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Journal articles on the topic 'Mathematical principles'

Author: Grafiati

Published: 18 May 2024

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1

Killeen, Peter R. "Mathematical principles of reinforcement." Behavioral and Brain Sciences 17, no. 1 (March 1994): 105–35. http://dx.doi.org/10.1017/s0140525x00033628.

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AbstractEffective conditioning requires a correlation between the experimenter's definition of a response and an organism's, but an animal's perception of its behavior differs from ours. These experiments explore various definitions of the response, using the slopes of learning curves to infer which comes closest to the organism's definition. The resulting exponentially weighted moving average provides a model of memory that is used to ground a quantitative theory of reinforcement. The theory assumes that: incentives excite behavior and focus the excitement on responses that are contemporaneous in memory. The correlation between the organism's memory and the behavior measured by the experimenter is given by coupling coefficients, which are derived for various schedules of reinforcement. The coupling coefficients for simple schedules may be concatenated to predict the effects of complex schedules. The coefficients are inserted into a generic model of arousal and temporal constraint to predict response rates under any scheduling arrangement. The theory posits a response-indexed decay of memory, not a time-indexed one. It requires that incentives displace memory for the responses that occur before them, and may truncate the representation of the response that brings them about. As a contiguity-weighted correlation model, it bridges opposing views of the reinforcement process. By placing the short-term memory of behavior in so central a role, it provides a behavioral account of a key cognitive process.

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Atmaja, I. Made Dharma. "Prinsip Induksi Matematika dalam Pengambilan Keputusan Organisasi." CENDEKIA : Jurnal Penelitian dan Pengkajian Ilmiah 1, no. 4 (April 14, 2024): 115–31. http://dx.doi.org/10.62335/v1519165.

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The principle of mathematical induction can be an effective tool in organizational decision making. Although these principles have the potential to increase efficiency, reduce uncertainty, and increase accuracy in organizational decision making, their application is limited and has not been fully exploited. Studies need to be conducted to bridge this gap by strengthening the understanding and application of the principles of mathematical induction in the context of organizational decision making. By considering the gaps that occur, it is necessary to conduct research on "The Principle of Mathematical Induction in Organizational Decision Making". This research provides an overview of how the principles of mathematical induction can bridge this gap and improve the quality of decision making in an organizational context. The research method used in this research is a qualitative approach and literature study which involves analysis of relevant literature related to the principles of mathematical induction in the context of organizational decision making. The conclusions from this research are: 1) Applying the principles of mathematical induction in organizational decision making can strengthen efficiency, reduce uncertainty, and increase accuracy in decision making; 2) In applying the principles of mathematical induction in organizational decision making, there are obstacles and challenges that need to be overcome; and 3) Utilizing the principles of mathematical induction involves the use of structured methods, in-depth analysis, and a more objective approach.

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3

Abboud, Mahmoud. "Arabic grammar by mathematical principles." Lebanese Science Journal 21, no. 2 (December 27, 2020): 230–39. http://dx.doi.org/10.22453/lsj-021.2.230-239.

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In mathematics, any equation is formed from specific elements; these elements are connected to each other according to a system of relationships (Borowski, 1995). This system allows us to build the general rule for the equation or the mathematical issue; similarly, the sentence is formed from elements that have grammatical properties, which can be transformed to mathematical data. Hence, the elements or the words that carry the grammatical properties of the sentence correlate to each other to form a mathematical relation; this mathematical relation forms the theory of sentence construction. Therefore, the analysis process is correct when we can collect mathematical data contained within the elements; in other words, we indicate the mathematical data contained in the words located in a specific sentence. These mathematical data will form the elements of the mathematical theory of the Arabic sentence.

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Nemer Abboud, Mahmoud. "Arabic Grammar by Mathematical Principles." Lebanese Science Journal 21, no. 2 (February 13, 2022): 252–61. http://dx.doi.org/10.22453/lsj-021.2.252-261.

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In mathematics, any equation is formed from specific elements; these elements are connected to each other according to a system of relationships (Borowski, 1995). This system allows us to build the general rule for the equation or the mathematical issue; similarly, the sentence is formed from elements that have grammatical properties, which can be transformed to mathematical data. Hence, the elements or the words that carry the grammatical properties of the sentence correlate to each other to form a mathematical relation; this mathematical relation forms the theory of sentence construction. Therefore, the analysis process is correct when we can collect mathematical data contained within the elements; in other words, we indicate the mathematical data contained in the words located in a specific sentence. These mathematical data will form the elements of the mathematical theory of the Arabic sentence.

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5

Patterson, Jim. "Physical principles versus mathematical rigor." Physics Teacher 38, no. 4 (April 2000): 214. http://dx.doi.org/10.1119/1.880508.

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6

Kieu, Tien D. "Quantum Principles and Mathematical Computability." International Journal of Theoretical Physics 44, no. 7 (July 2005): 931–42. http://dx.doi.org/10.1007/s10773-005-7070-y.

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7

Muraskin, Murray. "Mathematical aesthetic principles and nonintegrable systems." Physics Essays 28, no. 3 (September 5, 2015): 399–412. http://dx.doi.org/10.4006/0836-1398-28.3.399.

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8

Solodov, Alexander A. "MATHEMATICAL PRINCIPLES OF BUILDING RATING SYSTEMS." Statistics and Economics, no. 1 (January 1, 2016): 75–82. http://dx.doi.org/10.21686/2500-3925-2016-1-75-82.

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9

Latinčić, Dragan. "Possible principles of mathematical music analysis." New Sound, no. 51 (2018): 153–74. http://dx.doi.org/10.5937/newso1851153l.

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The text is a summary of many years of research in the domains of micro-intervals, metric-rhythmic projection of the spectrum harmonics, and the establishment of a link with mathematics, more precisely, geometry, with a special focus on the application of the Pythagorean Theorem. Mathematical music analysis enables the establishment of methods for constructing right, obtuse, and acute musical triangles as well as projections of their edges (sides), which are recognized in trigonometry as the functions of angles: the sine, cosine, and so on; as well as the establishment of methods for constructing spectral and scalar (intonative-temporal) trigonometric unit circles with their function graphs.

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10

Watkinson, Adam C., and Keith R. Brain. "BASIC MATHEMATICAL PRINCIPLES IN SKIN PERMEATION." Journal of Toxicology: Cutaneous and Ocular Toxicology 21, no. 4 (January 2002): 371–402. http://dx.doi.org/10.1081/cus-120016396.

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11

Wu, Xuemou, Xiangjun Feng, and Dinghe Guo. "Pansystems philosophy and its mathematical principles." Kybernetes 30, no. 9/10 (December 2001): 1087–109. http://dx.doi.org/10.1108/03684920110405575.

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12

Ting-he, Lu, Jin Jun, and Hang Yong-zhen. "The mathematical principles of vibration reductor." Applied Mathematics and Mechanics 7, no. 4 (April 1986): 355–63. http://dx.doi.org/10.1007/bf01898225.

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13

Jensen, Erik Ottar, Emilie Madeline Hersaa Nehammer, and Anna Louise Eriksen. "Enhancing Mathematical Reasoning in Primary School with the Strategic Board Game Othello." European Conference on Games Based Learning 17, no. 1 (September 29, 2023): 289–95. http://dx.doi.org/10.34190/ecgbl.17.1.1524.

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This study explores how the board game Othello can enhance primary school students' mathematical reasoning. Mathematical reasoning is increasingly emphasized in international mathematics curricula, yet both teachers and students face challenges in teaching and learning this important skill. Research shows that strategic games, like Othello, can develop thinking abilities related to mathematical reasoning by providing a context for students to engage in reflective thinking, anticipate future moves, and develop reasoning strategies. However, there is a need to understand how teachers can effectively utilize these games in the classroom to foster mathematical reasoning. We address this, through a design-based research approach consisting of a hermeneutic literature study and the development of design principles for a teaching intervention in a fifth-grade classroom. Data from the intervention is collected through participant observations and group interviews. The findings suggest that Othello can serve as a context for students to engage in mathematical reasoning by making and justifying claims and presenting logical arguments. The study proposes three design principles to scaffold mathematical reasoning during Othello gameplay. These principles focus on introducing and reinforcing the use of the "if...then" formulation, promoting exploratory talk, encouraging reflection on strategies, and fostering collaborative reasoning. The results indicate that the design principles positively impacted students' ability to reason mathematically. This paper contributes to the field of mathematics education and game-based learning by providing a practice-oriented perspective on designing mathematical instruction for reasoning using a specific board game in a primary school setting. The findings offer insights into the potential of strategic board games like Othello to enhance students' mathematical reasoning skills. The design principles proposed in this study can guide teachers in developing effective instructional approaches to support students' mathematical reasoning development.

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Trowell, Sandra Davis. "SONA: An Activity for Exploring the GCF." Mathematics Teaching in the Middle School 24, no. 2 (October 2018): 116–22. http://dx.doi.org/10.5951/mathteacmiddscho.24.2.0116.

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15

Demidov, Aleksandr, Ekaterina Kosarina, Olga Krupnina, and Natalya Mikhailova. "Mathematical Principles of X-Ray Computer Tomography." Vestnik MEI, no. 3 (June 22, 2022): 136–46. http://dx.doi.org/10.24160/1993-6982-2022-3-136-146.

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Loginova, L., E. Seslavina, and A. Seslavin. "MATHEMATICAL METHODS AND BASIC PRINCIPLES OF TRANSPORTATION." Transport Business of Russia, no. 4 (2021): 84–87. http://dx.doi.org/10.52375/20728689_2021_4_84.

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17

Kopp, Audrey. "The Folktale: Linking Story to Mathematical Principles." Humanistic Mathematics Network Journal 1, no. 14 (1996): 42–44. http://dx.doi.org/10.5642/hmnj.199601.14.15.

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18

Михеєва, Анастасія Миколаївна, Олег Миколайович Петріщев, and Александр Владимирович Богдан. "Principles of acousto-optical cells mathematical modeling." Electronics and Communications 20, no. 4 (May 30, 2016): 61–72. http://dx.doi.org/10.20535/2312-1807.2015.20.4.69910.

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19

Stewart, Ian G. "The principia: mathematical principles of natural philosophy." Studies in History and Philosophy of Science Part A 35, no. 3 (September 2004): 665–67. http://dx.doi.org/10.1016/j.shpsa.2004.06.012.

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20

Sufrin, Bernard. "Principles of Computer Programming: A Mathematical Approach." Science of Computer Programming 13, no. 1 (December 1989): 117–19. http://dx.doi.org/10.1016/0167-6423(89)90018-x.

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21

Newton, Isaac, and Alan E. Shapiro. "The Principia: Mathematical Principles of Natural Philosophy." Physics Today 53, no. 3 (March 2000): 73. http://dx.doi.org/10.1063/1.883005.

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22

Chen, P. J. "Mathematical principles of a new interferometric system." Il Nuovo Cimento B Series 11 106, no. 9 (September 1991): 983–1001. http://dx.doi.org/10.1007/bf02728342.

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23

Nev, Olga A., and Hugo A. Van Den Berg. "Mathematical Models of Microbial Growth and Metabolism: A Whole-Organism Perspective." Science Progress 100, no. 4 (November 2017): 343–62. http://dx.doi.org/10.3184/003685017x15063357842583.

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We review the principles underpinning the development of mathematical models of the metabolic activities of micro-organisms. Such models are important to understand and chart the substantial contributions made by micro-organisms to geochemical cycles, and also to optimise the performance of bioreactors that exploit the biochemical capabilities of these organisms. We advocate an approach based on the principle of dynamic allocation. We survey the biological background that motivates this approach, including nutrient assimilation, the regulation of gene expression, and the principles of microbial growth. In addition, we discuss the classic models of microbial growth as well as contemporary approaches. The dynamic allocation theory generalises these classic models in a natural manner and is readily amenable to the additional information provided by transcriptomics and proteomics approaches. Finally, we touch upon these organising principles in the context of the transition from the free-living unicellular mode of life to multicellularity.

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24

Gün, Özge, and Fatih Taş. "An Evaluation of Mathematical Tasks Designed by Pre-Service Teachers Within the Framework of Task Design Principles." International Journal for Mathematics Teaching and Learning 22, no. 2 (December 9, 2021): 17–32. http://dx.doi.org/10.4256/ijmtl.v22i2.372.

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It is important to support pre-service teachers in terms of mathematical task design so as to increase the success of their future teaching. The purpose of this study was to evaluate mathematical tasks designed by pre-service primary and elementary mathematics teachers within the framework of task design principles. For this purpose, a total of 43 tasks corresponding to the learning objectives in primary and elementary school mathematics curriculum were examined through content analysis. Results revealed that pre-service teachers have considered aim of task, classroom organization, students’ prior knowledge and multiple start point principles for all or most of their tasks; measurement and evaluation principle for almost half of their task; and instruction for using materials and student’s misconceptions and difficulties principles for very few of their tasks. This study can provide teacher educators with a guideline for improving their programs to support pre-service teachers in terms of mathematical task design.

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25

Gupta, Dittika, and Lara K. Dick. "Launching mathematical success." Teaching Children Mathematics 25, no. 4 (January 2019): 249–52. http://dx.doi.org/10.5951/teacchilmath.25.4.0249.

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Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014) calls for integrating into the classroom real-world activities that connect mathematical ideas to other subjects and contexts. Motivated by the desire to make these connections, we devised a paper airplane design task to engage students in various STEM concepts.

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26

Jumaev, M. I. "Some psychological and pedagogical principles of mathematical education." Professional education in the modern world 10, no. 4 (January 30, 2021): 4310–20. http://dx.doi.org/10.20913/2618-7515-2020-4-15.

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The article deals with the construction of regular inscribed polygons, which are of great scientific and practical importance. As a result of solving such problems, new formations arise, new systems of connections are formed, new properties, qualities of the mind (flexibility, depth, awareness), which mark a progressive shift in mental development. This is why the effect of math training is directed at this side of the psyche. To increase its developing effect, it is necessary to take into account the specifics of thinking, the ratio of age and individual mental characteristics of schoolchildren. Let us now consider the problem of humanizing higher education. Humanitarianization presupposes, first of all, the introduction of a young person to the humanitarian culture of mankind. In other words, humanitarization is usually seen as an additional and necessary component of professional education. The author draws attention to the issues of humanitarization of mathematical education in Uzbekistan for further improving the system of teaching mathematical science at all levels of education, support the effective work of teachers, expand the scale and increase the practical significance of research, and strengthen ties with the international community.

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27

Perminov, Y. A. "Methodology Principles of Mathematical Training of Vocational Teachers." Education and science journal 1, no. 5 (March 3, 2015): 36. http://dx.doi.org/10.17853/1994-5639-2013-5-36-53.

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28

Yudianto, E., F. F. Firmansyah, P. S. B. S. Akbar, R. Nisyak, F. A. Maudi, and A. N. Saputri. "Lamp control using the principles of mathematical logic." Journal of Physics: Conference Series 983 (March 2018): 012064. http://dx.doi.org/10.1088/1742-6596/983/1/012064.

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29

Wain-Hobson, Simon. "Virus Dynamics: Mathematical Principles of Immunology and Virology." Nature Medicine 7, no. 5 (May 2001): 525–26. http://dx.doi.org/10.1038/87836.

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30

Nevin, John A. "Mathematical principles of reinforcement and resistance to change." Behavioural Processes 62, no. 1-3 (April 2003): 65–73. http://dx.doi.org/10.1016/s0376-6357(03)00018-4.

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31

Quill, Timothy J. "The Mathematical Principles of Automatic Pharmacokinetic Infusion Controllers." International Anesthesiology Clinics 33, no. 3 (June 1995): 83–90. http://dx.doi.org/10.1097/00004311-199503330-00007.

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32

Mujumdar, Arun S. "A Review of: “Mathematical Principles of Heat Transfer”." Drying Technology 24, no. 2 (March 2006): 245. http://dx.doi.org/10.1080/07373930600559233.

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33

Maia Neto, José Raimundo. "John Craige's Mathematical Principles of Christian Theology (review)." Journal of the History of Philosophy 30, no. 3 (1992): 456–57. http://dx.doi.org/10.1353/hph.1992.0052.

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34

Chen, Fu, Junkang Zou, Lingfeng Zhou, Zekai Xu, and Zhenyu Wu. "Improvements on Recommender System Based on Mathematical Principles." OALib 10, no. 07 (2023): 1–9. http://dx.doi.org/10.4236/oalib.1110281.

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35

van der Giessen, E., and F. G. Kollmann. "On Mathematical Aspects of Dual Variables in Continuum Mechanics. Part 1: Mathematical Principles." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 76, no. 8 (1996): 447–62. http://dx.doi.org/10.1002/zamm.19960760807.

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36

Omran, Mahamed G., and Andries Engelbrecht. "Time Complexity of Population-Based Metaheuristics." MENDEL 29, no. 2 (December 20, 2023): 255–60. http://dx.doi.org/10.13164/mendel.2023.2.255.

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This paper is a brief guide aimed at evaluating the time complexity of metaheuristic algorithms both mathematically and empirically. Starting with the mathematical foundational principles of time complexity analysis, key notations and fundamental concepts necessary for computing the time efficiency of a metaheuristic are introduced. The paper then applies these principles on three well-known metaheuristics, i.e. differential evolution, harmony search and the firefly algorithm. A procedure for the empirical analysis of metaheuristics' time efficiency is then presented. The procedure is then used to empirically analyze the computational cost of the three aforementioned metaheuristics. The pros and cons of the two approaches, i.e. mathematical and empirical analysis, are discussed.

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37

Thomas, Christine, and Carmelita Santiago. "Spotlight on the Principles/Standards: Building Mathematically Powerful Students through Connections." Mathematics Teaching in the Middle School 7, no. 9 (May 2002): 484–88. http://dx.doi.org/10.5951/mtms.7.9.0484.

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Connections in mathematics can be implemented in ways that create excitement in the classroom, develop in students a love for doing mathematics, and foster students' natural inclination for pursuing mathematical tasks. According to the Curriculum and Evaluation Standards for School Mathematics, “If students are to become mathematically powerful, they must be flexible enough to approach situations in a variety of ways and recognize the relationships among different points of view” (NCTM 1989, p. 84). Principles and Standards for School Mathematics (NCTM 2000) further asserts that students develop a deeper and more lasting understanding of mathematics when they are able to connect mathematical ideas. The 1989 and 2000 Standards clearly delineate the power and importance of connections in the mathematics curriculum. This article examines and compares curricular recommendations for connections in the two documents.

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Əzizxan oğlu Eyyubov, Ramazan, Leyla Elxan qızı Bayramova, and Zeynəb Mirsəməd qızı Sadıqova. "Computer architecture and John von Neumann principles." SCIENTIFIC WORK 15, no. 2 (March 9, 2021): 11–15. http://dx.doi.org/10.36719/2663-4619/63/11-15.

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The program is stored in the machine's memory from any external device. The control device organizes its execution, taking into account the program in memory. The mathematical-logical device performs mathematical and logical calculations in accordance with the entered commands. Thus, the computer performs calculations without human assistance. Key words: computer, software, device, information, scheme

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39

Goldberg, Dorothy. "In Celebration: Newton's Principia, 1687–1987." Mathematics Teacher 80, no. 9 (December 1987): 711–14. http://dx.doi.org/10.5951/mt.80.9.0711.

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Three hundred years have passed since the publication in 1687 of Philosophiae Naturalis Principia Mathematica (The mathematical principles of natural philosophy). Sir Isaac Newton's great scientific treatise, commonly known as the Principia, was published in London on 5 July 1687.

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40

Koirala, Hari P., and Phillip M. Goodwin. "Middle-Level Students Learn Mathematics Using the U.S. Map." Mathematics Teaching in the Middle School 8, no. 2 (October 2002): 86–90. http://dx.doi.org/10.5951/mtms.8.2.0086.

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Middle school educators have widely accepted the importance of interdisciplinary curricula (Cook and Martinello 1994), and Principles and Standards for School Mathematics argues that mathematics should be linked with other subject areas at all levels (NCTM 2000). According to Principles and Standards, “thinking mathematically involves looking for connections, and making connections builds mathematical understanding” (p. 274). Therefore, connecting mathematics to other disciplines has become particularly important.

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41

Kozlov, K. O. "MODELING PRINCIPLES OF SPATIALLY DISTRIBUTED RADAR SYSTEMS." Issues of radio electronics, no. 3 (March 20, 2018): 7–10. http://dx.doi.org/10.21778/2218-5453-2018-3-7-10.

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The physical and mathematical principles of bistatic radar are considered in the article, the essential characteristics are considered when constructing a mathematical model of a spatially distributed radar system. The necessity of software implementation of such a model for further investigation of bistatic radars is substantiated. The article discusses the necessity of upgrading radar equipment to improve the quality of the detection and identification of small flying machines and means of achieving this. Discusses the physical and mathematical principles of non-emitting radar system with diversity receiver and the transmitter upon detection of air targets on the background of the underlying surface, are analyzed essential when constructing mathematical models of spatially-separated radar systems. Provides a general description of the scheme, non-emitting radar station and timing diagram of signals within the system with diversity receiver and the transmitter. Analyzed analytical expressions for modeling non-emitting radar - which allows you to analyze the system in different variations, on the basis of the results obtained by theoretical calculations and experimental studies. The necessity of a software implementation of this model for further research on bistatic radar.

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Karamyshev, Anton N., and Zhanna I. Zaytseva. "“MATHEMATICA” IN TEACHING STUDENTS MATHEMATICS." Práxis Educacional 15, no. 36 (December 4, 2019): 610. http://dx.doi.org/10.22481/praxisedu.v15i36.5937.

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The relevance of the topic of the article is due to the process of modernization of higher mathematical education in Russia, which has led to a significant change in curricula and the need to look for ways and forms of training that would allow students to learn the necessary material within the time granted for studying, while obtaining the maximum necessary amount of skills, knowledge, and competencies. The objective of the article is to justify the ways and principles of the development and implementation of new pedagogical and information technologies in the educational process, the organization of professional education of students in technical areas based on the integration of mathematics and computer science. The leading method of the study of this problem is the methodological analysis and subsequent synthesis, which, by analyzing the didactic content of the sections in mathematics and the possibilities of the computer mathematical environment called Mathematica, reveals the necessary methods and ways of developing and using modern computer technologies in the mathematical education of engineering students. It is proved that one of the main tools for implementing the methods for solving the indicated problem should be considered a computer, namely, the mathematical environment called Mathematica, and the basic principles of its systemic implementation in the educational process of the university have been identified. The materials of the article may be useful to teachers of mathematical disciplines of higher educational institutions, the computer programs and pedagogical software products created in Mathematica can serve as models for the development of similar pedagogical software products.

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43

Rao, Rojukurthi Sudhakar. "Different & Variable Natural Processes Not Opposed to Salvability of Human Mind’s Mathematical Principles." International Journal of Research Publication and Reviews 5, no. 1 (January 8, 2024): 2575–383. http://dx.doi.org/10.55248/gengpi.5.0124.0252.

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44

Suh, Jennifer M., Christopher J. Johnston, and Joshua Douds. "Enhancing Mathematical Learning in a Technology-Rich Environment." Teaching Children Mathematics 15, no. 4 (November 2008): 235–41. http://dx.doi.org/10.5951/tcm.15.4.0235.

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In Principles and Standards for School Mathematics (NCTM 2000), the Technology Principle asserts: “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning” (p. 24). More specifically, a technology-rich environment for mathematical learning influences five critical features of the classroom (Hiebert et al. 1997): the nature of classroom tasks, the mathematical tool as learning support, the role of the teacher, the social culture of the classroom, and equity and accessibility. An essential question when working in a technology-rich mathematics environment is how technology can be used (appropriately) to enhance the teaching and learning of mathematics.

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Superfine, Alison Castro, Wenjuan Li, and Mara V. Martinez. "Developing Preservice Teachers' Mathematical Knowledge for Teaching: Making Explicit Design Considerations for a Content Course." Mathematics Teacher Educator 2, no. 1 (September 2013): 42–54. http://dx.doi.org/10.5951/mathteaceduc.2.1.0042.

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Research has highlighted the nature of the mathematical work in teachers' practice. However, preservice mathematics coursework often too narrowly focuses on the development of common content knowledge and not enough on the development of specialized content knowledge, a kind of mathematical knowledge that is specific to the work of teaching mathematics. We offer three design principles that have informed a mathematics content course for elementary preservice teachers, and we provide learning outcomes data that suggest the overall content course experience supports specialized content knowledge development. We provide relevant examples from our own work to illustrate how we have applied these design principles in our local context. Our aim is to begin a dialogue about principled design considerations for content courses for preservice teachers.

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Odil Kizi, Urolbaeva Shokhsanam. "THE CONTENT OF MATHEMATICAL DEVELOPMENT OF PRESCHOOLERS." International Journal of Pedagogics 03, no. 03 (March 1, 2023): 37–39. http://dx.doi.org/10.37547/ijp/volume03issue03-07.

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This topic deals with the problem of mathematical education of pre-schoolers. The content of mathematical development of children, its structure and approaches to the development of the content of mathematical development is given on the basis of program documents "From birth to school", "Childhood". Here is the implementation of the principles of mathematics, a personality-oriented approach, developing learning in the formation of mathematical representations of preschool children of older groups.

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Caldon, Patrick, and Aleksandar Ignjatović. "On mathematical instrumentalism." Journal of Symbolic Logic 70, no. 3 (September 2005): 778–94. http://dx.doi.org/10.2178/jsl/1122038914.

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AbstractIn this paper we devise some technical tools for dealing with problems connected with the philosophical view usually called mathematical instrumentalism. These tools are interesting in their own right, independently of their philosophical consequences. For example, we show that even though the fragment of Peanos Arithmetic known as IΣ1 is a conservative extension of the equational theory of Primitive Recursive Arithmetic (PRA). IΣ1 has a super-exponential speed-up over PRA. On the other hand, theories studied in the Program of Reverse Mathematics that formalize powerful mathematical principles have only polynomial speed-up over IΣ1.

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Pečiuliauskienė, Palmira. "Application of Statistical Methods in Education Sciences: the Didactical Principles in the Educational Means Prepared by Bronislovas Bitinas." Pedagogika 124, no. 4 (December 2, 2016): 47–57. http://dx.doi.org/10.15823/p.2016.50.

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Based on works of professor B. Bitinas this article analyses educational materials on applying statistical methods in education sciences. The educational materials on applying statistical methods in education sciences can be classified into two groups: methodological group (the application of mathematical statistics in quantitative research) and technological group (computer software for processing quantitative research data). The article analyses application of didactical principles in the methodological group and the technological group. Didactical principles provide direction for learning process and govern contents, methods and organisation of learning. Different didactical principles can be used when preparing educational materials on the applying statistical methods in education as principle of the availability and principle of relation between the theory and practise. Application of statistical methods in education sciences is influenced by technological tools used for processing statistical data. These tools changed from electronic calculating machines (ECM) to modern computers with modern statistical programs. Technological change influences didactical principles applied for preparing educational materials on applying statistical methods in education sciences. The comparative analysis of learning materials on applying statistical methods in education sciences prepared by Professor B. Bitinas shows that the principle of availability was an important principle at the time of the processing statistical data using the ECM. This principle is less important when statistical data is processed using modern statistical computer programs. Didactical principle of the relation between theory and practice was important in the early (the eighth-ninth decade of XX century) and later stages (the twentyfirst century.) Professor B. Bitinas prepared both methodological (the usage of mathematical statistics into quantitative research) and technological (computer software for quantitative research data processing) learning means. The didactical principles in the methodological and technological learning means are different. The principle of the availability and the principle of relation between the theory and practise dominate in the methodological learning means. The principle of systematization and continuity is important in technological learning means.

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Staples, Megan, and Melissa M. Colonis. "Making the Most of Mathematical Discussions." Mathematics Teacher 101, no. 4 (November 2007): 257–61. http://dx.doi.org/10.5951/mt.101.4.0257.

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The importance of mathematical discourse and its connection to developing conceptual understanding, communication, and reasoning is well documented throughout NCTM's Principles and Standards for School Mathematics (2000). For example, NCTM's Learning Principle emphasizes the role of discourse in supporting student learning, noting that “classroom discourse and social interaction can be used to promote the recognition of connections among ideas and the reorganization of knowledge (Lampert 1986)” (NCTM 2000, p. 21). The skillful facilitation of discussions is something both novice and experienced teachers find challenging. Most teachers can recall a well-planned lesson that did not unfold as expected. From this article, we hope readers gain insight into planning mathematically focused, collaborative discussions. We illuminate three key aspects of the pedagogy of teachers who were successful in consistently organizing whole-class discussions. These teachers created learning environments aligned with NCTM's vision of good practice, where students were given conceptually demanding tasks, worked together to develop ideas, and consistently were asked to make sense of mathematics.

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Sriraman, Bharath. "Discovering Steiner Triple Systems through Problem Solving." Mathematics Teacher 97, no. 5 (May 2004): 320–26. http://dx.doi.org/10.5951/mt.97.5.0320.

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Principles and Standards for School Mathematics (NCTM 2000) calls for instructional programs that emphasize problem solving and that have the goal of helping students develop sophistication with such mathematical processes as representation, mathematical reasoning, abstraction, and generalization. In particular, the Problem Solving Standard suggests that teachers should choose problems that further the mathematical goals of the class. Problem solving can be viewed as a process through which teachers can help students think mathematically, which Schoenfeld (1985, 1992) defines as developing a mathematical point of view. It includes valuing the processes of representation and abstraction and having the predisposition to generalize them. In this article, I describe my attempt to implement problem solving as a teacher of ninthgrade algebra. I had two explicit goals in mind. The first goal was to use carefully chosen problemsolving situations as a setting for an extended mathematical investigation that leads to the discovery of Steiner triple systems. The second goal was to use problem-solving situations to help students think mathematically, that is, to construct representations and to engage in mathematical reasoning, abstraction, and generalization.

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