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.
Sean P. Yee, George J. Roy, and LuAnn Graul
Micah S. Stohlmann
An escape room can be a great way for students to apply and practice mathematics they have learned. This article describes the development and implementation of a mathematical escape room with important principles to incorporate in escape rooms to help students persevere in problem solving.
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.
LouAnn H. Lovin
Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.
Amber G. Candela, Melissa D. Boston, and Juli K. Dixon
We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.
Ryan Seth Jones, Zhigang Jia, and Joel Bezaire
Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.
Kelly Hagan and Cheng-Yao Lin
April 2020's GPS department provides tasks for each grade band that invite students to reason with age-appropriate number theoretic concepts.