Building sets, video games, and scatterplots may seem unrelated, but when they are combined into a problem-based learning (PBL) lesson, these elements join to create a unique learning experience. PBL lessons drive instruction by focusing learning and activities around a central challenge or question while providing a relevant, captivating, and…

Engineering-based modeling activities provide a rich source of meaningful situations that capitalize on and extend students' routine learning. By integrating such activities within existing curricula, students better appreciate how their school learning in mathematics and science applies to problems in the outside world. Furthermore, modeling…

When the author returned to teaching after several years in graduate school, she came armed with knowledge and visions of a student-centered classroom. Her experiences in a doctoral program taught her much about effective mathematics instruction and rekindled her desire to teach. However, a student-centered classroom reflected a major shift in…

With the adoption of the Common Core State Standards for Mathematics (CCSSM), many teachers are changing their classroom structure from teacher-directed to student-centered. When the author began designing and using problem-based tasks she saw a drastic improvement in student engagement and problem-solving skills. The author describes the Cake…

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical…

One challenge that middle school teachers commonly face is finding insightful, hands-on applications when teaching basic mathematical concepts. One concept that is a foundation of middle school mathematics is the notion of "linear functions." Although a variety of models can be used for linear equations, such as temperature conversions,…

This article describes a mathematics session in which students explored a challenging combinatorics task, a topic shown to be difficult for students when taught traditionally. The students developed a progression of personal representations, increasingly symbolic and abstract, which they used to find a solution and justification. (Contains 8…

This article elaborates on the basics of problem-based learning units and tips for implementation. The problem-based learning unit described focuses on the course of action involved in purchasing a new car. (Contains 2 figures.)