Ever try to captivate students with real-world applications only to discover that they live in a very different world? Assigning an Extreme Word Problem activity to students alleviates this dilemma by placing the authorship of a problem squarely into the hands of learners. Rather than trying to be hip and finding word problems that resonate with…

Teachers put a great deal of energy into searching for ways to engage each and every student. Some of these efforts fail. Others look promising one day, only to become less effective as the novelty wears off. Teachers want their students to feel ownership of their learning. They also believes that students engage more when learning mathematics…

The article uses vignettes to illustrate a small group of of grade 5 students who worked on different types of temperature problems (Wessman-Enzinger and Tobias 2015). The Common Core State Standards for Mathematics (CCSSM) recommends including contexts, such as temperature, paired with the introduction to integers in grade 6 and integer…

Engaging in argumentation can lead to an increase in the development of critical-thinking skills, not to mention academic achievement, emotional maturity, and academic and communication skills. If argumentation is such an effective format for developing rigorous academic ideas, how might it be used in discussion-oriented classrooms to engage…

As middle school teachers, the authors want their students to develop voice and agency because they want them to be able to make productive decisions about how to approach mathematics, communicate mathematics, and use mathematics to interpret and transform the world in which they live. They use this article to present two vignettes that examine…

Research on teacher professional learning has shown that formative assessment can improve student learning more than most instructional practices. Empirical evidence indicates that thoughtfully implemented formative assessment practices improve students' learning, increase students' scores, and narrow achievement gaps between low-achieving…

Sustaining engagement with a mathematics task is not a novel suggestion for effective mathematics teaching. "Principles and Standards for School Mathematics" (2000) specified that "students need to know that a challenging problem will take some time and that perseverance is an important aspect of the problem-solving process and of…

Two mathematics teachers in a small rural school decided to create a task that would engage seventh graders. The goal of the real-world activity was to help students develop geometric and spatial reasoning and to support their understanding of volume of rectangular prisms. The impetus for the task came from the teachers' desire to engage students…

Although educators agree that making connections with the real world, as advocated by "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), is important, making such connections while addressing important mathematics is elusive. The authors have found that math content coupled with the instructional strategy of…

Students engage in proportional reasoning when they use covariance and multiple comparisons. Without rich connections to proportional reasoning, students may develop inadequate understandings of linear relationships and the equations that model them. Teachers can improve students' understanding of linear relationships by focusing on realistic…

Statistics standards found in the Common Core (CCSSI 2010) and other state standards require considerable instructional time and focus for students to develop the depth and breadth of understanding necessary. In this article, the authors offer an approach to teaching a statistics unit that combines student choice with authentic and sustained…

The Common Core's Standards for Mathematical Practice encourage teachers to develop their students' ability to reason abstractly and quantitatively by helping students make sense of quantities and their relationships within problem situations. The seventh-grade content standards include objectives pertaining to developing linear equations in…

Lesson study cultivates teachers' capacity for formative assessment by placing student thinking front and center throughout. Lesson study is a form of professional development in which a team of teachers determines a mathematical focus, collaboratively studies student thinking about the topic, designs a lesson about this content, implements the…

Watching a debate can help people understand multiple points of view. At the conclusion of a debate, a consensus might occur after a deep analysis and discussion of the issues. Most students will participate in a class debate at some point in their schooling, but chances are that debate will not take place in math class. What could there be to…

Instead of reserving the study of probability and statistics for special fourth-year high school courses, the Common Core State Standards for Mathematics (CCSSM) takes a "statistics for all" approach. The standards recommend that students in grades 6-8 learn to summarize and describe data distributions, understand probability, draw…