Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

Cultures need to accurately record dates and times for various societal purposes, ranging from knowing when to plant crops to planning travel. In ancient times, the sun and moon were used as measurement devices because of the scientific understanding of the physical world at that time. Ancient timekeepers monitored celestial events and either used…

All students should be provided with opportunities to develop conceptual understanding prior to procedural fluency. To develop students' conceptual understanding, teachers must learn such skills as how to select, plan, and enact cognitively demanding tasks (CDT) and to evaluate evidence of student learning. Therefore, teachers need opportunities…

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…

How does one look for mathematical structure? Finding structure is a challenging yet accessible activity for all students. This article describes a lesson in which seventh graders engaged with mathematical structure. The setting was a seventh-grade prealgebra classroom in a suburban school. The classroom teacher was co-author Tatyana Finkelstein.…

With international exams (PISA and TIMSS) producing results every three or four years, there is near continual talk of East Asian dominance in mathematics education. Beyond the reporting of scores, some studies have compared mathematics teaching in these countries with U.S. instruction. However, researchers are not (usually) grade school math…

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

Just as ready-made clothes may not provide a perfect fit for all bodies, math lessons may not be a perfect fit for all students. Published instructional tasks, including problems in mathematics textbooks, often need to be tailored to be meaningful, relevant, or accessible to each student. Ways are possible to take high-level reasoning tasks and…

Implementing Universal Design for Learning (UDL) principles can provide solutions for general educators in inclusive mathematics environments. Any lesson can be planned to provide learning experiences appropriate for meeting diverse learning needs. This article explores an example of both how to approach a topic in middle school mathematics and…

This article presents major results of TIMSS, along with practical suggestions and questions that mathematics teachers can ask themselves in terms of how to apply the results to the improvement of their practice.

Presents a way to design lesson plans that takes into account four modes of communication (oral, written, visual, and kinesthetic) and four audiences (self, partner, small group, and whole class) and that allows for reflection based on the NCTM Standards. (MKR)

Cell phone coverage areas arouse students' curiosity in a lesson that engages students with area as a measure that relates to, but is different from, linear measure. Each distinct set of activities (stations) blends concepts and skills to align with and transcend state standards. In reflecting on the lesson planning and implementation, we…

The purpose of this lesson on classifying triangles is to aid students' discovery of the different characteristics of equilateral, isosceles, and scalene triangles through computer explorations using Geometric Supposer or GeoExplorer software. (MKR)

Describes how one teacher is converting her traditional mathematics classroom into one that more closely reflects the NCTM Standards and shows how communication between professionals can result in rewarding changes in teaching and learning. Presents activities involving data analysis appropriate for middle school students. Includes reproducible…

This article describes a professional development model in which middle-grades teachers focused on algebraic thinking as part of their participation in a mathematics academy.