The paper aims to present the extent to which the application of the concrete mathematical and musical play contributes to the child's cognitive development. The research was conducted in two international schools in Belgrade, using the play titled 'Musical Monkeys'. The results of the research have shown that this kind of approach in working with…

Lines and angles are essential for students because of geometry and its many applications in daily life. However, there are still many students who have difficulty grasping the material. Therefore, it is necessary to design learning using the right approach, context, and media. This study aims to produce a learning trajectory that can assist…

We present a typology for characterizing online student-facing mathematics platforms that examines how they position students as learners, exemplified by 9 commonly used platforms. We identify three types of student learning experiences: instruction and practice, practice and support, and conceptual games and activities, and describe each one in…

Teaching educational materials to others enhances the teacher's own learning of those to-be-taught materials, although the underlying mechanisms remain largely unknown. Here, we show that the learning-by-teaching benefit is possibly a retrieval benefit. Learners (a) solved arithmetic problems (i.e., they neither taught nor retrieved;…

We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the…

These notes discuss several related problems in geometry that can be explored in a dynamic geometry environment. The problems involve an interesting property of hexagons.

Verification and validation are essential aspects of mathematics and beyond in STEM, but these constructs are not consistently defined in research nor in curricula documents. In this theoretical paper, we argue that verification and validation are largely characterized as binary judgments by teachers and researchers about what students do. We then…

The purpose of this study is to investigate how students' in senior grade of the high school participate in and interpret the transformational geometry activities integrated with cultural context. 5 students in senior grade participated in this study, all of whom live in Aydin district of Turkey. The main design of the study is qualitative.…

This paper introduces a percentage activity based on the context of "Black Friday" discounts. The aim of the study was to reveal the existing and new conceptions of the 7th grade students regarding the topic of percentage calculation. The activity was designed considering the students' prior knowledge in the concept of "Ratio and…

The current study examined pictorial and written descriptions of mathematics teaching and learning among a cohort of 120 students (aged 11 to 14 years) in three different lower secondary schools in Ankara, Turkey. A classroom environment with students working in groups or pairs and engaging in open-ended questions or tasks was unavailable. The…

Connections is one of the Process Standards set forth by the National Council of Teachers of Mathematics (NCTM 2000), whereby teachers provide students with learning opportunities to "recognize and apply mathematics in contexts outside of mathematics." Similarly, the Standards for Mathematical Practice (NGA Center and CCSSO 2010) call…

Dude Perfect has one of the most popular YouTube channels in the United States. The task in this article is one of several activities the author has integrated into mathematics lessons in ways that engage students and that are connected to Dude Perfect videos (Stohlmann 2019). The author describes how he planned and implemented purposeful…

Mixed numbers and fraction in general have been a problem for students not only in understanding the concept of itself, but also in understanding the operation of it, such as addition. Thus, supporting students in learning addition of mixed numbers is needed. The aim of this study is to develop a local instructional theory and materials related to…

In this article, the author describes how to help develop students' conceptual understanding of fractions through the tactical card-based game Nearest to One. Nearest to One promotes number-sense based strategies for comparing fractions, such as benchmarking (e.g., Is the fraction greater or less than one-half?) and building to the next whole,…

The Zen concept of beginner's mind describes how one's level of awareness can open one's mind to growth and possibilities, an attitude that would be beneficial for many mathematics students. In this naturalistic case study, two small groups of middle years students engage in the same mathematical task, one group demonstrating the characteristics…