Programming as a mathematical activity

Programming in undergraduate mathematics is an opportunity to develop various mathematical skills. This paper outlines some topics covered in a second year, optional module ‘Programming with Mathematical Applications’ that develop mathematical thinking and involve mathematical activities, showing that practical programming can be taught to mathematicians as a mathematical skill

Motivating Students to Learn a Programming Language: Applying a Second Language Acquisition Approach in a Blended Learning Environment

Learning a programming language typically involves acquisition of new vocabulary, punctuation, and grammatical structures to communicate with a computer. In other words, learning a programming language is like learning a human language. A recent study showed that programmers use language regions of the brain when understanding source code and found little activation in other regions of the brain devoted to mathematical thinking. Even though programming code involved mathematical operations, conditionals, and loop iterations, researchers found that programming had less in common with mathematics and more in common with human language

Types of mathematical thinking implemented in the learn process of functional programming

Context: This article presents and analyzes the results of a research carried out in a classroom, in the context of the learning of functional programming at university level in Systems Engineering and Computing program, from the application of the types of mathematical thinking and their use in the DrRacket programming language. The purpose was to establish links between the types of mathematical thinking and computer programming (for first-semester students). Methodology: For the development of the research, we worked with a group of first-year students, applying the proposed methodology of mathematical thinking. The evaluations, based on the types of mathematical thinking, were made in another group that was receiving the subject by conventional methods. In this group only the evaluative tests were carried out; no monitoring of their learning was done. Results: The results show great advantages when articulating mathematics and computer programming within the context of a subject that gives meaning to both areas. Conclusions: It is concluded that functional programming is learned in an easier way when it is related to the types of mathematical thinking and vice versa

Beyond jam sandwiches and cups of tea: An exploration of primary pupils' algorithm‐evaluation strategies

The long-standing debate into the potential benefit of developing mathematical thinking skills through learning to program has been reignited with the widespread introduction of programming in schools across many countries, including England where it is a statutory requirement for all pupils to be taught programming from five years old. Algorithm is introduced early in the English computing curriculum, yet, there is limited knowledge of how young pupils view this concept. This paper explores pupils’ (aged 10-11) understandings of algorithm following their engagement with one year of ScratchMaths (SM), a curriculum designed to develop computational and mathematical thinking skills through learning to program. 181 pupils from six schools undertook a set of written tasks to assess their interpretations and evaluations of different algorithms that solve the same problem, with a subset of these pupils subsequently interviewed to probe their understandings in greater depth. We discuss the different approaches identified, the evaluation criteria they used and the aspects of the concept that pupils found intuitive or challenging, such as simplification and abstraction. The paper ends with some reflections on the implications of the research, concluding with a set of recommendations for pedagogy in developing primary pupils’ algorithmic thinking

Supporting the Algebra I Curriculum with an Introduction to Computational Thinking Course

The Louisiana Workforce Commission predicts a 33.6% increase in computer science and mathematical occupations by 2022 and the Bureau of Labor Statistics foresees a 16% increase in computer scientists from 2018-2028. Despite these opportunities for job and financial security, the number of Louisiana students enrolled in a nationally accredited computing course is less than 1%, compared to national leaders California and Texas which have 3% and 3.8% of students respectively. Furthermore, the international assessments of mathematical literacy, PISA and TIMMS, both report American students continue to fall further behind their international peers in mathematics achievement. This thesis rejects these statistics as definitive and attempts to contribute to an expansion of the mathematical libraries of a computational thinking course that a teacher could use to support a standards-based Algebra I course. The framework presented in this thesis supports the Louisiana State University (LSU) STEM Pathway course entitled Introduction to Computational Thinking (ICT). The course introduces students to a systematic problem-solving approach in which they learn to solve problems computationally, that is, through abstraction, decomposition, and pattern recognition. ICT utilizes the functional programming language Haskell in the educational programming environment “CodeWorld” in order to create pictures and animations. Jean Piaget, the great child cognitive development psychologist, proclaimed “The goal of intellectual education is not to know how to repeat or retain ready-made truths”; rather, one becomes educated by “learning to master the truth by oneself” (Piaget, 1973). Because of the graphical outputs that one can easily code in CodeWorld, students have the ability to explore an algebraic concept with a computer programmed model, alongside the textbook’s given table, equation and graph. This thesis provides additional projects for supporting the Algebra I curriculum through LSU’s ICT course and an overview of the history of computing with an emphasis on highlighting some of the attempts that were undertaken within the past 80 years to use computational thinking and programming to support problem solving across disciplines, including the humanities, math and sciences

Profile of Student Algebraic Thinking with Polya's Problem-Solving Strategy: Study on Male Students with Field Independent Cognitive Style

This study aims to describe the profile of students' algebraic thinking with Polya's problem solving strategy in completing a linear program conducted on male students with field independent cognitive style. This research is exploratory research with qualitative approaches. In accordance with the purpose of the study, the subject (single subject) were male student with field independent cognitive style. Single subject were screened from 119 participants (male students in grade X) at a high school in the city of Mataram, Indonesia. The criteria for determining a single subject are male students with field independent cognitive style, and having the highest math scores on linear algebra material. The research instrument consisted of the main instrument (researcher/human instrument) which interacted directly with the subject to explore the subject's algebraic thinking profile, and research aid instruments consisting of the GEFT test, mathematical ability test, linear programming tasks, and interview guidelines. Through Polya's problem solving, the students' algebraic thinking profile has been described, where the subject has represented mathematical ideas using algebraic expressions, the subject interprets algebraic expressions; the subject uses symbolic representations, formulations, and expressions of equations using algebraic conventions; and the subject can interpret the solution

Research questions and approaches for computational thinking curricula design

Teaching computational thinking (CT) is argued to be necessary but also admitted to be a very challenging task. The reasons for this, are: i) no general agreement on what computational thinking is; ii) no clear idea nor evidential support on how to teach CT in an effective way. Hence, there is a need to develop a common approach and a shared understanding of the scope of computational thinking and of effective means of teaching CT. Thus, the consequent ambition is to utilize the preliminary and further research outcomes on CT for the education of the prospective teachers of secondary, further and higher/adult education curricula

Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science