scholarly journals Computational Thinking in Mathematics and Computer Science: What Programming Does to Your Head

2021 ◽  
Vol 11 (1) ◽  
pp. 346-363
Author(s):  
Al Cuoco ◽  
Paul Goldenberg

How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and mathematics come together to inform and shape our interpretation of a classical result in mathematics: Euclid's algorithm that finds the greatest common divisor of two integers.

Author(s):  
Thiago Schumacher Barcelos ◽  
Ismar Frango Silveira

On the one hand, ensuring that students archive adequate levels of Mathematical knowledge by the time they finish basic education is a challenge for the educational systems in several countries. On the other hand, the pervasiveness of computer-based devices in everyday situations poses a fundamental question about Computer Science being part of those known as basic sciences. The development of Computer Science (CS) is historically related to Mathematics; however, CS is said to have singular reasoning mechanics for problem solving, whose applications go beyond the frontiers of Computing itself. These problem-solving skills have been defined as Computational Thinking skills. In this chapter, the possible relationships between Math and Computational Thinking skills are discussed in the perspective of national curriculum guidelines for Mathematics of Brazil, Chile, and United States. Three skills that can be jointly developed by both areas are identified in a literature review. Some challenges and implications for educational research and practice are also discussed.


1967 ◽  
Vol 60 (4) ◽  
pp. 358
Author(s):  
B. L. Foster

Since integer division reduces to repeated subtraction, Euclid's algorithm for finding the greatest common divisor may be recast in terms of subtraction. This is done, for example, in Trakhtenbrot,1 for automatic machine computation.


2018 ◽  
Vol 26 (2) ◽  
pp. 165-173
Author(s):  
Ievgen Ivanov ◽  
Artur Korniłowicz ◽  
Mykola Nikitchenko

Summary In this paper we present a formalization in the Mizar system [2, 1] of the correctness of the subtraction-based version of Euclid’s algorithm computing the greatest common divisor of natural numbers. The algorithm is written in terms of simple-named complex-valued nominative data [11, 4]. The validity of the algorithm is presented in terms of semantic Floyd-Hoare triples over such data [7]. Proofs of the correctness are based on an inference system for an extended Floyd-Hoare logic with partial pre- and post-conditions [8, 10, 5, 3].


2018 ◽  
Vol 18 (02) ◽  
pp. e15 ◽  
Author(s):  
Jacqueline M. Fernández ◽  
Mariela E. Zúñiga ◽  
María V. Rosas ◽  
Roberto A. Guerrero

Computational Thinking (CT) represents a possible alternative for improving students’ academic performance in higher level degree related to Science, Technology, Engineering and Mathematics (STEM). This work describes two different experimental proposals with the aim of introducing computational thinking to the problem solving issue. The first one was an introductory course in the Faculty of Physical, Mathematical and Natural Sciences (FCFMyN) in 2017, for students enrolled in computer science related careers. The other experience was a first attempt to introduce CT to students and teachers belonging to not computer related faculties at the National University of San Luis (UNSL). Both initiatives use CT as a mean of improving the problem solving process based on the four following elementary concepts: Decomposition, Abstraction, Recognition of patterns and Algorithm. The results of the experiences indicate the relevance of including CT in the learning problem solving issue in different fields. The experiences also conclude that a mandatory CT related course is necessary for those careers having computational problems solving and/or programming related subjects during the first year of their curricula. Part of this work was presented at the XXIII Argentine Congress of Computer Science (CACIC).


Author(s):  
Thiago Schumacher Barcelos ◽  
Ismar Frango Silveira

On the one hand, ensuring that students archive adequate levels of Mathematical knowledge by the time they finish basic education is a challenge for the educational systems in several countries. On the other hand, the pervasiveness of computer-based devices in everyday situations poses a fundamental question about Computer Science being part of those known as basic sciences. The development of Computer Science (CS) is historically related to Mathematics; however, CS is said to have singular reasoning mechanics for problem solving, whose applications go beyond the frontiers of Computing itself. These problem-solving skills have been defined as Computational Thinking skills. In this chapter, the possible relationships between Math and Computational Thinking skills are discussed in the perspective of national curriculum guidelines for Mathematics of Brazil, Chile, and United States. Three skills that can be jointly developed by both areas are identified in a literature review. Some challenges and implications for educational research and practice are also discussed.


Author(s):  
Chris Bleakley

Chapter 1 traces the origins of algorithms from ancient Mesopotamia to Greece in the 2th century BC. The oldest known algorithms were inscribed on clay tablets by the Babylonians more than 4,000 years ago. The clay tablets document algorithms ranging from geometry to accountancy. One tablet in particular - YBC 7289 - indicates knowledge of the Pythagorean Theorem thousands of years before its supposed invention by the ancient Greeks. The Greeks made other advances in algorithms. Euclid’s algorithm determines the greatest common divisor of two numbers. The Sieve of Eratosthenes finds prime numbers. Both algorithms proved to be important stepping stones to modern cryptography - the mathematics of secret messages.


2013 ◽  
Author(s):  
Jerry Lodder ◽  
David Pengelley ◽  
Desh Ranjan

2020 ◽  
Vol 12 (9) ◽  
pp. 152
Author(s):  
Gregor Milicic ◽  
Sina Wetzel ◽  
Matthias Ludwig

Due to its links to computer science (CS), teaching computational thinking (CT) often involves the handling of algorithms in activities, such as their implementation or analysis. Although there already exists a wide variety of different tasks for various learning environments in the area of computer science, there is less material available for CT. In this article, we propose so-called Generic Tasks for algorithms inspired by common programming tasks from CS education. Generic Tasks can be seen as a family of tasks with a common underlying structure, format, and aim, and can serve as best-practice examples. They thus bring many advantages, such as facilitating the process of creating new content and supporting asynchronous teaching formats. The Generic Tasks that we propose were evaluated by 14 experts in the field of Science, Technology, Engineering, and Mathematics (STEM) education. Apart from a general estimation in regard to the meaningfulness of the proposed tasks, the experts also rated which and how strongly six core CT skills are addressed by the tasks. We conclude that, even though the experts consider the tasks to be meaningful, not all CT-related skills can be specifically addressed. It is thus important to define additional tasks for CT that are detached from algorithms and programming.


2019 ◽  
Vol 29 (1) ◽  
pp. 53-64
Author(s):  
Kevin P Waterman ◽  
Lynn Goldsmith ◽  
Marian Pasquale

AbstractUsing an example of a grade 3 science unit about population changes during competition for resources, we describe how we integrated computational thinking (CT) into existing curriculum identifying three levels of depth of integration: identifying connections that already exist, enhancing and strengthening connections, and extending units to include activities that more explicitly develop students’ CT. We discuss students’ understanding of the relationship between a simple model of an ecosystem and the actual phenomenon it represents, their engagement with the unit’s data-gathering and data analysis activities, their ability to engage in sense-making regarding data they generated and analyzed, and how collectively the study supports their understanding of the complex system. This example module is part of “Broadening Participation of Elementary School Teachers and Students in Computer Science through STEM Integration and Statewide Collaboration,” a National Science Foundation-funded collaboration among Massachusetts teacher educators, researchers, teachers, and state-level education administrators that developed and implemented a number of elementary grade, CT-integrated science and mathematics curriculum modules. Collectively, these modules are designed to develop practices related to several key CT topics: abstraction, data, modeling and simulation, and algorithms. These CT topics support the development of core skills related to, but not exclusively the domain of, computer science. The strategy of integrating CT into core elementary STEM subject areas was intended to cultivate CT practices in support of science learning.


Author(s):  
Antim Panghal

Solving a problem mean looking for a solution, which is best among others. Finding a solution to a problem in Computer Science and Artificial Intelligence is often thought as a process of search through the space of possible solutions. On the other hand in Engineering and Mathematics it is thought as a process of optimization i.e. to find a best solution or an optimal solution for a problem. These reduce search space and improve its efficiency. At each and every step of search,it select which have the least futility. In this paper ,We categorize the different AI search and optimization techniques in a tabular form on the basis of their merits and demerits to make it easy to choose a technique for a particular problem.


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