Students often instrumentally use variables and unknowns without considering the variational thinking behind them. Using parameters to modify the coefficients or unknowns in equations or systems of linear equations (without altering their structure) involves consciously incorporating variational thinking into problem-solving. We will test the…

The identification in this study with the aim is to describe how difficult it is for students to think reflectively when solving math problems, especially in linear programming material. Based on the purpose of this study, the type of research is qualitative with a descriptive exploratory approach. Data collection techniques used are: (1) test…

In this article, examples are shown to demonstrate how open-ended mathematical activities can be used in the classroom. Open-ended activities give students opportunities to apply their understanding in unfamiliar contexts without the pressure of finding one perfect solution.

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…

Background: Problem-solving as a vehicle to develop independent thinking skills is mostly underestimated and is often either overlooked or not given adequate attention within the existing South African mathematics curriculum. Consequently, numerous learners often display limited skills or lack skills to adequately crack Mathematics problems by…

The use and understanding of mathematics is a crucial component of the physical sciences. Much work has been done in physics education research and science education more broadly to determine persistent difficulties with mathematics. This work has led to the development of numerous problem solving strategies aimed at helping learners approach…

Bachelors and graduate students are offered in the course of teaching computational informatics, the ability to solve nonstandard mathematical problems, which, as a rule, are not included in the content of teaching computational informatics. The article aimed to analyze the application effectiveness of non-standard mathematical problems in the…

This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what…

Increasing availability of digital devices in elementary school classrooms presents exciting new opportunities for teachers to support the teaching and learning of mathematics. Although many of the math applications available for these devices focus on drill and practice of mathematical procedures, screencasting apps can help support effective…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data…

Research over the past few decades points to ways precalculus and calculus courses can be strengthened to improve student learning in these courses. This research has informed the development of the Algebra and Precalculus Concept Readiness (APCR) and the Calculus Concept Readiness (CCR) assessments. In this article, the authors present three…

Student errors are springboards for analyzing, reasoning, and justifying. The mathematics education community recognizes the value of student errors, noting that "mistakes are seen not as dead ends but rather as potential avenues for learning." To induce specific errors and help students learn, choose tasks that might produce mistakes.…

This paper discusses some difficulties in teaching introductory courses to programming, paying particular attention to their mathematical nature. We consider some aspects, which have not been commented in detail in textbooks and often neglected by course outlines and schedules. Some of these are constructing complex conditions, exceeding array…

The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…