More Language Arts, Math, and Science for Students with Severe Disabilities

Diane Browder-Boswell, Fred Spooner, Diane Browder, Fred Spooner

• Publisher: Brookes Publishing
• Year: 2015
• Print ISBN: 9781598573176
• eBook ISBN: 9781598576474
• Topic: Education
• Subtopic: Inclusive Education

How can today's educators teach academic content to students with moderate and severe developmental disabilities—while helping all students meet Common Core State Standards? This text has answers for K-12 teachers, straight from 37 experts in special and general education. A followup to the landmark bestseller Teaching Language Arts, Math, and Science to Students with Significant Cognitive Disabilities, this important text prepares teachers to ensure more inclusion, more advanced academic content, and more meaningful learning for their students. Teachers will have the cutting-edge research and recommended practices they need to identify and deliver grade-aligned instructional content—leading to more opportunities and better quality of life for students with severe disabilities.

PREPARE TEACHERS TO

• skillfully adapt lessons in language arts, math, and science for students with disabilities
• align instruction with Common Core State Standards
• select target skills and goals
• differentiate instruction using appropriate supports and assistive technologies
• balance academic goals and functional skills
• make the most of effective instructional procedures such as peer tutoring, cooperative learning, and co-teaching
• maintain high expectations for student achievement
• promote generalization by embedding instruction into ongoing classroom activities
• assess students' progress and make adjustments to instruction

PRACTICAL MATERIALS: Detailed vignettes based on the authors' real-life experiences, teaching examples and guidelines that illustrate recommended practices, helpful figures and tables, resource lists, and suggestions for incorporating technology into teaching and learning.

SECTION III

Teaching Common Core Mathematics and Teaching Science

CHAPTER 8

Beginning Numeracy Skills

Alicia F. Saunders, Ya-yu Lo, and Drew Polly

Janette, a fifth grader with moderate autism, attends a general education math class with her same-age peers. The general education teacher, Ms. Karon, designs lessons with activities using principles of universal design for learning so that Janette can participate successfully. In the inclusive class, Janette uses a calculator and a peer buddy as supports. Initially, Janette often needed the help of her peers to perform the most basic math skills, such as creating sets, counting with one-to-one correspondence, and adding with manipulatives. To improve Janette’s basic math skills, Ms. Adams, Janette’s special education teacher, has been working with Janette daily on early numeracy skills using evidence-based practices, such as constant time delay and least intrusive prompting. During one inclusive math class, Ms. Karon was teaching her students about division and many were having difficulty. She posed the problem “12 ÷ 3 = ?” Janette picked up the 12 counting chips in front of her and 3 set makers and quickly divided the 12 chips into 3 groups and then touched the number 4 response card. Her peer buddy shouted out to the teacher, “Ms. Karon, look! Janette solved the problem. The answer is 4!” Everyone was so proud of Janette. Later that day, Ms. Karon approached Ms. Adams and told her that if Janette had been exposed to the kind of intensive instruction she was receiving beginning in early grades, Janette would likely be able to perform grade-level math problems. Her early numeracy skill impairments were preventing Janette from accessing the general education math curriculum to the fullest extent possible.

The increasing emphasis on addressing student learning deficiencies in mathematics has been prevalent in both general education and special education (National Mathematics Advisory Panel, 2008; Sarama & Clements, 2009; Stigler & Heibert, 1999). Examination of the causes of mathematics deficiencies and potential ways to support struggling students, including students with severe disabilities, raises the question, “What foundational mathematical skills and understandings do these students lack?” In this chapter early numeracy (EN) skills and their importance as building blocks for children’s mathematical understanding are described. EN skill descriptions are followed by research-based practices for teaching these critical skills and the specific steps educators can use to teach them.

IMPORTANCE OF EARLY NUMERACY SKILLS

Children’s mathematical understanding in real life and in upper grades in school is empirically linked to their understanding of numbers, including what they are and how they relate to one another (Leinwand, 2012). Mathematics educators hold the term number sense as a broad phrase that includes multiple concepts and skills related to numbers. Teachers often describe students using phrases such as, “They have very little number sense,” or “My students have a strong understanding of numbers.” The National Council of Teachers of Mathematics (NCTM; 2000) defined number sense as an individual’s ability to understand numbers and operations and use these concepts and strategies to make mathematical judgments and for more complex problem solving (McIntosh, Reys, & Reys, 1992).

Sample skills that fall under the umbrella of number sense and are discussed in this chapter include 1) rote counting; 2) number identification; 3) representation of numbers and counting with one-to-one correspondence; 4) creating sets; 5) composing and decomposing numbers; 6) early measurement concepts, such as identifying things as bigger/smaller and quantities as more/less; and 7) patterning. This list is not exhaustive of all skills that are encompassed under the term number sense; however, these skills are important for students with severe disabilities to master.

Regardless of whether EN skills are referred to by their individual skills or with the broad phrase number sense, research indicates that students’ early mathematical understandings strongly influence later success in mathematics (Denton & West, 2002; National Mathematics Advisory Panel, 2008). Krajewski (2005) found that children’s mathematical knowledge prior to first grade was a strong predictor of future quantitative understanding. Researchers who have studied gaps between populations of students found that students who struggle in mathematics lacked opportunities to develop EN skills, which are often provided prior to formal schooling and in the early years of school (Hiebert, 1986). It is critical for all students to develop EN skills so that they can function in the 21st century (Kilpatrick, Swafford, & Findell, 2001). Students who lack EN skills struggle to develop mathematical understandings far beyond their first years of school. Impairments in EN skills also prevent students such as Janette from fully accessing the general mathematics curriculum. Essentially, students who lack EN skills when entering formal schooling, including those with severe disabilities, need intensive, sound instruction in order to help develop the skills and bridge gaps (Gersten & Chard, 1999).

Mathematics educators (e.g., Fuson, 2004; Richardson, 2011; Sarama & Clements, 2009) have proposed empirically based trajectories and progressions of how children develop EN skills and number sense. In each of these trajectories and progressions, there are some skills that are foundational for success in students’ understanding of mathematical concepts. For students with severe disabilities, these progressions provide a starting point that educators and curriculum developers can use to develop instructional materials (Browder et al., 2012; Jimenez, Browder, & Saunders, 2013). By understanding foundational EN skills, and how to develop these skills in children through sound instructional pedagogies, teachers will be better prepared to develop the number sense of their students with severe disabilities.

RESEARCH-BASED PRACTICES FOR TEACHING EARLY NUMERACY SKILLS

Unlike most students without disabilities who often develop EN skills prior to any formal schooling, students with severe disabilities do not develop these skills without direct and intensive instruction (Judge & Watson, 2011; Morgan, Farkas, & Wu, 2009). Because EN skills are fundamental for mastering advanced knowledge in mathematics in later years of life (Denton & West, 2002; Jordan, Glutting, & Ramineni, 2010; Jordan, Kaplan, Ramineni, & Locuniak, 2009), it is especially important for students to receive effective, scientifically supported instruction in EN skills in very early grades (National Mathematics Advisory Panel, 2008). Even with this early EN skills instruction, students with severe disabilities may need additional focus on these skills during the elementary school years. Jimenez and colleagues (2013) found that EN skills for students with severe disabilities could still be developed between the ages of 5 and 11 with evidence-based practices.

Literature on mathematics instruction for students with severe disabilities traditionally has shown a primary focus on functional mathematics skills such as money computation, purchasing, budgeting, and banking (Browder & Grasso, 1999). With a shift to include students with severe disabilities in addressing academic content standards as a result of federal legislation (e.g., the No Child Left Behind Act of 2001 [PL 107-110]), slightly more research has become available on academic mathematics instruction for this student population. Browder, Spooner, Ahlgrim-Delzell, Harris, and Wakeman (2008) conducted a meta-analysis of 68 studies published between 1975 and 2005 that involved teaching academic mathematics skills to students with significant cognitive disabilities (i.e., developmental disabilities, autism, and moderate or severe intellectual disability) to identify evidence-based instructional practices. They found that systematic instruction with explicit prompting, prompt fading (e.g., least intrusive and constant time delay), and feedback is an evidence-based practice for teaching numbers, operations, and measurement skills to students with significant cognitive disabilities. In addition, in-vivo instruction, in which students applied their learning to real-world situations, was found to produce greater effects in students’ learning than those studies without in-vivo instruction.

In the following sections, two types of instructional methods—systematic instruction and explicit instruction—that have produced positive learning in EN skills for students with severe disabilities are briefly discussed.

Systematic Instruction for Teaching Early Numeracy Skills

Systematic instruction refers to a well-designed plan of teaching that targets and evaluates a student’s learning when given controlled and meaningful opportunities to practice the skills to reach mastery. It often involves specific procedures for systematically prompting and reinforcing operationalizing defined responses (Collins, 2007; Snell & Brown, 2011). In systematic instruction for teaching mathematics skills to students with severe disabilities, defined response prompts and explicit prompt fading are essential (Browder et al., 2008). Response prompting instructional strategies, including time delay, system of least prompts, and simultaneous prompting, have received strong evidence of effectiveness in interventions for students with moderate to severe disabilities (Wolery, Ault, & Doyle, 1992). Although research on the use of these strategies in teachi...

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• List of Figures
• List of Tables
• About the Reproducible Materials
• About the Editors
• About the Contributors
• Foreword Martin Agran
• Preface
• Acknowledgments
• I. Greater Access to General Curriculum
• II. Teaching Common Core Language Arts
• III. Teaching Common Core Mathematics and Teaching Science
• IV. Alignment of Curriculum, Instruction, and Assessment
• Index