There has been a lack of research into conceptually teaching the structure of contextual problems to kindergarten students. This is despite the popularity of contextual problems and the difficulties that students have with them. This study focuses on creating a textless, image-based application that uses the Triplet Structure Model to teach about…

The author seeks to use the limited contact time they have with students to engage them not only in academic pursuits but also in a discussion of the divine mission of humans. Since this can be difficult to meaningfully do in a math class, the author is continually searching for meaningful, engaging points of contact between mathematics and…

Should proof by induction be reserved for higher levels of mathematical instruction? How can teachers show students the nature of mathematics without first requiring that they master algebra and calculus? Proof by induction is one of the more difficult types of proof to teach, to learn, and to understand. Thus, this article delves deeper into…

The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at building the pattern of a structure sense as a profile of the structure sense in group property. Using a qualitative study, the structure sense of group property was explored through lecturing activity of…

While it is commonly accepted that Learning Analytics (LA) tools can support teachers' awareness and classroom orchestration, not all forms of pedagogy are congruent to the types of data generated by digital technologies or the algorithms used to analyse them. One such pedagogy that has been so far underserved by LA is exploratory learning,…

It is of critical importance, in particular, for mathematics teachers who will teach future generations to understand and do mathematical proofs. It is important to determine future teachers' beliefs about and difficulties with proofs because their knowledge of this issue affects their teaching. This study aims to determine and compare the proof…

The purpose of this paper was to review literature on the Cultural Historical Activity Theory (CHAT) and how it has been used to understand the mediation between emerging technologies and teaching and learning in a mathematics classroom. Specifically, it aimed at understanding the genesis of CHAT and further analyzing the studies that have…

This study reports the academic benefits of peer tutoring in algebra for middle school students. A total of 380 students enrolled in grades 7th and 8th participated in the study. Two peer tutoring sessions took place during each week (10 weeks). Interactions between peers lasted 20 to 25 minutes for each session. The typology of tutoring was fixed…

Circle, ellipse, parabola, hyperbolic curves are defined as conic sections from the intersection of a coni with a plane at different angles. These curves can be found in different positions depending on the different angles. In this case, rotation transformation can be applied to the curves so that their major axes are brought to the horizontal…

A phenomenographic study at a research university identified five categories of description for how STEM (science, technology, engineering, and mathematics) instructors conceptualize the design and redesign of undergraduate courses. These categories form a hierarchical outcomes space with increasing complexity of awareness of the phenomenon. The…

This study explores the effects of number structure characteristics on student thinking in solving missing-value proportion problems. Prior research has documented that the presence of an integer ratio is beneficial, particularly if the integer relationship is within the same measure space. Less information on student performance is available,…

This study explores relationships among prospective secondary teachers' skills of attending to relevant mathematics elements in students' answers, interpreting students' mathematical understanding, and proposing instructional actions. Thirty prospective secondary mathematics teachers analyzed three high school students' answers to three problems…

Early career K-grade 2 teachers in a yearlong project explored discourse and mathematical argumentation through monthly professional development (PD) sessions. The goal of the project was to develop an understanding of the types of K-grade 2 tasks that promote argumentation, the types of discourse and argumentation that K-grade 2 students engage…

The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students' attention. We present and compare various examples of how…

Students' beliefs that mathematical abilities are fixed can cause long-standing problems with motivation and learning. Hence, teachers should notice such problematic beliefs about identity among their students and handle them adequately. We used written descriptions of classroom situations to determine whether preservice mathematics teachers (n =…