Dual-credit courses expose high school students to college-level content and provide the opportunity to earn college credits, in part to smooth the transition to college. With the Tennessee Department of Education, we conduct the first randomized controlled trial of the effects of dual-credit math coursework on a range of high school and college…

Linear programming (LP) is an application of graphing linear systems that appears in many Algebra 2 textbooks. Although not explicitly mentioned in the Common Core State Standards for Mathematics, linear programming blends seamlessly into modeling with mathematics, the fourth Standard for Mathematical Practice (CCSSI 2010, p. 7). In solving a…

The problems of geometry and mechanics have driven forward the generalization of the concepts of number and function. This shows how application and generalization together prevent that mathematics becomes a mere formalism. Thoughts are signs and signs have meaning within a certain context. Meaning is a function of a term: This function produces a…

As more K-12 students with disabilities enroll in online courses, virtual schools and programs are working to make courses accessible through stronger course design. When course designers approach the issue of accessibility, they must comply with legal requirements and mitigate the challenges many students with disabilities face for literacy and…

This study examines the power of cognitive and noncognitive variables to predict students' performance in algebra. We investigated students' prior year's assessment scores and demographic characteristics to predict eighth-grade algebra scores. Using California statewide assessment data, we explored predictive factors in three regression models.…

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the…

Introduction: Visually impaired students (that is, those who are blind or have low vision) have difficulty accessing curricular material in mathematical textbooks because many mathematics texts have visual images that contain important content information that are not transcribed or described in digital versions of the texts. However, little is…

5th graders (n=527) were randomly assigned to self-explain worked examples (WE) or solve problems during a yearlong study. WE students learned more algebra skills when given algebra worked examples on an end-of-year transfer measure. Comparing attempts, conceptual, and mechanical correctness by condition, results demonstrated that the condition…

Prior work has found benefits of interpersonal closeness, or rapport, on student learning, but has primarily investigated its impact on learning outcomes, not learning processes. Moreover, such work often analyzes the direct impact of dyadic features like rapport on learning, without considering the role played by individual factors, such as…

In this paper, we document the results of the implementation of a series of activities related to an optimisation problem. The objective is describing how the construction of mathematical meanings is promoted when the students face the problem through different representations. The activities, addressed towards 15 year old students, surge from a…

Rational number understanding is a critical building block for success in more advanced mathematics; however, how rational number magnitudes are conceptualized is not fully understood. In the current study, we used a dual-task working memory (WM) interference paradigm to investigate the dominant type of strategy (i.e., requiring verbal WM…

Desmos Battleship is an engaging activity in which students can improve their visualisation skills, and deepen their understanding of linear functions and circles by making connections between algebraic and graphical representations. The Desmos Battleship activity was used in a Saturday STEM (Science, Technology, Engineering, and Mathematics)…

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

Multiple reports highlight the increasingly quantitative nature of biological research and the need to innovate means to ensure that students acquire quantitative skills. We present a tool to support such innovation. The Biological Science Quantitative Reasoning Exam (BioSQuaRE) is an assessment instrument designed to measure the quantitative…

The importance of laying a foundation for algebraic reasoning at a young age is increasingly being emphasized. In this article, the authors report on an activity that elicits in a natural way algebraic strategies that in a later stage of learning algebra are crucial for solving equations. The activity brings about the students' spontaneous use of…