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…

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…

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…

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…

The balance model is often used for teaching linear equation solving. Little research has investigated the influence of various representations of this model on students' learning outcomes. In this quasi-experimental study, we examined the effects of two learning environments with balance models on primary school students' reasoning related to…

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning…

In 2007 Georgia instituted a flexibility policy through which school districts enter into performance contracts with the state, receiving waivers from state rules, provisions, and guidelines in exchange for agreeing to meet annual accountability targets. The performance contracts are intended to incentivize innovations that increase achievement…

These are the appendixes for the report, "District Changes in Student Achievement and Local Practice under Georgia's District and School Flexibility Policy." Five appendixes are included in the document: (1) About the study; (2) Data and methods; (3) Supporting analysis; (4) Survey instrument; and (5) Interview protocol. [For the full…