The purpose of this study was to describe the design results of problem-solving question used to measure mathematical thinking type abstraction for junior high school students. The data analysis that used in this study is qualitative. This is design research which is divided into five stages, namely: Preliminary design, focus group discussion, trial, interview, and retrospective analysis. Based on the results of FGD, trial and interview, it was found that the question classified as problem-solving question, and could be used to measure mathematical thinking types abstraction, seen from the results of the subject answers that give rise the activities of abstraction which are observation of patterns, specialization, generalization, conjecturing, and testing conjectures. Observation of patterns can be seen from the subject that resolves the problem by observing the patterns. Specialization appears from the completion of the subject by looking at a specific example. Generalization is seen from the solution that describes a pattern into a general form. Conjecturing is composing allegations in solving problems. The last testing conjectures which is a process of checking and testing of guesses, whether the assumptions taken are right and correct.
This study aims to analyze or examine the mathematical thinking student type of reasoning in completing problem-solving question. The subjects in this study were 29 students from one of the schools in Palembang, totalling 29 students will be taken 6 students after the test. The instrument used in this study is a problem solving question totalling 2 items. In this research the mathematical thinking is more focused on the ability of reasoning which is divided into 3 types namely deductive and inductive. The results of the analysis of mathematical thinking type reasoning show that from question number 1 there are three different answers from 6 subjects, from the answers and results of their interviews can be concluded that in working on number one, 3 students use deductive reasoning, 2 students use inductive reasoning and 1 student is wrong in using formulas, and from question number 2 of the six students only three can meet the three indicators of inductive reasoning, most only arrive at the stage of expression of generality.
This study is design research aimed to describe the design result of problem-solving question that can be used to measure mathematical thinking type representation. The process of this study consists of five stages, namely: preliminary design, focus group discussions (FGD), trials, observation and interview, and retrospective analysis. The subjects of this study are three students. The technique for data analysis was qualitative. The instrument consists of test and directive interview. Based on preliminary design and FGD stages, researchers have designed two problem-solving questions. Based on the results of the trials, observations and interviews, all these questions can lead students’ mathematical thinking type representation. This is illustrated by the results of research subjects’ answers when working on questions that showing symbolic representation, numeric representation, and visual representation. Symbolic representation is seen from the completion of students who use symbols to solve problem number 1 and 2. Visual representation is seen from students resolve the problems using images to solve problem number 2. Numeric representation is seen from students solving problems using a trial and error strategy and then doing mathematical calculations to make sure the correctness of answers. This is done by students in working on questions number 1.
Mathematical thinking is a thought process in developing a mathematical perspective that involves other mathematical abilities such as modeling, reasoning, proving, symbolization, representation, abstraction, and mathematization. This study aims to describe the design results of problem-solving question that can be used to measure mathematical thinking type mathematization. This research is design research consisting of five stages, namely: preliminary design, focus group discussions, trials, observations and interviews, and retrospective analysis. The instrument consisted of test, observation, and interview. Data analysis uses qualitative methods. Based on data analysis, the problem-solving questions that are designed can already measure mathematical thinking type mathematization. This can be theoretically seen from the results of focus group discussions, which states the questions have been based on content, construct and language. Illustrated from the results of the trial, the strategies that have been used by the subject specifically on question number 1 is by making pictures and using certain mathematical formulas. Which solution illustrates that the subject has geometrization and formalization capabilities. Whereas in problem number 2, the mathematical ability that arises is connecting and formalization because in solving problems most subjects associate certain mathematical concepts and ideas with use facts, concepts and rules of mathematics.
This study aims to describe the mathematical thinking of 13-year-old students through problem-solving. Mathematical thinking consist of several aspects, namely: reasoning, abstraction, symbolization, and representation. The respondents were 6 students. The instruments used were tests and interviews. Tests are used two problem-solving. The data collection used qualitative approach. The conclusion is deductive dominant in reasoning. The formal form and geometrization are dominant in mathematization. All aspect of abstraction appears on students’ answer. Reasoning seen when students use prior knowledge and prior concept to solve problems. Abstraction appears when students find a particular form (pattern) of the problem being solved. mathematization appear when students visualize problems and use algebraic concepts to solve the problem.
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