Penggunaan Model Pembelajaran Snow Cube Throwing Berbasis Eksplorasi dalam Meningkatkan Kemampuan Intuisi Matematis Siswa

AbstrakModel pembelajaran snow cube throwing dikembangkan untuk melatih kemampuan intuisi siswa melalui kegiatan menebak/memperkirakan pola dari masalah-masalah eksplorasi yang diberikan. Sesuai dengan kekhasan model pembelajaran ini, siswa dapat berlatih banyak soal berbasis eksplorasi. Banyaknya soal-soal eksplorasi yang diberikan akan membantu siswa dalam mempertajam kemampuan intuisinya. Penelitian ini bertujuan menganalisis peningkatan kemampuan intuisi matematis yang mendapat pembelajaran SCTBE, eksploratif dan ekspositori ditinjau secara keseluruhan dan berdasarkan kategori sekolah. Penelitian ini merupakan penelitian kuasi eksperimen dengan rancangan non-equivalent pre-test and post-test control-group design. Populasi penelitian adalah siswa kelas VIII dari tiga sekolah di Kota Cimahi. Pemilihan sampel dalam penelitian kuantiatatif didasarkan pada teknik strata dan kelompok. Tes kemampuan intuisi matematis yang digunakan berbentuk uraian yang terdiri dari 5 soal. Hasil penelitian menunjukkan bahwa: Secara keseluruhan peningkatan kemampuan intuisi matematis siswa yang memperoleh pembelajaran snow cube throwing berbasis eksplorasi lebih baik dari siswa yang memperoleh pembelajaran eksploratif dan ekspositori; ditinjau berdasarkan kategori sekolah, pembelajaran snow cube throwing berbasis eksplorasi lebih cocok digunakan pada sekolah kategori tengah yang memiliki karakteristik aktif dan mandiri. The Use of Exploration-Based Snow Cube Throwing Learning Model in Improving Students' Mathematical Intuition AbilityAbstractThe snow cube throwing learning model was developed to practice students' intuition ability through guessing/predicting patterns of the given exploration problems. Following the uniqueness of this learning model, students can practice many exploration-based questions. The number of exploratory questions given will help students sharpen their intuitive abilities. This study aims to analyze the improvement of mathematical intuition ability that obtained SCTBE, explorative, and expository learning reviewed as a whole and based on school categories. This research was a quasi-experimental study with a non-equivalent pre-test and post-test control-group design. The study population was class VIII students from three schools in Cimahi City. Sample selection in quantitative research is based on strata and group techniques. The mathematical intuition ability test used is in the form of a description consisting of 5 questions. The results showed that: Overall improvement in mathematical intuition ability of students who obtained snow cube throwing based on exploration learning was better than students who obtained explorative and expository learning; based on the school category, snow cube throwing based on exploration learning is more suitable for middle category schools that have active and independent characteristics.

Mathematical Intuition: impact on non-math major undergraduates

The research question being investigated in this paper is how to improve the learning of calculus for non-math major students whose interests are primarily non mathematical. The study explores the impact of an intuitive approach applied to the concepts of limits and integration. The survey was carried on 1st year engineering students taking the Calculus-1 course. The students had already had a brief encounter with the topics in high school. They were surveyed about their outlook towards the concepts of limits and integration using the same pre and post inquiry form. The post analysis was conducted after introducing both the topics through an intuitive approach. The survey was analyzed for statistical significance using the Mc Nemar’s statistical test, which studies the impact of an intervention. Survey analysis indicated an improved understanding for the students and a positive change in their approach towards the topics.

Ignite the Spark of Wisdom——Thinking on the Cultivation of Elementary Students’ Mathematical Intuition Thinking Ability

In the learning process of primary mathematics, intuitive thinking remains an important section for students to analyze and solve mathematical problems, which has played an irreplaceable role in enlightening and developing the underlying intellectual and non-intellectual factors of students. By analyzing and comparing the relevant theories and research results regarding mathematical intuition thinking, as well as taking into account the learning characteristics of elementary students, the author has summarized four kinds of strategies suitable for training the mathematical intuition thinking ability of elementary students.

Charles Peirce and Bertrand Russell on Euclid

Both Charles Sanders Peirce (1839–1914) and Bertrand Russell (1872–1970) held that Euclid’s proofs in geometry were fundamentally flawed, and based largely on mathematical intuition rather than on sound deductive reasoning. They differed, however, as to the role which diagramming played in Euclid’s emonstrations. Specifically, whereas Russell attributed the failures on Euclid’s proofs to his reasoning from diagrams, Peirce held that diagrammatic reasoning could be rendered as logically rigorous and formal. In 1906, in his manuscript “Phaneroscopy” of 1906, he described his existential graphs, his highly iconic, graphical system of logic, as a moving picture of thought, “rendering literally visible before one’s very eyes the operation of thinking in actu”, and as a “generalized diagram of the Mind” (Peirce 1906; 1933, 4.582). More generally, Peirce personally found it more natural for him to reason diagrammatically, rather than algebraically. Rather, his concern with Euclid’s demonstrations was with its absence of explicit explanations, based upon the laws of logic, of how to proceed from one line of the “proof” to the next. This is the aspect of his criticism of Euclid that he shared with Russell; that Euclid’s demonstrations drew from mathematical intuition, rather than from strict formal deduction.

Epistemology and rationality of intuition and imagination in the field of mathematics

This paper aims to contribute to the clarification of the role of mathematical intuition and imagination in the constitution of mathematical knowledge, evidencing its epistemological and procedural characteristics. For that, an "epistemology of intuition and imagination" in the field of mathematics is outlined (suggested) emphasizing the need to adopt a dynamic conception of mathematics. In this context, intuition and imagination present themselves as forms of mathematical experience that give access, through paths that are not purely logical, to mathematical knowledge. Its epistemological and rationality characteristics, a rational of a non-logical nature, are highlighted by several examples, resources for moving the ideas involved. The epistemological study of intuition and imagination also allows highlighting its ontology, constituted of more relations than objects. From the pedagogical point of view, we discuss the formative character of philosophical studies involving intuition and imagination, mainly related to creativity in mathematics. Keywords: Mathematical knowledge; Mathematical experience; Epistemology of intuition and imagination; Creativity in mathematics.

The Effectiveness Of Using The Dunn And Dunn Model In Teaching The Unit Of Regular Fractions For Fifth-Grade Primary Students In Developing Achievement And Mathematical Intuition Skills

The current study aimed to reveal the effectiveness of using the Dunn and Dunn model in teaching the unit of regular fractions for fifth-grade primary students in developing achievement and mathematical intuition skills. The study sample was tested from fifth grade students in the first semester of Mosa ben Nosier school at Tabuk City, and they (30 students) were divided into two district groups; the first half (15 students) were allocated into the experimental group and the other half (15 students) made up the control group. After preparing and utilizing the instruments, the results of the research revealed the following: statistic between the mean scores of students of the experimental and control groups in the cognitive achievement test related to the unit of regular fractions in the first semester in favor of the average of the students of the experimental group, as it was found that there was a statistically significant difference at the level (0.01) between the average scores of students of the experimental group in the pre and post applications in the achievement test Cognitive, and in favor of the mean of post-application. The results also demonstrated that there were statistically significant differences between the control group and the experimental group in the mathematical intuition test as a whole, and in its components in the post-application for the benefit of the experimental group. Furthermore, the results indicated that to and statistically significant differences between the pre application and post application of the experimental group in the sport as a whole test intuition, and in its components in favor of the dimensional application, and in light of the results, this current study presents a number of recommendations as Encouraging math teachers to use the Dunn and Dunn model of learning styles to develop students' achievement and mathematical skills.

Intuitionism in the Philosophy of Mathematics: Introducing a Phenomenological Account

ABSTRACT The aim of this paper is to establish a phenomenological mathematical intuitionism that is based on fundamental phenomenological-epistemological principles. According to this intuitionism, mathematical intuitions are sui generis mental states, namely experiences that exhibit a distinctive phenomenal character. The focus is on two questions: what does it mean to undergo a mathematical intuition and what role do mathematical intuitions play in mathematical reasoning? While I crucially draw on Husserlian principles and adopt ideas we find in phenomenologically minded mathematicians such as Hermann Weyl and Kurt Gödel, the overall objective is systematic in nature: to offer a plausible approach towards mathematics.