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Journal articles on the topic 'Computational Mathematics'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 June 2025

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1

Dean, Walter. "Computational Complexity Theory and the Philosophy of Mathematics†." Philosophia Mathematica 27, no. 3 (2019): 381–439. http://dx.doi.org/10.1093/philmat/nkz021.

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Abstract Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof.

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Mezhoud, Salim. "Language Mathematics and Mathematics Language, Reading from Computational Linguistics." Mathematical Linguistics 1, no. 1 (2021): 7–24. http://dx.doi.org/10.58205/ml.v1i1.140.

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The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language using technical terms and grammatical conventions that are peculiar to mathematical discourse, supplemented by a highly specialized symbolic notation for mathematical formulas. mathematical characterizations of various notions of linguistic complexity include also computational linguistics, philosophical logic, knowledge representation as a branch of artificial intelligence, theoretical computer science, and computational psychology. Mathematical linguistics has initially served as a foundation for computational linguistics, though its research agenda of designing machines to simulate natural language understanding is clearly more applied. Inductive methods have gained the upper hand in applied computational linguistics The question is whether mathematics is a language, or that language is mathematical, and how computational linguistics employs language as mathematics.

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Azevedo, Greiton Toledo de, Marcus Vinicius Maltempi, and Arthur Belford Powell. "Contexto Formativo de Invenção Robótico-Matemática: Pensamento Computacional e Matemática Crítica." Bolema: Boletim de Educação Matemática 36, no. 72 (2022): 214–38. http://dx.doi.org/10.1590/1980-4415v36n72a10.

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Resumo Neste artigo buscamos identificar e compreender as características do contexto formativo em Matemática de estudantes quando produzem jogos digitais e dispositivos robóticos destinados ao tratamento de sintomas da doença de Parkinson. Norteados pelas ideias da metodologia qualitativa de pesquisa, interagimos com alunos do Ensino Médio visando a construção de um jogo eletrônico com dispositivo robótico, chamado Paraquedas, destinado a sessões de fisioterapia de pacientes com Parkinson. Os alunos foram estimulados a propor e desenvolver ideias em ambientes voltados à experimentação e invenções eletrônicas para beneficiar pessoas em sociedade. Os dados foram analisados à luz dos pressupostos teóricos do Pensamento Computacional e da Matemática Crítica e consistem de discussão-análises do desenvolvimento científico-tecnológico, colaborativo-argumentativo e inventivo-criativo de tecnologias, indo além dos muros da sala de aula de Matemática. Como resultado, identificamos as seguintes características do contexto formativo em Matemática: independência formativa; imprevisibilidade de respostas; aprendizagem centrada na compreensão-investigação-invenção; e conexão entre áreas de conhecimento. Compreendemos que tais características se originam e mutuamente se desenvolvem dinâmico e idiossincraticamente nas concepções de planejamento, diálogo e protagonismo dos sujeitos, os quais fomentam a exploração de problemas aberto e inéditos de Matemática em-uso e descentralizam a formalização excessiva do rigor de objetos matemáticos como ponto nevrálgico à formação em Matemática.

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4

Russell, Susan Jo. "Principles and Standards: Developing Computational Fluency with Whole Numbers." Teaching Children Mathematics 7, no. 3 (2000): 154–58. http://dx.doi.org/10.5951/tcm.7.3.0154.

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Principles and Standards for School Mathematics (NCTM 2000) emphasizes the goal of computational fluency for all students. It articulates expectations regarding fluency with basic number combinations and the importance of computational facility grounded in understanding (see a summary of key messages regarding computation in Principles and Standards in the sidebar on page 156). Building on the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and benefiting from a decade of research and practice, Principles and Standards articulates the need for students to develop procedural competence within a school mathematics program that emphasizes mathematical reasoning and problem solving. In fact, learning about whole-number computation is a key context for learning to reason about the baseten number system and the operations of addition, subtraction, multiplication, and division.

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Annamalai, Chinnaraji. "Computation and Calculus for Combinatorial Geometric Series and Binomial Identities and Expansions." Journal of Engineering and Exact Sciences 8, no. 7 (2022): 14648–01. http://dx.doi.org/10.18540/jcecvl8iss7pp14648-01i.

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Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and computational equations for solving today’s scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with combinatorial geometric series, and innovative binomial theorems. Combinatorics involves integers, factorials, binomial coefficients, discrete mathematics, and theoretical computer science for finding solutions to the problems in computing and engineering science. The combinatorial geometric series with binomial expansions and its theorems refer to the methodological advances which are useful for researchers who are working in computational science. Computational science is a rapidly growing multi-and inter-disciplinary area where science, engineering, computation, mathematics, and collaboration use advance computing capabilities to understand and solve the most complex real-life problems.

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Abramovich, Sergei. "Computational Triangulation in Mathematics Teacher Education." Computation 11, no. 2 (2023): 31. http://dx.doi.org/10.3390/computation11020031.

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The paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser used as background for (what is called in the paper) computational triangulation in the context of four digital tools. Computational problem solving and problem formulating are presented as two sides of the same coin. By revealing the hidden mathematics of Fibonacci numbers included in the Brain Teaser, the paper discusses the role of computational thinking in the use of the well-ordering principle, the generating function method, digital fabrication, difference equations, and continued fractions in the development of computational algorithms. These algorithms eventually lead to a generalized Golden Ratio in the form of a string of numbers independently generated by digital tools used in the paper.

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7

Matevossian, Hovik A., and Francesco dell’Isola. "“Computational Mathematics and Mathematical Physics”—Editorial I (2021–2023)." Axioms 12, no. 9 (2023): 824. http://dx.doi.org/10.3390/axioms12090824.

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Based on the papers published in the Special Issue of the scientific journal Axioms, here we present the Editorial Article “Computational Mathematics and Mathematical Physics”, the main topics of which include both fundamental and applied research in computational mathematics and differential equations of mathematical physics [...]

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8

Webb, Nigel, M. Beilby, and G. McCauley. "Introduction to Computational Mathematics." Mathematical Gazette 71, no. 457 (1987): 243. http://dx.doi.org/10.2307/3616782.

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MTW, Zhongying Chen, Yuesheng Li, Charles A. Micchelli, and Yuesheng Xu. "Advances in Computational Mathematics." Journal of the American Statistical Association 95, no. 450 (2000): 690. http://dx.doi.org/10.2307/2669442.

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10

Fillion, Nicolas. "Conceptual and Computational Mathematics†." Philosophia Mathematica 27, no. 2 (2019): 199–218. http://dx.doi.org/10.1093/philmat/nkz005.

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Lenstra Jr., H. W., Steven M. Serbin, Stig Larsson, Ohannes Karakashian, J. Thomas King, and Ewald Quak. "Book Review: Mathematics of Computation 1943--1993: A half-century of computational mathematics." Mathematics of Computation 66, no. 219 (1997): 1367–75. http://dx.doi.org/10.1090/s0025-5718-97-00877-6.

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Nocar, David, George Grossman, Jiří Vaško, and Tomáš Zdráhal. "The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry." Computation 11, no. 11 (2023): 222. http://dx.doi.org/10.3390/computation11110222.

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This article explores the accessibility of symbolic computations, such as using the Wolfram Mathematica environment, in promoting the shift from informal experimentation to formal mathematical justifications. We investigate the accuracy of computational results from mathematical software in the context of a certain summation in trigonometry. In particular, the key issue addressed here is the calculated sum ∑n=044tan⁡1+4n°. This paper utilizes Wolfram Mathematica to handle the irrational numbers in the sum more accurately, which it achieves by representing them symbolically rather than using numerical approximations. Can we rely on the calculated result from Wolfram, especially if almost all the addends are irrational, or must the students eventually prove it mathematically? It is clear that the problem can be solved using software; however, the nature of the result raises questions about its correctness, and this inherent informality can encourage a few students to seek viable mathematical proofs. In this way, a balance is reached between formal and informal mathematics.

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Mainzer, Klaus. "The Digital and the Real Universe. Foundations of Natural Philosophy and Computational Physics." Philosophies 4, no. 1 (2019): 3. http://dx.doi.org/10.3390/philosophies4010003.

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In the age of digitization, the world seems to be reducible to a digital computer. However, mathematically, modern quantum field theories do not only depend on discrete, but also continuous concepts. Ancient debates in natural philosophy on atomism versus the continuum are deeply involved in modern research on digital and computational physics. This example underlines that modern physics, in the tradition of Newton’s Principia Mathematica Philosophiae Naturalis, is a further development of natural philosophy with the rigorous methods of mathematics, measuring, and computing. We consider fundamental concepts of natural philosophy with mathematical and computational methods and ask for their ontological and epistemic status. The following article refers to the author’s book, “The Digital and the Real World. Computational Foundations of Mathematics, Science, Technology, and Philosophy.”

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Duffy, Austen C. "Where do computational mathematics and computational statistics converge?" Wiley Interdisciplinary Reviews: Computational Statistics 6, no. 5 (2014): 341–51. http://dx.doi.org/10.1002/wics.1313.

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Turner, Raymond. "Computational Abstraction." Entropy 23, no. 2 (2021): 213. http://dx.doi.org/10.3390/e23020213.

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Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code; without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure and seeks to find a more concrete one. Abstraction does the reverse: it starts with concrete structures and abstracts away. While formal accounts of representation are easy to find, abstraction is a different matter. In this paper, we provide an analysis of data abstraction based upon some contemporary work in the philosophy of mathematics. The paper contains a mathematical account of how Frege’s approach to abstraction may be interpreted, modified, extended and imported into type theory. We argue that representation and abstraction, while mathematical siblings, are philosophically quite different. A case of special interest concerns the abstract/physical interface which houses both the physical representation of abstract structures and the abstraction of physical systems.

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Mendrofa, Netti Kariani. "Computational Thinking Skills in 21st Century Mathematics Learning." JIIP - Jurnal Ilmiah Ilmu Pendidikan 7, no. 1 (2024): 792–801. http://dx.doi.org/10.54371/jiip.v7i1.3780.

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Computational thinking skills are a crucial mental skill in the 21st century, enabling individuals to solve problems, understand data, and make decisions with a structured and computational-based approach. Integrating computational thinking skills in mathematics learning has an important role in preparing students to become skilled in thinking computationally in the 21st century. The method used in this research is library research in which relevant data are collected from sources such as books, dictionaries, journals, magazines, and others without the need to conduct direct investigations in the field. Applying computational thinking in mathematics learning will foster skills such as decomposition (breaking down a problem into manageable parts), pattern recognition, abstraction, and algorithm design as well as developing analytical and abstract thinking skills.

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Pérez, Arnulfo. "A Framework for Computational Thinking Dispositions in Mathematics Education." Journal for Research in Mathematics Education 49, no. 4 (2018): 424–61. http://dx.doi.org/10.5951/jresematheduc.49.4.0424.

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This theoretical article describes a framework to conceptualize computational thinking (CT) dispositions—tolerance for ambiguity, persistence, and collaboration—and facilitate integration of CT in mathematics learning. CT offers a powerful epistemic frame that, by foregrounding core dispositions and practices useful in computer science, helps students understand mathematical concepts as outward oriented. The article conceptualizes the characteristics of CT dispositions through a review of relevant literature and examples from a study that explored secondary mathematics teachers' engagement with CT. Discussion of the CT framework highlights the complementary relationship between CT and mathematical thinking, the relevance of mathematics to 21st-century professions, and the merit of CT to support learners in experiencing these connections.

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Elwes, Richard, and Rob Sturman. "Developing computational mathematics provision in undergraduate mathematics degrees." MSOR Connections 18, no. 2 (2020): 59–65. http://dx.doi.org/10.21100/msor.v18i2.1097.

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Over the last ten years we have comprehensively embedded computational mathematics, and in doing so programming, into the undergraduate mathematics degree programmes at the University of Leeds. This case study discusses some of the practical, organisational and pedagogical issues we encountered, and how we addressed them.

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Laghrib, A., L. Afraites, M. Nachaoui, and A. Ghazdali. "Special Issue: Recent Developments of Optimization and Computational Mathematics." Statistics, Optimization & Information Computing 11, no. 1 (2023): 1. http://dx.doi.org/10.19139/soic-2310-5070-1741.

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The evolution of mathematics gave rise to several new fields, among them we can find Data Science and someapplications to mathematics and computer science. Recently, Data science is considered as a dynamic and attractive research area with numerous usability in other scientific fields, such as: Machine Learning, Data Mining and computer science, especially in Image Processing. For that and to closely follow the evolution of Data Science using recent mathematical tools, we propose this special issue which contains a number of papers on various mathematical tools, optimization and their applications. This special issue contains carefully selected articles from the first edition of the conference ``International Conference on New Trends of Applied Mathematics (ICNTAM)”, which is held at B\'{e}ni Mellal, Morocco from 19 to 21 May 2022.

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Bass, Hyman. "Computational Fluency, Algorithms, and Mathematical Proficiency: One Mathematician's Perspective." Teaching Children Mathematics 9, no. 6 (2003): 322–27. http://dx.doi.org/10.5951/tcm.9.6.0322.

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In recent years, few aspects of mathematics education have been as much discussed and debated as the notions of computational fluency and algorithms. A National Research Council report, Adding It Up: Helping Children Learn Mathematics (Kilpatrick, Swafford, and Findell 2001), offers an image of what it means to have skill with mathematics, or mathematical proficiency. This concept is helpful for moving beyond these debates. Mathematical proficiency includes five components: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (Kilpatrick, Swafford, and Findell 2001, p. 116). That these components are not separate but fundamentally intertwined is important to note. This article illustrates some of the ways in which the goal of computational fluency and an appreciation of mathematical algorithms are related to this larger concept of mathematical proficiency.

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Tomasiello, Stefania, Carla M. A. Pinto, and Ivanka Stamova. "Computational Mathematics and Neural Systems." Mathematics 9, no. 7 (2021): 754. http://dx.doi.org/10.3390/math9070754.

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E, Weinan. "Machine Learning and Computational Mathematics." Communications in Computational Physics 28, no. 5 (2020): 1639–70. http://dx.doi.org/10.4208/cicp.oa-2020-0185.

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Clune, Megan. "Computational thinking in primary mathematics." Set: Research Information for Teachers, no. 3 (December 20, 2019): 43–50. http://dx.doi.org/10.18296/set.0151.

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Daly, Tim. "Scripta Manent: Publishing Computational Mathematics." Notices of the American Mathematical Society 59, no. 02 (2012): 1. http://dx.doi.org/10.1090/noti797.

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Vigo-Aguiar, Jesus, Juan Carlos Reboredo, and Higinio Ramos Calle. "Topics of contemporary computational mathematics." International Journal of Computer Mathematics 89, no. 3 (2012): 265–67. http://dx.doi.org/10.1080/00207160.2012.649131.

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Della Dora, Jean, and François Robert. "Noël Gastinel and computational Mathematics." Linear Algebra and its Applications 78 (June 1986): 237–47. http://dx.doi.org/10.1016/0024-3795(86)90027-3.

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Gottliebsen, Hanne, Tom Kelsey, and Ursula Martin. "Hidden verification for computational mathematics." Journal of Symbolic Computation 39, no. 5 (2005): 539–67. http://dx.doi.org/10.1016/j.jsc.2004.12.005.

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Gadanidis, George, Ricardo Scucuglia Rodrigues da Silva, Janette Hughes, Steven Floyd, and Immaculate Namukasa. "Computational Literacy & Mathematics Education." Revista Internacional de Pesquisa em Educação Matemática 12, no. 4 (2022): 1–23. http://dx.doi.org/10.37001/ripem.v12i4.3144.

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Computer programming has permeated many fields as a tool to model phenomena and processes and to make new discoveries. Curricula in many jurisdictions have been revised to use computer languages across K-12, and in some cases in mathematics education. The literature suggests that while digital media in mathematics education can be used as tools that serve our purposes, they also serve to reorganize knowledge. This paper investigates the interactions among computer programming and mathematics teaching and learning. Our data sources are a) Ontario curriculum documents, b) resources developed by our team in Ontario and in Brazil, and c) our research in Ontario and Brazil. diSessa’s idea of computational literacy serves as a theoretical framework and as an analytical lens for conceptualizing how the integration of computer programming may alter the structure and experience of school mathematics.

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Wang, Junping. "Selected topics in computational mathematics." Frontiers of Mathematics in China 7, no. 2 (2012): 197. http://dx.doi.org/10.1007/s11464-012-0195-4.

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Churchhouse, R. F. "Computational mathematics and computer science." Education and Computing 8, no. 4 (1993): 331–37. http://dx.doi.org/10.1016/0167-9287(93)90423-x.

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Bailey, David H., and Jonathan M. Borwein. "Experimental mathematics and computational statistics." Wiley Interdisciplinary Reviews: Computational Statistics 1, no. 1 (2009): 12–24. http://dx.doi.org/10.1002/wics.1.

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Vabishchevich, P. N. "Works of A.A. Samarskii on Computational Mathematics." Computational Methods in Applied Mathematics 9, no. 1 (2009): 5–36. http://dx.doi.org/10.2478/cmam-2009-0002.

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Abstract This is a review of the main results in computational mathematics that were obtained by the eminent Russian mathematician Alexander Andreevich Samarskii (February 19, 1919 – February 11, 2008). His outstanding research output addresses all the main questions that arise in the construction and justification of algorithms for the numerical solution of problems from mathematical physics. The remarkable works of A.A. Samarskii include statements of the main principles re- quired in the construction of difference schemes, rigorous mathematical proofs of the stability and convergence of these schemes, and also investigations of their algorith- mic implementation. A.A. Samarskii and his collaborators constructed and applied in practical calculations a large number of algorithms for solving various problems from mathematical physics, including thermal physics, gas dynamics, magnetic gas dynam- ics, plasma physics, ecology and other important models from the natural sciences.

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Revshenova, Makhabbat, Esen Bidaibekov, Victor Kornilov, et al. "Professional competence development when teaching computational informatics." Cypriot Journal of Educational Sciences 16, no. 5 (2021): 2575–85. http://dx.doi.org/10.18844/cjes.v16i5.6360.

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Bachelors and graduate students are offered in the course of teaching computational informatics, the ability to solve non-standard mathematical problems, which, as a rule, are not included in the content of teaching computational informatics. The article aimed to analyze the application effectiveness of non-standard mathematical problems in the course of teaching computational informatics, elaboration of constructive computational solution algorithms of inverse problems for differential equations, during which the bachelors and graduate students develop own professional competencies. The research conducted a review of previous literature on the topic. Formulation of the inverse problem for differential equations for the investigation of which the computational mathematics finite difference methods are applied, is presented. In the course of investigation, it was revealed that at elaborating the constructive computational algorithms of its solution, the bachelors and graduate students develop not only fundamental knowledge in the field of applied and computational mathematics, computational informatics methods, but also develop the professional competences, including computational thinking. Key words: professional competence; computational informatics; computational mathematics methods; non-standard.

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Maharani, Swasti, Vera Dewi Susanti, Tri Andari, Ika Krisdiana, and Indra Puji Astuti. "Trend Publication of Computational Thinking in Mathematics Education: Bibliometric Review." JIPM (Jurnal Ilmiah Pendidikan Matematika) 12, no. 1 (2023): 22. http://dx.doi.org/10.25273/jipm.v12i1.17654.

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Computational thinking and mathematics are closely related, namely mathematics plays a role in overcoming challenges and understanding concepts in computational thinking, while computational thinking ultimately simplifies and abstracts situations by formulating and presenting problems in mathematical form. The purpose of this study is to identify trends and research patterns with the topic of computational thinking in mathematics education using bibliometric analysis. Data is obtained from the dimensions database which has been refined through 4 stages (identification, screening, eligibility, and inclusion). The results showed that the peak of publications related to computational thinking in mathematics education research occurred in 2022. The Journal of Science of Education and Technology became the most influential journal with the most citations, namely 877 citations even though it only with 7 publications. The United States is the most influential country in this field because of the good number of publications, the number of citations is the highest of any other country. There are three research focuses related to computational thinking in mathematics education research on the dimensions database from 2013-2023, namely, 1) mathematics, study, teacher; 2) problem, child, learning; 3) student, steam, CT skill

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Beshley, Andriy, Ihor Borachok, Olha Ivanyshyn Yaman, et al. "60th anniversary of birthday of professor Roman Chapko." Journal of Applied and Numerical Analysis 1, no. 1 (2023): 135–37. http://dx.doi.org/10.30970/ana.2023.1.135.

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On October 26, 2023, the distinguished Ukrainian mathematician Roman Chapko, Doctor of Sciences, Professor in the Department of Computational Mathematics of the Faculty of Applied Mathematics and Informatics at Ivan Franko National University of Lviv, Ukraine, has turned 60. He is renowned in the broad mathematical community in Ukraine and beyond for his significant contributions to numerical analysis, computational mathematics, and mathematical modeling. His decades-long scientific activity has earned him a high reputation and has significantly elevated the standing of Ukrainian mathematics and science as a whole.

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Ilić, Svetlana. "Computational estimation: Theoretical and methodological foundations." Metodicka praksa 23, no. 2 (2020): 105–20. http://dx.doi.org/10.5937/metpra2001105i.

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The practical significance of computational estimation is noticeable in everyday life, but the place and role of estimation within mathematical abilities is also important. The paper presents the theoretical and methodological foundations of the concept of computational estimation, the development of estimation skills, and it gives a systematic overview of computational estimation strategies. Computational estimation, due to its nature, has not been much examined and a small number of papers that have tested the effectiveness of the teaching instruction have been observed. However, the results so far suggest that it is possible to develop the estimation ability in both children and adults, and that this contributes to mathematical flexibility, better achievement and attitudes towards mathematics. The place of estimation in the curricula was examined and methodical recommendations for teaching were given. Computational estimation should be integrated into as many mathematics teaching content as possible, and new research suggests that estimation skills should be developed from preschool age.

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Bianca, Carlo. "Mathematical and computational modeling of biological systems: advances and perspectives." AIMS Biophysics 8, no. 4 (2021): 318–21. http://dx.doi.org/10.3934/biophy.2021025.

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<abstract> <p>The recent developments in the fields of mathematics and computer sciences have allowed a more accurate description of the dynamics of some biological systems. On the one hand new mathematical frameworks have been proposed and employed in order to gain a complete description of a biological system thus requiring the definition of complicated mathematical structures; on the other hand computational models have been proposed in order to give both a numerical solution of a mathematical model and to derive computation models based on cellular automata and agents. Experimental methods are developed and employed for a quantitative validation of the modeling approaches. This editorial article introduces the topic of this special issue which is devoted to the recent advances and future perspectives of the mathematical and computational frameworks proposed in biosciences.</p> </abstract>

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Anwar, Vita Nova, Darhim Darhim, Suhendra Suhendra, and Elah Nurlaelah. "Exploring the Characteristics of Digital Pedagogy Model for Developing Computational Thinking in Mathematical Problem Solving." JTAM (Jurnal Teori dan Aplikasi Matematika) 8, no. 1 (2024): 137. http://dx.doi.org/10.31764/jtam.v8i1.17419.

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Challenges in the 21st century are increasingly complex, technology is developing rapidly and competition is getting tougher. Therefore we need quality human resources that can keep up with and anticipate the times. The use of technology involves computational thinking (CT) skills which are closely related to the problem-solving process. The stages in computational thinking are part of mathematical thinking, meaning that learning mathematics can support students' CT skills. Through the development of digital pedagogical models in CT integrated mathematics learning, it can improve problem-solving skills. This research uses design based implementation research with 4 phases including; preliminary research, prototyping, results, and design principle. The participants were 28 grade 8 junior high school students who took part in two rounds of experiment in direct CT activities and digital CT activities. In this paper, we present an iterative mathematical problem-solving process in the digital pedagogy model. The computational task, environment, tool and practices were iteratively improved over two rounds to incorporate CT effectively in mathematics. The results from CT environment demonstrated that direct CT activities are more effective than digital CT activities in mathematical problem-solving. Based on empirical research, we summarize the characteristic of the digital pedagogy model from computational tasks, computational environment and tools, and computational practices in mathematical problem solving.

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Kashicyna, Yu, and Marina Vasileva. "Methods of Formation of Computational Skills Using Information Technologies." Profession-Oriented School 9, no. 6 (2022): 42–47. http://dx.doi.org/10.12737/1998-0744-2021-9-6-42-47.

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The article is based on the main key ideas of the concept of the development of Russian mathematical education, one of which is the idea of using information technologies in mathematical education as a basis for advancing at the world level. The article introduces mathematics teachers to the possibilities of using interactive simulators for the formation of students ' computational skills in the process of organizing oral and written counting in a playful form. Methodological recommendations on the topic "Actions with decimals" are given. The article is addressed to teachers and students of pedagogical universities, methodologists, mathematics teachers.

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Nystrom, J. F. "Tensional computation: further musings on the computational cosmography." Applied Mathematics and Computation 120, no. 1-3 (2001): 211–25. http://dx.doi.org/10.1016/s0096-3003(99)00248-9.

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Sanford, John F., and Jaideep T. Naidu. "Computational Thinking Concepts for Grade School." Contemporary Issues in Education Research (CIER) 9, no. 1 (2016): 23–32. http://dx.doi.org/10.19030/cier.v9i1.9547.

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Early education has classically introduced reading, writing, and mathematics. Recent literature discusses the importance of adding “computational thinking” as a core ability that every child must learn. The goal is to develop students by making them equally comfortable with computational thinking as they are with other core areas of early education. Computational thinking does not come naturally and requires training and guidance. This paper argues for the inclusion of computational thinking in tandem with mathematics. As an example, the paper demonstrates spreadsheet applications that can be utilized concurrently with early mathematical concepts. It demonstrates that at this time, spreadsheets are the best medium for inculcating computational thinking but recognizes that advances in technology may favor other digital approaches in time.

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Kissane, Barry. "The Scientific Calculator and School Mathematics." Southeast Asian Mathematics Education Journal 6, no. 1 (2016): 29–48. http://dx.doi.org/10.46517/seamej.v6i1.38.

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Scientific calculators are sometimes regarded as important only for obtaining numerical answers to computational questions, and thus in some countries regarded as inappropriate for school mathematics, lest they might undermine the school curriculum. This paper argues a contrary view that, firstly, numerical computation is not the principal purpose of scientific calculators in education, and secondly that calculators can play a valuable role in supporting students’ learning. Recent developments of calculators are outlined, noting that theirprincipal intention has been to make calculators easier to use, align their functionality with the school mathematics curriculum and represent mathematical expressions in conventional ways. A model for the educational use of calculators is described, with four key components:representation, computation, exploration and affirmation. Examples of how these might impact positively on school mathematics are presented, and suggestions are made regarding good pedagogy and curriculum with calculators in mind. The paper concludes that scientific calculators represent the best available technology to provide widespread access to some ICT in the mathematics curriculum for all students in the SEAMEO region.

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Ramasamy, Subburaj. "Computational Mathematics for Software Reliability Engineering." Journal of Combinatorics, Information & System Sciences 44, no. 1-4 (2020): 217–44. http://dx.doi.org/10.32381/jciss.2019.44.1-4.12.

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Braack, Malte, Dietmar Gallistl, Jun Hu, Guido Kanschat, and Xuejun Xu. "Sino–German Computational and Applied Mathematics." Computational Methods in Applied Mathematics 21, no. 3 (2021): 497–99. http://dx.doi.org/10.1515/cmam-2021-0102.

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Abstract This short article serves as an epilog of the thirteen preceding papers in this special issue of CMAM. All contributions are authored by participants of the 7th Sino–German Workshop on Computational and Applied Mathematics at the Kiel University. The topics cover fourth-order problems, solvers and multilevel methods, a posteriori error control and adaptivity, and data science.

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Arnold, Douglas, and Thierry Goudon. "The SMAI Journal of Computational Mathematics." SMAI Journal of Computational Mathematics 1 (2015): 1–3. http://dx.doi.org/10.5802/smai-jcm.1.

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Little, John B. "Book Review: Computational Mathematics with SageMath." Bulletin of the American Mathematical Society 57, no. 3 (2020): 515–21. http://dx.doi.org/10.1090/bull/1690.

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Walker, Henry M. "Mathematics with computing and computational science." ACM SIGCSE Bulletin 45, no. 2 (2013): 7. http://dx.doi.org/10.1145/2490868.2490871.

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Arnon, Dennis S. "Workshop on environments for computational mathematics." ACM SIGGRAPH Computer Graphics 22, no. 1 (1988): 26–28. http://dx.doi.org/10.1145/48155.48158.

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Lorenz, R. "COMPUTATIONAL MATHEMATICS: Full Steam Ahead-Probably." Science 299, no. 5608 (2003): 837–38. http://dx.doi.org/10.1126/science.1081280.

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O'Leary, D. P. "Teamwork: computational science and applied mathematics." IEEE Computational Science and Engineering 4, no. 2 (1997): 13–18. http://dx.doi.org/10.1109/99.609827.

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