Introduction to the Special Series: Mathematics and Learning Disabilities

Increased attention is being paid to students who demonstrate difficulty in learning and applying mathematics concepts. The purpose of this special series was to address issues related to students and mathematics learning disabilities (LD). We identify Response to Intervention (Rtl) as it relates to early mathematics instruction and a multi-tiered service delivery system. Further, because Rtl has focused primarily on young children and the prevention of LD, we present information about older students who have been identified as having mathematics LD and provide strategies for helping them access the general education curriculum. Six papers on various mathematics topics, grade levels, and service delivery will be provided in this special series. Authors report findings on research efforts and offer implications for practice. BRIAN R. BRYANT, Ph.D., The University of Texas at Austin. DIANE PEDROTTY BRYANT, Ph.D., The University of Texas at Austin. Development and application of mathematical competence is a critical educational goal for all students, including those who have learning disabilities (LD). Yet, research on understanding mathematics disabilities and how they affect learning has lagged behind comparable work in reading disabilities. Likewise, when compared to the well-established research base in early reading difficulties, far less attention has been paid to early difficulties in mathematics and identification of mathematics disability (D. Bryant, Smith, & Bryant, 2008). Similarly, research on adolescent students with mathematics disabilities is limited at best. Fortunately, in recent years, researchers have been paying increased attention to students who demonstrate challenges in learning and applying mathernatics skills and concepts (D. Bryant, 2005; Chard et al., 2005; Fuchs & Fuchs, 2005; Gersten, Jordan, & Flojo, 2005; Jitendra et al., 2005; Jordan, Hanich, & Kaplan, 2003; Kroesbergen & Van Luit, 2003; Maccini & Gagnon, 2006; Miller, & Hudson, 2007; Montague, 2006). This special series on mathematics and LD is intended to add to this growing research base. The specific purpose of this special series is to address two primary issues related to students and mathematics learning disabilities. First, at a time when Response to Intervention (Rtl) is the focus of considerable attention and discussion in the educational community, we seek to identify key Rtl issues as they relate to early mathematics instruction, particularly as they pertain to a multi-tiered service delivery system. Second, because Rtl has focused primarily on young children and prevention of LD, we present information about older students who have been identified as having mathematics LD and provide strategies they can use to access the general education curriculum. Volume 31, Winter 2008 In this introduction, we (a) describe characteristics of students who have difficulties in mathematics, (b) overview the purposes of Rtl and the multi-tiered service delivery system, (c) discuss briefly elementary and secondary math instruction, and (d) introduce the articles that constitute the special series and the authors who contributed to the series. Characteristics of Students with Mathematics Difficulties Mathematical difficulties are persistent and evident from the early elementary grades through secondary levels (Garnett, 1987). With respect to the early grades, Gersten et al. (2005) examined several kindergarten through grade 2 studies that compared students who exhibited mathematical difficulties to their typically achieving peers. Learning problems were found in arithmetic combinations (i.e., basic facts), counting strategies (e.g., counting all, counting on), and number sense (e.g., basic counting techniques, understanding of size of number, number relationships). Based on their findings, Gersten and his colleagues suggested that, over a period of time, limited mastery of arithmetic combinations (basic facts) was a "hallmark" of mathematics difficulties. In a study on mathematics difficulties with students in grades 2 through 12, D. Bryant, Bryant, and Hammill (2000) identified 29 specific mathematics behaviors associated with math LD based on a search of the research and theoretical literature (see Table 1). They then asked a group of LD teachers to rate the frequency with which students exhibited the identified mathematical skills. A rank ordering of responses showed that certain mathematics problems were troublesome for students with mathematics weaknesses across ages. Not surprisingly, word problems were ranked as most problematic for students with learning disabilities and math weaknesses. Table 1 shows the ranking of the mathematical difficulties, in decreasing order of frequency, exhibited by students with LD and math weaknesses. D. Bryant et al. (2008) further surveyed the literature and identified specific behaviors associated with math calculation and problem solving demonstrated across the grades. Students with calculations difficulties may demonstrate problems with some or most of the following skills: • Identifying the meaning of signs (e.g., -i-, -, x, <, =, >, %, 2) • Remembering answers to basic arithmetic combinations (e.g., 8-1-9 = ?, 7 x 7 = ?) • Using effective counting strategies to calculate answers to arithmetic problems. • Understanding the commutative property (e.g., 5 + 3 = 8 and 3 H5 = 8) • Solving multi-digit calculations that require regrouping • Misaligning numbers • Ignoring decimal points Word problem-solving difficulties may be observed in any of the following skills: • Reading the problem • Understanding the meaning of the sentences • Understanding what the problem is asking • Identifying extraneous information that is not required for solving the problem • Developing and implementing a plan for solving the problem • Solving multiple steps in advanced word problems • Using the correct calculations to solve problems An examination of the behaviors cited across the studies demonstrates that difficulties are broad-based and exhibited across a wide array of mathematics content. While individual students with mathematics LD may exhibit only one or two of the listed behaviors, they are more likely to exhibit pervasive difficulties (D. Bryant et al., 2008). Given the mathematics difficulties demonstrated by students with LD, prevention and intervention are critical components to include as part of instructional delivery (Fuchs & Fuchs, 2001). Overview ofthe Purposes of Rtl and the Tiered Service Delivery System For years, LD diagnoses were based primarily on a discrepancy between intelligence test scores and achievement test scores. The Individuals with Disabilities Education Improvement Act IDEA 2004 allows for either the IQ-achievement discrepancy model or the newly conceived Rtl approach for identifying learning disabilities. With the Rtl approach, once students have been identified as having low achievement and learning at a rate below that of the their nondisabled peers, they may be identified as having learning disabilities (provided they meet exclusionary clause criteria) (Vaughn & Fuchs, 2003). Vaughn (2002) described one Rtl approach as a prevention and intervention model for struggling readers in the early grades. The 3-Tier Reading Model provides a framework for a data-driven delivery of differentiated instruction for all students (Vaughn Gross Center for Reading and Language Arts [VGCRLA], 2005) that can be generalized to mathematics or any other academic area. Tier 1 consists of evidence-based core instruction for all students, including struggling students receiving concurrent services in Tier 2 and Tier 3 (D. Bryant & Bryant, 2007). Tier 2 provides supplemental instruction and ongoing progress monitoring to students who have been identified as achieving below their averageand above-average-performing peers. The classroom teacher Learning Disability Quarterly