Use a framework to evaluate a tool: Is it mathematically sound? Does it offer opportunities for student engagement with little distraction? Will it afford students the chance to develop their own ideas? This article provides a framework that teachers can use to evaluate technological tools. The authors evaluate two examples that are designed to…

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Student thinking, a learning cycle, and procedural fluency are discussed in this article, which is the second installment in the series. [For the first installment in this series see "Promoting a Conceptual Understanding…

Take a moment to think about the students class. What are their mathematical strengths? How can a teacher know a mathematical strength when they see it? Can teachers identify at least one mathematical strength for every student? More important, how are teachers using students' strengths in their mathematics classrooms? Teaching is a complex…

Teachers have found that engaging students in justification can help students deepen and retain mathematical knowledge, gain a greater sense of ownership over the material, and improve communication and representation skills (Staples, Bartlo, and Thanheiser 2012). Student engagement in a justification activity can also lead to more equitable…

A presentation on the Budapest Seminars in Mathematics Education website, inspired the author to try a new approach while teaching a unit on quadrilaterals in his Geometry for K-8 Teachers course, a class primarily composed of undergraduate students interested in teaching at the elementary or middle school level. The author designed a lesson that…

To help alleviate the struggle in choosing effective apps to use in the classroom, Taylor Harrison presents a list of qualities supported by research, that teachers can use to discern at a glance whether an app can potentially be an effective learning tool for their students. This list of qualities was produced through an extensive review of…

Students who are adept in modeling with mathematics have the capability to use mathematics in situations that arise in everyday life. The German Tank problem described in this article created the expectation that student reasoning was rooted in logical deductions (NCTM 2000). By engaging in this problem, students grappled with challenging…

To improve mathematics achievement of U.S. students and to assure that "what and how students are taught should reflect not only the topics within a certain academic discipline, but also the key ideas that determine how knowledge is organized and generated within that discipline" are dual goals of the Common Core State Standards for…

More teachers are trying out the flipped classroom model in which content is delivered outside of class time, typically through online videos and "homework," and follow-up activities are done in class. This model frees up more class time for inquiry and discussion. This article focuses on the self-learning portion of the flipped learning…

An important goal of school mathematics is to enable students to formulate, approach, and refine problems beyond those they have studied, allowing them to organize and consolidate their mathematical thinking. To achieve this goal, students should be encouraged to develop expertise in a variety of areas, such as problem solving, reasoning and…

In education, it is common to set aside older curriculum documents when newer ones are released. In fact, some instructional leaders have encouraged the "out with the old, in with the new" process by asking teachers to turn in all copies of the older document. Doing so makes sense when the old curriculum document is incompatible with the new.…

As middle school mathematics becomes more abstract, it is imperative for teachers to introduce concepts in ways that are interesting and meaningful to students. Since her students struggled at times to stay engaged in mathematics and seemed to have difficulty developing conceptual understanding, the author looked for ways to create learning…

Spatial abilities help students identify features of various shapes and the relationship that exists among these features. Being able to mentally manipulate images and tell what those images represent are important spatial skills. Research has highlighted the relationship between mathematics performance and spatial abilities. This article's…

Mathematics and science are natural partners. One of many examples of this partnership occurs when scientific observations are made, thus providing data that can be used for mathematical modeling. Developing mathematical relationships elucidates such scientific principles. This activity describes a data-collection activity in which students employ…

Proportional reasoning is both complex and layered, making it challenging to define. Lamon (1999) identified characteristics of proportional thinkers, such as being able to understand covariance of quantities; distinguish between proportional and nonproportional relationships; use a variety of strategies flexibly, most of which are nonalgorithmic,…