This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with…

Generalization is considered to be an essential part of mathematical reasoning and proving, and it has many definitions in mathematics education research. Despite its centrality, teachers often have difficulty identifying and responding to generalization in students' work. In this study, we focus on preservice teacher's (PTs) ability to describe…

Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

In this study, hypothetical samples of students' work on a task involving pattern generalizations were used to examine the characteristics of the ways in which 154 elementary prospective teachers (PSTs) paid attention to students' work in mathematics. The analysis included what the PSTs attended to, their interpretations, and their suggestions for…

Twelve college students learned to tact the names of notes and rhythms and play them when presented with compound stimuli (visuals of notes and rhythms on a musical staff). In Experiment 1, we assessed generalization by presenting novel notes, rhythms, and compound stimuli not previously paired together. In the second experiment, we added a…

This paper aims to assess the impact of the reciprocal teaching strategy on the academic performance of student-teachers enrolled in the Higher Professional Diploma (HDE) program at Ajman University, United Arab Emirates. The study adopts a quasi-experimental design, employing pre- and post-tests and a control-experimental group configuration. The…

Slow reading has long been viewed as a teaching technique that engages students more deeply with course readings. Little systematic research, however, has been done to understand how this pedagogical strategy works in college classrooms. This study investigated how slow reading techniques promoted deep learning among undergraduate college students…

The study reported in this article investigated the appropriateness of Mathematical Knowledge in Teaching of three pre-service primary school teachers (PSTs), teaching an informal statistical inference (ISI) lesson to primary school students. Using an ISI framework and the Knowledge Quartet framework, the presence and appropriateness of the PSTs'…

This paper describes a study that used a novel method to investigate conceptual difficulties with mathematical induction among two groups of undergraduate students: students who had received university-level instruction in formal mathematical induction, and students who had not been exposed to formal mathematical induction at the university level.…

The purpose of the study is to evaluate how prospective mathematics teachers (PMTs) modify tasks to facilitate students' learning of pattern generalization through the use of their mathematical knowledge for teaching. Case study, which is a type of qualitative research method, was used to determine the mathematical characteristics that PMTs use…

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

Inherent in the Common Core's Standard for Mathematical Practice to "look for and express regularity in repeated reasoning" (SMP 8) is the idea that students engage in this practice by generalizing (NGA Center and CCSSO 2010). In mathematics, generalizing involves "lifting" and communicating about ideas at a level where the…

We perform dynamic investigation of two surprising geometrical properties, each of which involves additional properties. In the first task the property belongs to two regular polygons with the same number of sides and with one common vertex. It is found that all the straight lines that connect corresponding vertices of the two polygons intersect…

Adults with intellectual disability may not learn safety skills needed to maintain the safety of those within their communities. Basic life-saving skills are valued by community members and increase independent and integrated living and employment opportunities. This study used an instructional package consisting of modeling, task analysis, and…