A NEW UNCONSCIOUS PARADIGM AT THE HEART OF MATHEMATICS AND PHYSICS

It is already the case that philosophical foundations of mathematics and physics, need a serious critical analysis and revision of a number of generally accepted assumptions. In the future, this work may lead to a shift in the paradigm related to mathematics and physics. The article deals with the problem of the ideas of actual and potential infinity being not distinguished in the «fragmented thinking» of many mathematicians. We consider it necessary to differentiate between the concept of «representation of a number by an infinite decimal fraction» and the concept of «writing a numeral». A real number can be written in different ways, but every number must be uniquely represented using an infinite decimal fraction. First of all, we overcome the ambiguity of the representation of number 1 by assuming a potentially infinite set of signs of a periodic fraction and an actually infinite set of signs of a non-periodic fraction. This leads to the following harmonious scientific and philosophical system required by broad-minded scientists. 1. Every real number, including 0, (9) is represented by a single point of a continuous number line. 2. Every irrational number in decimal representation, unlike a rational number, does not have the last digit. 3. Real space, as well as past and future time are not mathematically equal and are referents of potentially and actually infinite, countable and uncountable sets. 4. The motion of a quantum micro-object, as a fundamental particle, is mathematically imaginary because a quantum particle has a countable set of points in time that is insufficient to move temporally and an uncountable set of points in space that is excessive for moving along the trajectory. Therefore, the motion of a quantum particle can be described as the path of a point in the plane of a complex variable.

1 Slash 100%: gamification of mathematics with hybrid QR-based card game

Mathematics is important in our life and society. However, gamification of mathematics is rare for the topics such as fractions and decimals. This paper presents the development of an educational mathematics game called One Slash One Hundred Percent (1 Slash 100%). It is the hybridization of conventional card game and Quick Response (QR). This research aims to study how the respondents explore the card game to master decimal, fraction and percentage. The testing was conducted among secondary school students in Kuching, Sarawak, Malaysia (n=12; age=14). The respondents were asked to answer a set of questions in pre-test and post-test question. The results were promising where the analysis showed a significant difference between pre (M=14.3, SD=2.103) and post-test scores (M=17.6, SD=2.234). Thus, gamification of mathematics using hybrid card game increases their mastery of decimal, fraction and percentage.

PENGEMBANGAN PERANGKAT PEMBELAJARAN PENJUMLAHAN DAN PENGURANGAN PECAHAN DESIMAL UNTUK KELAS V SEKOLAH DASAR DENGAN PENDEKATAN MATEMATIKA REALISTIK

ABSTRACTThe aim of this reseach is to describe learning device development process, to produce good learning device, and to describe the effectivity of device learning development in adding and subtracting decimal fraction using realistic mathematics in fifth grade at elementary school. This reseach using Plomp’ model. This model have four phases: preliminary investigation, design, realization/constructio, test, evaluation, and revision ; and implementation. This reseach produces: good learning device with criteria: (a) validity, the validator gives minal good apprasial at each document ; (b) practice. indicator of practicality of this device is teacher ability to manage the learning is in good category; (c) effectivity. Indicator of effectivity of this device is students activity fulfill effective criteria, suitable with ideal time and goal learning reach 82,75% ; (2) mathematic realistic are effectively with criteria; (a) clasical student learning result is 92,85%, (b) the teacher ability to manage the learning process is in good criteria. (c) the student activity fulfill effective criteria, (d) the student response of the learning process is positiveKeywords: learning device, Adding and substracting, decimal fraction, Realistic Mathematic. ABSTRAK Penelitian ini bertujuan untuk mendeskripsikan proses pengembangan perangkat pembelajaran, menghasilkan perangkat pembelajaran yang baik, dan mendeskripsikan keefektifan pembelajaran operasi penjumlahan dan pengurangan pecahan desimal di kelas V Sekolah Dasar dengan pendekatan matematika realistik. Model pengembangan yang digunakan sebagai acuan adalah model Plomp. Model pengembangan ini meliputi lima fase yaitu fase investigasi awal (preliminary investigation), fase desain (design), fase realisasi/konstruksi (realization/construction), fase tes, evaluasi dan revisi (test, evaluation, and revision), dan fase implementasi (implementation). Penelitian ini menghasilkan (1) perangkat pembelajaran yang baik dengan kriteria : (a) kevalidan, hasil penilaian validator terhadap perangkat pembelajaran mencapai 82,75 %; (2) Pembelajaran matematika realistik untuk mengajarkan operasi penjumlahan adalah minimal dalam kategori baik; (b) kepraktisan, diindikasikan dengan kemampuan guru mengelola pembelajaran berada dalam kategori baik; (c) keefektifan, dengan indikator aktivitas siswa memenuhi kriteria efektif sesuai dengan waktu ideal dan ketuntasan hasil belajar siswa secara klasikal mencapai 82,75 %; (2) Pembelajaran matematika realistik untuk mengajarkan operasi penjumlahan dan pengurangan pecahan desimal dengan kriteria : (a) hasil belajar siswa tuntas dengan persentase ketuntasan secara klasikal mencapai 92,85 %; (b) kemampuan guru mengelola pembelajaran berada dalam kategori baik; (c) aktivitas siswa memenuhi kriteria efektif; (d) respon siswa terhadap pembelajaran positif.Kata Kunci: Perangkat Pembelajaran, Penjumlahan dan Pengurangan Pecahan, Desimal, Pendekatan Matematika Realistik.

What is qualimetry? May we measure quality in points?

We are introducing the “Model standard of the public library”, where I once read that "scores can be expressed from zero to ten". Is it worth talking about quality in general, if we allow that one of the indicators can be zero? The evaluation of quality is the subject of the study of science, which is called qualimetry The one of founders of qualimetry was G. Azgaldov. However, there are still a lot of people willing to write about the evaluation of quality so that not a word to say about qualimetry. They did not read the books of Azgaldov, and some even dispense with the term qualimetry. Without knowing the qualimetry, we make an obvious methodological error in the assessment of quality. What can be done with digital indicators "from zero to ten"? It's obvious: fold it! You can also divide the amount obtained by the number of indicators: you get a certain "average"... with "zero" quality for one indicator. The quality of the "individual indicator" does not compensate for the lack of quality in another indicator. Too much quality in one does not cover shortcomings in the other: quality in quantitative terms is not summarized. Each indicator should be expressed in the form of a decimal fraction, with the norm (the standard of quality) being the score of 1. The cumulative quality of the object is expressed by multiplying the indicators. There can not be at least one indicator equal to zero (multiplying any integer by zero yields zero). Even if at least one indicator from many equals 0.1 or 0.2, the cumulative index falls so low that it makes us ashamed to talk about any quality! Another interesting and very important regularity for us is connected with the number of parameters for which an estimate is made - as the number of parameters increases, the quality assurance problems increase dramatically. Thus, a conditionally "permissible" cumulative estimate of 0.7 with a number of indicators equal to 7 can be obtained only if each of them is not lower than 0.9. It is necessary to think whether it is worthwhile to express an abstract "score" on the evaluation of the quality of work, which in one case "pulls" for two thousand hours, and in another characterizes the work of the library for many years?

PENGEMBANGAN PERANGKAT PEMBELAJARAN PENJUMLAHAN DAN PENGURANGAN PECAHAN DESIMAL UNTUK KELAS V SEKOLAH DASAR DENGAN PENDEKATAN MATEMATIKA REALISTIK

ABSTRACTThe aim of this reseach is to describe learning device development process, to produce good learning device, and to describe the effectivity of device learning development in adding and subtracting decimal fraction using realistic mathematics in fifth grade at elementary school. This reseach using Plomp’ model. This model have four phases: preliminary investigation, design, realization/constructio, test, evaluation, and revision; and implementation. This reseach produces: good learning device with criteria: (a) validity, the validator gives minal good apprasial at each document; (b) practice. Indicator of practicality of this device is teacher ability to manage the learning is in good category; (c) effectivity. Indicator of effectivity of this device is students activity fulfill effective criteria, suitable with ideal time and goal learning reach 82,75% ; (2) mathematic realistic are effectively with criteria; (a) clasical student learning result is 92,85%, (b) the teacher ability to manage the learning process is in good criteria. (c) the student activity fulfill effective criteria, (d) the student response of the learning process is positive Keywords: learning device, Adding and substracting, decimal fraction, Realistic Mathematic. ABSTRAK Penelitian ini bertujuan untuk mendeskripsikan proses pengembangan perangkat pembelajaran, menghasilkan perangkat pembelajaran yang baik, dan mendeskripsikan keefektifan pembelajaran operasi penjumlahan dan pengurangan pecahan desimal di kelas V Sekolah Dasar dengan pendekatan matematika realistik. Model pengembangan yang digunakan sebagai acuan adalah model Plomp. Model pengembangan ini meliputi lima fase yaitu fase investigasi awal (preliminary investigation), fase desain (design), fase realisasi/ konstruksi (realization/ construction), fase tes, evaluasi dan revisi (test, evaluation, and revision), dan fase implementasi (implementation). Penelitian ini menghasilkan (1) perangkat pembelajaran yang baik dengan kriteria : (a) kevalidan, hasil penilaian validator terhadap perangkat pembelajaran mencapai 82,75 %; (2) Pembelajaran matematika realistik untuk mengajarkan operasi penjumlahan adalah minimal dalam kategori baik; (b) kepraktisan, diindikasikan dengan kemampuan guru mengelola pembelajaran berada dalam kategori baik; (c) keefektifan, dengan indikator aktivitas siswa memenuhi kriteria efektif sesuai dengan waktu ideal dan ketuntasan hasil belajar siswa secara klasikal mencapai 82,75 %; (2) Pembelajaran matematika realistik untuk mengajarkan operasi penjumlahan dan pengurangan pecahan desimal dengan kriteria : (a) hasil belajar siswa tuntas dengan persentase ketuntasan secara klasikal mencapai 92,85 %; (b) kemampuan guru mengelola pembelajaran berada dalam kategori baik; (c) aktivitas siswa memenuhi kriteria efektif; (d) respon siswa terhadap pembelajaran positif. Kata Kunci: Perangkat Pembelajaran, Penjumlahan dan Pengurangan Pecahan, Desimal, Pendekatan Matematika Realistik.

The Analysis of Students’ Ability of Decimal Numeral Multiplication of the Fifth Grade Students

This study aimed to (1) describing Learning multiplication of decimal fractions in V grade,(2) The students' ability in completing the multiplication of decimal fractions, (3) The constraints which were faced by students in completing the multiplication of decimal fractions and the solutions to overcome those obstacles. The type of this study was descriptive quantitative and qualitative research. The subjects of this study were the fifth grade students of SD Negeri 2 Penarukan, consisted of 20 students and teachers in V class. The object of this study were (1) Learning multiplication decimal fraction in V grade, (2) The students' ability in completing the multiplication of decimal fractions, (3) The constraints which were faced by students in completing the multiplication of decimal fractions and the solutions to overcome those obstacles. The observation, test, interview, and documentation were used to collect the data. The data were analyzed using descriptive quantitative and qualitative approach. The results showed (1) Learning multiplication decimal fractions was categorized good with a value of 84 , (2) the average test results in classical 59.9 with low category with the highest indicators is to solve everyday problems which involves multiplication of various fractions 55.25% and the lowest indicator is determining the results of multiplication operations of various fractional 88.5 %, (3) The constraints faced by students are: forget the concept of decimal fractions multiplication operations, forget to put coma at the end of the answer and students are still confusein completing the essay task. The solution to overcome those constraints aregiving students a lot of exercises regarding the multiplication of decimal fractions. So that students are better trained and familiar with the particular multiplication exercises.