Baseball. Subway line. Maps. A flower. Each of these contexts involves some form of varying motion or constant change over time: the bi-directional motion of a fly ball, the speed of a subway car, or the growth of a flower until bloom. This article does not highlight students' calculus problem-solving abilities, but rather describes a set of…

Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…

In this paper, I present a homework system that supports a flipped classroom environment using only a textbook for students' first contact with the material. Motivated by David Pengelley's homework system, each unit of material has four key components: Core Assignments, Conceptual Assignments, In-class Worksheets, and Follow-up Assignments. The…

Two studies (Trautwein 2007 and Dettmers et al. 2010) show a positive correlation between high-quality homework and mathematics achievement. Students who completed their homework assignments scored better on assessments. However, these studies also showed no relationship between time spent on homework and resulting student achievement. This helped…

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or…

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks…

Writing about mathematics holds a wealth of benefits for students. When students are given opportunities to write in math class, it helps develop mathematical thinking and language, encourages self-reflection, and provides a better way to organize ideas. Many teachers incorporate journaling and other types of reflective writing into their…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

It is common for freshmen students to enter Calculus I with a wide range of levels of preparation and mastery of background material. In addition, many of the students struggle with the adjustment from high school to college. In an effort to help the students to solidify their understanding of concepts as they progress through the course, as well…

The Literacy Design Collaborative (LDC) incorporates challenging literacy standards into middle grades and high school content areas within a variety of academic disciplines, not just English/language arts courses. The Mathematics Design Collaborative (MDC) provides schools with instructional tools needed to help teachers understand and implement…

This article will describe a writing assignment designed for use in a liberal arts college whose mission stresses effective written communication both within and across disciplines. In this assignment, students write three separate solutions to the same mathematics problem: one for a mathematical peer, a second for a contemporary that does not…

Flipped classrooms and inquiry-based learning (IBL) have each become popular in their own right, leading to a natural question: Why not combine these two great ideas? Although flipping a class usually involves students reading or watching videos before class, and IBL focuses on allowing and encouraging students to develop material on their own,…

The overarching purpose of this document is to define a new vision for mathematics instruction that explicitly attends to the needs of English Language Learners (ELLs), addressing the interdependence of language and mathematics. The sections in this report are devoted to (1) making clear that the grade-level college- and career-readiness…

We consider a variety of writing assignments used for two general education mathematics courses. The student writing ranges from brief informal pieces to more formal assignments that address the full scope of a course, with an emphasis on encouraging students to have a richer experience of mathematical people and ideas and of their own learning.…