Quantitative Reasoning for Professionals is a two-semester general education sequence that teaches basic and intermediate algebra through the lens of quantitative reasoning. In this course sequence, we emphasize communication and inference-making while teaching practical algebra skills for students in programs such as business, nursing, and social…

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…

Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. In this article I…

Introductory and remedial courses in college mathematics often serve as a gateway to student success. However, these university courses have seen little innovation despite historically low success rates. We sought to address deficits of the traditional lecture model and enhance student learning in an introductory college algebra course through the…

A common challenge among mathematics professors is to structure a course so that students are motivated to complete enough work to master the material without creating an unmanageable grading workload. We will discuss a strategy that the author devised to successfully confront this challenge (after many other failed attempts): using online surveys…

During the author's eighteen-year tenure as a high school mathematics teacher, there has been one question that she has yet to answer: "Why don't students do homework?" On the basis of research, many factors may lead to a student leaving homework undone. A student may lack the drive to complete work out of school. Or a student may choose…

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…

This paper describes the linear algebra class I taught during Spring 2014 semester at Adelphi University. I discuss the details of how I flipped the class and incorporated elements of inquiry-based learning as well as the reasoning behind specific decisions I made. I give feedback from the students on the success of the course and provide my own…

At a time when the debate continues over whether homework is overused, optional, or essential or favors well-off students over those with little home support, teachers must understand ways in which effective homework strategies can help narrow the achievement gap. Vatterott (2009, p. 94) argues convincingly that the "old paradigm" of…

This article reports on techniques of teaching abstract algebra which were developed to achieve multiple student objectives: reasoning and communication skills, deep content knowledge, student engagement, independence, and pride. The approach developed included a complementary combination of inquiry-based learning, individual (not group) homework…

Continuous feed and bleed ultrafiltration, modeled with the gel polarization model for the limiting flux, is shown to provide a rich source of non-linear algebraic equations that can be readily solved using numerical and graphical techniques familiar to undergraduate students. We present a variety of numerical problems in the design, analysis, and…

The flipped classroom model of teaching can be an ideal venue for turning a traditional classroom into an engaging, inquiry-based learning (IBL) environment. In this paper, we discuss how two instructors at different universities made their classrooms come to life by moving the acquisition of basic course concepts outside the classroom and using…

Higher education in the United States is facing a failure-rate crisis in entry-level mathematics courses. In this article, the authors describe an innovative, technology-enhanced hybrid course model that has significantly improved course completion and content mastery outcomes in general education (GE) mathematics courses. The model relies on five…

Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. "Math Remediation for the College Bound" fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some…

Three dysfunctional behaviors of basic algebra students are described: Silence as Camouflage, Wing and a Prayer, and Ignorance is OK. These behavior patterns are explained, and beneficial teaching methods that address the weaknesses are presented.