The objective of this work is to show an educational path for combinatorics and graph theory that has the aim, on one hand, of helping students understand some discrete mathematics properties, and on the other, of developing modelling skills through a robust understanding. In particular, for the path proposed to middle-school students, we used a…

Academic scholars face a difficult challenge when attempting to grasp the intricate world of mathematics. The complexity of mathematical concepts often lies hidden beneath layers of formulas and procedures, obscuring their true essence. Traditional educational resources often fall short in conveying the profound meaning behind these concepts,…

A key topic throughout school geometry is measurement--namely, distance, area, and volume. This article focuses on one key idea for finding and justifying the area of two-dimensional (2D) shapes: area-preserving transformations. Although especially pertinent to geometry teachers, this article highlights a vertical connection of ideas progressing…

Active learning techniques are generally considered to be any classroom activities in which students become an active participant in learning, instead of a passive listener to a lecture. Service learning activities are generally experiential (real life) and reflective problem-based learning activities in which students enrolled in an academic…

The "Aboriginal: How Are We Doing Report" is an annual, public-facing report focusing on Indigenous students in B.C. The data in this report provides teachers, schools, school districts and the Ministry of Education and Child Care with important information on how Indigenous students are developing and identifies areas for interventions…

This Framework builds upon the foundation of the 2010 Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework published since 1995. The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in implementing the 2010 standards in their…

John Lamb, a professor of mathematics education and a teacher of high school precalculus, describes how he developed a way to use the elements of the game Angry Birds® as a platform to engage his students with the concepts of parabolas and vectors. The game could be categorized as a type of microworld game in which students interact with the…

Population models are often discussed in algebra, calculus, and differential equations courses. In this article we will use the human population of the world as our application. After quick looks at two common models we'll investigate more deeply a model which incorporates the negative effect that accumulated pollution may have on population.

This article presents an example of how middle school teachers can lay a foundation for calculus. Although many middle school activities connect directly to calculus concepts, the authors have decided to look in depth at only one: the concept of change. They will show how teachers can lead their students to see and appreciate the calculus…

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

Today's classrooms are much different from those of yesterday. The increased diversity of learners, students' familiarity and attraction to technology, and the improved availability of technology in education have made it increasingly possible for teachers to use various forms of technology in instruction. The responsibility for addressing these…

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…

This project was coordinated and funded by the California Partnership for Achieving Student Success (Cal-PASS). Cal-PASS is a data sharing system linking all segments of education. Its purpose is to improve student transition and success from one educational segment to the next. Cal-PASS' standards deconstruction project was initiated by the…

There has been much debate in recent years as to the amount and type of mathematical knowledge that teachers need to acquire. One set of recommendations is provided by the Mathematical Education of Teachers (MET) report, produced jointly by the American Mathematical Society and the Mathematical Association of America. This paper reports on efforts…