This paper analyses student views on an e-learning intervention that incorporated a content development tool and computer algebra systems, aimed at improving performance and applicability of mathematics knowledge. The study deliberately relied on open source tools, with high usability both online and offline, that can be customized to address the…

The purpose for this correlational, explanatory study was to explain the influence of the length of the school day on the mean Partnership for Assessment of Readiness for College and Careers (PARCC) scores on the 2016 Grade 8 Mathematics and 2016 Algebra II tests for students in various socioeconomic strata. The Grade 8 Mathematics sample included…

Texas provides a unique opportunity to examine teachers without standard university preparation, for it prepares more teachers through alternative pathways than any other state. We find two advantages for mathematics and science teachers prepared in the standard way. First, since 2008 they have been staying in the classroom longer than those who…

Standards-based grading (SBG) is an assessment/grading system that attaches scores to the mastery level of specific learning objectives. This methodology is gaining momentum in the K-12 environment but has been largely overlooked at the post-secondary level. In this paper, I will discuss the implementation of this practice in a College Algebra…

Latent classes of effective and non-effective Algebra I teachers were established using measurements of teacher promoted engagement, teacher promoted understanding, and classroom management from the Measures of Effective Teaching Project (MET Project) database. Historically, robust measures of effective teaching exist in the literature; however,…

We investigated whether early algebra lessons that explicitly aimed to elicit mathematical discussions (shift-problem lessons) invoke more and qualitatively better mathematical discussions and raise students' mathematical levels more than conventional lessons in a small group setting. A quasi-experimental study (pre- and post-test, control group)…

While the lion's share of mathematics education research in linear algebra has been concerned with the conceptual aspects of students' learning, this study focuses on procedural knowledge that undergraduates can develop in a typical first-year course. The study analyzes the methods that a large cohort of second-semester students applied in a final…

This article shares analysis regarding quantum mechanics students' metarepresentational competence (MRC) that is expressed as they engaged in solving an expectation value problem, which involves linear algebra concepts. The particular characteristic of MRC that is the focus of this analysis is students' critiquing and comparing the adequacy of…

This paper focuses on the mathematical sensemaking by women of color in the USA as part of the global effort of dismantling deficit narratives about historically marginalized groups of students. Following Adiredja's anti-deficit framework for sensemaking, this cognitive study invited a group of women of color to share their understanding of basis…

In this paper we share a classroom implementation of a task about basis in linear algebra, which was originally developed for research about the topic. The task asks students to construct an everyday situation that captures the definition of basis, and then to critique it mathematically. Using this task, the original research study uncovered…

The purpose of this note is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of geometry and algebra.

An important goal in school algebra is to help students notice the covariational nature of functional relationships, how the values of variables change in relation to each other. This study explored 102 Year 7 (12 to 13-year-old) students' covariational reasoning with their constructed graphs for figural growing patterns they had generalised. A…

Mathematics faculty created a model for intermediate algebra integrating principles from the science of learning. The redesigned curriculum revolved around two big ideas (solving and graphing) and provided students with information about the formation of long-term memories, the benefits of distributed practice, the impact of physiological aspects…

We propose a divisibility criterion for elements of a generic Unique Factorization Domain. As a consequence, we obtain a general divisibility criterion for polynomials over Unique Factorization Domains. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities for college and high school…

The Rural Math Innovation Network (RMIN) is a 4-year project that launched in January 2017 after receiving a $2.9 million Investing in Innovation (i3) development grant from the U.S. Department of Education (ED) and matching funds from the private sector. Virginia Ed Strategies and rural local education agencies (LEAs) in Virginia are implementing…