We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…

Every day, students collect, organize, and analyze data to make decisions. In this data-driven world, people need to assess how much trust they can place in summary statistics. The results of every survey and the safety of every drug that undergoes a clinical trial depend on the correct application of appropriate statistics. Recognizing the…

A teacher is doing something right when his high school students--kids with limited English, no less--form groups and begin discussing a lesson on quadratic equations at the start of class, without any teacher direction. Bondie, Gaughran, and Zusho describe "discussion routines" that teachers at International Community High School in the…

Mathematics teachers face the challenge of integrating calculator use in their classrooms. Calculators provide advantages for students when performing calculations and they can provide teachers with a versatile instructional tool. Students face high-stakes mathematics tests each year in middle school and must take Regents and college entrance…

As part of an outreach program, we integrated chemistry apps with blogging to enhance the learning experience of students in and outside the classroom. Our outreach program involved college mentors who participated in the development and implementation of chemistry lessons alongside the classroom teacher. Three technology-rich modules that focused…

The purpose of the study is to present research focused on validating the four algebra cognitive models in Gierl, Wang, et al., using student response data collected with protocol analysis methods to evaluate the knowledge structures and processing skills used by a sample of SAT test takers.

For decades, every chemical engineer has been asked to have a background in separations. The required separations course can, however, be uninspiring and superficial because understanding many separation processes involves conventional graphical methods and commercial process simulators. We utilize simple, user-­friendly mathematical software,…

The purpose of this study was to describe elementary preservice teachers' difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on…

Background: Multiplication and division by fractions are among the most troublesome concepts in the elementary mathematics curriculum. Recent studies have shown that preservice elementary teachers in the United States do not have deep understandings of these concepts. Effective ways to improve preservice teachers' conceptual understanding of these…

The logic and methodological concepts behind the application of a quantitative methodology to the problem of effective resource utilization in the New York State suburban schools is detailed. The goal of the study was to determine the best composition of available "factors of production," measured in dollar amounts by function, that…