampling to determine 3 research subjects (high, medium and low mathematical abilities). The stages that were passed were the lecturer making questions, assessment criteria, conducting tests, scoring and assessment ending with data reduction assisted by MS Excel. The data obtained was that there were 16.67% students in the high mathematical ability category, 75% in the medium category and 8.33% in low mathematical ability. MS excel calculations show that the average value of students' mathematical ability is 52.78, so it is in the medium category. Students with high mathematical abilities are very good at understanding the material on odd numbers as well as irrational numbers, both on prime numbers and need guidance on prime numbers. Understanding of prime numbers is very good, good for even numbers as well as odd numbers but needs improvement in irrational numbers for students with moderate mathematical abilities. Students with low mathematical abilities have a good understanding of prime numbers, understand enough material for odd and even numbers and have no clue about irrational numbers.

This study aims to describe the profile of solving problems of derivatives of algebraic functions. This type of research is a qualitative research with a qualitative descriptive approach based on the problem solving stages of Polya. The determination of the research subject was based on the results of daily mathematics tests for the 2021/2022 school year and recommendations from the mathematics teacher. Data collection was carried out by giving assignments and interviews. The results of this study indicate that: 1) the stages of understanding the problems of students with high, medium and low mathematical abilities are identifying problem information, namely things that are known and asked through statements and command sentences correctly. 2) the stage of making a problem-solving plan for students with high mathematical abilities uses the concept of derivatives of algebraic functions to correctly determine the speed and acceleration, students with moderate mathematical abilities are right to the wrong speed and acceleration, while students with low mathematical ability to determine the correct speed and acceleration are wrong. 3) the stage of carrying out the problem-solving plan for students with high mathematical abilities carrying out the problem-solving plan correctly, students with mathematical abilities carrying out the problem-solving plan at the right speed but not the right acceleration, while students with low mathematical ability carrying out the problem-solving plan incorrectly. 4) the stage of re-examining the problem solving of students with high mathematical abilities checked again correctly, students with medium and low mathematical abilities did not re-check their answers.

This study aims to describe students' mathematical understanding in solving mathematical problems from the perspective of Skemp's theory of understanding which consists of instrumental understanding and relational understanding. This type of research is descriptive qualitative in which students' mathematical understanding in solving exponential problems is described based on the results of mathematical understanding tests and interviews. This research was conducted in class X SMA Darul Faqih Indonesia and the research subjects were taken from students with high, medium, and low mathematical abilities, each of which was represented by two subjects from each category.The results of this study indicate that students with high mathematical abilities are able to find mathematical relationships, apply them, and explain the reasons, which include relational understanding. Students with moderate mathematical ability are able to apply memorized procedures in finding solutions to problems but are unable to explain the reasons, which include instrumental understanding. Meanwhile, students with low mathematical ability have low mathematical understanding because they are unable to meet the indicators of relational understanding and instrumental understanding. This study recommends that students with low mathematics abilities are trained to apply mathematical theory to increase their understanding into instrumental understanding while students with moderate mathematical abilities are trained to find mathematical theory to increase their understanding into relational understanding.

Mathematical ability is the ability required by students to solve a problem, students with high abilities will find it easy to solve problems because they have a good understanding of concepts, whereas students with low abilities will find it difficult to solve problems because they do not understand concepts correctly, which is what causes students to make conceptual errors. A condition when students experience a conceptual error is called a misconception. This research is a qualitative study that has the purpose to describe the misconceptions at each level, such as high mathematical ability, moderate mathematical ability, and low mathematical ability on quadrilateral material and alternatives to overcome them. The subjects in this study were 3 students who were selected using purposive sampling. In this study, students were given a mathematical ability test so that they could be grouped according to their level, then misconceptions were analyzed using a misconception test with the modified CRI method and continued with a diagnostic interview. The results showed that students with low mathematical abilities experienced more misconceptions than other abilities. The three subjects experienced misconceptions in determining the shapes which include rectangular shapes and the nature of rectangular. The causes of misconceptions are caused by pictures, students' abilities, and incomplete reasoning. The alternatives that can be done to overcome misconceptions are providing cognitive conflict, providing scaffolding, and re-explanation.
 Keywords: misconception, quadrilateral, mathematical ability, alternative to overcome misconceptions.

The aim of this research is to describe junior high school students' critical thinking skills in solving congruence problems based on mathematical abilities. Critical thinking skills are a person's cognitive process in interpreting, analyzing, evaluating, inferring, explaining and self-regulating in the process of making reflective and focused judgments. This research is a qualitative descriptive study. The research took place at As - Syafiah Loceret Islamic Middle School, Nganjuk. Subjects were selected based on their level of mathematical ability, namely one student each with high, medium and low mathematical ability. Researchers act as the main instrument and data collector. Data collection techniques using mathematics ability tests, mathematics assignments, and semi-structured interviews. The research results showed that junior high school students in solving congruence problems demonstrated interpretation skills: categorization and decoding; analytical skills: examination of ideas, identification of arguments and analysis of arguments; evaluation skills : claim assessment and argument assessment; inference skills: questioning claims, alternative thinking and drawing conclusions, explanation skills: presentation of problems, justification of procedures and articulation of arguments, self-regulation skills: self-research. Students' critical thinking skills appear optimally in students with high mathematical abilities as evidenced by the emergence of all sub-indicators of critical thinking skills, less so in students with moderate mathematical abilities as evidenced by less than optimal identification of arguments for certain questions and the absence of alternative thinking for the mathematical tasks presented. Meanwhile, students with low mathematical abilities find it difficult so that their analysis, evaluation, inference, explanation and self-regulation skills are not perfect.

This study is descriptive research that aims to describe students' collaborative problem solving (CPS) skills in solving mathematics problems. The subjects in this study were 6 students at grade XI consisting of 2 students with high mathematical abilities, 2 students with moderate mathematical abilities, and 2 students with low mathematical abilities. The six of them were divided into 3 groups consisting of 2 students with different mathematical abilities. The three groups were given mathematics problems to be solved collaboratively. The results of this study were analyzed using the semiotic Peirce model approach which uses a trichotomous relationship between representamen (Z), interpretant (I), and object (O) to show the CPS process that occurs. The results of the study show that students' CPS skills vary. The CPS process of high and moderate mathematical ability students is running quite well. Meanwhile, the CPS process of high and low mathematical ability students and moderate and low mathematical ability students was not as good as expected because of the little interaction or discussion between the members of the group in solving problems

Introduction. Learning mathematics accompanied by understanding is an essential component of factual and procedural knowledge skills practical for students in solving real-life problems. Errors in solving systems of linear equations in two variables (SPLDV) among students can be caused by various factors, including students' lack of understanding of this concept, so this problem must be studied in depth by utilizing task with scaffolding. The research aimed to explore the potential of a task to foster mathematical understanding of students from the image-having layer to the property noticing layer in the learning context of a system of linear equations in two variables (SPLDV). Study participants and methods. The study involved three students in grade 8 at a junior high school in Indonesia. They were selected based on their mathematical ability (low, moderate, and high) based on their accumulated score reports in grade 7 and information from the teacher who taught them. This study employed a qualitative research approach, data collection was carried out by giving task to students, observing, and interviews them while doing the task, and data analysis began with transcription and organizing the results of interviews and student task, followed by identification and classification of difficulties faced by students. The results. The study showed that student with low mathematical ability has difficulty recognizing patterns or relationships between coefficients and variables in equations. Even with the help of scaffolding, the student still did not succeed in strengthening her understanding to complete the task given, so her understanding only shifted slightly from the image having layer and could not move completely to the property noticing layer. Next, a student with moderate mathematical ability had a sufficient understanding of the concept of variables and coefficients. However, she still needed additional help to complete task, especially in determining the value of variable. She was observed to be already at the property noticing layer of understanding because she had been able to identify the property of two linear equations in two variables that is equivalence and complete the task given. Lastly, the student with high mathematical ability could understand the relevant mathematical concepts well. She could complete the task assigned well despite folding back and scaffolding. Thus, this student's understanding reached the property noticing layer. Conclusions. The research showed differences in the growth of mathematical understanding from the image having layer to the property noticing layer among junior high school students with low, medium, and high mathematical ability. The student with lower math skills was only slightly shifted from the image having layer and could not be transferred completely to the property noticing layer. The student with moderate mathematical ability had reached the layer of understanding properties because she was able to identify equivalent properties of two linear equations in two variables and complete the given task. Lastly, the student with high mathematical skills has reached the layer of property noticing.

This research aims to describe the profile of written mathematics communication in the mathematics problems solving of SMP in terms of the mathematics ability. This research is a qualitative research because the main data about the accuracy, completeness, and fluency of written mathematics communication in the form of written words. Subjects consisted of one student with high, medium, and low mathematics ability. The results of research indicate that the accuracy of written mathematics communication of students with high and medium mathematics ability is equally accurate for any information submitted. The accuracy of written mathematics communication of students with low mathematics ability is accurate to write the things that are known and asked and use rule. The completeness of written mathematics communication of students with high mathematics ability is complete for any information submitted. The completeness of written mathematics communication of students with medium mathematics ability is complete for information submitted except calculation. The completeness of written mathematics communication of students with low mathematics ability is complete for information submitted except for drawing/sketching and performing calculations. The fluency of written mathematics communication students with high and medium mathematics ability is equally fluent. The fluency of written mathematics communication students with low mathematics ability is not fluent.

Argumentation is an essential mathematical skill employed in mathematical literacy. Argumentation is an individual's ability to think critically to provide reasons based on facts to make conclusions that solve problems. A qualitative approach is used in this study to describe students' argumentation in solving mathematical literacy problems based on mathematics ability level. The research subjects were three twelfth-grade students: one with high mathematics ability, one with moderate mathematics ability, and one with low mathematics ability, which was selected purposively. Data are collected through mathematical literacy problem tests and interviews. The data are analyzed using McNeill and Krajcik's argumentation components: claim, evidence, reasoning, and rebuttal in solving mathematical literacy problems. The results showed that students with high mathematical abilities could formulate and perform the procedures at the evidence indicator; connect information for reasoning indicators; provide general solutions, represent and assess the mathematical solutions at the rebuttal indicators; and make a correct claim. Students with moderate mathematical ability could apply mathematical concepts although made a miscalculation at the evidence indicator; connect information for reasoning indicators; provide partially correct solutions; represent and evaluate the sufficiency of the mathematics solutions at the rebuttal indicator; and make a correct claim. Meanwhile, students with low mathematical ability miss a crucial concept and make miscalculations at the evidence indicator; connect information for reasoning indicators; provide and represent partially correct solutions but cannot evaluate the sufficiency of the mathematics solutions at the rebuttal indicator; provide a correct claim.
 Keywords: Argumentation, McNeill Argumentation, Mathematical Literacy Problems, Mathematical Abilities.