The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…

Standards for Technological Literacy: Content for the Study of Technology was released in April 2000 by the International Technology Education Association (ITEA, 2000). This was the first attempt by the ITEA to set forth comprehensive specifications regarding what students should know and be able to do within each of four grade bands from…

Using a national sample of students' writing from the National Study of Writing Instruction, this study examines the current state of writing in the mathematics classroom and the extent to which enactments align with the intentions established in the research base and curricula articulated by NCTM and the CCSS-M. Over 3,000 writing assignments…

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

Current reform efforts challenge teachers to create more student-centered classrooms focused on high quality classroom discourse (NCTM, 2014). There are difficulties, however, teachers face in bringing this vision to fruition. Over the past three years, we have worked with a group of 7-12 teachers supporting their efforts to implement high quality…

"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…

When confronted with a challenging problem, many solvers may at first think that not enough information has been provided. If, however, they suspect that the problem is solvable, this feeling typically influences them to persevere as well as monitor and reflect on their efforts. In this article the authors present four nonroutine tasks that they…

Addressing the direction of high school mathematics in the 21st century, this resource builds on the ideas of NCTM's Principles and Standards for School Mathematics and focuses on how high school mathematics can better prepare students for future success. Reasoning and sense making are at the heart of the high school curriculum. Discover the…

Composition of functions is one of the five big ideas identified in NCTM's "Developing Essential Understanding of Functions, Grades 9-12" (Cooney, Beckmann, and Lloyd 2010). Through multiple representations (another big idea) and the use of The Geometer's Sketchpad[R] (GSP), students can directly manipulate variables and thus see dynamic visual…