A group of eighth-graders was presented with a two-day lab exploring graph theory as an enrichment experience. With the school's winter break looming, students were weary of solving linear equations, and this topic was intended to inject some new life into the classroom. In addition to learning about a completely new topic, they would be exposed…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

Every student has mathematical strengths beyond knowing basic facts, solving problems quickly, or showing work clearly. In this article, the author presents Smiles as an "on-ramp" task that supports students working together by unveiling and leveraging mathematical strengths. Nielsen describes on-ramp mathematics tasks as scaffolds that…

Building sets, video games, and scatterplots may seem unrelated, but when they are combined into a problem-based learning (PBL) lesson, these elements join to create a unique learning experience. PBL lessons drive instruction by focusing learning and activities around a central challenge or question while providing a relevant, captivating, and…

The plight of refugees has recently received considerable media coverage. Yet, little attention is given to groups who are internally displaced. The purpose of this article is to model one way to teach about internally displaced peoples, drawing on the Rohingya crisis as a specific example. We first provide a background of the Rohingya crisis, and…

"When you hear hoofbeats, look for horses, not zebras." This common saying in medicine (often attributed to Theodore Woodward, MD, of the University of Maryland School of Medicine) advises doctors to stick to the expected or likely diagnosis, rather than anticipating an unusual or atypical one. As a result, uncommon medical diagnoses are…

The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance,…

Youth involved in 4-H projects have been engaged in science-related endeavors for years. Since 2006, 4-H has invested considerable resources in the advancement of science learning. The new Minnesota 4-H Science of Agriculture Challenge program challenges 4-H youth to work together to identify agriculture-related issues in their communities and to…

"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…

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…

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…

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

In "Principles to Actions: Ensuring Mathematical Success for All," NCTM (2014) defines productive struggle as students delving "more deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions" (p. 48). Hiebert and Grouws (2007, p. 387)…

What "is" mathematics? What does it mean to "do" mathematics? The answers to these two questions critically influence the ways in which learners respond to a mathematical problem. On the other hand, if they see questions as having only one correct answer and as needing to be solved in one particular way, they will be prone to…

With the advent of No Child Left Behind (2002), the academic expectations of students with disabilities have changed. Students with disabilities are now held to the same academic standards as their peers without disabilities. Furthermore, the 2004 provisions in the Individuals With Disabilities Education Improvement Act state that students with…