Current reforms in mathematics education advocate the development of mathematical learning communities in which students have opportunities to engage in mathematical discourse and classroom practices which underlie algebraic reasoning. This article specifically addresses the pedagogical actions teachers take which structure student engagement in…

Concept-focused quiz questions required College Algebra students to write about their understanding. The questions can be viewed in three broad categories: a focus on sense-making, a focus on describing a mathematical object such as a graph or an equation, and a focus on understanding vocabulary. Student responses from 10 classes were analyzed.…

Nationwide, schools are pushing for more students to take Algebra I in eighth grade, prior to formally entering high school. The algebra-for-all movement has been intended to alleviate equity issues which held minority and low-income students back from entering a college-preparatory path in high school. Students with the needed content,…

This design-based research project investigated the development of functional thinking in algebra for the upper primary years of schooling. Ten teachers and their students were involved in a sequence of five cycles of collaborative planning, team-teaching, evaluating and revising five lessons on functional thinking for their students over one…

We describe an attempt by a former mathematics teacher to read an undergraduate mathematics proof aided by discussions with a mathematician using the language of mathematical problem solving. The literature on successful approaches to reading mathematics is scarce at the secondary and undergraduate levels. Shepherd, Selden and Selden (2012)…

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an…

Research on flipped instruction with English Language Learners (ELLs) is sparse. Data-driven flipped research conducted with ELLs primarily involves adult learners attending a college or university. This study examined the academic performance of secondary ELLs who received flipped instruction in an algebra course at a newcomer school compared to…

It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students' learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a…

Students with mathematics learning disabilities (MLD) have a weak understanding of fraction concepts and skills, which are foundations of algebra. Such students might benefit from computer-assisted instruction that utilizes evidence-based instructional components (cognitive strategies, feedback, virtual manipulatives). As a pilot study using a…

Student Mobility is increasing on Long Island, NY, the site of the present study related to the demographic changes of increasing immigration and poverty. Mobile students often struggle academically, and are at risk for school drop-out or failure. Mobility is sometimes combined with other risk factors such as gender, ethnicity, limited English,…

In this paper, we describe how database instructors can teach Relational Algebra and Structured Query Language together through programming. Students write query programs consisting of sequences of Relational Algebra operations vs. Structured Query Language SELECT statements. The query programs can then be run interactively, allowing students to…

Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…

Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

In this paper, we investigate which aspects are overriding in the concept images of monotonicity of Finnish tertiary mathematics students, i.e., on which aspects of monotonicity they base their argument in different types of exercises related to that concept. Further, we examine the relationship between the quality of principal aspects and the…

Recently, a new cognitive style approach was introduced, which refers to two types of visualizers. This approach is based on neuropsychological evidence and neuroimaging results, which suggest the existence of two distinct imagery subsystems, the object and the spatial imagery subsystems. The goal of the study was twofold: first to examine a…