Educators in forty-five states and the District of Columbia are hard at work interpreting and implementing the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010). This work typically involves teacher participation in professional development activities focused on developing an understanding of the content standards as well as the…

The quadrilaterals problem is a particularly rich task, applicable to in-service teachers as well as to the students they teach. The ways in which students engage in this task, the strategies they use, and the mathematics that results align well with this "MT" Focus Issue on flexible mathematical thinking. The authors offer their observations of…

Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…

"Reasoning and sense making should occur in every classroom every day," states "Focus in High School Mathematics: Reasoning and Sense Making" (NCTM 2009, p. 5). As this book suggests, reasoning can take many forms, including explorations and conjectures as well as explanations and justifications of student thinking. Sense making, on the other…

The National Council of Teachers of Mathematics (NCTM) has consistently recognized communication as essential to reform-oriented mathematics teaching (NCTM 1991, 2000). In this article, the authors propose a strategic mix of univocal and dialogic discourse that, when used in conjunction with an "inductive model of teaching," can promote…

An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos. The activities exposed the students to nonlinear patterns and modeling. The rate-of-change investigations related the ideas of intercept and slope to the changing equilibrium. The chaotic model intrigued them and was useful…

The Country Data Project was developed for eighth-grade students of Milwaukee public schools to make them understand the importance of numbers by making them interpret the full descriptions of people of various countries by analyzing the numbers summarizing the population distribution of the respective country. The results prove that the project…

This article describes the collaboration between an eighth grade teacher and two college professors in the design and implementation of in vivo field experiences that help preservice secondary school mathematics teachers connect theories of learning with instructional practice.