Four teachers and a teacher educator move from guided notes to strings in a series of problems that support students in increased engagement, reasoning, sense making, and problem solving.
Rob Wieman, Lindsay Freedman, Paul Albright, Deb Nolen, and Jessica Onda
Steve Ingrassia and Molly Rawding
Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to firstname.lastname@example.org. If published, the authors of problems will be acknowledged.
Deanna Pecaski McLennan
Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton
We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.
Sean P. Yee, George J. Roy, and LuAnn Graul
As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.
Matt Enlow and S. Asli Özgün-Koca
Equality is one of the main concepts in K–12 mathematics. Students should develop the understanding that equality is a relationship between two mathematical expressions. In this month's GPS, we share tasks asking students one main question: how do they know whether or not two mathematical expressions are equivalent?
Scott Corwin, Michelle Cascio, Katherine Emerson, Laura Henn, and Catherine Lewis
Our middle school mathematics department used lesson study to investigate how to introduce fractions division to our sixth-grade students. We highlight our learnings during the Study and Plan phases, describe our observations during the lesson, and provide tips for educators interested in using lesson study to study their own content.
Manouchehri Azita, Ozturk Ayse, and Sanjari Azin
In this article we illustrate how one teacher used PhET cannonball simulation as an instructional tool to improve students' algebraic reasoning in a fifth grade classroom. Three instructional phases effective to implementation of simulation included: Free play, Structured inquiry and, Synthesizing ideas.
Aline Abassian and Farshid Safi
This article dives into the importance of engaging students in investigating the mathematics of businesses that pressure their members to recruit new members as a basis for success, also referred to as multi-level marketing (MLM). The mathematics behind these businesses are discussed, and a sample student task is given.
Trena L. Wilkerson
How has NCTM leadership shaped the evolution of teaching and learning mathematics? What are your expectations for NCTM leadership?