"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly…

School algebra serves as the language of mathematics and a foundational subject for learning advanced mathematics courses. This makes developing learners' proficiency in algebra the most desirable instructional goal of school mathematics. Despite having such importance emphasis, however, studies indicate that the vast majority of learners are…

Statisticians have developed propensity score methods to improve generalizations from studies that do not employ random sampling. However, these methods rely on assumptions whose plausibility may be questionable. We introduce and discuss bounding, an approach that is based on alternative assumptions that may be more plausible. The bounding…

Flipped classrooms serve as a new pedagogical approach for teaching and learning, which involves switching from the traditional teacher-centred academic agenda. Unlike the traditional classroom model, the flipped classroom enables students to understand the lesson better while learning at their own pace and enhancing their communication skills…

This study aims to evaluate the effectiveness of the online learning platform Brilliant.org in improving the academic performance of 60 tenth-grade students from four public schools in the city of Barranquilla, Colombia. A quasi-experimental design with two groups will be used: an experimental group that will use Brilliant.org platform to learn…

Introductory courses in biology often lack sufficient emphasis on quantitative skills and interdisciplinary problem solving, leaving many students unprepared for more advanced biology coursework and hampering their ability to pursue biology research careers. MathBench Biology Modules were created to enhance the quantitative skills of biology…

Rural schools face particular challenges with teacher quality. The Northeast Tennessee College and Career Ready Consortium was a collaborative reform effort among rural schools with a key goal of improving the quality of instruction in math and science to support its efforts to expand academically rigorous courses. This study examines progress…

We investigated how high school mathematics course placement contributes to inequalities in college preparation for students categorized as "English Learners" (ELs), especially "long-term" English Learners (LTELs). We devised a base-2 enumeration approach that allowed us to process complex transcript data from one school…

Acceleration refers to placing students in advanced courses to meet their individual learning ability. The problem of focus in this study was that the increased placement of students in advanced courses was often associated with negative impacts, including a lack of readiness, as well as emotional and social immaturity. As such, the purpose of…

Mathematics is not just memorized facts, but rather it is understanding how to approach and solve problems, and problem-solving requires linguistic proficiency. Too often, English learners' (ELs) relatively low math performance is dismissed due to their supposed "limited" English proficiency. Taking this perspective, a constructivist…

Using data from the Educational Longitudinal Study of 2002-2006, the authors investigated the effects of advanced math course taking on math achievement and college enrollment and how such effects varied by socioeconomic status and race/ethnicity. Results from propensity score matching and sensitivity analyses showed that advanced math course…

This report examines the placement of Teacher for America (TFA) teachers and examines their impact on the learning gains of their students during the 2013-14 school year. Sets of eligible TFA teachers were identified in 2013-14 from which the subset of teachers assigned to teach language arts and/or mathematics to students in grades 3 through 10…

Everyone knows that there is racial inequality in achievement returns from advanced math; however, they do not know why black students and white students taking the same level of math courses are not leaving with the same or comparable skill levels. To find out, the author examines variation in course coverage by the racial composition of the…

This paper reports findings of a post test experimental control group design conducted to investigate the role of modified Moore learning approach on improving students' mathematical understanding and proving abilities. Subjects of study were 56 undergraduate students of one state university in Bandung, who took advanced abstract algebra course.…

Many mathematicians and curriculum bodies have argued in favour of the theory of formal discipline: that studying advanced mathematics develops one's ability to reason logically. In this paper we explore this view by directly comparing the inferences drawn from abstract conditional statements by advanced mathematics students and well-educated arts…