Programming is an interdisciplinary practice with applications in both mathematics and computer science. Mathematics concerns rigor, abstraction, and generalization. Computer science predominantly concerns efficiency, concreteness, and physicality. This makes programming a medium for problem solving that mediates between mathematics and computer…

Research on geometric transformations suggests that early learners possess intuitive understandings grounded in motion metaphors, transitioning to mappings. The processes through which students transition between these two conceptions are not fully understood. We propose that Vygotskian hybridizing (related to Vygotsky's articulation of everyday…

Geometric concepts are fundamental to early geometry education, and developmentally appropriate practices are crucial for teaching them to young children. Robotic coding is an effective tool in many areas of early mathematics and has significant potential in teaching geometric concepts. This study aimed to test the impact of a research-based…

Mathematics achievement is positively associated with coding in the classroom. By making mathematical relationships visible to students as they code, teachers leverage rich connections between block-based computer programming and mathematical sense making. In this article, the authors describe strategies for adapting a Code.org lesson integrating…

Grounded in problem-based learning and with respect to four mathematics domains (arithmetic, random events and counting, number theory, and geometry), we designed a series of programming-based learning tasks for middle school students to co-develop computational thinking (CT) and corresponding mathematical thinking. Various CT concepts and…

The goal of this paper is to explore dynamic geometry environments (DGE) as a type of computer programming language. Using projects created by secondary students in one particular DGE, we analyse the extent to which the various aspects of computational thinking--including both ways of doing things and particular concepts--were evident in their…

Studies have shown that learning mathematics through programming can be complex and that the programming itself might even hamper students' learning. However, few studies have focused on the role of the teacher and the teacher-student interaction that aims to support students' learning when using programming. The present study examines a didactic…

The robotics context is suggested as a context that supports the learning of the sciences including mathematics. The present study investigates how the robotics context affects students' motivation for learning mathematics. Two groups of seventh-grade students participated in the present research: a robotics class (32 students) and a regular class…

This work covers a three-week program designed to provide undergraduate students with a background in structural chemistry and materials science. Sessions are based on the programming of regular polyhedra and their geometrical relationships by using an object-oriented language (i.e., POV-Ray). Three lectures introduce the basics of programming…

The aim of study to investigate the effects of block-based game development activities carried out on the goal-based scenario approach on the geometry achievement and computational thinking skills of seventh-grade students and to reveal their opinions regarding the process. The study used a one-group pretest-posttest experimental model an…

We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion…

Scratch is a tool for initial learning of programming, but also for creating educational and entertainment content, making mathematical and scientific projects, simulating and visualizing experiments. This paper examines the effectiveness of Scratch's application in mathematics, in the study of basic geometric shapes. The analysis has shown that…

This article reports on a research project that examined the ways that 10-year-old students, who were using Scratch for coding, engaged with mathematical ideas. Interactive software is emerging that has cross-curricula implications and facilitates thinking in rich, problem-solving environments. Scratch, a free-to-use graphical programming…

Background and Context: Learners struggle with conceptual understanding of introductory programming concepts such as variables, expressions, and loops. Objective: We examine whether and how designed activities for conceptual exploration support preliminary engagement with and learning of foundational and often hard-to-grasp programming concepts…

This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists,…