The aim of this article is to shift the notion of 'sites' as places of work peculiar to continuous professional development (CPD) to a theoretical level, independent of, yet intimately connected to, their physical meanings, for example universities and schools. Most CPD initiatives have to contend with at least one of these two sites, in which…

Mathematics classrooms have reflected little change over the past century, consisting of the learning of inert, disjoint procedures with few connections between mathematics concepts and students' everyday experiences. However, problem posing, that is, the reformatting of existing problems and the generation of new ones, has been promoted by the…

This mixed qualitative and quantitative methods study addressed the effect of technology on college algebra and survey of calculus students' understanding. This research study was conducted in fall 2016 on eight college algebra classes with a total of 315 students, and in summer 2017, on two survey of calculus classes with a total of 40 students…

The purpose of this study was to determine if student on-task behavior varied when a) the One Teach/One Assist co-teaching model was applied or b) when the Team Teaching model was applied using an alternating treatment design for four students in a co-taught Algebra I classroom. Results show that participants experienced increased on-task behavior…

In the context of a generic harmonic oscillator, we investigated students' accuracy in determining the period, frequency, and angular frequency from mathematical and graphical representations. In a series of studies including interviews, free response tests, and multiple-choice tests developed in an iterative process, we assessed students in both…

The article provides a report on the comparison of Opportunities to Learn algebra and eighth grade students' algebra achievement in three countries: Botswana, Singapore and the United States. The study used student and teacher data from the Trends in International Mathematics and Science Study (2011 and 2015). By using a multilevel regression…

Teaching mathematics by project-based learning (PBL) method on the use of educational technology offers an innovative teaching pedagogy at college. The "World Culture Art Created with Calculus Graphs of Equations" poster project was designed by the first author and was completed in the pilot Calculus course during the spring 2016…

This report examines the effects of taking math in 12th grade on several academic outcomes, including high school grade point average, A-G course completion, college enrollment, and college persistence. We also investigate whether particular types of math courses (for example, Calculus or Statistics) are especially beneficial for students'…

This report examines the impact of taking a math course in twelfth grade on L.A. Unified students' science, technology, engineering, and math (STEM) college course taking and academic achievement. We also investigate whether particular types of math courses (for example, Calculus or Statistics) are especially beneficial for students' postsecondary…

Quantifier Elimination is a procedure that allows simplification of logical formulas that contain quantifiers. Many mathematical concepts are defined in terms of quantifiers and especially in calculus their use has been identified as an obstacle in the learning process. The automatic deduction provided by quantifier elimination thus allows…

Many students with learning disabilities (LD) in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic…

Patterns are a ubiquitous phenomenon. They exist in nature's plant species emerging as a complete order from truncated matter. Patterns are also present in the fine arts where the aesthetic properties of form exist and conjugate through paintings and sculptures. Mathematical patterns, the focus of this position paper, dominate financial scenarios,…

In this research, I set out to elucidate the relationships that might exist between students' conceptual understanding upon which they draw in their proof activity. I explore these relationships using data from individual interviews with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of…

Many students with learning disabilities (LD) in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic…

This study posed and studied a solution to a prevailing tension in online education: the online medium is fundamentally connective and yet students often report feelings of social isolation. The study compared two online interventions -- both into a student's fluency in the language of functions and graphs, a major focus of a student's transition…