Integer operations are typically introduced in sixth grade, but they are a consistent area of struggle among these students. This struggle also inhibits their understanding of algebraic computations involving positive and negative terms. In this article, the author provides introductory tasks and models for adding and subtracting integers that can…

The mathematics of budgeting and space can lead to a justice-oriented experience for elementary students as they design a proposal for an inclusive playground. The authors' work focused on creating the space for elementary children to see the interconnectedness between mathematics and a community social injustice, lack of inclusive playground…

In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…

How might fourth graders address the problem of measuring the size of a leaf? And why might their classroom teachers choose such a shape to measure? One group of fourth-grade students in an urban Australian school were interested in knowing the sizes of leaves on a passionfruit vine growing at their school. The children were excited after a visit…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Connections among the mathematics, science, and engineering disciplines have been recognized and affirmed in national standards. For example, the application of mathematical ideas and skills within science has been highlighted in national science standards for over 20 years. More recently, the Next Generation Science Standards (NGSS; NGSS Lead…

A powerful way to build students' mathematical power and agency is through Teaching Mathematics for Social Justice (TMfSJ), where students read and write the world with mathematics (Gutstein, 2005). Reading the world with mathematics uses mathematics to understand relations of power, resource inequities, and disparate opportunities between…

Access to drinking water is becoming more limited as drought persists across continents. This article highlights a particularly impacted group of students due to increasing drought conditions and upstream river pollution near their reservation. While there are related water and modeling standards across the K-12 Next Generation Science Standards…

In this article, we extend Liao's test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be…

This article details how a team of fourth-grade teachers in Rockingham County, Virginia used the Inquiry Design Model (IDM) to deepen student understanding of Barbara Johns and the Moton Student Strike's fight for racial justice in Virginia and to reframe their overall approach to Black history in general. Although Rockingham County Schools are…

Increasing pupil mobility has led to widespread concern among parents, educators, and policymakers regarding its negative effects on academic performance. An important issue in examining mobility effects in longitudinal school achievement comparisons is providing accurate estimates. The presence of pupil mobility suggests that we should model…

In this paper, we build on a previously developed notion of 'learning as Making' to examine mathematics thinking and learning in a highly transformative and technological Making environment: one that involves a handheld 3D printing technology which enables 3D models to be created instantly via one's moving hand. In particular, we present two…

Mathematical modeling involves using mathematics to represent, analyze, and make predictions or decisions about real- world situations. Garfunkel and Montgomery (2016) elaborate on six components of the mathematical modeling process, including identifying the problem, making assumptions and identifying variables, doing the math, analyzing and…

As computational models are becoming more widely used with the release of "A Framework for K-12 Science Education" (NRC 2012) and the "Next Generation Science Standards" ("NGSS"; NGSS Lead States 2013), these models are reshaping the way science is practiced in increasingly diverse classrooms. For students classified…

In this article, the authors present a 5E learning cycle for fifth grade that focuses on using a model of matter to explain the properties they observe, and how those properties can help identify whether two objects are made of the same type of matter. That model also helps explain phenomena such as why a specific material floats, no matter how…