KNOWLEDGE IN PRACTICE OF TEACHING RATIO AND PROPORTION: A CASE OF TWO IN-SERVICE PRIMARY TEACHERS

This study draws upon an ongoing research in investigating the knowledge in practice regarding Mathematics Content Knowledge (MCK) and Mathematics Pedagogical Content Knowledge (MPCK). It investigated the enactment of teachers’ knowledge in teaching practice. I use mixed method to explore two in-service primary teachers’ MCK and MPCK understanding categories on ratio and proportion and analysed teaching practice in the same content with developed framework regarding exploratory factor analysis for video observation. The result indicated that some teachers’ respond on written assessment could be observed in practice. However, the students misconception on ratio and proportion which were explored in written assessment were seldom appear in teaching practice due to no task for students to reveal misconception. Keywords: MCK, MPCK, knowledge in practice, ratio and proportion, Indonesi

DESCRIBING SECONDARY STUDENTS’ GEOMETRIC PROBLEM SOLVING BY SEX

Students efforts in solving mathematical problems often involve the describing of data within the problem. One of the problems that often arises in mathematics is the problem of geometry. In this research, problem solving geometry of male and female students are described. The geometry problem solving written test was delivered, specifically the application of trigonometry in Geometry. This research was conducted by taking 17 eleventh grade students as participants and 2 students as research subjects. The results of the study show that Problem solving between male and female students has difference in the stages of planning, executing, and looking back. While at the stage of understanding is same. The differences can be caused by several factor such as a memory that occurs or post solution strategy to solve a given problem. Implication of study expected to be able to provide a deeper description of geometry problem solving so that in making geometry questions consider this research

Hubungan Keyakinan Siswa Tentang Matematika dan Pembelajarannya dengan Kemampuan Matematika

Abstrak Keyakinan merupakan dasar pikiran yang dapat memengaruhi pola pikir dan pandangan seseorang terhadap sesuatu sebelum bertindak. Keyakinan siswa tentang matematika adalah cara pandang siswa dalam menilai matematika, sedangkan keyakinan siswa terhadap pembelajaran matematika adalah cara pandang siswa dalam memelajari, memahami, dan menyelesaikan permasalahan matematika. Kemampuan matematika adalah kemampuan intelektul yang dimiliki siswa dalam pembelajaran matematika. Pada penelitian ini peneliti ingin mengetahui bagaimana hubungan keyakinan siswa terhadap matematika dan pembelajarannya terhadap kemampuan matematika. Jenis penelitian yang digunakan dalam penelitian ini adalah penelitian expost facto menggunakan uji korelasi karena untuk mengetahui hubungan antara variabel (keyakinan siswa tentang matematika dan pembelajarannya) dan variabel (kemampuan matematika siswa). Populasi dalam penelitian ini adalah siswa SMP Negeri 1 Sidoarjo kelas VIII yang berjumlah siswa. Teknik pengambilan sampel pada penelitian ini yaitu dengan mengambil dari jumlah populasi sehingga sampel yang diambil siswa. Instrumen pada penelitian ini berupa angket keyakinan siswa tentang matematika dan pembelajarannya dan tes kemampuan matematika. Teknik pengolahan dan analisis data pada penelitian ini menggunakan uji korelasi. Hasil pengujian korelasi pada penelitian ini menunjukkan hubungan yang signifikan antara keyakinan siswa tentang matematika dan pembelajaranya dengan kemampuan matematika siswa dengan Rhitung . Berdasarkan tabel kriteria korelasi, nilai ini berada pada rentang nilai yang menunjukkan bahwa korelasi antar variabel sangat kuat. Kata Kunci: Keyakinan, keyakinan matematika, kemampuan matematika Abstract Belief is the basis of thought that can influence ones mindset and view to something before acting. Students beliefs about mathematics are students perspective in assessing mathematics, while students beliefs about mathematics learning are the way students see in learning, understanding, and mathematics problem solving. Mathematics ability is the intellectual ability possessed by students in mathematics learning. In this study the researchers wanted to know how the students beliefs relate to mathematics and their learning to mathematical abilities. The type of research used in this study was expost facto research using correlation tests because to determine the relationship between variables x (students beliefs about mathematics and learning) and y variables (students mathematical abilities). The population in this study were students of SMP Negeri 1 Sidoarjo VIII class which amounted to students. The sampling technique in this study is taking of the population so that the sample is taken students. The instrument in this study was in the form of student confidence questionnaires about mathematics and learning and tests of mathematical abilities. Processing and data analysis techniques in this study used descriptive statistics and inferential statistics. The results of the correlation test in this study indicate a significant relationship between students beliefs about mathematics and their learning with students mathematics ability with Rcount . Based on the correlation criteria table, this value in the range of which indicates that the correlation between variables is very strong. Keywords: belief, mathematics belief, mathematics abilit

ANALYSIS OF LEARNER’S CONJECTURE ABILITY IN SOLVING OPEN-ENDED PROBLEMS

Conjecture will always be used by learners in problem solving, because the conjecture itself is tied to activities such as logical reasoning, translating problems, analyzing and evaluating an information to obtain valid decisions related to problem solving, where the conjecture is also able to develop the learning process of the learner in making a statement, especially with the help of open problems in its application,  Which can make learners morecreative. This research aims to illustrate the conjecture ability of learners in open-ended problems with descriptive types of research and qualitative approaches  to number pattern material, especially generalizing patterns. The subjects of the study are four learners who have a high and moderate level of mathematical ability and are willing to take part in interviews. The results showed that  all subjects have not been able to perform every stage on constructing the conjecture, especially in the stage of arguing the conjecture and there is one subject who does not do the stage of proof of the conjecture because it is confident in the formula that has been given by the teacher. So that learning activities are needed in which there is problem solving that collects the ability of learners' contours,  open-ended problems can also be one of the problem choices that can help students build their thought processes independently, and not bound by the formula of teachers or books

Horizontal and Vertical Mathematization Processes of Junior High School Students in Solving Open-Ended Problems

Mathematization is converting information from problems into mathematical models. The mathematization process is divided into horizontal and vertical mathematization. This descriptive qualitative research aimed to describe junior high school students' horizontal and vertical mathematization process in solving open-ended problems. The subjects are three students with good, medium, and poor mathematical problem-solving abilities. The instruments used were interview guidelines, mathematical problem-solving ability tests, and open-ended problem tests with topics area and perimeter of rectangles and circles. This research shows the horizontal and vertical mathematization process in solving open-ended problems. The horizontal mathematization process was; identifying the information and topics area and perimeter from the problem; representing the problem into some rectangle and circle figures and expressing the problem in the subject’s own words; writing the mathematics language; finding the regularity of the relations to find the possible solutions; and making mathematical models. The vertical mathematization process was; using mathematical representations with symbols and formulas related to the area and perimeter of rectangles and circles; using formal algorithms; customizing and combining some models to get the correct answers; making logical arguments to support the solution and other possible solutions that suit the problem; and generalizing the solution using the concepts of area and perimeter of rectangles and circles to solve similar problems. Every student may have different strategies and solutions when solving open-ended problems

The Decision Making Process of High School Students with High Mathematical Ability in Solving Social Arithmetic Problems

The decision making process is the individual steps in choosing an appropriate alternative choice from the various alternatives available to solve the problem. The purpose of this study is to describe the decision making process of high school students with high mathematical abilities in solving social arithmetic problems. The research approach used in this study is qualitative research. While the type of research is a qualitative descriptive study. The process of collecting data uses several instruments consisting of mathematics ability tests, social arithmetic problem solving tests, and interview guidelines. This research was conducted on 11th grade high school students in one of the state high schools in Sidoarjo. The subjects of this study consisted of one student with high mathematical abilities. The data collection method in this study began with the provision of mathematics ability tests for all students followed by selecting one subject with high mathematical ability through several considerations. The next step, the subject is given a problem solving test and interviewed to get the decision making process carried out by the subject. The results showed that students with high mathematical abilities carried out a series of activities in the stages of the decision making process, namely define the decision, understand the context, identify the options, prioritise the options, evaluate the consequences, review the decisions, and take actions

JUNIOR HIGH SCHOOL STUDENTS’ STRATEGY IN SOLVING GEOMETRY PROBLEM BASED ON MATHEMATICS ABILITY

Abstract This research aims to describe Junior High School students’ strategy in solving geometry problem based on mathematics ability. This is a descriptive research with qualitative approach. Subject was chosen from test of mathematics ability result. Subjects are students in class IX-i SMPN 1 Gresik who already studying 3D figure with flat side material. Data research taken from three subject with high mathematics ability and three subject with medium mathematics ability who are given test of solving geometry problem and interview. Based on data analysis, it found that student with high mathematics ability consider writing an equation or open sentences (WE) strategy, drawing picture, acting it out, and using model (DP) strategy, guessing and checking (GC) strategy and logical reasoning (LR) strategy. While student with medium mathematics ability consider writing an equation or open sentences (WE) strategy, drawing picture, acting it out, and using model (DP) strategy, and guessing and checking (GC) strategy. Based on data analysis, teacher are suggested to create learning activity that can stimulate student in using logical reasoning so that their logical reasoning can be developed. Keywords: strategy, geometry problem, mathematics abilit

Cognitive Processes of High Mathematics Anxiety Student in Solving Area Conservation Problem

Area conservation is a concept to modify the shape or position of a geometrical figure without changing its area. Skipping the concept of area conservation in learning area measurement causes students’ difficulties in this topic. One of students’ activity in math class is problem solving which is a cognitive process of the brain to search a solution for a given problem. Cognitive process is an activity that consist of receiving, processing, and using information. Cognitive process may affected by mathematics anxiety. Mathematics anxiety is a condition in which students experience unexplained anxiety during learning mathematics. This study is qualitative descriptive research which aimed at describing the cognitive processes of high mathematics anxiety student in solving area conservation problem. The data were collected by using mathematics anxiety test, area conservation problem test, and interview. The result showed that at the stage of receiving information, high mathematics anxiety students read the given problem and observe the given figures. At the stage of processing the information, the students devising plan by linked the received information with their knowledge, solving the problem, and evaluating the obtained solution. Student with high mathematics anxiety use the concept of area conservation to modify some figures. Moreover, high mathematics anxiety student did a simple estimation to determine the area of the given figures. At the stage of using information, student with high mathematics anxiety re-explain the given problem, the idea to solve the problem, every single steps in solving problem, and the obtained solution

Students Mathematical Connection in Problem Posing

Abstract Mathematics is a complex discipline, while in the learning process mathematics is taught to students in stages and divided into several chapters. Therefore, it requires mathematical connection skills to connect the concepts that have been learned to obtain meaningful knowledge Mathematical connection is students’ ability to use connection on inter-concepts in mathematics, connection with other disciplines, and apply mathematical ideas in the context of everyday life. Problem posing is an activity that can be used to see students’ mathematical connection. Problem posing is an activity to formulate or to make a question of the given situation and then try to solve it. One of the types of problem posing is pre-solution posing, which focuses on making questions based on the situation or information that will provide an open problem that can develop students mathematical connections. Semi-structured situation is one of the situations on problem posing that ask students to pose a problem from open condition which has chance to be completed by applying prior mathematical knowledge or concepts. This study is a qualitative descriptive research with two subjects which representing each category. This study used mathematical abilities test, mathematical problem posing test and interview to obtain the data. After that, The data obtained were analyzed by doing data condensation, data display and then drawing and verifying conclusions based on mathematical connection indicators. The results of the study has shown that each subject uses different connections in each aspects of. Students mathematical experiences influence the mathematical connections that students use in problem posing. Keywords: Mathematical Connection, Problem Posin

Development of Interactive Module Based on Realistic Mathematics Education for the Material of Numbers

During the Covid 19 pandemic, which required distance or online learning makes learning material difficult for students to understand, especially number material in junior high schools. One of the ways that teachers can use to facilitate students in learning is by taking approaches, one of which is the Realistic Mathematics Education (RME) approach. To support online learning where students can study independently with teacher guidance so that learning media is very important. One of the learning media developed is an interactive module based RME. The purpose of this research is to describe how the process of developing interactive modules based on realistic mathematics education on numbers and how the results of developing interactive modules are measured from the aspects of validity, practicality, and effectiveness as an alternative learning media. This study used research and development methods, the model used in this research was ADDIE (Analysis, Design, Development, Implementation, and Evaluation). The subjects of this study were 15 students in grade 7 junior high school. The test results showed that the module is valid with a percentage of 76,13% valid, from teachers 92,49% practical, from students 86,33% practical, and 88,66% effectiveness. The uniqueness of this interactive module is that it has interactive features such as videos, practice questions, and related learning media.  Based on the research conducted, the interactive modules can be said to be a good mathematics learning medium