Mathematics requires thinking but also pattern recognition. Recent research indicates that perceptual learning (PL) interventions facilitate discovery of structure and recognition of patterns in mathematical domains, as assessed by tests of mathematical competence. Here we sought direct evidence that a brief perceptual learning module (PLM)…

Recent federal legislation, such as the "No Child Left Behind Act" of 2001 and the "Education Sciences Reform Act (ESRA)" of 2002, has insisted that educational evaluations use rigorous research designs with quantitative outcome measures. In particular, the Institute of Education Sciences (IES) at the U.S. Department of…

This study examined how mathematical modeling activities within a collaborative group impact on students' perceived 'value' of mathematics. With a unified framework of Makiguchi's theory of 'value', mathematical disposition, and identity, the study identified the elements of the value--beauty, gains, and social good--with the observable evidences…

This study is part of a larger research program aimed at studying mental mathematics with objects other than numbers. It concerns operations on functions in a graphical environment with Grade-11 students. Grounded in the enactivist theory of cognition, particularly in problem-posing, the study aims to characterize students' mathematical activity…

We examine the impact of a teacher development program based on a functions approach to algebra on 7th grade students' understanding of equations. We focus on how students' score gains relate to their teachers' initial level of mathematics performance. Students from participating teachers' and their control peers completed a mathematics assessment…

Objective: In recent years, developmental education (DE) reform has led to a restructuring of the placement process, redesigning of course instructional modalities, or implementing student support services to supplement developmental coursework. In Florida, recent legislative changes allowed students to opt out of placement testing and enroll…

The Alabama State Department of Education (ALSDE) was grappling with several issues including: (1) A respectable rate of growth in student achievement for both fourth- and eighth-grade math in the state of Alabama, as measured by the National Assessment of Educational Progress (NAEP), but below the national average; and (2) A growing concern about…

The purpose of mathematics competitions, and in our case the South African Mathematics Olympiad (SAMO), is to promote problem solving skills and strategies, to generate interest and enthusiasm for mathematics and to identify the most talented mathematical minds. SAMO is organised in two divisions--a junior and a senior division--over three rounds.…

The U.S. educational system is undergoing rapid and substantial changes with many states grappling with the adoption of the Common Core State Standards in Mathematics (CCSSM). Important research questions remain unanswered regarding the potential efficacy of the CCSSM to improve student math performance compared with students around the globe.…

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…

In this article, the author contributes to the growing body of scholarship on critical mathematics pedagogy. In particular, the author advances this scholarship by outlining how critical pedagogy in the mathematics classroom can support students to engage in transformational resistance. Using a critical practitioner research approach, the author…

The transition to Common Core State Standards for Mathematics has created a need for high-quality professional learning on content and pedagogy. This is especially true for algebra 1 teachers in Florida, where students must pass a standards-based exam as a requirement to earning a high school diploma. Time, distance, and cost constraints can get…

This dissertation investigated whether math course sequence from 8 th to 9th grade influenced 9th grade math motivation, defined as perceived competence in math, sense of belonging in math, importance of math, and math anxiety. Two competing hypotheses were proposed suggesting that a more accelerated math curriculum (Algebra 1 in 8th grade versus…

I describe a method of evaluating the integral of 1/r[superscript 2] with respect to r that uses only algebra and the concept of area underneath a curve, and which does not formally employ any calculus. This is useful for algebra-based introductory physics classes (where the use of calculus is forbidden) to derive the work done by the force of one…

Acid-base equilibrium is one of the most important and most challenging topics in a typical general chemistry course. This article introduces an alternative to the algebraic approach generally used in textbooks, the graphical log "C" method. Log "C" diagrams provide conceptual insight into the behavior of aqueous acid-base systems and allow…