Creative posters in the classroom can inspire students to become engaged and motivated in learning art. Within the classroom, there are many places to put posters so that students can read them (especially when they get bored in the classroom) - on the cabinets, near the chalkboard, on the teacher's desk and any spare space on the wall. There is…

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

Sometimes the best mathematics problems come from the most unexpected situations. Last summer, a Corvette raced down a local quarter-mile drag strip. The driver, a family member, provided the spectators with time and distance-traveled data from his time slip and asked "Can you calculate how many seconds it took me to go from 0 to 60…

"Low threshold, high ceiling" tasks are accessible to diverse learners; invite a wide range of approaches; and hold the potential to further challenge, strengthen, and extend everyone's mathematical reasoning. In this article, the authors present a family of Brick Pyramid problems as examples of "low threshold, high ceiling"…

Many teachers of required secondary school mathematics classes are introducing statistics and probability topics traditionally relegated to college or AP Statistics courses. As a result, they need guidance in preparing lesson plans and orchestrating effective classroom discussions. In this article, the authors will describe the students' learning…

Reaction workup can be a complex problem for those facing novel synthesis of difficult compounds for the first time. Workup problem solving by systematic thinking should be inculcated as mid-graduate-level is reached. A structured approach is proposed, building decision tree flowcharts to analyze challenges, and an exemplar flowchart is presented…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics,…

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Holidays and seasonal activities provide excitement and a change of pace for teachers and students alike. They also offer perfect backdrops for mathematical tasks that can be related to other topics and themes in the classroom. "Problem Solving in All Seasons, Prekindergarten-Grade 2" delivers thirty-two appealing, real-world situations,…

This article illustrates the importance of one's initial thoughts in problem solving through an entertaining example.

As we typically teach in an introductory mechanics course, choosing a "good" coordinate frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely powerful problem-solving tool. While the former idea is typically discussed in the context of…

In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…

The following kinematics problem was given to several students as a project in conjunction with a first-semester calculus-based physics course. The students were asked to keep a journal of all their work and were encouraged to keep even their scrap paper. The goal of the project was to expose the students to the process of doing theoretical…

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

A well-known mathematical puzzle regarding a worm crawling along an elastic rope is considered. The resulting generalizations provide examples for use in a teaching context including applications of series summation, the use of the integrating factor for the solution of differential equations, and the evaluation of definite integrals. A number of…