Penanaman Karakter Penalaran Matematis dalam Pembelajaran Matematika melalui 1 Pola Pikir Induktif-Deduktif

One of the mathematics learning purposes is using reasoning in patterns and properties, mathematical manipulation in making generalization, compiling evidence, or explaining mathematical ideas and statements. Mathematical learning based on behaviorism has been seen as less successful in instilling character of mathematics reasoning. Therefore, it is necessary to find alternative learning not only teaching but instilling character of mathematical reasoning. This paper offers constructivist in mathematics learning, which is one of the ways to involve the use of inductive-deductive thinking. Activities that involve students learning to use the inductive-deductive mindset needs to be designed and implemented by teachers. Using inductive thinking can be conditioned, especially in the process of understanding a concept or generalization. Deductive thought patterns can be conditioned to improve mathematical reasoning, for example, in the proofing. The mindset of inductive and deductive mathematical reasoning is difficult to separate in the mathematical reasoning therefore it is regarded involving the use of inductive-deductive thinking

SECONDARY SCHOOL MATHEMATICS TEACHERS’ PERCEPTIONS ABOUT INDUCTIVE REASONING AND THEIR INTERPRETATION IN TEACHING

Inductive reasoning is an essential tool for teaching mathematics to generate knowledge, solve problems, and make generalizations. However, little research has been done on inductive reasoning as it applies to teaching mathematical concepts in secondary school. Therefore, the study explores secondary school teachers’ perceptions of inductive reasoning and interprets this mathematical reasoning type in teaching the quadratic equation. The data were collected from a questionnaire administered to 22 teachers and an interview conducted to expand their answers. Through the thematic analysis method, it was found that more than half the teachers perceived inductive reasoning as a process for moving from the particular to the general and as a way to acquire mathematical knowledge through questioning. Because teachers have little clarity about inductive phases and processes, they expressed confusion about teaching the quadratic equation inductively. Results indicate that secondary school teachers need professional learning experiences geared towards using inductive reasoning processes and tasks to form concepts and generalizations in mathematics

Critical review of geometry in current textbooks in lower secondary schools in Japan and the UK

This paper reports on an initial analysis of current best-selling textbooks for lower secondary schools in Japan and the UK (specifically Scotland) using an analytic framework derived from the study of the textbooks in the “Trends in International Mathematics and Science Study” (TIMSS). Our analysis indicates that, following the specification of the mathematics curriculum in these countries, Japanese textbooks set out to develop students’ deductive reasoning skills through the explicit teaching of proof in geometry, whereas comparative UK textbooks tend, at this level, to concentrate on finding angles, measurement, drawing, and so on, coupled with a modicum of opportunities for conjecturing and inductive reasoning

DESCRIBE REASONING OF STUDENTS IN COMPLETING THREE-DIMENSIONAL PROBLEM-SOLVING

This study aims to describe reasoning by highly capable subjects (ST), medium-impacted subjects (SS), and low-ability subjects (SR) in completing three-dimensional problem-solving tasks. This research is a qualitative descriptive research. Instruments in this study are researchers as the main instrument guided by the task of solving problems Mathematics and interview guidelines are valid. The subjects of this study were students of class XI IPA C consisting of 3 people (high-ability subject (ST), medium-skilled subjects (SS), and low-ability subjects (SR)). The research process follows the steps of: (a) formulating the reasoning indicator in solving Mathematics problem, (b) formulating the supporting instrument (valid problem solving task of Mathematics and interviewing), (c) did research subject taking, (d) perform data retrieval to uncover students' reasoning in Mathematical problem solving, (e) do triangulation techniques to obtain valid data  (f) perform analysis of student reasoning data in problem solving, (g) conduct discussion of result of analysis, (h) make a conclusion of research result. The results of a highly capable subject study show: 1) in understanding the problem using inductive reasoning type analogies, 2) planning completion using inductive reasoning, 3) carrying out the settlement plan using inductive and deductive reasoning, 4) re-examining using common procedures. While for the subject of moderate ability and low-ability subjects in solving problems only meet one reasoning indicator that is filed allegations (inductive type of analogy) is at the stage of understanding the problem. By looking at the students' abilities teachers need to provide non-routine questions so that students are better trained in reasoning and able to develop students' communication skills both in the learning process and in the community environment

Peningkatan Penalaran Siswa Dalam Pembelajaran Matematika Menggunakan Pendekatan Induktif (Ptk Pada Siswa Kelas Vii Smp Negeri 1 Kedunggalar Semester Ganjil Tahun 2015/2016)

The purpose of this research is to improve students’s reasoning in mathematics learning using an inductive approach. This research is a classroom action research. The subject of recipient action in this study were VII C grade students of Secondary School 1 Kedunggalar, while the subject of implementing measures is a mathematics teacher. The implementation of action class was performed for two cycle, four meetings. The data was collected by observation, documentations, test methods and field notes. To insure the validity of data it used triangulation of source and triangulation of techniques. The technique of analysis data used by reduction of data, presentasion of data and verification of data. The results showed an increasing of students learning mathematics reasoning using inductive approach seen from the percentage of: (1) the student is able to forward allegations from 8,57% up to 71,43%; (2) the student is able to perform mathematical manipulations from 28,57% up to 77,14%; (3) the student is able to appeal conclusions from 14,28% up to 74,28%; (4) the student is able to explain from 8,57% up to 71,43%. It can be concluded that the application of inductive approach in teaching mathematics can improve students’s reasoning

DEDUCTIVE OR INDUCTIVE? PROSPECTIVE TEACHERS’ PREFERENCE OF PROOF METHOD ON AN INTERMEDIATE PROOF TASK

The emerging of formal mathematical proof is an essential component in advanced undergraduate mathematics courses. Several colleges have transformed mathematics courses by facilitating undergraduate students to understand formal mathematical language and axiomatic structure. Nevertheless, college students face difficulties when they transition to proof construction in mathematics courses. Therefore, this descriptive-explorative study explores prospective teachers' mathematical proof in the second semester of their studies. There were 240 pre-service mathematics teachers at a state university in Surabaya, Indonesia, determined using the conventional method. Their responses were analyzed using a combination of Miyazaki and Moore methods. This method classified reasoning types (i.e., deductive and inductive) and types of difficulties experienced during the proving. The results conveyed that 62.5% of prospective teachers tended to prefer deductive reasoning, while the rest used inductive reasoning. Only 15.83% of the responses were identified as correct answers, while the other answers included errors on a proof construction. Another result portrayed that most prospective teachers (27.5%) experienced difficulties in using definitions for constructing proofs. This study suggested that the analytical framework of the Miyazaki-Moore method can be employed as a tool to help teachers identify students' proof reasoning types and difficulties in constructing the mathematical proof

An approach to mathematical induction - starting from the early stages of teaching mathematics

It is well-known that the method of proof by mathematical induction often creates serious problems to students who encounter these proofs in secondary schools. It is therefore important to prepare the students for understanding and the application of the method of mathematical induction. For this purpose, our students should develop the abilities to notice, compare, generalize, conjecture by analogy and conjecture by inductive reasoning. On the other hand, the examples showing that conjectures suggested by inductive reasoning could be incorrect, should be pointed out at early stages. In that way, we show the students the need of proving the conjectures as well as finding the methods for proving. In this paper we mention a number of such examples through which the students at early stages of teaching mathematics are induced to inductive reasoning, but we also mention examples which illustrate how cautious one has to be when accepting hypotheses obtained by inductive reasoning

An approach to mathematical induction - starting from the early stages of teaching mathematics

It is well-known that the method of proof by mathematical induction often creates serious problems to students who encounter these proofs in secondary schools. It is therefore important to prepare the students for understanding and the application of the method of mathematical induction. For this purpose, our students should develop the abilities to notice, compare, generalize, conjecture by analogy and conjecture by inductive reasoning. On the other hand, the examples showing that conjectures suggested by inductive reasoning could be incorrect, should be pointed out at early stages. In that way, we show the students the need of proving the conjectures as well as finding the methods for proving. In this paper we mention a number of such examples through which the students at early stages of teaching mathematics are induced to inductive reasoning, but we also mention examples which illustrate how cautious one has to be when accepting hypotheses obtained by inductive reasoning

ANALISIS KEMAMPUAN PENALARAN INDUKTIF MATEMATIS MAHASISWA PENDIDIKAN MATEMATIKA UNIVERSITAS PAPUA

This research was conducted to analyze the mathematical Inductive reasoning abilities of students’ mathematics education UNIPA. Research on inductive mathematical reasoning skills using qualitative methods using observation techniques, tests and interviews. The results showed that the mathematical inductive reasoning abilities of mathematics education students UNIPA were mostly in the moderate category. Students' inductive reasoning ability on each indicator is the ability to present mathematical statements in writing or drawings of 66.66%, the ability to submit suspicions by 26.66%, mathematical manipulation ability of 29.44%, ability to compile evidence, provide reasons or evidence for some solutions of 5.82%, finding patterns or traits of mathematical symptoms to generalize of 30.27%, examining validity of arguments 11.32% and drawing conclusions from statements of 5.27%.   DOI: https://doi.org/10.30862/jhm.v1i2.104