This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…

Facilitating meaningful discourse directly supports what students should be able to do with respect to the third of the eight Standards for Mathematical Practice (SMP 3) in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010): "Construct viable arguments and critique the reasoning of others" (p. 6). Following best…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

Natural disasters often receive massive media attention. The headlines can engage students to think mathematically and scientifically about the world around them. 'Principles and Standards for School Mathematics' explicitly encourages instruction where students "recognize and apply mathematics in contexts outside of mathematics" (NCTM…

The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

The twenty-first century has seen an increased call to train students to craft mathematical arguments. The third of the Common Core's (CCSS) Standards for Mathematical Practice (SMP 3) (CCSSI 2010) calls for all mathematically proficient students to "construct viable arguments" to support the truth of their ideas and to "critique…

The Common Core has emphasized reading for comprehension, including making inferences. However, little is known about the instructional materials included in core literacy programs for teaching inferences. The purpose of this study was to determine the frequency of background, anaphoric, predictive, and retrospective inferences in instructional…

The Common Core State Standards for Mathematics (CCSS-M) aim to engage students in complex mathematical practices, including modeling, reasoning, and argumentation. Currently, little is known about how teachers' daily instruction supports these practices. This study draws upon data from daily logs completed by third-, fourth-, and fifth-grade…

Watching a debate can help people understand multiple points of view. At the conclusion of a debate, a consensus might occur after a deep analysis and discussion of the issues. Most students will participate in a class debate at some point in their schooling, but chances are that debate will not take place in math class. What could there be to…

Comprehending expository reading material is a challenge for many students. Research has shown that students' expository reading comprehension can improve with the help of text structure instruction. The purpose of this article is to present teachers with a framework for effectively implementing text structure instruction in their classrooms.…

Students often have difficulty comprehending informational text. Results from a meta-analysis by Hebert, Bohaty, Nelson and Brown (2016) indicated that text structure instruction is effective for improving reading comprehension of expository text. This article presents evidence-based practices for teaching informational text structures to improve…

High-quality professional development is needed to prepare teachers to help students learn how to conduct online academic research and meet Common Core State Standards for English Language Arts. This study created and evaluated a Web-based professional development program with five instructional modules designed to prepare middle-school teachers…

The population of emerging bilinguals (EBs) is rapidly growing across the United States leaving many teachers wondering how best to teach these students to read and write effectively in English. Concurrently, and as a result of the Common Core State Standards, elementary school students are required to produce more sophisticated writing than ever…

International rankings show children in the United States perform well below average in mathematics. There are also large mathematics achievement gaps between children of lower- and higher-socioeconomic status. As today's teachers face these challenges, they are also faced with the pressures of sweeping educational reforms that arrived with the…

A fundamental claim for Common Core State Standards (CCSS)-aligned assessments is that they will lead to better teaching practices. The purpose of this study is to seek evidence in support of this claim by surveying teachers about their instructional practices, test preparation strategies, and test score use both before and after the introduction…