This article describes a framework of Standards-Based Grading suitable for use in a variety of mathematics courses. We detail our experience adapting this framework to various courses, ranging from Pre-calculus to Differential Equations, at four different institutions, including both small liberal arts colleges and large universities, and in class…

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…

This paper investigates the advantages of using a two-step homework system. First, technology is used to collect and grade traditional homework. Then, students are expected to present and explain problems from their assignments in class. Several versions of implementation are discussed for different course levels and sizes. Through these methods,…

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…

Too often our students submit incomplete homework that is disorganized, unclear, and nonlinear. Typesetting with LATEX, although time consuming for those new to the software, strengthens communication by forcing organization and proper notation required by the precise, formal language of mathematics. In this manuscript we report on a study of 42…

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…

This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…

In this article we describe a partially flipped Introductory Linear Algebra course developed by three faculty members at two different universities. We give motivation for our partially flipped design and describe our implementation in detail. Two main features of our course design are team-developed preview videos and related in-class activities.…

Although the use of traditional just-in-time teaching techniques has long been viewed positively by students and instructors in undergraduate calculus courses, past studies in this area have not addressed gains in student achievement with respect to specific calculus topics. This paper investigates the latter by administering modified just-in-time…

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…

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…