The purpose of this work is to explore alternative geometric pedagogical perspectives concerning justifications to 'fast' multiplication algorithms in a way that fosters opportunities for skill and understanding within younger, or less algebraically inclined, learners. Drawing on a visual strategy to justify these algorithms creates pedagogical…

Productive failure has shown positive effects on conceptual and transfer measures, but no clear effects on procedural measures. It is therefore an open question whether, and to what extent, productive failure methods may be used to enhance the learning of procedural skills. A typical productive failure study focuses on a single, complex concept;…

Examining the use of conceptual frameworks such as the instructional hierarchy (IH) to drive academic interventions represents an important area of inquiry in order to understand why an intervention was effective. However, to date, the IH has only been examined retroactively to explain the effectiveness of math interventions and has not been used…

In this study, we used hierarchical linear modeling to examine restricted-use 2011 National Assessment of Educational Progress (NAEP) data to explore relationships between principal-reported time spent on the different NAEP responsibilities of mathematics coaches and specialists (MCSs) and the achievement scores of approximately 37,400…

Textbooks have a long history of explicitly and implicitly supporting heteronormative ideologies and effectively erasing marginalized populations, such as people who identify as queer, by exclusion. Students view textbooks as an authority over content and spend large portions of in and out of class time interacting with their textbooks. Because…

Common divisor is one of the concepts that started to be learned in secondary school and forms the basis of many concepts. But students generally have difficulty in making sense of it. The purpose of this study is to investigate concept formation processes of common divisor through a case study on seven sixth grade students. To do this, we…

The researcher conducted a qualitative case study of two sessions of a preservice teacher tutoring a student with a learning disability on Algebra 1 content. In this study, the focus was the tutor's use of gestures overlaid on the students' offloaded work on paper to help the student make sense of the problems. The student also demonstrated how…

Research on puppets in Intermediate Phase mathematics is in its infancy. According to Vygotsky, play affords a playful element that can optimise learning opportunities. However, many mathematics teachers are unfamiliar with the integration of pedagogy of play (PoP) (in this case, puppetry). The aim of this paper is to report on one participant's…

In this mixed-methods research, the relationship between four factors of individual online learners and their mathematics self-concept was explored. In addition, the challenges the students faced in learning mathematics online during the Coronavirus disease (COVID-19) pandemic were determined. The participant students were from two mathematics…

This article discusses Cigugur indigenous communities' custom in carrying out calculation practices to determine the best time to start house construction activities. The realist ethnography approach was used in this study through exploratory research. The ethnomathematics design adopted four elements: generic questions, initial answers, critical…

In this paper, I aim to explore what role persuasion plays in the early education of children. Advocating Wittgenstein, I claim that persuasion involves imparting to a pupil about a particular world-picture ("Weltbild") by showing rather than explaining. This because we cannot introduce a child to the hinges of a world-picture through a…

Research on elementary students' reasoning on patterning problems with pictorial representations has illustrated that students can visualize structure in patterns in different ways. In this paper, we offer a characterization of students' spatial structures and numerical structures and explain how the link between these two structures can support…

Positioning teachers as designers of curricular resources invites opportunities for exploration at the intersection of content, pedagogy, and design. As researchers accepting greater responsibility for preparing teachers to maintain a commitment to their pedagogical vision in practice, this work seeks to cultivate the imagination of humanistic…

Responding constructively to unexpected events during a lesson is a particularly challenging facet of teaching. This study aimed to investigate how a secondary school mathematics teacher responded to learners' unexpected or unplanned offers in the teaching of algebra. A total of three sequential lessons were video recorded and the quality of the…

In order to enhance students learning environments, mathematics lecturers need to prepare suitable materials in their lessons. So improving the materials in textbooks based on learning theories is so important to enhance the ability of students in mathematics learning through problem solving activities. The purpose of this qualitative case study…