For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

Drawing on evidence from the Longitudinal Investigation of the Effect of Curriculum on Algebra Learning (LieCal) Project, issues related to mathematics curriculum reform and student learning are discussed. The LieCal Project was designed to longitudinally investigate the impact of a reform mathematics curriculum called the Connected Mathematics…

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)…

These proceedings are a written record of the research presented at the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Mazatlán, Mexico, virtually beginning May 27, 2021 and in-person June 2-6, 2021. The conference was originally scheduled to take place…

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…

Should all students take Algebra 2? Florida seemed to say "no" this spring with the passage of a law striking it from graduation requirements. Texas said much the same in legislation Republican Gov. Rick Perry signed this week that also backs away from Algebra 2 for all. Those steps come as the Common Core State Standards for math set…

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…