Education leaders in Virginia use early access to Algebra I as one method to provide students more time to take college preparatory courses in high school, thereby increasing students' likelihood of graduating prepared for college and careers. Yet, little data are available for these leaders to examine whether their approach is warranted. Members…

This document provides the two appendixes that accompany the full report, "Algebra I and College Preparatory Diploma Outcomes among Virginia Students Who Completed Algebra I in Grades 7-9." Appendix A, "Methods," details the data sources, study population, and analysis methods used in the study. Appendix B, "Supporting…

Algebraic competence is a major determinant of college access and career prospects, and equal sign knowledge is taken to be foundational to algebra knowledge. However, few studies have documented a causal effect of early equal sign knowledge on later algebra skill. This study assessed whether second-grade students' equal sign knowledge…

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

Many studies have shown that visual representations can enhance student understanding of STEM concepts. However, prior research suggests that visual representations alone are not necessarily effective across a broad range of students. To address this problem, we created a novel, scaffolded form of diagrammatic self-explanation in which students…

National standards and frameworks for mathematics, computer science, and technology emphasize the importance of teaching all children computational thinking (CT) skills. These skills are important for preparing citizens that are literate in science, technology, engineering, and mathematics and for participation in a society that is rapidly…

Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence…

This study examined pre-service primary teachers' (PSPTs) mathematics performance on a set of question items measuring at the sixth grade level in Hong Kong. These items covered the five learning strands of the local primary mathematics curriculum -- number, algebra, measures, shape and space, and data handling. The participants of the study were…

Competence in fractions is important in achieving advanced mathematics such as algebra and calculus. To foster students' understanding of fractions, intervention studies have found number lines to be an effective representational tool. Yet, it is unclear whether or not number lines are equally effective regardless of the ways in which they are…

The aim of this study was to examine 6th-grade students' mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations,…

This study sought to answer the following questions: (1) Is it feasible to develop Academic Key Performance Indicators (KPIs) and collect data on them across member urban school districts? (2) Are comparisons between districts on academic performance measures valid and reliable? (3) Do districts collect and maintain requested KPI data in a way…

This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode…

In this study, it was aimed both to examine middle school students' perceptions of the concept of pattern and to reveal if the metaphoric perceptions which the students created in relation to the concept of pattern changed according to the variable of grade level. The metaphors in relation to the concept were carried out via the…

There are different perspectives in the literature on the examination of visual images used in course books. In this study, illustrations from the visuals used in geometry in the lower learning area of school mathematics were examined and summarized first by researchers and then by teachers and students. For many students, the mathematics…

Stopping rules for fixed-form tests with graduated item difficulty are intended to stop administration of a test at the point where students are sufficiently unlikely to provide a correct response following a pattern of incorrect responses. Although widely employed in fixed-form tests in education, little research has been done to empirically…