Argumentation is an important mathematical practice, highlighted by research and policy documents that describe ways to structure reform-oriented classrooms (Nardi and Knuth 2017; NCTM 2000; NGA Center and CCSSI 2010). Participating in argumentation can enhance students' mathematics learning as they make sense of mathematical ideas, provide…

Nationally, there is a rise in students with multidimensional identities--as newcomers, emergent bilinguals, students of color, and/or those with disabled and neurodiverse identities--in schools who are disproportionately represented in intervention programs and lower-tracked mathematics pathways. This article leverages the incredible power that…

The authors asked a group of students during a classroom research study to analyze data sets containing different amounts of noise. The authors use the word "noise" to refer to statistical variability. The four students in the group were finishing seventh grade and participating in summer mathematics instruction. The authors carefully…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) emphasizes eight teaching practices for effective mathematics teaching, one of which is to "use and connect multiple representations" (NCTM 2014, p. 24). An action that describes how teachers might promote this practice is to "allocate substantial…

Minecraft is an open world survival computer game that was originally created in Sweden in 2011 and later purchased by Microsoft® in 2014. It is among the most popular computer games with students of all ages because it gives players a sense of ownership and opportunities for creative exploration. The game has three unique features: (1) no clear…

The International Association for the Evaluation of Educational Achievement (IEA) Research for Education series represents a further effort by IEA to capitalize on it's unique datasets, so as to provide powerful information for policymakers and researchers. Each report focuses on a specific topic and is produced by a dedicated team of leading…

Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…

In education, "dialogue protocols," or "protocols," are structured guidelines that were developed to promote meaningful and efficient communication and learning. They are "vehicles for building the skills--and culture-- necessary for collaborative work. The authors share protocols that were found to transform practices…

This article describes a project in which students investigate the question: What dihedral angles between pairs of mirrors in a kaleidoscope result in perfectly symmetric images? The unit culminates with students building their own kaleidoscopes. This content aligns with parts of the Common Core's standards for fifth grade (classify…

If teachers have a deeper comprehension of their students' reading ability, it may lead to students' improved literacy and understanding of the subject. The account presented in this article of the author's growing interest in mathematical literacy specifically involves mathematical reading. This shift in interest began with a six-week…

This is a companion piece to "Professional Learning Community: Improving Mathematical Problem Solving for Students in Grades 4 through 8. Facilitator's Guide. REL 2019-002" (ED595201). It contains handouts to accompany each of the sessions included in the facilitator's guide.

There is a growing interest in using a flipped classroom format in day-to-day teaching. Direct computer-based individual instruction outside the classroom and interactive group learning activities inside the classroom are the two essential components of the flipped classroom model. By watching instructional videos, students can work through some…

Do your students need more opportunities do develop number sense and reasoning? Are you looking to get your students energized and talking about mathematics? Have you wondered how practical, replicable, and engaging activities would complement your mathematics instruction? This guide answers the question "What could I do differently?" by…

Do your students think they can model ratios with sets of discrete objects and combine them to show the addition of ratios? Do they believe that equivalent ratios are based on additive relationships rather than multiplicative ones? What tasks can you offer what questions can you ask to determine what your students know or don't know and move them…

When teaching algebra concepts to middle school students, the author often hears questions that echo her own past confusion as a young student learning to write linear equations using data tables that show only input and output values. Students, expected to synthesize the relationship between these values in symbolic representation, grow…