The goal in this article is to support teachers in better understanding what it means to model with mathematics by focusing on three key decision-making processes: Simplification, Relationship Mapping, and Situation Analysis. The authors use the Theme Park task to help teachers develop a vision of how students engage in these three decision-making…

Many teachers are using the Five Practices model to guide them in orchestrating whole-class mathematics discussions that focus on understanding: (1) anticipate an array of possible student-generated solution strategies to a mathematical task before implementing the lesson; (2) monitor students' work as they grapple with the task; (3) select a…

Tape diagrams, also known as strip diagrams, bar models, fraction strips, or length models, are linear representations that can be used to effectively model quantitative relationships during problem solving. Tape diagrams are a powerful model recommended by the Common Core, but they are relatively new to teachers and students in the United States.…

Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…

Engaging students in studies about conservation and sustainability can support their understanding of making environmental conscious decisions to conserve Earth. This article aims to contribute these efforts and direct students' attention to how they can use mathematics to make environmental decisions. Contributors to iSTEM: Integrating…

Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…

In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

In this article, the author shares how his fourth-grade students' creative thinking concerning a long-standing research problem stimulated changes in his instructional strategies. He begins by providing an example which illustrates that the standard tool of democracy, the plurality vote, suffers serious deficiencies: "The winner can be the…

A new mathematical tool, known as Engage, Explore, Explain (EEE) model, was developed that was simple for teachers to use, could guide them as they planned exploratory experiences, and was useful to teach mathematics for understanding. The EEE model provides a lesson structure for teachers to use with almost any mathematics topic and can easily be…

Presents examples of direct modeling and invented strategies of students for problem solving. Teachers are encouraged to capitalize on children's abilities to use these invented strategies and in time guide the student toward a standard, more efficient strategy. (AIM)

Proposes a system to help at-risk students develop problem solving skills. Provides some teaching methods and evaluation ideas. (KHR)