This study reports on the design and implementation of an equity-focused, project-based algebra curriculum in two advanced eighth-grade classrooms. We document with substantial detail a promising approach to capturing how students demonstrate and build robust mathematical understandings in ways that strongly connect to equity issues. We illuminate…

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We…

Problem posing is a learning approach that trains students to be able to process and communicate mathematical problems based on information obtained. This study aims to describe the ability of high school students to pose problems on the topic of the system of linear equations in two variables (SLETV). This study used a quantitative descriptive…

Majority of the students regarded algebra as one of the difficult areas in mathematics. They even find difficulties in algebraic expressions. Thus, this investigation was conducted to identify common errors in algebraic expressions of the preservice teachers. A descriptive method of research was used to address the problems. The data were gathered…

We propose that by more closely aligning interdisciplinary work in (a) numeracy education for medication dosage calculations and (b) model-driven design for medical devices that are used for delivery of medication we may help address the incident-rate in incorrect medication calculations and delivery, given that such devices commonly require the…

Nationwide, students with disabilities struggle to develop foundational skills across content areas (National Center for Education Statistics, 2012, 2013). Researchers and national organizations have suggested that many students' achievement problems stem from failing to develop fluency with basic facts and skills in reading, mathematics, and…

A key aim of mathematics teaching is for children to develop appropriate and efficient strategies for solving tasks. The analysis presented in this paper moves beyond the exploration of changes in the strategies that children employ to solve tasks and extends to observation and exploration of changes that occur when their overall solving approach…

Students who score within the bottom quartile on cognitive measures of math aptitude have been identified as at-risk for low performance in chemistry courses, with less attention as to "why" such differential performance persists. At-risk students struggle most differentially on assessment items related to the mole concept and…

This study examined gender differences in the early mathematical skills of children at risk of developing mathematical difficulties. Of a total sample of 1091 children (49% girls and 51% boys), we observed authentic children who scored low at 33 months with the assessment material MIO (Mathematics, Individual and Environment). Cut-off for low…

Brief experimental analysis (BEA) is a methodology of rapidly implementing interventions and observing the effect each has on student performance. Extensive research exists demonstrating the utility of BEA in identifying effective reading interventions for students, but comparatively little research exists regarding BEA and mathematics. The…

Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

Adult learners preparing for university level study have varying degrees of prior experience, confidence, ability, motivation and need when it comes to mathematical tasks. The development of numeracy skills is a core aspect of university preparation, with many university courses requiring a certain level of mathematical literacy. The standard…

Previous theoretical research has revealed conceptual similarities among a number of mathematical learning theories and theories regarding language acquisition. This intersection of ideas led to a novel framework defining four stages of mathematical learning: Receiving, Replicating, Negotiating Meaning, and Producing. Through qualitative research…

In this article, we report on a three-pronged effort to create a hypothetical learning progression for quantification in science. First, we drew from history and philosophy of science to define the quantification competency and develop hypothetical levels of the learning progression. More specifically, the quantification competency refers to the…

Facing increased pressure to improve retention and graduation rates, engineering departments are increasingly scrutinizing whether they are getting their desired outcomes from core mathematics coursework. Since mathematics courses are a significant source of attrition and many engineering faculty are unhappy with students' mathematical abilities,…