This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…

The growing use of programming in mathematics classrooms presents a challenge linked to implementation in general and task design in particular. This article presents design ideas for mathematical problems incorporating programming in which the focus remains mainly on learning mathematics and less on learning programming. The article starts by…

Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…

The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

This paper aims at using a Use-Modify-Create approach to explore students' mathematical problem solving by means of computational thinking (CT) and programming activities. The data collection method is participant observation, in which the researcher also has the role as teacher, guiding the group activities. In our study, two groups of students…

As computational thinking (CT) is new to teachers, they need support on how CT integration will work. This study examines the use of a hypothetical learning trajectory (HLT) to support teachers in integrating computational thinking into mathematics lessons utilizing GeoGebra. By employing the educational design research (EDR) methodology, the…

Background: Empirical studies have revealed students' development of computational thinking (CT) and mathematical thinking (MT) during programming-based mathematical problem-solving, highlighting specific CT concepts or practices that serve as learning goals or outcomes. However, implementing programming-based mathematics instruction requires…

We report on a case study of eight grade 5 to 6 students (ages 12-14) involved in a three-day "digital-making summer camp" focused on mathematical problem-solving through block-based programming combined with programmable electronics. Data analysis focused on the computational thinking (CT), mathematics, and problem-solving challenges…

In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…

A Prolog program consists of a set of facts and rules rather than imperative statements, commonly used in most other programming languages. Therefore, the Prolog language is used to encode logic, from which the inference engine deduces logical conclusions. In this article, we argue that the use of the Prolog language can be useful to help students…

Physics, even though it is guided by simple principles, tends for many topics to be obscured in the mathematics redundancy. MATLAB®, as interactive software for computer algebra, has already had an important impact on the way physics is taught by educators. It has also had a substantial impact on the way research is performed by students to…

Games are an everyday part of most students' lives. Games engage students and provide opportunities to foster perseverance in problem solving. When implemented in the mathematics classroom, game-based learning can have similar positive benefits. Students can enjoy mathematics and develop important life skills that will help them in their current…

This research investigates the impact of mathematical problems created with Scratch on the problem-solving skills of 8th-grade middle school students. The research was based on the descriptive design of mixed research approaches. In this direction, the research model was single-group pretest-posttest design, which is a weak experimental design…

This paper describes a 54-hour summer institute for grades 6-12 mathematics and science teachers (N = 19) with a comprehensive approach to preparing teachers to use computational thinking (CT) in their classrooms, including training in Python computer programming with Lego® Mindstorms® robotics, mathematics content sessions, and opportunities to…

Probability is generally considered one of the most challenging areas to teach in mathematics education due to its intricate nature. However, the simulation-based teaching method can increase students' accessibility significantly to the probability problems because it enables students to resolve the problems with minimal mathematical skills. By…