As more chemical engineering students enter careers beyond the field, students need more guidance in applying their problem solving skills to a challenges beyond the plant or refinery. Since Fall 2019, we have implemented case-based learning across our Material and Energy Balances course to help students practice chemical engineering thinking as a…

Sequences are an important topic--not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns…

Mistakes can be a source of frustration for teachers and students in mathematics classrooms because they reveal potential misunderstandings or a lack of learning. However, increasing evidence shows that making mistakes creates productive pathways for learning new ideas and building new concepts (Boaler 2016; Borasi 1996). Learning through…

Creativity is more important than ever in today's knowledge-based economy. Although many students doubt their own creativity, very few exercises are designed to help them access this ability. We believe that self-expression and self-reflection are important for understanding personal creative ability. Jung introduced the mandala to promote these…

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…

Parents in the United States expect their students to have homework; and students, especially in middle school and high school, expect daily homework assignments from their teachers. However, it is difficult to create effective homework assignments. Despite the challenges involved, the authors believe that homework "can" be an important…

Artificial satellites are easily observed most nights when the weather is fine. The website called "Heavens Above" at www.heavens-above.com will help locate these satellites flying over one's location. It also includes how bright they will appear. The direction of travel of each satellite in the night sky also indicates the type of satellite. For…

Studies in cognitive science have verified that working memory (where the brain solves problems) can manipulate nearly all elements of knowledge that can be recalled automatically from long-term memory, but only a few elements that have not previously been well memorized. Research in reading comprehension has found that "lecture notes with…

Gaming, an integral part of many students' lives outside school, can provide an engaging platform for focusing students on important disciplinary core concepts as an entry into developing students' understanding of these concepts through science practices. This article highlights how S'cape can be used to support student learning aligned with the…

In this article, the author describes the pedagogical benefits of giving students individually unique homework exercises from an exercise template. Evidence from a test of this approach shows statistically significant improvements in subsequent exam performance by students receiving unique problems compared with students who received traditional…

In the early 1990s, the National Science Foundation funded many research projects for improving statistical education. Many of these stressed the need for classroom activities that illustrate important issues of designing experiments, generating quality data, fitting models, and performing statistical tests. Our paper describes such an activity on…

Presents a method to make precalculus college freshmen accountable to the class for doing at least some of their assigned homework problems by making each student an expert on one or more of the assignments. (ASK)

Eight techniques for studying mathematics that can be taught during regular classroom instruction are presented and discussed with illustrations of their classroom use. (MNS)

Suggested are ways that problem solving can be integrated into existing college courses. Modification of assignments, reduction of class examples, developing the structure of knowledge, finding time to teach process skills, and developing student awareness are discussed. A self-assessment form for students is included. (CW)

Presents an alternate form of assignment, called "Special Problems," that incorporates writing in journals into the mathematics classroom. The method requires students to provide process narratives to accompany selected homework exercises. Allows the teacher to monitor the student's thought processes and development. (MDH)