Facilitating students' transition from less to more mathematically productive engagement in discussions is an important area of investigation. Research on mathematical whole-class discussions has consistently identified facilitating students' mathematical autonomy as a central component of this transition. Additionally, research commonly infers…

Increased efforts are needed to meet the demand for high quality mathematics in early years classrooms. Despite the foundational role of geometry and spatial reasoning for later mathematics success, the strand receives inadequate instructional time and is limited to concepts of static geometry. Moreover, early years teachers typically lack both…

We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing…

This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

To what extent can instructional design be based on principles for instilling a culture of problem solving and conceptual learning? This is the main focus of the study described in this paper, in which third grade students participated in a one-year course designed to foster problem solving and mathematical reasoning. The design relied on five…

Previous studies have provided that when learning shapes for the first time, young children tend to use the prototype as the reference point for comparisons, but often fail when doing so since they do not yet think about the defining attributes or the geometric properties of the shapes. Most of the time, elementary students learn geometric…

The purpose of this study is to investigate the mathematical literacy of the 15-year-old students in terms of PISA mathematical literacy questions. The research model of this study is the survey model in the quantitative models. The sample of this study was composed of 1.227 students who received formal education in five different types of schools…

This study explores the effects of the "presence of external representations of a mathematical object" (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric…

In this article, Teachers use "studio" time to review videotaped classroom episodes, learn about students' developmental levels in geometry, and increase students' use of mathematical language and vocabulary.This article has a twofold purpose: (1) to share the power of opening the classroom door to a community of professional…

A computational experiment that investigates single-walled carbon nanotubes (SWNTs) has been developed and employed in an upper-level undergraduate physical chemistry laboratory course. Computations were carried out to determine the electronic structure, radial breathing modes, and the influence of the nanotube's diameter on the…

A computational experiment that investigates the optical activity of the amino acid valine has been developed for an upper-level undergraduate physical chemistry laboratory course. Hybrid density functional theory calculations were carried out for valine to confirm the rule that adding a strong acid to a solution of an amino acid in the l…

This study examines socioeconomic status (SES), English language proficiency (ELP), vocabulary proficiency (VP), and math proficiency (MP) of students to determine if SES, as determined by the Free and Reduced Lunch Program (FRL), as well as English language proficiency (ELP) and vocabulary proficiency (VP), as measured by CELLA scale scores and…

This report describes the longitudinal development of one student, Drew, in terms of his unit concepts in area and volume measurement situations across Grades 2 through 5. Data were collected during individual interviews and an open-response assessment within the context of a four-year longitudinal teaching experiment. Results indicate that Drew's…

This research reports on data and analysis investigating the sharing of ideas and strategies from the level of a small group to the level of the whole class (and vice versa) in a fourth grade mathematics classroom utilizing digital technology. This research takes a sociocultural perspective positioning meaning and learning as shaped by mediational…

Mathematics is an important discipline, providing crucial tools, such as problem solving, to improve our cognitive abilities. In order to solve a problem, it is better to envision and represent through multiple means. Multiple representations can help a person to redefine a problem with his/her own words in that envisioning process. Dynamic and…