Algorithms and Logic as Programming Primers (original) (raw)

Elementary Math to Close the Digital Skills Gap

Proceedings of the 10th International Conference on Computer Supported Education, 2018

All-encompassing digitalization and the digital skills gap pressure the current school system to change. Accordingly, to 'digi-jump', the Finnish National Curriculum 2014 (FNC-2014) adds programming to K-12 math. However, we claim that the anticipated addition remains too vague and subtle. Instead, we should take into account education recommendations set by computer science organizations, such as ACM, and define clear learning targets for programming. Correspondingly, the whole math syllabus should be critically viewed in the light of these changes and the feedback collected from SW professionals and educators. These findings reveal an imbalance between supply and demand, i.e., what is over-taught versus under-taught, from the point of view of professional requirements. Critics claim an unnecessary surplus of calculus and differential equations, i.e., continuous mathematics. In contrast, the emphasis should shift more towards algorithms and data structures, flexibility in handling multiple data representations, logic; in summary-discrete mathematics.

Teaching Discrete Mathematics to Computer Science Students

Formal Methods Teaching, 2019

Discrete Mathematics is an inevitable part of any undergraduate computer science degree programme. However, computer science students typically find this to be at best a necessary evil with which they struggle to engage. Twenty years ago, we started to address this issue seriously in our university, and we have instituted a number of innovations throughout the years which have had a positive effect on engagement and, thus, attainment. At the turn of the century, a mere 2% of our first-year students attained a 1st-class mark (a mark over 70%) in the discrete mathematics course whilst over half of the class were awarded a failing grade (a mark under 40%). Despite the course syllabus and assessment remaining as difficult as ever (if not more challenging), and despite maintaining the same entrance requirements to the programme whilst more than tripling the class size, for the past two years, two-thirds of the class attained a first-class mark whilst less than 2% of the class failed. In this paper, we describe and motivate the innovations which we introduced, and provide a detailed analysis of how and why attainment levels varied over two decades as a direct result of these innovations.

A New Course “Algebra + Computer Science”: What Should Be Its Outcomes and Where It Should Start

Doklady Mathematics

The words “Programming is the second literacy” were coined more than 40 years ago [13], but never came to life. The paper develops and details that old slogan by proposing that the mainstream mathematics education in schools should merge with education in computer science/programming. Of course, this means a deep structural reform of school mathematics education. We are not talking about adapting the 20th century mathematics to the 21st century—as it outlined in [10, 19], we mean the 21st century mathematics education for the 21st century mathematics. To the best of our knowledge, this paper is perhaps the first known attempt to start a proper feasibility study for this reform. The scope of the paper does not allow us to touch the delicate socio-political (and financial) sides of the reform, we are looking only at general curricular and didactic aspects and possible directions of the reform. In particular, we indicate approaches to development of a Domain Specifiic Language (DSL) as...

Better understanding mathematics by algorithmic thinking and computer programming

Teaching Mathematics and Computer Science, 2020

Tamás Varga’s mathematics education experiment covered not just mathematics, but also other related topics. In many of his works he clearly stated that computer science can support the understanding of mathematics as much as mathematics supports informatics. On the other hand, not much later than the introduction of the new curriculum in 1978, personal computers started to spread, making it possible to teach informatics in classes and in extracurricular activities. Varga’s guided discovery approach has a didactic value for other age groups as well, not only in primary school. Its long-lasting effect can be observed even in present times. Having reviewed several educational results in the spirit of Tamás Varga, we have decided to present an extracurricular course. It is an open study group for age 12-18. Students solve problems by developing Python programs and, according to our experiences, this results in a deeper understanding of mathematical concepts. Subject Classification: 97B1...

Programming as a mathematical instrument: the implementation of an analytic framework

2020

During the past decade, there has been a renewed recognition of programming as an important digital competence to be developed as part of the general education of all students, and of its particular relationship to mathematical competence. This has been recognized in changes to curricula in many countries: in France, Finland, and Sweden, for example, programming is included in mathematics curricula. In Sweden, where the study described in this paper took place, programming was in 2018 included in mathematics from year 4 in lower secondary school. In upper secondary school, programming is to be used as a tool for mathematical problem solving.

Empowering mathematics education through programming

Journal of Mathematics and Science Teacher

One of my last assignments at the university of Gothenburg was to teach a sequence of three seminars in programming for prospective teachers (n=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.

MATHSCRATCH -BRINGING PROGRAMMING AND MATHEMATICAL SKILLS INTO HIGHER EDUCATION

2017

According to some authors, the success of students' integration in the courses of Differential and Integral Calculus all depends on their obtained basic knowledge in mathematics, which should have been acquired during the Secondary School. This knowledge is also essential for the first year in any Engineering Degree at the Superior level. It is from this compatibility that a better integration of students in the courses arises. A link between secondary and higher education is urgently needed, reducing the degree of demotivation that may lead to early school dropout with consequent implication in academic failure. However, a growing multiplicity in the basic training of students, with significantly different grades of access in mathematics, causes difficulties not only in Mathematics-based courses but also in courses of Introduction to Programming. Project members have already studied both problems. In this scenario, the integration of students in higher education, namely in Engineering degrees, is essential. Concurrently the recruitment of students to these areas of knowledge is in visible decline. Therefore, strategies to prevent students from deterring from these areas by introducing new processes of teaching and learning are needed. It is also important to draw a plan that fosters positive attitudes towards mathematics to reinforce self-efficacy. This intervention has to be carried out in higher education from a very early phase and has to gather a set of strategies that reverse the students' alienation in the areas of mathematics. Either by reorganizing the functioning and evaluation of courses or by constructing instruments that facilitate the learning process and that promotes student involvement. The "MathScratch" project aims at the creation of products (games/animations) on a Mathematics theme, in basic and elementary concepts that are considered essential for the integration of students in higher education in engineering degrees using Scratch programming. These resources will later be placed on a platform for the use of the 1st year students with difficulties in mathematics. We intend to support students and facilitate their integration into higher education by creating a sustainable structure that includes projects carried out through the 2016/2017 academic year, identifying the major difficulties experienced in areas of knowledge which are considered essential.

Algorithmics In Secondary School: A Comparative Study Between Ukraine And France

This article is devoted to the teaching and learning of Algorithmics, discipline at the intersection of Informatics and Mathematics. We focus on the didactic transposition of Algorithmics in secondary school in France and Ukraine. Based on epistemological and didactical frameworks, we identify the general characteristics of the approaches in the two countries, taking into account the organization of the contents and the national contexts (in the course of Mathematics in France and in the course of Informatics in Ukraine). Our results give perspectives to understand the place that Algorithmics can hold in the teaching and learning of Mathematics and Informatics.

Discrete mathematics at university level. Interfacing mathematics, computer science and arithmetic

2018

Discrete mathematics is a recent field linked with Computer Science. We discuss its place in university mathematics curricula and in the particular case of France, where it has difficulties to find its place. We make explicit the didactical challenges posed by discrete mathematics at university level, and present DEMIPS network and its plans to tackle them. Through two detailed examples we discuss the reasons for teaching Discrete Mathematics at university level, and illustrate our conclusions.