In the article, we prove 18 inequalities involving inradius, a length of one side and one additional element of a given triangle. 14 of these inequalities are the necessary and sufficient conditions for the existence and uniqueness of such a triangle. All proofs are based on standard methods of calculus and can serve as a good demonstration of the…

This article describes research on the use of a differentiated approach in assessing students' academic achievements during mathematics lessons. The study used theoretical and empirical research methods. In particular, normative documents and scholarly literature were reviewed, and in 2021, the study conducted a survey of online mathematics…

The aim of the current study was to investigate whether exposing teachers to theoretical and empirical background information regarding pedagogical aspects of geometrical thinking would affect their noticing abilities. Forty-one in-service Mathematics teachers participated in this study. The research tools used in the study included a lesson taken…

The interplay between mathematics teachers' beliefs and practices has been widely investigated and research has examined how teachers' beliefs about mathematics, teaching and learning change when participating in continuing professional development (CPD). In this paper, I track teachers' self-reported beliefs and practice changes as they…

Teachers and caregivers use children's books (i.e., trade books) to support mathematics learning in school and home settings; shared book reading offers a unique opportunity to support students' understanding of operations and schema development. No prior studies have examined the representations of addition, subtraction, multiplication, and…

Purpose: The aim of this paper is to describe teachers' professional development in Lesson Study (LS) as processes situated in Semiosphere and generated by the unevenness due to different cultural traditions. The authors characterise teachers' professional development in two LS experiments as processes generating new knowledge to point out their…

This study lies within the field of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the…

In this paper, we present a novel solution of the quadrature of a parabola based on application of Ramanujan's formula for the partial sum of the square roots of the first "n" natural numbers. We also derive a new formula for calculating of area of a parabolic segment and we apply the result to a generalization of some classical theorems…

This study described the experiences of a group of seven sixth-grade teachers and the participation of their emergent bilingual students (EBs) during the implementation of an instructional protocol designed to provide students with opportunities to engage in mathematical reasoning through discourse. The Discursive Mathematics Protocol (DMP) is…

Across three studies and empirical papers, this dissertation focuses on the ways embodied, choreographic sense-making practices can expand the means and ends of STEM learning with respect to mathematics and computation. Specifically, this work demonstrates how practices for developing rule-based improvisational choreography map generatively onto…

There is a plethora of textbooks to choose from. While most textbooks contain the same content, teachers need to understand the textbook they have chosen to support their students' learning, as textbooks can significantly impact student learning and teacher instruction. When searching for a way to understand the various textbooks, my research…

Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a…

This study used a mixed-methods design to examine teachers' responses to professional learning on mathematics differentiation. Grade 3 classroom teachers (N = 28) attended four 2-h professional learning sessions and an additional 2 h individually on differentiation and completed pre- and post-surveys with quantitative and short response items…

Considering the prevalence of mathematics teacher shortages in the United States, together with declining enrollments in teacher preparation programs, it is crucial for districts and teacher preparation programs alike to investigate new recruitment initiatives. In this pilot study, a university aimed to increase high school students' interest in…

Discrete time models, one linear and one non-linear, are investigated, both with a herbivore species that consumes a basal food source species. Results are presented for coexistence of the species and to illustrate chaotic behaviour as parameters are varied in the non-linear model. The results indicate the benefit of fertilization in terms of the…