Count Me in! K–5: Including Learners with Special Needs in Mathematics Classrooms


Judy Storeygard

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  • Chapters
  • Front Matter
  • Back Matter
  • Subject Index
  • Dedication

    To Eli Freeman and Nathan Joseph, with love. May you have teachers as dedicated and knowledgable as those who contributed to this book.


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    Teachers are the lever in making change. We know that teachers can increase student progress by taking on the study of the complex, multifaceted task of teaching mathematics. This can be accomplished, in part, through learning about what research suggests has worked to increase student performance. Yet teachers who seek effective practices in teaching mathematics to students with special needs will find that the amount of research-based strategies for mathematics instruction pales in comparison to the expansive array of strategies for use with students with special needs in literacy. Teaching mathematics is intellectually challenging, as is teaching students with learning disabilities. The combination can be doubly difficult. These are the very reasons why this book is so significant and its value so unique.

    Simply put, Judy Storeygard focuses on the learning issue rather than the label—or formal diagnosis. By emphasizing the characteristics of learning needs, she focuses on an approach that helpfully responds to the needs of students across disabilities. Building on multitiered prevention systems used in many states, she moves away from consistently starting with a focus on the “gaps” in students' knowledge. She instead moves to identifying strengths in students' prior knowledge—a sounder first step. She emphasizes the behaviors students present every day in the classroom and finds ways to combat the tendency to step in and do the work for the students. In its place is this press for acknowledging and identifying capabilities and potential contributions from which to build. This welcome approach is the underlying framework for the book—in essence minimizing what the student cannot do and maximizing the student's opportunities to respond.

    In Count Me In!, Judy steps out in front and illustrates how this change to more effective mathematics teaching can occur through the shared examples drawn from the work of classroom teachers. In the spirit of her last book, My Kids Can, she continues to hold high expectations for all learners by crafting chapters that move beyond the labeling of students. She details ways to uncover some of the complex barriers to learning challenges, and shows how teachers can respond to a variety of misconceptions on their own.

    Count Me In! showcases authentic environments in classrooms using a feature called “Voices From the Field.” Here, classroom teachers directly communicate their wisdom about the very purposeful choices they make. These conversations result in suggestions ranging from practical ideas that are applicable to Monday morning, as well as thoughtful, broad-based reflections that provide the foundations for an overarching philosophy about working with students with disabilities. The book addresses the challenges teachers confront every day in building the following for students:

    • Capacity for learning mathematics
    • Cognitive flexibility
    • Ability to organize, plan, and self-monitor
    • Development of useful strategies
    • Skill in expressing mathematical ideas

    By asking questions along the way, Judy reveals how to identify the organizational, behavioral, and cognitive skills necessary for students with special needs to derive meaning from a variety of activities. She then describes specific ways to provide additional support if any weaknesses in these skills are diagnosed.

    Because approximately 80 percent of students' time in mathematics class is spent working on mathematics problems, Judy's emphasis on a problem-solving approach to instruction that promotes and supports sense-making is critical. Peppered with the verbatim dialogue from problem-solving sessions and samples of student work, she helps readers to see the moves necessary to help kids make sense of problem situations and to communicate their mathematical ideas. She paints vivid pictures of classrooms where the teacher's language and organization are shared in think-alouds; these bring the process of building a safe environment for learning and cultivating a culture of acceptance to the forefront.

    It is important for all teachers to know, when reading this book, that it is not about the fear of facing the challenge of learning to teach mathematics to students with disabilities in a potentially new way. It is about the complex task of doing so—and how others who've gone before can support their colleagues. Teachers' voices are central to this work, and the mantra in one classroom, effective effort plus time equals success, holds true for teachers as well as students.

    As one of the teachers in the book said to her students, “If you'd like help getting started, please come join us.”

    Karen Karp
    Professor of Mathematics Education at the University of Louisville


    This book is a product of collaboration with a group of dedicated teachers, colleagues, and parents. Their insight and commitment has been essential to the process of conceiving, writing, and revising Count Me In!

    In many ways, parents have inspired this book. Listening to their concerns about their children's education, and seeing their determination for their children's teachers to see their children's strengths as well as their needs, has greatly increased my awareness and understanding. I give special thanks to Nancy Isaacs, Laurie Brennan, Lenworth Hall, Janet Altobello, and Karen Economopoulos for their poignant and honest accounts of their children's educational experiences.

    The Educational Research Collaborative at TERC provided me with funding to pursue publication. My colleagues, Arusha Hollister and Myriam Steinback, have been unfailingly generous in their support and astute feedback. Andee Rubin has been particularly helpful in advising me about the technology-related pieces, providing examples from her research project, INK-12: Teaching and Learning Using Interactive Ink Inscriptions in K-12; Curtis Killian has been an invaluable resource in creating graphics and offering general technological support. Karen Mutch-Jones and Amy Brodesky (Education Development Center colleague) have lent their wisdom about students with special needs.

    I am also very grateful for my knowledgeable colleagues from the Professional Development Study Group who provided me with excellent comments on several chapters. In addition, Deborah Schifter, Marion Reynolds, and Connie Henry subsequently read revised versions.

    In addition to the talented contributing teacher-authors, many other excellent teachers have played a part in informing my thinking and in allowing me to observe and write about their outstanding teaching. Excerpts from these observations are included in the book.

    I want to thank Eileen Backus, Sara Gardner, Linda Jackson, Amy Monkiewicz, Lisa Nierenberg, Karin Olson-Shannon, Dee Watson, and Sara Wolff.

    Jessica Allan and Cassandra Seibel at Corwin have guided and encouraged me throughout. Finally, I would like to thank my family for their love and support.

    Publisher's Acknowledgments

    Corwin gratefully acknowledges the contributions of the following reviewers:

    • Roxie Ahlbrecht
    • Teacher Leader, NBCT
    • Second Grade, Math
    • Robert Frost Elementary School
    • Sioux Falls, SD
    • Carol Amos
    • Teacher, Math
    • Twinfield Union School
    • Kennett Square, VT
    • Sue Delay
    • Learning Support Teacher
    • Cedar Hills Elementary School
    • Oak Creek, WI
    • Susan German
    • Teacher, Math and Science
    • Hallsville Middle School
    • Hallsville, MO
    • Jennifer Harper
    • Fourth-Grade Teacher
    • Cavendish Town Elementary
    • Proctorsville, VT
    • Debra Howell
    • Teacher, Monte Cristo
    • Elementary
    • Granite Falls, WA
    • Diane K. Masarik
    • Assistant Professor of Teacher
    • Education, Math and Science
    • University of Wisconsin—Eau
    • Claire
    • Eau Claire, WI
    • Edward Nolan
    • Mathematics Department
    • Chairperson
    • Montgomery County PS
    • Market, MD
    • Renee Peoples
    • Teacher Leader, Math
    • Swain West Elementary
    • Bryson City, NC

    About the Author

    Judy Storeygard has been a senior research associate at TERC for the past 20 years, an independent, not for profit research and development organization whose mission is to improve mathematics and science education.

    She has a long-term interest in and passion about the mathematics education of students with special needs and from underrepresented populations. Collaborating with teachers has been a prime focus of her work. She has also taught students with learning disabilities and behavioral disorders, and supervised graduate students in a moderate special needs certification program. As a member of the board of the Massachusetts Tourette Syndrome Association for over 15 years, she cochaired the Tourette Syndrome Association Conference for Educators from 1998 to 2002. At TERC, she has been a member of the ERC Fellowship Committee, an initiative that seeks recent PhDs or EdDs whose research focuses on enhancing teaching and learning opportunities in math and science for children, youth, and adults from historically nondominant communities.

    Count Me In! is a continuation of the work she has done for the past decade. The Annenberg Challenge Fund and the National Science Foundation, Research in Disabilities Education division, have funded much of her work. Other roles that have resulted from these projects include contributing author to Models of Intervention in Mathematics: Reweaving the Tapestry (Fosnot, 2010); editor of the collection of video and written cases written with elementary mathematics teachers, My Kids Can: Making Math Accessible to All Learners, K–5 (2009); contributing editor to Working with the Range of Learners: Classroom Cases in the Investigations in Number, Data, and Space (TERC) second edition; and coauthor for publications in the journals Teaching Children Mathematics (2007) and Teaching Exceptional Children Plus (2005).

    About the Contributors

    Zachary Champagne taught fourth and fifth grade in a large urban district in North Florida for 13 years. Currently, he is working on a two-year grant as a district facilitator for the Florida Center for Research In Science, Technology, Engineering, and Mathematics (FCR-STEM). He was the 2010 Teacher of the Year for his county and finalist for the Macy's Florida Teacher of the Year. He also was the 2006 recipient of the Presidential Award for Excellence in Mathematics and Science Teaching. He believes strongly in making mathematics concepts concrete and applicable to all of his students, and he works to show his students that “mathematics makes sense.”

    Nikki Faria-Mitchell is a third-grade teacher in the Boston Public Schools. She is also part of a project called Using Routines as an Instructional Tool for Developing Students' Conceptions of Proof—a collaboration of TERC, Education Development Center (EDC), and Mt. Holyoke College. She has also participated in and facilitated many Developing Mathematical Ideas workshops. She is especially interested in facilitating mathematical conversations that include all learners and allow her students to take ownership of their math learning.

    Abbie Fox is a third-grade teacher in Natick, Massachusetts. She is passionate about helping kids apply their math skills in science and engineering and loves to incorporate technology projects into her teaching. She also facilitates lesson study with her colleagues, a form of professional development in which teachers codevelop lessons, observe one another's teaching, and take a close look at student's mathematical understandings.

    Tiffany Young Frank is a preK teacher in the Boston Public Schools. She remembers being a young struggling math student. As a teacher, she has been committed to teaching all students, especially children of color, the intricacies of early math concepts with a focus on hands on instruction. In 2007, she was a Fund for Teachers fellow, and traveled to Melbourne, Australia (home to the Early Numeracy Project) to investigate effective research-based math instruction. She was also a part of rewriting and testing new math ideas for the TERC Investigations program for kindergarten students. She hopes her learning will enrich her teaching, her students, and her community.

    Elizabeth Henshaw Harrington is a second-grade teacher on the north shore of Boston. As a person who struggled with math as a student, she was surprised to find she loves to teach math. She hopes her students will always love math and feel confident about the amazing work of which they are capable.

    Sherri Neasman is a fifth-grade teacher in Boston Public Schools. She enjoys teaching all subjects; however, she most enjoys teaching math. As a child, she remembers “doing” math, but not being able to articulate exactly what was being “done.” Because of this, she participated in the Title IIB math project, which sought to bridge the gap in the language of math learning between upper elementary and middle school grades. She is a member of the Grade 5 Assessment Preview Team whose goal is to examine the language of the exams and tests. She also tutors elementary and middle school math after school.

    Lisa Nguyen is a fifth-grade teacher in the Boston Public Schools. She has also been a leader in several professional development projects related to elementary school math. She is dedicated to her practice in developing student mathematical thinking. Her focus is on developing students' ability to explain and challenge one another's mathematical thoughts by using math language.

    Danielle Silverman is currently an elementary math resource room teacher for the Boston Public Schools. As a former math coach for the district, she continues to work collaboratively with the elementary math department to facilitate districtwide professional development on response to intervention (RTI) and the Investigations curriculum. She also facilitates Developing Mathematical Ideas workshops for Boston Public Schools and works as a consultant for TERC. In addition to advocating for special education students and their mathematical learning needs, she enjoys spending time with her new baby boy, traveling, reading, photography, and spending time on Nauset Outer Beach on Cape Cod.

    Heather Straughter taught fourth and fifth grade in the Boston Public Schools for eight years. She looped with her students and thoroughly enjoyed teaching them for two years. She was also a Developing Mathematical Ideas facilitator and leader in professional development for other teachers. She left teaching in 2005 to become a stay-at-home mom and is enjoying using what she knows about teaching with her now elementary-aged son.

    Ana Vaisenstein has been working in the Boston Public Schools since 1998. She has taught kindergarten through fifth grade to English language learners and has coached teachers in mathematics. She is currently teaching a third-grade sheltered English immersion class. She enjoys observing students explain their ideas to one another and make sense of problems together.

  • Conclusion

    What does it look like to teach mathematics that focuses on sense-making to a range of students in inclusive classrooms?

    The preceding chapters provide a framework and examples to address the question posed in the introduction. The examples offer teachers resources and strategies to help them meet the challenge of teaching mathematics to diverse learners, and to dispel some common myths:

    • There are “tips” and “procedures” that can make teaching in inclusive classrooms straightforward.
    • Students with special needs cannot learn mathematics unless they are told what to do.
    • “Good teaching” for all children is enough for students with special needs to succeed in mathematics.
    Complexity of Teaching in Inclusive Mathematics Classrooms

    Teachers who understand the complexity of teaching in inclusive classrooms have written each “Voices From the Field” segment. The process is anything but simple. As Karp and Voltz (2000) state,

    Being a successful weaver of lessons for diverse groups of students requires the ability to integrate effectively what is known about the content (in this case, mathematics), what is known about how to teach it, and what is known about the students to whom it is taught. (p. 27)

    A major theme of each chapter is how purposeful these teachers are—how thoroughly they plan in order to meet their students' needs. They not only plan for each lesson, but they also plan to build the culture of acceptance that is the foundation of an inclusive mathematics classroom. Ms. Gordon establishes a routine for extra help earlier in the year, announcing to the class, “At the round table, I'm going to do some more problems like this with a small group. If you'd like some help getting started, please come join us.”

    As a resource teacher, Ms. Tarlow makes it a point to interview students if she observes that they are struggling with a math concept. By spending this time with the students, she learns what they know, what they still need to practice, and how they approach a task. Ms. Tran uses sentence frames as a starting point to help her students who are learning English get accustomed to expressing their mathematical ideas as they learn mathematical terms. These sentence frames are open-ended, giving students a structure that facilitates their thinking. All of these teachers show a command of math content, pedagogical strategies, and knowledge of their students.

    Making Sense of Mathematics

    All of the teachers who contributed to this book expect their students to make sense of mathematics, and they provide supports and resources that facilitate their students' understanding of mathematical concepts. They might use technology, as Mr. Daniels does when he makes a fraction number line on the SMART Board that his student can use flexibly as she masters the concept of equivalent fractions. They might develop structures, as Ms. Gatto does with her regularly scheduled “turn-and-talks,” during which students talk in pairs about a particular concept. Ms. Gatto takes her students through a carefully orchestrated sequence so that they are aware of the purpose of and expectations for their roles during turn-and-talk. These strategies are very different from what often happens for students with special needs in mathematics class. Too often, they are presented with a series of steps and procedures to follow and not engaged in mathematical discourse that helps build their ability to grasp mathematical ideas.

    Making Mathematics Explicit

    “Good teaching for all” is not enough to help students with special needs succeed in the inclusive math classroom. As stated previously, the voices from the field in this book reveal the purposefulness and intentionality these teachers bring to their practice. While they expect that their students with special needs can and will learn mathematics, they also realize that they need to put in place supports and meticulously sequenced activities and lessons to make the mathematics explicit and the expectations for class assignments clear. Ms. West knew that some of her first-grade students would struggle to solve a story problem on their own without acting it out first. She plans a guided math group and acts out the problem with real objects first, asking questions, and naming the strategies students use to indicate the important mathematics in the problem. Ms. Thompson knew that her student, Michael, who needed support with cognitive flexibility, did not apply his knowledge of place value when he used rote procedures, and became confused when trying to solve problems in multiple ways. She observes and thinks through the times that Michael has been successful. After noting that he could break numbers apart and multiply the parts, she helps Michael develop his strength into a reliable strategy. When Ms. Miller asks her students to evaluate each other's solutions, she communicates her goals and expectations clearly to the students: “I want you to particularly notice how each of the students organized their factor pairs. I also want to check in to see how you figured out which numbers are factors.” Throughout the lesson, she emphasizes the mathematics and clarifies students' comments about their organization and justification for deciding which numbers are factors and multiples.

    In all of these examples and the many others in the book, the emphasis is on sense-making, along with providing the resources, tools, and structures that support the students to develop mathematical understanding. The focus on making sense implies that the students themselves are doing the thinking, that is, it is not coming from adults who “spoon feed” them. When Ms. Gatto decides to interview her students about what they learned from her turn-and-talk sessions (in which partners discuss a mathematical strategy, make a prediction, or evaluate an answer to her problem), Berlyn, one of her students who struggled with attention, shows remarkable insight. He comments that talking with his classmates helps him get his ideas out, and they work out ideas together. He adds, “I think it keeps me focused.” The students described in this book, like Berlyn, are taking responsibility for their learning. It is only when students see themselves as learners can we “count them in,” as members of a mathematical learning community.

    Glossary and Resources


    Ableism is a term that refers to society's discrimination against people with disabilities, also known as physicalism, handicapism, and disability oppression.

    Useful Resources and References
    Griffin, P., Peters, M. L., Smith, R. M. (2007). Ableism curriculum design. In M.Adams, L. A.Bell, & P.Griffin (Eds.), Teaching for diversity and social justice (
    ed.). New York: Taylor & Francis.
    Hehir, T. (2005). Eliminating ableism in education. In L. I.Katzman (Ed.), Special education for a new century.Cambridge, MA: Harvard Educational Publishing Group.
    Abstract Thinking

    The American Heritage Stedman's Medical Dictionary (2002) defines abstract thinking as “thinking characterized by the ability to use concepts and to make and understand generalizations, such as of the properties or pattern shared by a variety of specific items or events.” In math, an example is generalizing about number patterns or properties of operations. Young children are often able to engage in abstract thinking earlier than was previously believed. However, children with certain disabilities, such as autism spectrum disorder, tend to have difficulty with abstract thinking.

    Useful Resources and References
    Abstract thinking. (2002). In American Heritage Stedman's medical dictionary.Boston: Houghton Mifflin Company.
    Seo, K. H., & Ginsburg, H. P. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. H.Clements, J.Sarama, & A. M.DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 91–104). Hillsdale, NJ: Lawrence Erlbaum.
    Steen, L. A. (1999). Twenty questions about mathematical reasoning. In L.Stiff (Ed.), Developing mathematical reasoning in Grades K–12 (pp. 270–285). Reston, VA: NCTM Yearbook.

    Accommodations are changes that teachers make in the way tasks are taught or the classroom environment is structured so that children with disabilities can learn along with their classmates.

    Useful Resources and References
    National Dissemination Center for Children with Disabilities (NICHCY) (
    National Center for Learning Disabilities (NCLD). (2006). Accommodations for students with LD. Retrieved from
    Asperger's Syndrome

    Asperger's syndrome is a developmental disability characterized by normal intelligence, motor clumsiness, unusual and intense interests, a limited ability to appreciate social nuances and develop friendships, impaired nonverbal communication such as facial expressions and body language, and strong preference for routine and consistency. The DSM-V (American Psychiatric Association, 2012) is now including Asperger's under autism spectrum disorders.

    Useful Resources and References
    National Institute of Neurological Disorders and Stroke (
    American Psychiatric Association. (2000). Diagnostic and statistical manual of mental disorders (DSM IV).Washington, DC: Author.
    Attwood, T. (2005). What is Asperger's syndrome? Retrieved from
    Attention Deficit Hyperactivity Disorder (ADHD)

    Attention deficit hyperactivity disorder is a neurological-based condition that is characterized by the following behaviors that occur over a period of time: distractability, short attention span, and impulsiveness. There are three subtypes: (1) predominantly hyperactive-impulsive, (2) predominantly inattentive, and (3) combined hyperactive-impulsive and inattentive. Most children have this combined type of ADHD.

    Useful Resources and References
    National Institute of Mental Health, U.S. Department of Health and Human Services (
    National Resource Center on ADHD (
    American Psychiatric Association (2000). Diagnostic and statistical manual of mental disorders (DSM IV).Washington, DC: Author.
    Flick, G. L. (2010). Managing ADHD in the K–8 classroom.Thousand Oaks, CA: Corwin.
    Autism Spectrum Disorder

    Autism spectrum disorder is a developmental disability that usually begins in infancy or early childhood. The characteristics include deficits in social responsiveness and interpersonal relationships, abnormal speech and language development, and repetitive or stereotyped behaviors. In addition, the children with autism often have atypical sensory responses, such as to certain sounds or textures. Each of these symptoms varies from mild to severe. They will present in each individual child differently.

    Useful Resources and References
    National Institute of Mental Health, U.S. Department of Health and Human Services (
    American Psychiatric Association (2000). Diagnostic and Statistical Manual of Mental Disorders (DSM IV).Washington, DC: Author. (See for proposed changes in the next edition.)
    Cognitive Flexibility

    Flexible cognition entails the ability to adapt to a variety of task demands, to consider and respond to multiple aspects of a task, and to consider multiple representations of an object or event.

    Useful Resources and References
    Deak, G. O. (2003). Flexible problem solving in children.Advances in child development and Behavior, 31, 271–326.
    Homer, B. D., & Hayward, E. O. (2008). Cognitive and representational development in children. In K. B.Cartwright (Ed.), Literacy processes: Cognitive flexibility in learning and teaching (pp. 19–41). New York: Guilford Press.
    Spiro, R., Feltovich, P., & Coulson., R. L. (2004). Cognitive flexibility theory. In Theory into practice database. Retrieved from
    Common Core State Standards Initiative

    As detailed on the website,, the Common Core State Standards Initiative is a state-led effort coordinated by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO). Teachers, school administrators, and experts collaborated on the development of the standards in English language arts and mathematics. “The K–5 standards in mathematics were designed to provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals—which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications” (para. 1).

    Useful Resources and References
    National Council of Teachers of Mathematics (
    Council for Exceptional Children (CEC). Common Core Standards: What special educators need to know. Retrieved from

    Tomlinson (2001) notes,

    Differentiation consists of the efforts of teachers to respond to variance among learners in the classroom. Whenever a teacher reaches out to an individual or small group to vary his or her teaching in order to create the best learning experience possible, that teacher is differentiating instruction. (para. 2)

    When planning for differentiation, teachers need to consider the classroom: environment, curriculum, assessment, instruction, and classroom management.

    Useful Resources and References
    Hall, T., Strongman, N., & Meyer, A. (2011). Differentiated instruction and implication for UDL. Retrieved from
    Tomlinson, C. A. (2001). Differentiation of instruction in the elementary grades. In ERIC Digest. Retrieved from

    Disproportionality is the “inappropriate overidentification or disproportionate representation by race and ethnicity of children as children with disabilities” (U.S. Department of Education, n.d., para. 2).

    Useful Resources and References
    The Civil Rights Project (
    U.S. Department of Education, Office of Special Education Programs (n.d.). Topic: Disproportionality. Retrieved from,root,dynamic,TopicalBrief,7,
    Executive Function

    The National Center for Learning Disabilities (2010) describes executive function as “a set of mental processes that helps connect past experience with present action. People use it to perform activities such as planning, organizing, strategizing, paying attention to and remembering details, and managing time and space” (para. 1).

    Useful Resources and References
    Meltzer, L. (Ed.). (2007). Executive function in education: From theory to practice.New York: Guilford Press.
    Council for Exceptional Children. (2008). Improving Executive Function Skills—An Innovative Strategy that May Enhance Learning for All Children. Retrieved from
    National Center for Learning Disabilities. (2010). What is executive function? Retrieved from
    Expressive Language Disability

    “Children with an expressive language disorder have problems using language to express what they are thinking or need” (Medline Plus, 2010, sec. 2, para. 3). These children may struggle with organizing their thoughts, constructing sentences, finding the right words when speaking, have limited vocabulary, and leave words out. Children who are learning a second language may struggle to express themselves because they are in the process of language acquisition. They are sometimes misdiagnosed as having an expressive language disability.

    Useful Resources and References
    American Speech-Language-Hearing Association ( National Clearinghouse for English Language Acquisition ( Medline Plus. (2010). Language disorder—children. Retrieved from
    Gradual Release of Responsibility

    The gradual release of responsibility model represents a gradual transition from teacher's modeling of problem-solving strategies, for example, to the student's responsibility for demonstrating and articulating the use of a particular strategy.

    Useful Resources and References
    Teaching Literacy in the Turning Points School (
    Fisher, D., & Frey, N. (2008). Better learning through structured teaching: A framework for the gradual release of responsibility.Alexandria, VA: Association of Supervision and Curriculum Development.
    Keene, E. O., & Zimmermann, S. (1997). Mosaic of thought: Teaching comprehension in a reader's workshop.Portsmouth, NH: Heinemann.
    Individualized Education Program (IEP)

    The Individualized Education Program (IEP) is the centerpiece of the Individuals with Disabilities Education Act (IDEA). It is a process that is intended to ensure educational opportunity for students with disabilities. The IEP is an agreement that guides and documents specially designed instruction for each student with a disability based on the student's unique academic, social, and behavioral needs.

    Useful Resources and References
    U.S. Department of Education (
    Christie, C. A. & Yell, M. L. (2010). Individualized education programs: Legal requirements and research findings.Exceptionality, 18(3), 109–123.
    Council for Exceptional Children. (2005). Council for Exceptional Children's initial summary of selected provisions from Part B Proposed Regulations for the Individuals With Disabilities Education Act.Arlington, VA: Author.
    Council for Exceptional Children. (2012). Federal outlook for exceptional children: Fiscal year 2012.Arlington, VA: Author.
    U.S. Department of Education, Office of Special Education and Rehabilitative Services, Thirty-five Years of Progress in Educating Children With Disabilities Through IDEA, Washington, D.C., 2010.
    Interactive Whiteboard

    An interactive whiteboard (e.g., SMART Board) consists of an LCD projector that projects a computer desktop onto an interactive board. The easiest way to envision the interactive whiteboard is that the board becomes the computer and it is controlled with the teacher's hands or an interactive pen that can write and highlight documents and presentations on the computer. It allows for teachers and students to interact with the software on their computers. Most interactive whiteboards supply supplemental software that enhances the board with many other options including rulers, protractors, charts, graphs, and so forth.

    Useful Resources and References
    National Clearinghouse for Educational Facilities (
    Least Restrictive Environment (LRE)

    A least restrictive environment means that a student who has a disability should have the opportunity to be educated with nondisabled peers in an inclusive setting, to the greatest extent appropriate. To determine what setting is appropriate for a student, a school team reviews the student's needs and interests.

    Useful Resources and References
    National Dissemination Center for Children With Disabilities ( Wrightslaw (
    Memory Difficulties

    Students with memory problems in mathematics tend to have problems with either short-term memory, the active process of storing and retaining information for a limited period of time, or working memory, the ability to hold on to pieces of information until the pieces blend into a full thought or concept (e.g., reading each word until the end of a sentence or paragraph and then understanding the full content). The impairment might be more predominant with auditory memory or visual memory or both. Deficits in long-term memory (information that has been stored and that is available over a long period of time) are less likely to come up with mathematics learning for young children.

    Useful Resources and References
    Learning Disabilities Association of America (
    Mercer, C. D., & Miller, S. P. (1997). Educational aspects of learning disabilities.Journal of Learning Disabilities, 30 (1), 46–56.
    Sliva, J. (2004). Teaching inclusive mathematics to special learners, K–6.Thousand Oaks, CA: Corwin.

    Metacognition refers to an individual's ability to have insight into one's own thinking and knowing, to monitor one's own learning, and make adjustments when necessary. These metacognitive processes help an individual make meaning, and select and revise cognitive tasks, goals, and strategies.

    Useful Resources and References
    Math VIDS: Video Instructional Development Source (
    Fisher, R. (1998). Thinking about thinking: Developing metacognition in children.Early Child Development and Care, 141, 1–15.
    Flavell, J. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental enquiry.American Psychologist, 34, 906–911.
    Hennessy, S. (1993). Situated cognition and cognitive apprenticeship: Implications for classroom learning.Studies in Science Education, 22, 1–41.
    Nonverbal Learning Disorder (NVLD)

    Nonverbal learning disorder (also called nonverbal learning disability and NVLD) is a particular type of learning disability. Individuals with this disability are highly verbal, with their areas of deficit being in the nonverbal domains. The four major categories of dysfunction that often present themselves include a combination of learning, academic, social, and emotional issues. These may include the following:

    • Motoric (both fine and gross motor)
    • Visual-spatial-organizational (involving recall and perception)
    • Social (difficulties in understanding nonverbal communication and social cues, and difficulties adjusting to new situations and transitions)
    • Abstract reasoning (difficulties with problem solving and understanding spatial concepts)
    Useful Resources and References
    National Center for Learning Disabilities (
    Pervasive Developmental Disorder (PDD)

    Pervasive developmental disorder refers to a group of disorders, also sometimes referred to as autism spectrum disorders, characterized by delays in the development of socialization and communication skills, often accompanied by difficulty with changes in routine or familiar surroundings, and repetitive body movements or behavior patterns. Autism is the most characteristic and best studied PDD. Other types of PDD include Asperger's syndrome, childhood disintegrative disorder, and Rett syndrome.

    Useful Resources and References
    National Institute of Neurological Disorders and Stroke (
    Matson, J., & Sturmey, P. (Eds.). (2011). International Handbook of Autism and Pervasive Developmental Disorders.New York: Springer.
    Post-Traumatic Stress Disorder (PTSD)

    “Post-traumatic stress disorder is a type of anxiety disorder. It can occur after one has seen or experienced a traumatic event that involved the threat of injury or death” (U.S. National Library of Medicine, n.d., para. 1).

    Useful Resources and References
    Jaycox, L. (2004). CBITS: Cognitive behavioral intervention for trauma in schools.Frederick, CO: Sopris West Educational Services.
    Rice, K. F., & Groves, B. (2005). Hope and healing: A caregiver's guide to helping young children affected by trauma.Washington, DC: Zero to Three Press.
    U.S. National Library of Medicine. (n.d.). Post-traumatic stress disorder. In PubMed Health. Retrieved from
    Response to Intervention (RTI)

    Response to intervention is an initiative that integrates assessment and intervention within a multitiered prevention system to maximize student achievement and to reduce behavioral problems. Schools use data to identify students at risk for poor learning outcomes, monitor student progress, provide evidence-based interventions, and adjust the type and level of the interventions depending on a student's responsiveness, and to identify students with learning disabilities or other disabilities.

    Useful Resources and References
    National Center on Response to Intervention ( Fuchs, D., Fuchs, L. S., & Stecker, P. M. (2010) The “blurring” of special education in a new continuum of general education placements and services.Exceptional Children, 76(3), 301–325.
    Searle, M. (2010). What every school leader needs to know about RTI.Alexandria, VA: ASCD.

    Self-monitoring is the ability to observe and keep track of one's own academic and social behavior.

    Useful Resources and References
    Hallahan, D. P., & Kaurmman, J. M. (2000). Exceptional learners: Introduction to special education (
    ed.). Boston: Allyn & Bacon.
    Rutherford, R. B., Quinn, M. M. & Mathur, S. R. (1996) Effective strategies for teaching appropriate behaviors to children with emotional/behavior disorders.Reston, VA: Council for Children With Behavioral Disorders.
    Vaughn, S.Bos, C. S., & Schumm, J. S. (2000). Teaching exceptional, diverse, and at-risk students in the general education classroom (
    ed.). Boston: Allyn & Bacon.

    Self-regulation is “an active, constructive process whereby learners set goals for their learning and then attempt to monitor, regulate, and control their cognition, motivation, and behavior, guided and constrained by their goals and the contextual features in the environment” (Pintrich, 2000, p. 453).

    Useful Resources and References
    Collins, G. (2008). Self-regulation as related to the transfer of learning from one setting to another.Discoveries (National Institute for Learning Development), 25(1), 12–13.
    Pintrich, P. R. (2000). The role of goal orientation in self-regulated learning. In M.Boekaerts, P. R.Pintrich, & M.Zeidner (Eds.), Handbook of self-regulation (pp. 451–502). San Diego: Academic Press.
    Schunk, D. H. (2005) Commentary on self-regulation in school contexts.Learning and Instruction, 15, 173–177.
    Zimmerman, B. J. (2008). Investigating self-regulation and motivation: Historical background, methodological developments, and future prospects.American Educational Research Journal, 45(1), 166–183.
    Zimmerman, B. J., & Campillo, M. (2003). Motivating self-regulated problem solvers. In J. E.Davidson & R. J.Sternberg (Eds.), The nature of problem solving (pp. 233–262). New York: Cambridge University Press.
    Universal Design for Learning (UDL)

    Universal design for learning is a set of principles for curriculum development and teaching that give all individuals equal opportunities to learn. UDL provides a plan for developing instructional goals, methods, materials, and assessments that work for everyone—not a single, one-size-fits-all solution, but rather, flexible approaches that can be individualized. The UDL guidelines are organized according to the three main principles of UDL that address (1) representation, (2) expression, and (3) engagement.

    Useful Resources and References
    Center for Applied Special Technology (CAST) (
    National Center for Universal Design for Learning (
    Rose, D. H., & Meyer, A. (Eds.). (2006). A practical reader in universal design for learning.Cambridge, MA: Harvard Education Press.


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    CORWIN: A SAGE Company

    The Corwin logo—a raven striding across an open book—represents the union of courage and learning. Corwin is committed to improving education for all learners by publishing books and other professional development resources for those serving the field of PreK–12 education. By providing practical, hands-on materials, Corwin continues to carry out the promise of its motto: “Helping Educators Do Their Work Better.”

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