Contribution: This article compares student success via different pathways in which students take mathematics courses required for engineering degrees. Background: Mathematics courses are an integral part of engineering curriculum. Many institutions require or recommend the order in which students take Calculus II, Multivariable Calculus,…

Teacher-directed and self-directed learning have been compared across various contexts. Depending on the settings and the presentation of material, mixed benefits are found; the specific circumstances under which either condition is advantageous are unclear. We combined and reanalyzed data from two experimental studies investigating the effects of…

Low passing rates in developmental mathematics have been a serious concern for community colleges for many years. A course in Quantitative Literacy (QL) offers non-STEM students an alternative option to introductory algebra as a path to a degree. This paper describes the implementation and evolution of QL at the Borough of Manhattan Community…

This study examined the effects of two teaching treatments [multiple-representation instruction (MR) and traditional algorithmic instruction (TA)] on students' performance on mathematics problems that integrated fractions, decimals, and percent. Using a 2 × 2 crossover design, the effect of the teaching treatments and their sequences on student…

Scholars propose that contextual problems can be used to ground students' understanding of mathematical ideas, and recent curricular trends have resulted in a plethora of resources that introduce and develop new mathematical ideas through contextual problems (CPs). Given the tension between this approach and the traditional role of CPs as…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

This article describes a learning trajectory on expressions and equations based on the sixth-grade Common Core State Standards for Mathematics (NGA/CCSSO, 2010). A classroom teaching experiment using design research (Lamberg & Middleton, 2009) was conducted. The data was analysed using Corbin and Strauss' (2014) Constant Comparative method and…

In this article we advance characterizations of and supports for elementary students' progress in generalizing and representing functional relationships as part of a comprehensive approach to early algebra. Our learning progressions approach to early algebra research involves the coordination of a curricular framework and progression, an…

The purpose of this project was two-fold. First, it would provide an opportunity for students to complete the developmental math course sequence more quickly, thereby enabling students to proceed to a college-level mathematics course sooner. To accomplish this, the classroom was designed with computer-assisted homework courses that blended…

We detail a learning progressions approach to early algebra research and how existing work around learning progressions and trajectories in mathematics and science education has informed our development of a four-component theoretical framework consisting of: a curricular progression of learning goals across big algebraic ideas; an instructional…

This investigation tried to determine if a statistically significant relationship exists between different sequences of enrollment in remedial mathematics and grades obtained in college algebra classes at Jacksonville State University. Groups consisting of five different enrollment sequences in mathematics were studied. The data collected supports…