This study used the RBC+C model to reveal the abstractions of the 6th-grade students in the process of transition to the parallelogram area formula. Also, constructing parallelogram area information was employed as a teaching experiment based on the basic interpretive approach, one of the qualitative research methods. The study participants…

This qualitative case study investigated how computational models can help students engage in scientific practice and influence their emotional, epistemic, and conceptual aspects. Twenty-four sixth-graders were guided to conduct scientific practices as they predicted and modified the computational models on food web using StarLogo Nova. Three…

Strategies are an important component of self-regulated learning frameworks. However, the characterization of strategies in these frameworks is often incomplete: (1) they lack an operational definition of strategies; (2) there is limited understanding of how students develop and apply strategies; and (3) there is a dearth of systematic and…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

Student growth percentiles (SGPs) are currently used by several states and school districts to provide information about individual students as well as to evaluate teachers, schools, and school districts. For SGPs to be defensible for these purposes, they should be reliable. In this study, we examine the amount of systematic and random error in…

Sources of longitudinal achievement data are increasing thanks partially to the expansion of available interim assessments. These tests are often used to monitor the progress of students, classrooms, and schools within and across school years. Yet, few statistical models equipped to approximate the distinctly seasonal patterns in the data exist,…

This article explains the process behind estimating a National Education Cost Model (NECM) and generating from that model projections of per-pupil costs to achieve 2016 national average outcomes (reading and math grades 3 to 8) across all districts in the United States, from 2019-20 to 2020-21. This article is a follow-up to a preliminary report…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

For the past decade, the accountability model associated with No Child Left Behind (NCLB) emphasized proficiency on end of year tests; with Every Student Succeeds Act (ESSA) the emphasis on proficiency within statewide testing programs, though now integrated with other measures of student learning, nevertheless remains a primary metric for…

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

Two objectives guided this research. First, this study examined how well teachers' tracking decisions contribute to the homogenization of their students' achievements. Second, the study explored whether teachers' tracking decisions would be outperformed in homogenizing the students' achievements by statistical models of tracking decisions. These…

Engaging students in studies about conservation and sustainability can support their understanding of making environmental conscious decisions to conserve Earth. This article aims to contribute these efforts and direct students' attention to how they can use mathematics to make environmental decisions. Contributors to iSTEM: Integrating…

Public schools with impressive records of serving lower-performing students are often overlooked because their average test scores, even when students are growing quickly, are lower than scores in schools that serve higher-performing students. Schools may appear to be doing poorly either because baseline achievement is not easily accounted for or…

Mediation analysis is a statistical approach used to examine how the effect of an independent variable on an outcome is transmitted through an intervening variable (mediator). In this article, we provide a gentle introduction to single-level and multilevel mediation analyses. Using single-level data, we demonstrate an application of structural…

Value-added approaches for attributing student growth to teachers often use weighted estimates of building-level factors based on "typical" schools to represent a range of community, school, and other variables related to teacher and student work that are not easily measured directly. This study examines whether such estimates are likely…