Work in teacher noticing has captured to what extent teachers notice students' thinking on paper and pencil tasks and technology tasks, yet no one study has considered how the same group of teachers notices across task types. This study used Jacobs et al.'s (Journal for Research in Mathematics Education, 2010, 41(2), pp: 169-202.) professional…

Mathematics education at the high school level is not working for many students. Although there has been steady improvement in mathematics learning at the elementary and middle school levels across the United States, for the past decade, student achievement has remained essentially flat at the high school level (NCES 2015, 2016). One possible…

In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

While the Common Core State Standards and state learning standards guide teachers in what mathematical content knowledge should be addressed as well as the processes and proficiencies necessary for developing mathematical competence, several student- and teacher-related factors may hinder student access to the general education curriculum for…

While one author was reading "The Simpsons and Their Mathematical Secrets by Simon Singh" (2013) in preparation for a presentation, the second author asked what in the book would be interesting to discuss. The topic of Klein bottles was on the first author's mind at that moment, so he tried to describe and explain the form to her--a real…

The phenomenon of outbreaks of dangerous diseases is both intriguing to students and of mathematical significance, which is exactly why the authors engaged eighth graders in an introductory activity on the growth that occurs as an epidemic spreads. Various contexts can set the stage for such an exploration. Reading adolescent literature like…

Mathematics education is replete with activities that explore real-world problems. A variety of these problems are added to lessons in the belief that merely applying mathematics knowledge to everyday contexts will enhance the transfer of that knowledge to other settings. However, these contexts are hypothetical rather than authentic. This…

Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics. The aim of the study was to examine teachers' conceptions of representation as a process in doing mathematics, and their perspectives on the role of representations in the teaching and learning of mathematics at the…

Technology use in mathematics often involves either exploratory or expressive modeling. When using exploratory models, students use technology to investigate a premade expert model of some phenomena. When creating expressive models, students have greater flexibility for constructing their own model for investigation using objects and mechanisms…

Calls for reform in mathematics education around the world state that proofs should be part of school mathematics at all levels. Turning these calls into a reality falls on teachers' shoulders. This paper focuses on one secondary school teacher's reactions to students' suggested proofs and justifications in elementary number theory. To determine…

This article is concerned with the professional development of mathematics teachers. It starts with a need, identifies a problem, and suggests some ways of coping with the problem. The need is for teachers to develop mathematical communication and reflection skills in their practice. There is a widespread agreement that these skills are an…

The goal of this article is to help teachers both recognize and capitalize on classroom opportunities so that students can be meaningfully engaged in mathematical proof. To do so, the authors discuss students' thoughts about proof and their abilities to construct arguments. They also offer suggestions for teachers that are intended to support…

Mathematical argumentation is an important skill. It leads to the process of proof, which is one area that students are being asked to master by the end of secondary school. Encouraging explanation and justification in math class allows this skill to develop. Explaining and justifying their ideas forces students to think deeply about mathematics…

Content area literacy is a growing trend across the entire secondary school curriculum. Science, history, physical education, and mathematics teachers are being required to teach reading comprehension in their classrooms. Many resources are available to aid students' prereading, reading, and postreading skills. Typical activities include KWL…