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…

It is difficult but important for mathematics teachers to help students see themselves as capable mathematics learners, that is, to help each student develop a positive mathematics identity. A student's mathematics identity is a powerful influence on his or her engagement and participation in mathematics. Students act in ways that are consistent…

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…

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…

When finding the decimal equivalent of a fraction with 12 in the denominator, will it terminate or repeat? This question came from a seventh grader in author Erica Burnison's class as the student was pondering a poster generated by one of her classmates. Not only was the question intriguing, but it also affirmed the belief in the power of…

Teachers across all grade levels agree that problem solving and reasoning are areas of weakness in students. Assessments among U.S. students indicate that these weaknesses persist (NCTM 2014) in spite of repeated calls that date back more than thirty years for increased problem solving, reasoning, and sense making in our schools. The NCTM is…

A key characteristic of successful mathematics teachers is that they are able to provide varied activities that promote student learning and assessment. Web 2.0 applications can provide an assortment of tools to help produce creative activities. A Web 2.0 tool enables the student to enter data and create multimedia products using text, graphics,…

To help middle school students make better sense of decimals and fraction, the author and an eighth-grade math teacher worked on a 90-minute lesson that focused on representing repeating decimals as fractions. They embedded experimentations and explorations using technology and calculators to help promote students' intuitive and conceptual…

Although it is not a new idea, discourse continues to be a topic of discussion among teachers, teacher educators, and researchers in mathematics education. The National Council of Teachers (NCTM) and the Common Core State Standards for Mathematics (CCSSM 2010) describe mathematics classrooms as discourse communities in which whole-class…

"Who has been to Dairy Queen® and purchased a Blizzard?®" Ms. Bosetti asked her students. During the summer, Bosetti had seen many of her former and future students at the local Dairy Queen enjoying Blizzard desserts and wondered, "Which Blizzard size is the best value?" She used this context for a ratios and proportions task…

While some students are enjoying days at the park or at the beach, forty middle school students are in a classroom solving challenging mathematics problems. The second Math Camp for middle school students was offered in 2013 at a western university for students from local school districts. For three days, these students met from 10 a.m. to 3 p.m.…

Raising expectations is nothing new. Every iteration of standards elevates the expectations for what students should know and be able to do. The Common Core State Standards for Mathematics (CCSSM) is no exception, with standards for content and practice that move beyond memorization of traditional algorithms to "make sense of problems and…

Using a nonroutine problem can be an effective way to encourage students to draw on prior knowledge, work together, and reach important conclusions about the mathematics they are learning. This article discusses a problem on the mathematical preparation of chocolate milk which was adapted from an old book of puzzles (Linn 1969) and has been used…

Statistics is the art and science of gathering, analyzing, and making conclusions from data. However, many people do not fully understand how to interpret statistical results and conclusions. Placing students in a collaborative environment involving project-based learning may enable them to overcome misconceptions of probability and enhance the…

Crime Scene for Mathematics Investigation (CSMI) was created as a small group, cooperative, self-selective grouping strategy to allow students to explore mathematics based on their own understanding and perceived readiness, much like the concept and application of literature circles in language arts. In essence, these self-chosen small groups met…