Applications of CAS in the Teaching and Learning of Discrete Mathematics

Durcheva, Mariana; Varbanova, Elena

doi:10.1007/s11786-017-0310-8

Cited by 11 publications

(6 citation statements)

References 1 publication

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“…Recently, the requirements for developing demonstrating and modeling programs have been intensifying, and, first of all, the requirements for interactivity, understandability, and simplicity of the interface used are increasing. Scientists such as Bobalova (2019), Durcheva and Varbanova (2017), Klima and Sigmon (2012) widely use the capabilities of the Maple computer algebra system and building interactive applications using the capabilities of the Maplets library.…”

Section: Interactive Submission Formmentioning

confidence: 99%

Maple Information Tools in the Study of Mathematical Logic Questions

Olenev¹

2023

European Proceedings of Computers and Technology

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Correspondence (truth) tables are the main model for the analysis of various logical expressions. Their applications go beyond the study of Boolean algebra. The Maple computer algebra system has a wide range of commands for working with propositions, obtaining and evaluating their truth, but the result of their execution is most often not represented in a perfectly normal form. The results obtained are undoubtedly useful, but do not contribute to the development of competencies in the field of modeling Boolean functions. In this case, using the programming methods of the Maple computer algebra system, as well as its ability to create interactive applications. The article presents the results of a study summarizing the experience of implementing computer algebra systems for modeling logical functions. To expand the possibilities, comply with the requirements of interactivity, the Maple computer algebra system was chosen as the main tool. The developed and presented interactive application allows you to automatically build Boolean functions based on their truth or falsity values and present the result in the form of perfect disjunctive or conjunctive normal forms. The authors presented the features of using the developed application. The main goal: to achieve an understanding of the process of building a model of Boolean functions, presented in a perfect disjunctive or conjunctive form, to help in the study of discrete mathematics, students of both technical and humanitarian specialties. In addition, evaluate your knowledge in this discipline.

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Section: Interactive Submission Formmentioning

confidence: 99%

Maple Information Tools in the Study of Mathematical Logic Questions

Olenev¹

2023

European Proceedings of Computers and Technology

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“…Understanding how computers work and their applications requires knowledge of discrete mathematics (Pollak, 2007). However, the special opportunities provided by technology are also pointed out in the context of teaching discrete mathematics (Durcheva & Varbanova, 2017;Weigand, 2014). In the context of a short Canadian experiment to explore the potential of introducing complex dynamical systems into curricula, it was discussed that the transition to a computer treatment involves as a fundamental element one or more types of discretization, for example of time, of space or of matter.…”

Section: Relevance Of Discrete Mathematicsmentioning

confidence: 99%

Teaching and learning discrete mathematics

Sandefur

Lockwood

Hart

et al. 2022

ZDM Mathematics Education

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In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes, topics, and mathematical practices that distinguish discrete mathematics. We then present potential benefits of focusing on discrete mathematics topics for mathematics education; in particular, we discuss the accessibility of topics in discrete mathematics, the connection to mathematical processes and affect, and the relevance of discrete mathematics in our current society. We also emphasize discrete mathematics from an international perspective, highlighting studies from the US, Italy, France, Chile, and Germany, which are across all school levels–primary, middle, and secondary school, and with some implications for post-secondary education. We particularly discuss discrete topics including number theory, combinatorics, iteration and recursion, graph theory, and discrete games and puzzles; we describe and situate these topics within literature. We also suggest the additional topics of game theory and the mathematics of fairness that we hope to see addressed in future studies.

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“…El trabajo matemático en torno a la generación de modelos presenta diferentes escenarios bajo los cuales se construyen de acuerdo a las características del fenómeno a modelar; en particular los modelos en tiempo discreto se presentan como el mejor método para describir el comportamiento de un fenómeno que se rastrea a partir de mediciones temporales igualmente espaciadas (Durcheva y Varbanova, 2017). En este sentido el proceso de comprender la manera en la cual se interrelacionan los individuos de una comunidad y la forma óptima en que éstos aprovechan los recursos que les proporciona su entorno, es una tarea compleja en la que se involucran elementos característicos de las poblaciones y objetos matemáticos propicios para describir Modelos de Crecimiento Poblacional: Enseñanza-Aprendizaje desde las Ecuaciones Recursivas Parra Formación Universitaria Vol.…”

Section: Modelos En Tiempo Discretounclassified

Modelos de Crecimiento Poblacional: Enseñanza-Aprendizaje desde las Ecuaciones Recursivas

2019

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Este artículo presenta los resultados obtenidos mediante una estrategia metodológica que involucra la noción de crecimiento poblacional, crecimiento restringido y ecuaciones recursivas, en el desarrollo de un curso de cálculo diferencial para la formación de ingenieros forestales. Se implementa un enfoque de investigaciónacción, que permite contrastar resultados entre dos grupos; experimental y control, con los cuales se valida la propuesta. Esta forma de trabajar las nociones en los grupos permitió identificar falencias en los diferentes tipos de representación usados en algunos objetos matemáticos como lo son función, sucesión y limite. Igualmente, el contraste final evidencia que el uso de contextos propios de la ingeniería fortalece el aprendizaje del cálculo diferencial.

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Applications of CAS in the Teaching and Learning of Discrete Mathematics

Cited by 11 publications

References 1 publication

Maple Information Tools in the Study of Mathematical Logic Questions

Maple Information Tools in the Study of Mathematical Logic Questions

Teaching and learning discrete mathematics

Modelos de Crecimiento Poblacional: Enseñanza-Aprendizaje desde las Ecuaciones Recursivas

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