Strong mathematics achievement is lacking in the United States, with motivation waning especially among mathematics and online students. Online mathematics students, in particular, struggle with self-regulation and self-efficacy (Kim, 2012; Sun & Rueda, 2012). Ryan and Deci (2017), in their well-established and empirical self-determination…

Federal legislation requires every student receive access to and make progress in the general curriculum. Teachers have reported difficulties in meeting this requirement for students with extensive support needs (ESN) who do not yet demonstrate foundational academic skills, such as in the areas of literacy and numeracy. Once students enter high…

We examined the influences of pre-solving pause time, algebraic knowledge, mathematics self-efficacy, and mathematics anxiety on middle-schoolers' strategy efficiency in an algebra learning game. We measured strategy efficiency using (a) the number of steps taken to complete a problem; (b) the proportion of problems completed on the initial…

High school mathematics achievement is crucial to the success of students as they advance through their education and prepare for careers, but most Georgia high school students are not high-achievers on state mandated mathematics assessments (GaDOE, 2019; Yu & Singh, 2018). The purpose of this qualitative study was to explore the life and…

A faculty development workshop, focused on incorporating universal learning strategies into developmental mathematics courses, was created and utilized in a developmental mathematics department at an open-enrollment, mid-western university to ascertain the best methods for dissemination of essential learning strategies to developmental math…

We present the basic theory of denesting nested square roots, from an elementary point of view, suitable for lower level coursework. Necessary and sufficient conditions are given for direct denesting, where the nested expression is rewritten as a sum of square roots of rational numbers, and for indirect denesting, where the nested expression is…

Let R be a ring with identity. Then {0} and R are the only additive subgroups of R if and only if R is isomorphic (as a ring with identity) to (exactly) one of {0}, Z/pZ for a prime number p. Also, each additive subgroup of R is a one-sided ideal of R if and only if R is isomorphic to (exactly) one of {0}, Z, Z/nZ for an integer n = 2. This note…

The set of functions {x[superscript q] | q[element of][real numbers set]} is linearly independent over R (with respect to any open subinterval of (0, 8)). The titular result is a corollary for any integer n = 2 (and the domain [0, 8)). Some more accessible proofs of that result are also given. Let F be a finite field of characteristic p and…

Spreadsheets provide a rich setting for first-year algebra students to solve problems. Individual spreadsheet cells play the role of variables, and creating algebraic expressions for a spreadsheet to perform a task allows students to achieve a glimpse of how mathematics is used to program a computer and solve problems. Classic optimization…

Community colleges are essential for United States higher education, but their students have low retention and graduation rates. Community college students assigned to mathematics remediation are particularly unlikely to graduate. Corequisite remediation (college-level coursework with additional support) has shown short-term increased student…

The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

This capsule is meant to address the most frequently asked questions about the academic performance of Miami-Dade County Public Schools (M-DCPS) during the 2022-2023 school year. M-DCPS received a District Performance Grade of "A" this academic year, and no traditional MDCPS school received a grade of "F". However, the…

The damped harmonic oscillator physics problem is a standard oscillation problem in calculus physics for pre-engineering students in a community college. The use of alternative linear algebra eigenvalue stability method is consistent with the upper engineering courses using control theory. The external force and friction damping would become the…

This study reports on the design and implementation of an equity-focused, project-based algebra curriculum in two advanced eighth-grade classrooms. We document with substantial detail a promising approach to capturing how students demonstrate and build robust mathematical understandings in ways that strongly connect to equity issues. We illuminate…

The gold-standard for evaluating the effect of an educational intervention on student outcomes is running a randomized controlled trial (RCT). However, RCTs may often be small due to logistical considerations, and resulting treatment effect estimates may lack precision. Recent methods improve experimental precision by incorporating information…