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Статті в журналах з теми "Programming (mathematics)"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 29 липня 2024

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1

Turskienė, Sigita. "Kompiuterinių matematikos sistemų programavimo kalbų lyginamoji analizė." Lietuvos matematikos rinkinys 44 (December 17, 2004): 377–82. http://dx.doi.org/10.15388/lmr.2004.31946.

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Анотація:

The paper analyses possibilities of programming languages of computer mathematics systems. The summary table of operations of 5 programming languages is presented. The advantages and disadvantages between programming languages of computer mathematics systems (MAPLE, MATHEMATICA, MATLAB) and professional programming languages (C/C++, PASCAL) are presented, too. That makes easier the application of computer mathematics systems in practice.

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2

Tasic, Milan, Predrag Stanimirovic, Ivan Stanimirovic, Marko Petkovic, and Nebojsa Stojkovic. "Some useful MATHEMATICA teaching examples." Facta universitatis - series: Electronics and Energetics 18, no. 2 (2005): 329–44. http://dx.doi.org/10.2298/fuee0502329t.

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Анотація:

We show how a computer algebra system in MATHEMATICA can be used in several elementary courses in mathematics for students. We have also developed an application in programming language DELPHI for testing students in MATHEMATICA.

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3

Stigberg, Henrik, and Susanne Stigberg. "Teaching programming and mathematics in practice: A case study from a Swedish primary school." Policy Futures in Education 18, no. 4 (December 17, 2019): 483–96. http://dx.doi.org/10.1177/1478210319894785.

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Анотація:

Programming and computational thinking have emerged as compulsory skills in elementary school education. In 2018, Sweden has integrated programming in mathematics education with the rationale that it fosters problem solving and logical thinking skills and motivates students to learn mathematics. We investigated how teachers introduce programming in mathematics education in a Swedish primary school using an explorative case study. We followed four mathematics teachers during the first semester in which programming was mandatory. They taught second-, sixth- and ninth-grade students. Our contributions are threefold: we provide an account of how programming is taught in mathematics education; we discuss how teachers reflect on the challenge of teaching programming in mathematics; and we report on students’ understanding of programming and their view on the relationship between programming and mathematics.

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4

Kwon, Misun. "Analysis of Mathematical Elements for Programming Education Presented in Finnish 1st and 2nd Grade Elementary Mathematics Textbooks." Korean Society of Educational Studies in Mathematics - School Mathematics 25, no. 3 (September 30, 2023): 385–406. http://dx.doi.org/10.57090/sm.2023.09.25.3.385.

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Since 2016, Finland has been implementing programming education in elementary school mathematics. This study analyzed Finnish first and second grade elementary mathematics textbooks and tutorials that reflected programming education. Previous studies on programming were analyzed to extract mathematical elements for programming instruction, and based on the extracted sequence, rules, selection, variables, possibilities, logic elements, functions, and algorithm, the contents of elementary mathematics textbooks in Finland were analyzed. As a result of the analysis, in Finnish mathematics textbooks, activities suitable for programming learning were evenly presented by utilizing all content elements as a whole, and a separate lesson for programming was also organized. In addition, the basic content of programming suitable for the student level was presented mathematically, and the level was changed and presented as the grade level went up. Looking at each element, activities for variables and logic elements accounted for a large part, and students were provided with opportunities to learn various mathematical elements related to programming during the first and second grades of elementary school. Based on these results, this study is expected to provide significant resources for applying programming to mathematics education in Korea.

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5

Swanier, Cheryl, Cheryl Seals, and Elodie Billionniere. "Visual Programming: A Programming Tool For Increasing Mathematics Achivement." i-manager's Journal of Educational Technology 6, no. 2 (September 15, 2009): 1–5. http://dx.doi.org/10.26634/jet.6.2.784.

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6

Daher, Wajeeh, Nimer Baya'a, and Otman Jaber. "Mathematics Preservice Teachers’ Preparation in Designing Mathematics-Based Programming Activities Rich in Metacognitive Skills." International Journal of Emerging Technologies in Learning (iJET) 18, no. 06 (March 21, 2023): 71–82. http://dx.doi.org/10.3991/ijet.v18i06.36965.

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Programming problems enrich the environment of mathematics learning, adding the flavor of technology to these problems. This is especially true when this programming is Scratch based, where Scratch is being used to make students’ learning of mathematics more meaningful. This role of programming in the mathematics classroom points at the importance of preparing mathematics teachers for designing mathematics-based programming problems activities. The present research describes one attempt to prepare mathematics preservice teachers in designing mathematics-based programming problems activities that could be used in the classroom to teach both programming and mathematics concepts. Twenty-three preservice teachers participated in the research, where they worked in eight groups of 2-3 members in each group. Data collected through observations based on video recordings of the sessions in which the preservice teachers discussed with the pedagogical supervisors the designed mathematics activities. The preparation model comprises of five stages related to the educational environment and to the design notions. The results show special importance for the concepts of struggle and devolution in designing this kind of activities, in addition to the concept of equilibrium between the creative and imitative thinking. The results also show the useful application of metacognitive skills when designing the activities, especially when designing the directions given to the students for solving each of the programming activities.

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7

Freeman, T. L., A. L. Peressini, F. E. Sullivan, and J. J. Uhl. "The Mathematics of Nonlinear Programming." Mathematical Gazette 73, no. 464 (June 1989): 170. http://dx.doi.org/10.2307/3619709.

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8

Bar-On, Ehud. "A programming approach to mathematics." Computers & Education 10, no. 4 (January 1986): 393–401. http://dx.doi.org/10.1016/0360-1315(86)90015-1.

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9

Zotos, Kostas. "Object-oriented programming in Mathematics." Applied Mathematics and Computation 188, no. 2 (May 2007): 1562–66. http://dx.doi.org/10.1016/j.amc.2006.11.025.

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10

Lingefjärd, Thomas. "Empowering mathematics education through programming." Journal of Mathematics and Science Teacher 4, no. 1 (January 1, 2024): em053. http://dx.doi.org/10.29333/mathsciteacher/13847.

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Анотація:

One of my last assignments at the university of Gothenburg was to teach a sequence of three seminars in programming for prospective teachers (<i>n</i>=37). The three seminars are given in the introduction of this manuscript. Since this was a course for prospective upper secondary teacher of mathematics, it was decided that it should be a course in programming for learning mathematics. This manuscript is a research article but also a manuscript about programming in GeoGebra, Python, and Wolfram Alpha. The examples I shared with my students led me to write a book about programming. See the reference list.

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11

Broley, Laura, France Caron, and Yvan Saint-Aubin. "Levels of Programming in Mathematical Research and University Mathematics Education." International Journal of Research in Undergraduate Mathematics Education 4, no. 1 (November 30, 2017): 38–55. http://dx.doi.org/10.1007/s40753-017-0066-1.

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12

Naganjaneyulu, V., Shaik Mohammed Ali, Mohd Irshad Ali, Masarath Jabeen, and Syed Naseeruddin. "Microsoft Mathematics as a Teaching and Learning Tool for Mathematics." International Journal of Management and Humanities 5, no. 4 (December 15, 2020): 55–59. http://dx.doi.org/10.35940/ijmh.b1140.125420.

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Анотація:

This article depicts how the utilization of Microsoft Mathematics(MM) programming has encouraged for educators to build up their capacities in two viewpoints: 1) solving tough problem 2) developing students focused instructing course of actions. The specified models explain that for a portion of the intense issues canbe introduced to the students, it is practically unworkable or extremely hard to physically make right drawings. To overcome this trouble, the utilization of MM programming has all the earmarks of being crucial. Furthermore, the utilization of this product can energize students close enough for trouble, fathoming, just as present a straightforward and persuading way regarding approve the arrangement. Moreover, learners can develop precise visual portrayals to display genuine circumstances productively by utilizing changes in MM programming. This can spare time widely so students can give more consideration on the practical aspects and comprehension. Astounding instructing assignments that take advantage of MM programming can likewise effectivelydevelop student’s mathematics understanding. Also an investigation is beingdone on engineering students after MM Training supports the statement of effectiveness of MM in teaching and learning process.

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13

Iyamuremye, Aloys, and Ezechiel Nsabayezu. "Mathematics and Science Teacher’s Conception and Reflection on Computer Programming with Scratch: Technological and Pedagogical Standpoint." International Journal of Education, Training and Learning 6, no. 1 (February 14, 2022): 11–16. http://dx.doi.org/10.33094/ijetl.v6i1.488.

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Анотація:

The current study investigates teachers' conception and reflection of computer programming from scratch in terms of technological and pedagogical standpoint. Mixed research approaches typically achievement tests and interviews were used to collect quantitative and qualitative data respectively. A total of twenty-one Mathematics and Science teachers were randomly selected to participate in the study. A paired t-test was used to analyze quantitative data from pre and post-test, while descriptive and interpretive analyses were used to analyze qualitative data from the interview. The results of the study showed that Mathematic and Sciences teachers have a great conception of scratch programming after attending scratch programming. There was a significant difference in mean between pre and post-test (p ˂ 0.05). It was also found that scratch is an effective pedagogical tool for teaching and learning Mathematics and Sciences. In addition, teachers expressed positive views of using scratch in teaching and learning Mathematics and Sciences as it helps them to visualize abstract content, motivate students, increase students' interest, critical thinking, and problem-solving skills, act as an assessment tool and increase student's academic performance.

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14

Herlina, Herlina, and Teady Matius Surya Mulyana. "ANALISIS PERSEPSI DAN HUBUNGAN PRESTASI BELAJAR MATEMATIKA DENGAN PRESTASI BAHASA PEMROGRAMAN." Jurnal Ilmiah Matematika dan Pendidikan Matematika 11, no. 1 (May 18, 2020): 1. http://dx.doi.org/10.20884/1.jmp.2020.12.1.1932.

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Анотація:

Mathematics is the basis before learning coding-based courses. This type of research is quantitative descriptive. Sample of 110 informatics engineering students. The results of the study showed a significant association of learning outcomes in mathematics with the achievement of learning programming languages. The magnification coefficient of 0.663 has a moderate and positive meaning. The contribution of mathematics in explaining programming languages is 43.97% and the remaining 56.03% is accepted by other variables. Students' perceptions of mathematics and programming languages consist of four levels of understanding, namely the five senses, analysis, interpretation and evaluation. Every level of dimension. On the sensory dimension of 31.9% mathematics has a close relationship with programming languages. In the dimensions of analysis and interpretation, the value of the percentage of perceptions that are almost the same namely 21.24% and 21.14% associate mathematical concepts with the concepts of programming languages. In the evaluation dimension of 20.6%, it shows that in programming languages, students need information other than mathematics, namely the purpose of the programming language that is being designed. Full Article

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15

Leksono, Ibut Priono, and Sri Rahmawati Fitriatien. "Development of Mathematic Learning Set Based On Pedagogical Content Knowledge to Improve Mathematics Problem Solving Ability." Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang 5, no. 1 (January 18, 2021): 159. http://dx.doi.org/10.31331/medivesveteran.v5i1.1529.

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Анотація:

This research use development research wich aim to product mathematic learning that include implementation plans and woksheets based on pedagogical content knowledge in order to improve mathematical problem solving ability. The development model that used in this research uses four stages starting with define, then continue with design stage, next the develop stage, and the last stage is disseminate stage, or better known as 4D model. The mathematical problems that used in this research include linear programming problems that are solved with the integer programming method. The results of validation for the result of learning tools show that the pedagogical content knowledge with 4D method are suitable to used with very good categories. Meanwhile, the trial results show that the pedagogical content knowledge learning tools produced are practical and effective. This is able to support an achievement of research object that is able to improve the ability of students to solve math problems for linear programe case by using integer programming method. Keywords: pedagogical content knowledge, problem solving, math problem, integer programming.

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16

Amalia, Rizki, Fadilah Fadilah, Mamay Komarudin, and Jaka Wijaya Kusuma. "Development of Mathematics E-Books in Improving Mathematical Literacy and Entrepreneurial Spirit." AL-ISHLAH: Jurnal Pendidikan 13, no. 3 (December 30, 2021): 2425–34. http://dx.doi.org/10.35445/alishlah.v13i3.987.

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This study aimed to create an e-book on mathematics learning for vocational high school students in grade XI, complete with liner program material, using the ADDIE model development methodology (Analysis, Design, Development, Implementation, Evaluation). Based on the findings of the development of e-books on linear programming material for grade XI students at vocational high school in Langsa Aceh majoring in Online Business and Marketing, it can be concluded that the media is valid for use in learning mathematics with linear programming materials, then effective in improving mathematical literacy and entrepreneurial spirit. Finally, practical media is used in mathematics learning, among other conclusions.

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17

Ionescu, Cezar, and Patrik Jansson. "Domain-Specific Languages of Mathematics: Presenting Mathematical Analysis Using Functional Programming." Electronic Proceedings in Theoretical Computer Science 230 (November 26, 2016): 1–15. http://dx.doi.org/10.4204/eptcs.230.1.

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18

Saez-Lopez, Jose-Manuel, Esteban Vazquez-Cano, and Maria-Luisa Sevillano-Garcia. "Scratch and visual block programming in mathematics: perceptions of preservice teachers in Columbia." Scientia Paedagogica Experimentalis 59, no. 1 (March 2022): 29–50. http://dx.doi.org/10.57028/s59-029-z1003.

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This research evaluates the use of visual block programming-based instruction and its possibilities in mathematics, from the perspective of future teachers. A visual programming environment was employed to introduce pre-service teachers to prepare mathematics activities and programming. The study followed a pre-experimental design with a sample of 65 pre-service teachers. A Wilcoxon test was used to evaluate the gains in the participants’ knowledge of computational concepts and attitudes towards Scratch as a pedagogic tool in mathematics. We analyzed open questions to evaluate the participants’ attitudes concerning programming applications, and their perception of advantages in the implementation of programming in mathematics. Although there is no significant improvement in learning, positive results were obtained for programming in the classroom, with significant improvements in motivation, active learning, fun, and the possibility of learning Cartesian coordinates and other mathematical concepts.

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19

Wainwright, Roger L. "Introducing functional programming in discrete mathematics." ACM SIGCSE Bulletin 24, no. 1 (March 1992): 147–52. http://dx.doi.org/10.1145/135250.134540.

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20

Geete, Prof Nitin, and Prof Saurabh Verma. "MATLAB APPLICATIONS FOR MATHEMATICS STUDENTS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (January 13, 2023): 3138–41. http://dx.doi.org/10.47191/ijmcr/v11i1.05.

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Анотація:

One of the oldest professions in human society is mathematics. It is closely tied to all stages of the development of human society's cognitive system. An essential tool for researching and resolving these real-world issues is mathematical modeling. A mathematical model is a structure that can be created mathematically by using the right tools and making the necessary, simplified assumptions about the underlying laws of a specific object and purpose in the real world. A mathematical model is an abstraction of real-world issues, to put it simply. Computer application technology has greatly influenced many different businesses as a result of computer progress. Among these, MATLAB is a piece of commercial math software that excels in applications for math in science and technology. One of the most widely used fourth-generation programming languages worldwide is MATLAB. It is one of the greatest environments for numerical analysis. Additionally, the most potent and effective language utilized in technical computing is MATLAB. It is designed to address mathematically notated challenges. It is employed in algorithm development and matrix calculations. Additionally, it enables us to run programmers written in any other programming language. It implies that MATLAB can make use of the advantages of other programming languages. It is extensively utilized in robotics, communications, control systems, signal processing, and image processing. This paper first examines MATLAB's benefits and discusses how to utilize it for mathematical operations and modeling.

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21

Farid, Muhammad, Muhammad Yahya, and Dian Atmasani. "The Correlation Between Digital Simulation Learning, Basic Programming, Mathematics and Students’ Knowledge: Optimizing Students’ Skill Program for Learning Results." Journal of Educational Science and Technology (EST) 7, no. 3 (December 21, 2021): 298. http://dx.doi.org/10.26858/est.v7i3.24538.

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Анотація:

The study aims to investigate students learning results of Mathematics, Digital Simulation, and Basic Programming subjects in Vocational High School 7 Takalar and to identify the correlation between students’ learning results on Mathematics and Digital Simulation Subjects and Basic Programming Subject. The research method was ex-post facto. The number of population was 210 and the samples were 63. Data were collected using documentation and test. Hypotheses were tested after performing Prerequisite Test. Results of the study show that: (1) students’ learning results in Mathematics were in the Good category. (2) students’ learning results in Digital Simulation were in the Good category. (3) students’ learning results in Basic Programming were in the Good category. (4) there is a strong correlation between students’ learning results in Mathematics and Basic Programming. (5) there is a strong correlation between students’ learning results in Digital Simulation and Basic Programming, (6) There is a Correlation between students’ learning results on Mathematics and Digital Simulation subjects and Basic Programming subject

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22

Heipcke, Susanne. "An example of integrating constraint programming and mathematical programming." Electronic Notes in Discrete Mathematics 1 (March 1999): 84. http://dx.doi.org/10.1016/s1571-0653(05)80001-0.

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23

Liberti, Leo, Stéphane Le Roux, Jeremy Leconte, and Fabrizio Marinelli. "Mathematical programming based debugging." Electronic Notes in Discrete Mathematics 36 (August 2010): 1311–18. http://dx.doi.org/10.1016/j.endm.2010.05.166.

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24

Cornet, B., V. H. Nguyen, and J. P. Vial. "Mathematical programming study 30." Mathematical Programming 41, no. 1-3 (May 1988): 119–21. http://dx.doi.org/10.1007/bf01580757.

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25

Hoffman, K. L., R. H. F. Jackson, and J. Telgen. "Mathematical programming study 31." Mathematical Programming 41, no. 1-3 (May 1988): 395–98. http://dx.doi.org/10.1007/bf01580778.

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26

Fiacco, Anthony V. "Mathematical programming study 21." Mathematical Programming 31, no. 1 (January 1985): 118–21. http://dx.doi.org/10.1007/bf02591865.

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27

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 (November 19, 2022): 1–23. http://dx.doi.org/10.37001/ripem.v12i4.3144.

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Анотація:

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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28

Octaria, Dina, Zulkardi Zulkardi, and Ratu Ilma Indra Putri. "Systematic Literature Review: How students learn linear programming with realistic mathematics education?" International Journal of Trends in Mathematics Education Research 6, no. 1 (March 30, 2023): 41–46. http://dx.doi.org/10.33122/ijtmer.v6i1.174.

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This study aims to investigate more deeply the material of linear programming with a realistic mathematics education (RME) approach. This research is a literature study with a descriptive qualitative research type with library research using various written sources such as articles from Springer, ScienceDirect, and Google Scholar. This study focuses on the characteristics of RME, the principles of RME, the steps of learning RME on linear programming material, and examples of implementing RME learning on linear programming material. From the results of previous research, it was found that using the RME approach can help students understand linear programming material. This is because real-life problems in linear programming are in line with realistic principles that exist in the RME principle, namely being able to apply mathematics in solving real-life problems and mathematics must start from problem situations that are meaningful for students.

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29

Klotz, Frederic S. "When Is a Program Like a Function?" Mathematics Teacher 79, no. 8 (November 1986): 648–51. http://dx.doi.org/10.5951/mt.79.8.0648.

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Анотація:

In some respects computer programming seems closely related to mathematics. Good programming requires the same combination of clear logic, attention to detail, and inventiveness that is characteristic of good mathematics. Yet many important concepts in programming—loops, pointers, arrays, and floating-point arithmetic, to name just a few are awkward to deal with in mathematical terms. Even the concept of a variable in computer science looks strange to someone accustomed to variables in mathematics.

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30

Dai, Siyang. "An approach to simulate basic concepts of mathematics with object-oriented programming." Theoretical and Natural Science 9, no. 1 (November 13, 2023): 123–31. http://dx.doi.org/10.54254/2753-8818/9/20240729.

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Анотація:

Traditional approaches to using data structures mainly focus on the improvement in algorithm efficiency but rarely take advantage of object-oriented programming that can simulate the definition of mathematic concepts in a way that is similar to human thinking mode, so traditional approaches cannot satisfy the need of simulating sets and their features and operations for mathematics studies. In this paper, the author pointed out the disadvantages of traditional ways, proposed a series of hypotheses describing the relationship between sets and classes such as inheriting and inclusion relationships and a way based on those hypotheses using features of object-oriented programming, and used C#, one of the best object-oriented programming languages, to simulate sets and their features. In addition, for each hypothesis, the author raised examples with C# codes that realize the theory in this paper, clearly showing the approach proposed in this paper and why it is both efficient and elegant.

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31

Elwes, Richard, and Rob Sturman. "Developing computational mathematics provision in undergraduate mathematics degrees." MSOR Connections 18, no. 2 (July 9, 2020): 59–65. http://dx.doi.org/10.21100/msor.v18i2.1097.

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Анотація:

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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32

Eto, H. "Relationship of mathematical programming with mathematics, economic/regional planning and other specialties." Scientometrics 45, no. 2 (June 1999): 311–24. http://dx.doi.org/10.1007/bf02458439.

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33

Jones, Matthew M., and Alison Megeney. "Programming in Groups: developing industry-facing software development skills in the undergraduate mathematics curriculum." MSOR Connections 18, no. 2 (July 9, 2020): 18–24. http://dx.doi.org/10.21100/msor.v18i2.1087.

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Анотація:

Programming is increasingly becoming an expected graduate skill for mathematics students. We argue in this article that programming should be given the same priority as any other graduate skill. Given the practical and philosophical constraints placed on undergraduate mathematics curricula, however, we acknowledge the difficulty in introducing, in a meaningful way, many of the core ideas of programming. We therefore present a case study of a second year course on an undergraduate mathematics programme that introduces Object Oriented Programming and aspects of software design, as well as key practical skill such as version control. We will argue that group assessment in this context is a more natural setting for students to be working and reflects more closely the experience of programming in industry; furthermore, it serves as a convenient platform to introduce students to aspects of software design and practical programming considerations. We will present an example of the type of assessment that can be used and how Version Control Systems like Git can be used to give students a more realistic experience of programming with the advantage of allowing tutors and other group members to track student work.

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34

Jones, Leslie, and Tim Smith. "Introductory Computer Programming Courses in Mathematics Curriculum." Teaching Mathematics and Computer Science 18, no. 1 (October 2020): 19–30. http://dx.doi.org/10.5485/tmcs.2020.0470.

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35

Dibiase, Julie. "Teaching Higher Order Mathematics through Graphics Programming." Journal of Educational Computing Research 15, no. 3 (October 1996): 261–81. http://dx.doi.org/10.2190/r2a6-lqt7-fpqw-u8f2.

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Анотація:

Most of the underlying concepts that pervade what is typically referred to as “higher” mathematics are relegated to the arena of the mathematical elite. The research presented here demonstrates that, given the proper pedagogical environment, these concepts are quite accessible for early high school students. Through SchemePaint, a graphics enhanced computer programming language, students learned the mathematical notion that a function can be a data object. Further, students were able to apply their knowledge of functions from within the graphics domain to solve novel mathematical problems. This work suggests the need for a more elaborate study of how such early conceptual introduction of advanced material may preclude some of the problems which have been documented to pervade the later stages of students' academic career.

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Laurent, Manon, Rosamaria Crisci, Pascal Bressoux, Hamid Chaachoua, Cécile Nurra, Erica de Vries, and Pierre Tchounikine. "Impact of programming on primary mathematics learning." Learning and Instruction 82 (December 2022): 101667. http://dx.doi.org/10.1016/j.learninstruc.2022.101667.

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VanDrunen, Thomas. "Functional programming as a discrete mathematics topic." ACM Inroads 8, no. 2 (May 16, 2017): 51–58. http://dx.doi.org/10.1145/3078325.

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BRIDGES, DOUGLAS, and STEEVE REEVES. "Constructive Mathematics in Theory and Programming Practice." Philosophia Mathematica 7, no. 1 (February 1, 1999): 65–104. http://dx.doi.org/10.1093/philmat/7.1.65.

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Hvorecký, Jozef. "On a connection between programming and mathematics." ACM SIGCSE Bulletin 22, no. 4 (November 1990): 53–54. http://dx.doi.org/10.1145/122153.122164.

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Shafto, Sylvia A. "Programming for learning in mathematics and science." ACM SIGCSE Bulletin 18, no. 1 (February 1986): 296–302. http://dx.doi.org/10.1145/953055.5635.

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Henderson, Peter B. "Discrete mathematics as a precursor to programming." ACM SIGCSE Bulletin 22, no. 1 (February 1990): 17–21. http://dx.doi.org/10.1145/319059.319070.

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Kiyoumarsi, Farshad. "Mathematics Programming based on Genetic Algorithms Education." Procedia - Social and Behavioral Sciences 192 (June 2015): 70–76. http://dx.doi.org/10.1016/j.sbspro.2015.06.011.

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Ploger, Don, and Margaret Carlock. "Mathematics and molecules: Exploring connections via programming." Journal of Mathematical Behavior 15, no. 4 (December 1996): 441–52. http://dx.doi.org/10.1016/s0732-3123(96)90028-0.

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Cline, K., J. Fasteen, A. Francis, E. Sullivan, and T. Wendt. "Integrating Programming Across the Undergraduate Mathematics Curriculum." PRIMUS 30, no. 7 (August 20, 2019): 735–49. http://dx.doi.org/10.1080/10511970.2019.1616637.

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Dubinsky, Ed. "Isetl: A programming language for learning mathematics." Communications on Pure and Applied Mathematics 48, no. 9 (1995): 1027–51. http://dx.doi.org/10.1002/cpa.3160480905.

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Buteau, Chantal, and Eric Muller. "Assessment in Undergraduate Programming-Based Mathematics Courses." Digital Experiences in Mathematics Education 3, no. 2 (November 28, 2016): 97–114. http://dx.doi.org/10.1007/s40751-016-0026-4.

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Cafolla, Ralph. "Piagetian Formal Operations and other Cognitive Correlates of Achievement in Computer Programming." Journal of Educational Technology Systems 16, no. 1 (September 1987): 45–55. http://dx.doi.org/10.2190/gw1p-7bbk-dvwr-w3tu.

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The purpose of this study was to determine if success in writing computer programs is related to level of cognitive development, verbal ability, and mathematics reasoning. Subjects were drawn from students enrolled in beginning computer programming classes. Each subject was given the School and College Ability Test (SCAT II) test to assess mathematics and verbal levels and the Inventory of Piaget's Developmental Tasks (IPDT) to assess level of cognitive development. The instructor's final examination was used as a measure of computer programming ability. This study supports prior research showing mathematics reasoning and verbal ability were each significant predictors of success in computer programming. Level of cognitive development, as defined by Piaget, also predicts success in computer programming ability. Regression analysis showed that level of cognitive development, when combined with verbal reasoning, is linearly predictive of programming ability.

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Sjöberg, Christer, Tove Risberg, Jalal Nouri, Eva Norén, and Lechen Zhang. "Programming as a tool for across-subjects learning in primary school." RUDN Journal of Informatization in Education 17, no. 3 (December 15, 2020): 179–89. http://dx.doi.org/10.22363/2312-8631-2020-17-3-179-189.

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Problem and goal. Computational thinking has been introduced in many countries around the world and teachers are working intensely to incorporate programming activities in the classroom. However, teachers are faced with several challenges due to the fact that there is still little research conducted focusing on programming education for younger children, that programming didactics is a rather new phenomenon for the K-9 educational system, and that K-9 teachers have little training with regards to programming. In Sweden for instance, programming has been introduced in several subjects and not as a subject in its own, which create a pressure on teachers to utilize programming as an instrument to teach and enhance learning of different subjects such as mathematics. Methodology. In this paper, we report on a larger lesson study conducted in a primary school (sixth grade) in Sweden with a total of 155 participating pupils. The aim of the lesson was to study whether the visual programming languages, Scratch , in particular, can be used to teach computational thinking, mathematics and social science in an interdisciplinary way. Results. Thus, the paper more specifically presents findings related to: 1) reflections of the use of lesson study methodology to develop programming education; 2) how programming can be utilized as an instrument to teach mathematics as well as social sciences in an interdisciplinary way; and 3) the didactical strategies employed by the teachers. Conclusion. The evidence from this study suggests that the interdisciplinary character of the lesson which incorporates learning goals of mathematics, social science and programming was highly beneficial. The pupils gained a better understanding of learning material by drawing, digitalizing and animating their ideas in Scratch .

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Iwamoto, S. "From Dynamic Programming to Bynamic Programming." Journal of Mathematical Analysis and Applications 177, no. 1 (July 1993): 56–74. http://dx.doi.org/10.1006/jmaa.1993.1243.

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Liberti, Leo, and Nelson Maculan. "Reformulation techniques in mathematical programming." Discrete Applied Mathematics 157, no. 6 (March 2009): 1165–66. http://dx.doi.org/10.1016/j.dam.2008.10.016.

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