Students with mathematics learning disabilities have a weak understanding of mathematical concepts that underlie success in Algebra I, such as ratios and proportional reasoning. In this study, researchers used a multiple baseline across participants design to evaluate the effects of a intervention based on a instructional trajectory of how students come to understand ratios through build-up, emergent unit, and unit strategies on performance on a test of ratio equivalence. Student performance during intervention indicated a functional relationship between the instruction and higher scores on a curriculum-based measure across three students. Student use of increasingly sophisticated strategies over the course of the intervention also increased. Results as well as possible implications and future research are discussed.

59% of fourth-grade students could not identify two rational numbers as equivalent or generate additional equivalent rational number relations (National Center for Educational Statistics, 2009). Less than half of eighth-grade students could correctly identify rational numbers given in ascending order or add two fractions with different denominators. If students have difficulties understanding mathematics, we would expect rational numbers to become increasingly more difficult to learn. Indeed, research points to not only quantitative performance differences between students with and without mathematics difficulties but also qualitative differences in the ways students who struggle to learn mathematics understand and approach problems involving rational numbers (Mazzocco & Devlin, 2008).Despite the differences students experience as they learn rational number equivalency concepts, few studies offer content and instructional guidance to practitioners to help improve understanding of rational number equivalency for students with severe learning difficulties. In the sections that follow, the author addresses (a) content, instructional practice, and mathematics difficulties students who struggle may face as they relate to rational numbers; (b) supplemental approaches to increasing proficiency in rational number concepts for students who struggle with mathematics; and (c) the research objectives of the present study.Many people view the Common Core State Standards Initiative (CCSS, 2010) as a possible catalyst for improving mathematical proficiency of children and adolescents in the United States. The CCSS offer direct guidance in content and practices regarding rational numbers. In terms of mathematical practices, the CCSS emphasize student reasoning and sense making of problem situations and solutions as well as those posed by other students, student use of visual models, mathematical structures, and relationships, and the ability to abstract concepts through making use of mathematical structure and expressing regularity in repeated reasoning. In terms of content, the CCSS define equivalence as the understanding of two fractions that are the same size or at the same point on a number line. Evidence of a student's growing understandings of rational number equivalence also includes the ability to recognize and generate simple 507780R SEXXX10.

Little to no information exists explaining the nature of conceptual gaps in understanding fractions for students with learning disabilities (LD); such information is vital to practitioners seeking to develop instruction or interventions. Many researchers argue such knowledge can be revealed through student's problem-solving strategies. Despite qualitative differences in thinking and representation use in students with LD that may exist, existing frameworks of student's strategies for solving fraction problems are not inclusive of students with LD. This exploratory study extends existing literature by documenting the strategies students with LD use when solving fraction problems. Clinical interviews were conducted with 10 students across the third, fourth, and fifth grades (N = 10). Results indicate students with LD used similar strategies as previously reported in research involving non-LD students, although the dominant strategy utilized was less advanced and the range of strategy use was relatively compact. Researchers suggest the nature of conceptual gaps students with LD display in their understanding of fractions originates from a malleable source. Implications for instruction and assessment are presented.

There is a critical need to mentor novice special education teachers to meet the current and projected teacher shortages. However, due to the various skill-levels of beginning special education teachers in schools and the small number of current special educators in each school who could serve as mentors, there is difficulty finding induction-level mentors that possess similar or the same teaching credentials or teaching assignments as mentees in the same schools or geographical regions. Electronic mentoring (e-mentoring) using technology initiates solutions as e-mentoring can provide synchronous and asynchronous mentoring opportunities which increase collaboration time and reduce feelings of isolation and increases efficacy among new teachers. The article presents the findings from research using a mixed methods design investigating novice special education teacher knowledge of professional competencies and the participant's perceptions of effectiveness of induction-level mentoring through the pilot use of an electronic mentoring program.