Designing a digital game using method, activities, contexts and problems which have been proved to be effective in mathematics education for a long time, will increase the effectiveness and success of the game. The purpose of this study was to reflect the digital game design process for the area concept. The design-based research method was used…

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and…

In combinatorics, combinatorial notation, e.g., C(n, r), is explicitly defined as a numerical value, a cardinality. Yet, we do not use another symbol to signify the set of outcomes--the collection of objects being referenced, whose cardinality is, for example, C(n, r). For an expert, this duality in notation, of signifying both cardinality and…

In the late 1800s and early 1900s, increases in metallurgic technology and better manufacturing methods made naval artillery a more powerful force. Guns could fire more powerful shells that could travel farther and hit a target with much greater accuracy. Torpedoes represented a major threat to even the most powerful of warships, forcing captains…

Understanding a mathematical concept in real-world situations is of practical importance and would be helpful to learn the concept in depth. One potential way to help students learn mathematical concepts in real-world situations would be to engage them with contextual problems. Exponential and logarithmic concepts are essential topics in higher…

We describe the results of a master's thesis in malware detection and discuss the connection to the learning goals of the project. As part of the thesis, we studied obfuscation of malware, conversion of files into images, image processing, and machine learning, a process of benefit to both the student and faculty. Malware detection becomes…

3D-printing technology has become increasingly important in recent years, offering many possibilities for mathematics teaching and learning. From our point of view, the field of calculus seems to be particularly suitable for the use of 3D-printing. Using the example of 3D-printed graphs of functions, the use of this technology in calculus is…

In order to participate proficiently in mathematical activity, a student needs to become fluent in both mathematical sign activity and speaking about the activity with signs. From the theoretical viewpoint of the philosophers Wittgenstein and Peirce, on the one hand, mathematics is seen as a sign game, while on the other hand experiments with…

Nat Banting, argues that the "invert and multiply" algorithm for division of fractions is, in fact, not an algorithm. He suggests that Liping Ma's (1999) algorithm, which involves writing the fractions with a common denominator and then dividing the numerator of the first fraction by the numerator of the second fraction, is better as it…

We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.

The purpose of this research is to identify prospective mathematics teachers' conceptual structure about the concept of "Integral". In this research, phenomenology design, one of the qualitative research designs, was used. A total of 35 prospective mathematics teachers, studying at a state university, participated in the research. The…

Young children show remarkably sophisticated abilities to evaluate others. Yet their abilities to engage in proportional moral evaluation undergoes protracted development. Namely, young children evaluate someone who shares "absolutely" more as being "nicer" than someone who shares "proportionally" more (e.g., sharing…

In this study, we examine the connections between real analysis concepts and secondary mathematics content. This is accomplished by conducting a textbook analysis of a commonly used real analysis textbook. Concepts from the real analysis textbook were mapped to the Common Core State Standards-Mathematics (2010) to determine the relationship…

In this article, the authors argue that teachers need to possess appropriate understanding and diverse pedagogies to successfully move learners from additive to multiplicative thinking. Herein, they offer five pedagogical strategies that teachers can use to help students make this transition. Some of the challenges of learning multiplicative…

This paper reports an overview of contemporary research on early childhood mathematics teaching and learning presented at recent mathematics education research conferences and papers included in the special issue (2020--4) of "ZDM Mathematics Education." The research covers the broad spectrum of educational research focusing on different…