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Mathematics
Glossary

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Absent curriculum: the curricular emphases that, for whatever reason, are not actually included in the school program.
Academic content mastery: the curricula in special education settings that is designed to parallel the primary content emphases taught in the general curriculum.
Access to the general curriculum: the opportunity and extent to which children with disabilities participate with students who are not disabled in the general education program.
Accommodations: adaptations that include changes in teaching strategies and student response processes related to teaching and learning (i.e., extended testing time, assistive technology). Accommodations do not include changes in standards, task content, or test items.
Acquisition: the initial stage of learning in which students acquire behaviors or skills that subsequently will need to be enhanced and maintained.
Action planning: a procedure used to develop a long-term strategy for the accomplishment of desired goals. Action planning involves the identification of goals as well as an analysis of the tasks or steps required to achieve the long-term goal.
Adaptations: a generic term that encompasses both accommodations and modifications. Both curricular and instructional adaptations may be used in their classroom according to their perceived acceptability by teachers.
Age appropriate: the design of instructional programs to be consistent with the chronological age of the students participating in the program (e.g., age appropriate arts programs, social skills training).
Alphabetic principle: the principle that written spellings represent spoken words.
Analytic rubrics: assessment guidelines that outline the specific criteria necessary to determine the level of an individual student's performance.
Annual goals: a requirement within IEPs in which yearly progress is projected in terms of learned skills or behaviors.
Apprenticeship programs: initiatives that place 11th- or 12th-grade students in work opportunities to develop specific skills related to a chosen career direction, such as a specific trade.
Arithmetic: a subcategory of mathematics that includes the study of number, concepts, and basic operations. Arithmetic is the foundation of elementary-level mathematics programs.
Assistive technology(AT): assistive technology includes learning accommodations that range from low-tech applications (e.g., tape player) to high-tech ones (e.g., FM systems for helping students concentrate on what is being said).
Augumentation: an approach to teaching life skills courses by augmenting existing classes to cover specific topics within meaningful, life-related domains.
Augumentative or Alternate communication (AAC): non-verbal language systems to facilitate enhanced communication by persons with disabilities (e.g., communication board, voice synthesizer).
Babbling: the child's use of consonant-vowel (CV) syllables.
Basal reading programs: commercially developed, grade-level-matched reading materials that serve as the core instructional program for most elementary-level reading curricula.
Basic skills: a curricular emphasis that focuses on the remediation of reading, mathematics, and/or writing skills.
Behavioral intervention plans (BIPs): a requirement under IDEA to develop written plans to address significant behavioral problems experienced by students with disabilities.
Block scheduling: an alternative approach to daily schedules in which larger time blocks are set aside for specific academic subjects.
Chaining: the instructional strategy that uses reinforcement to promote the acquisition of multiple, related behaviors (e.g., getting dressed).
Cherology: in sign language, the analogue to phonology in oral language, consisting of hand shape, location, movement, palm orientation (cf., manner, place, and voicing in phonology).
Classroom discourse: the language used for teaching and learning.
Classroom survival skills: the identification of specific skills within the general education classroom that are necessary for student success. Inventories of survival skills provide a basis for instructional planning.
Cohesive markers: linguistic devices that help listeners or readers understand how a story is tied together.
Collaboration: a team-oriented approach in which general and special educators work together to design and implement instructional programs for students with special needs, as well as programs for other students.
Collaborative teaching: see cooperative teaching.
Communication: sending and receiving ideas, feelings, thoughts, emotions, or information.
Comprehension monitoring: the strategies that help students think about how well they are understanding what they are reading and how they can address any reading problems they are having.
Comprehensive curriculum: a generic term which refers to the importance of designing programs for students with disabilities that incorporates information that is relevant at the current time and also meaningful in terms of eventual adult outcomes.
Constructivist approach: a teaching approach that incorporates instruction into meaningful activities, provides for self-regulated learning, demonstrates instructional responsiveness, and establishes learning communities in classrooms.
Consultation: a model of collaboration based on the assumption that the consultant has certain areas of expertise to be shared with the recipient (e.g., general education teacher).
Content enhancement: strategies to increase comprehension and tactics for retaining information over time. These strategies support the student in using existing material, particularly when the student is in a general education setting.
Contextual analysis: the identification of an unknown word based on its use in a sentence or passage. Contextual analysis utilizes a system of syntactic and semantic cueing.
Continuous reinforcement schedule: providing positive reinforcement subsequent to each occurrence of a specific behavior.
Conversational discourse: the language used for social interaction.
Cooperative learning: a learning arrangement in which students work together to achieve certain academic and behavioral skills.
Cooperative teaching: a team-based approach in which general and special educators share responsibilities for instructing classrooms that include students with and without disabilities. There are numerous models for implementing a cooperative teaching approach.
COPS: an error-monitoring strategy in writing for the organization of revising and editing activities. The strategy includes the following considerations: Capitalization, Overall appearance, Punctuation, and Spelling.
Corrective Mathematics: a commercial approach that uses direct instructional strategies to teach arithmetic and other mathematical skills to students.
Creative dramatics: a curricular emphasis in which students are given the opportunity to practice expressing the emotions and activities that are necessary for functioning within the world in general.
Criterion-referenced tests: the assessment of skills in terms of absolute levels of mastery rather than in comparison to a normative sample.
Curriculum-based assessment (CBA): this approach ties the collection of assessment data directly to the curricular content to be taught. It provides a basis for ongoing measurement and detects student progress in a way that enables teachers to modify curriculum and instruction.
Customized approaches: in science or social studies, instructional strategies that are designed by individual teachers to blend selected features of other programs and design a specialized approach for a given group of students.
Decoding-based programs: a skills-based, "bottom-up" program for reading characterized by the direct teaching of a sequence of skills that begins with an emphasis on the phonological basis of language and provides a foundation for the subsequent transfer of skills to actual reading.
Demands of adulthood: an orientation to curriculum design that uses adult outcomes as a basis for the development of programs for students of school age. An example is the program developed by Cronin and Patton (1993).
Differential reinforcement (DR): behavior change approaches based on reinforcement, for example, as tied to low rate (DRL), incompatible behaviors (DRI), alternative behaviors (DRA), or non-occurrence (DRO).
Differentiated instruction: strategies designed to adapt instruction in the general education classroom for students with variant learning needs.
Direct instruction: a widely used systematic instructional method which involves explaining, teaching, modeling, and practicing a skill as well as giving feedback on skill performance.
Directed reading thinking activity (DRTA): an approach commonly used in basal reading programs and by reading teachers in general to enable students to predict what they are about to read, read the material, and respond to questions. The approach focuses on a before/after strategy to reading comprehension.
Double deficit hypothesis: a hypothesis that focuses on an assumption of a core deficit experienced by readers with disabilities in the area of phonological processing in conjunction with problems related to naming speed.
Dramatic discourse: the language used in acting out scenes, stories, or plays, including scene (set), lighting, timing, physical appearance of the characters, and the pragmatics used by the characters.
Effective listening: the ability to receive information, apply meaning, and provide evidence of understanding what was heard.
Elaborated dialogue: an interactive dialogue between students and teachers that provides explicit modeling of strategies, critical evaluation of responses, questioning of students, and elaboration responses by students.
Embedding: combining two or more clauses into one to express more complex relationships.
Empowerment: a multifaceted concept, which involves the ability to earn respect and dignity. The ability to be self-determined is central to empowerment.
Explicit curriculum: the formal and stated curriculum that teachers and students are expected to follow.
Expository discourse: the language used for exposition, including description, explanation, and persuasion (also called argumentation).
Extinction: withdrawing and withholding reinforcement that was previously sustaining a behavior, leading to eventual reduction and elimination.
Fernald multisensory approach: a multisensory (VAKT) instructional strategy for students who have difficulty in reading, spelling, and writing.
Free, appropriate public education: school districts must provide special education and related services at no cost in order to ensure an appropriate education for students with disabilities.
Free-form drawing: the process of creating pictures to expand a student's imagination as well as promote the student's attention to detail and opportunities for social interaction.
Functional behavioral assessment (FBA): an assessment strategy to identify the functions or purpose of specific behaviors by placing them in the context of antecedent and consequent events.
Functional reading: a level of literacy necessary for information and protection, which subsequently allows an individual to derive meaning from, and use, job applications, newspaper advertisements, job instruction manuals, telephone books, and other sources.
Generalization: the learning stage categorized by the application of learned skills or behaviors to, for example, new environments and/or new skills and behaviors.
Goal planning: the process of identifying the steps needed to achieve particular goals.
Goal setting: the skill to determine the tasks or events that must be accomplished for certain outcomes to be obtained.
Graphic aids: materials such as charts, graphs, maps, models, pictures, or photographs that can be an effective tool to facilitate learning.
Graphic organizers: visual formats or structures that help students organize information for better comprehension. Examples include central story problem, story maps, and semantic mapping.
Hidden curriculum: important curricular considerations that are not explicitly stated and/or addressed (e.g., study skills).
High-incidence disabilities: a term that refers to students historically described as having mild disabilities. Unlike the term "mild," high incidence does not understate the need for specialized instruction.
Holistic approach: another term for a whole language program that focuses on the meaningfulness of language, stresses the importance of the child's language as a bridge to literacy, and includes speaking, listening, and, expressive writing as integral parts of literacy development.
Holistic rubrics: an assessment strategy that requires the teacher to assess and rate the overall quality of a student's work, such as by classifying it as outstanding, above average, acceptable, below average, or unacceptable.
Horizontal transitions: a concept that refers to the process through which students with special needs move from more restrictive to less restrictive settings (e.g., from self-contained classrooms to inclusive classrooms).
Hoyle gripper: a three-sided plastic device that requires the child to place two fingers and the thumb in the proper position to facilitate grip for pencils and other utensils.
Iconic word: a word whose form suggests its meaning (e.g., "blob").
Inclusive classrooms: general education classes in which students with disabilities and students who are not disabled study and learn together with the support of special education teachers, paraeducators, and/or others.
Individual educational program (IEP): a written document summarizing a student's learning program that is required for every student who qualifies for special education services. The major purposes of an IEP are to establish learning goals for an individual child, to determine services the school district must provide to meet those learning goals, and to enhance communication among parents and other professionals about a student's program.
Individualized transition planning (ITP): a statement of needed transition services is required beginning at age 14. Transition services are defined as a coordinated set of activities for a student, designed within an outcome-oriented process, which promotes movement from school to postschool activities including postsecondary education, vocational training, integrated employment, continuing and adult education, adult services, independent living, and/or community participation.
Individuals with Disabilities Education Act (IDEA): the 1997 update to the original Education for All Handicapped Children Act, which authorized funding to the states to assist in the development, expansion, and improvement of special education programs. The law includes the key provisions of free and appropriate public education, appropriate evaluation, individual educational programs, least restrictive environment, parent and student decision-making, and procedural safeguards.
Informal reading inventory (IRI): a common instrument to assess reading skills, which may contain a word-recognition inventory, oral reading passages, silent reading passages, and comprehension questions to accompany the passages.
Infusion approach: an effort to infuse life-related skills into academic subjects in order to make the instruction more career-relevant.
Inquiry approach: frequently used in science and social studies, this approach has a discovery orientation in which students seek to learn important concepts by exploring through experimentation and research.
Inquiry skills: in science, specific inquiry skills include observation, measurement, classification, data collection, prediction, data intrepretation, hypothsis formalation, and experimentation.
Integration: as a concept in special education, integration refers to the physical placement of students with disabilities in general education classrooms. The concept historically has not included focused attention on the provision of supports to enable these individuals to be successful.
Interactive unit: an approach to teaching mathematics developed by Cawley in which instructional options are outlined in a matrix that includes four teacher outputs (do, present, say, graphically symbolize) and four student response options (do, identify, say, and graphically represent).
Intermittent reinforcement schedules: non-continuous schedules that may be fixed or variable and may be designed on a ratio, interval, or duration basis.
Invented spellings: a component of some whole language programs, in which students initially write without concern for spelling accuracy.
Joint attending: adult and child jointly looking at an object or toy while the adult talks about it.
Joint referencing: adult and child pointing to an object or toy while the adult talks about it.
Language: an abstract, arbitrary, and rule-governed set of symbols.
Language experience approach (LEA): an approach that combines attention to listening, speaking, reading, and writing in order to establish a link between oral and written expression.. The process involves student dictation of stories that teachers transcribe for subsequent reading and revision.
Learning strategies: a cognitive orientation to learning, which provides students with a method for using their own abilities and knowledge to acquire, organize, and integrate new information.
Life Centered Career Education (LCCE): a program developed by Brolin that includes attention to 22 adult-relevant competencies, which are then divided into 97 sub- competencies. It also includes an assessment measure to accompany the program.
Life skills: specific skills that have adult relevance that can be incorporated into school curricula in order to prepare students for success in post-school environments.
Literate household: homes in which literate language and print are routine; these homes contain numerous printed materials and tools to create print (pens, pencils, computer), and provide opportunities for their children to interact with them.
Logical consequences: strategies that relate specific behavior management responses directly to the outcomes of the inappropriate behavior.
Look, Cover, Write, Check: a word-study method that involves looking at a word, saying the word, and then covering and writing the word before checking for accuracy.
Maintenance: the learning stage concerned with retention and accurate recall.
Mathematics: curricular area that involves quantities, relationships, and reasoning, in domains including arithmetic, geometry, algebra, and calculus.
Metacognitive ability: the ability to reflect on and manage one's own thinking and learning.
Metacognition: a set of skills that allow students to monitor their own behavior, and specifically to direct their own behavior in order to increase time spent on learning.
Metalinguistic ability: the ability to talk about language and its parts and to separate literal from figurative usages.
Metapragmatic ability: the ability to reflect on and manage the varying aspects of engaging in discourse in different settings.
Mild disabilities: a term referring commonly to students with learning disabilities, mild mental retardation, and emotional and behavioral disorders. The term understates the learning needs of these students and thus inadvertently may be used to question their need for specialized instruction.
Mixed script: the mixing of cursive and manuscript writing, which simplifies the task of learning letter forms and eliminates the need for transition from manuscript to cursive writing.
Modifications: changes in content or standards, which involves adjustments to content and tasks rather than instructional delivery (i.e., substitution of study of culture for a language requirement).
Morphology: the study of meaning units (i.e., morphemes) in words.
Narrative discourse: the language used in stories, including setting, character information, temporal order, causal relationships, and episode structure.
Natural consequences: a strategy in which a parent or teacher does not intervene in a particular situation but rather allows the natural consequences that follow from the situation to provide a learning opportunity for the child.
No Child Left Behind Act: an act passed in 2001 which, among other things, provided students with disabilities recognition as an important component of the school population and thus subject to the opportunities and accountability inherent in the act.
Norm-referenced tests: tests that attempt to compare student scores to other students and thus typically separate results into a distribution of scores.
Note-taking/outlining: the documentation of major ideas and relevant topics for later use to classify and organize information.
Organizational strategies: the methods children use to organize time, work setting, and tasks for learning.
Paraeducators: also referred to as paraprofessionals or teacher assistants, these persons frequently are key individuals in successful inclusion programs.
Peer assisted learning strategies (PALS): a strategy in which beginning readers are assisted in learning through paired instruction. Each member of the pair takes turns serving as a coach and a reader with the first coach being the reader at a higher achievement level who listens to, comments on, and reinforces the other student before the roles are reversed.
Peer-mediated strategies: a strategy in which the focus is on activities in which students with learning-related problems work collaboratively with their fellow students. Examples include peer tutoring and collaborative learning.
Peer tutoring: the pairing of two students for learning opportunities in a particular behavioral or academic area.
Personalized grading plans (PGP): a grading model with a series of steps including collaborative meetings with parents to discuss the purpose of grades, review the grading policies, implement the PGP, and evaluate the perceptions of the model and grades a student earns.
Phonetic analysis: a skill that allows students to decode unknown words using learned sound-symbol correspondences. Phonetic analysis builds on phonological awareness as students learn to apply the phonological system to the written word.
Phonological awareness: a set of skills related to success in decoding and the development of reading ability. Phonological awareness includes the following skills: discriminate between words and sounds, identify sounds within words, manipulate sounds in words, identify phonemes, and isolate sounds in words (in initial, medial, and final positions).
Phonology: the study of the sound system in a language and the basis for determining the correspondence between sounds and their graphic representation (i.e., letters).
Poetic discourse: the language of poetry, including choice and arrangement of language forms, rhythm, and sound.
Portfolio: a type of assessment that involves the evaluation and comparison of, for example, writing samples over time.
Positive reinforcement: a strategy for increasing the occurrence of the behavior or developing a learned skill by providing a positive reinforcer after its occurrence.
Postwriting stage: the final phase of the writing process that involves editing the craft aspects of writing as well as revising content. The goal of postwriting is to improve the written product.
Pragmatics: the rules governing how language is used (i.e., when, where, and under what circumstances).
Premack principle: the basis of contingency contract, the principle establishes an if-then proposition, thus making reinforcement contingent on performance of a particular behavior.
Presuppositions: assumptions the speaker makes about what the listener already knows about the topic at hand.
Prewriting: the first component in the writing process that involves planning and organizing. Activities that might encompass the prewriting component include reading, listening, and developing motivation and purpose to write.
Problem-centered collaboration: an approach to collaboration based on a systematic analysis of a challenging classroom (or student) situation and the identification and implementation of strategies for solving it.
Procedural facilitators: processes which allow students to think and talk to themselves about the writing process, and thus bridge the gap between oral and written language and enhance the writing process.
Process approach to writing: an instructional strategy for writing that stresses the meaning of the writing first and later introduces skills related to the components of written expression.
Proficiency: the learning stage concerned with accuracy and fluency.
Project MATH: developed by Cauley, this classic program provided an important foundation for transforming mathematics instruction for students with special needs from rote learning to conceptualization and understanding.
PURPOSE: a direct instructional approach that contains seven steps on which lesson plans can be composed.
RAP: a paraphrasing strategy that incorporates the following steps: Read a paragraph, Ask yourself what the main ideas and details in the paragraph were, and Put the main idea and details into your own words.
Reading rate: the rate at which one reads, which may include skimming, scanning, rapid reading, and careful, study-type reading.
Reasoning: in mathematics, the underlying ability that enables students to be successful at problem solving.
Recipical teaching: strategies used in various curricula areas, most notably in reading, in which teachers and students take turns asking each other questions that relate to, for example, predicting, summarizing, and explaining what has been read.
Repeated readings: an approach also known as multiple oral readings that is based on the assumption that limiting the number of possible responses results in an increased probability of accuracy.
Report writing: the various skills necessary to organize and present ideas on paper in a meaningful and appropriate way. These skills include topic selection, note-taking, organization of ideas, outlining, spelling and punctuation, and sentence structure.
ReQuest: a process of reading and reciprocal questioning between students and teachers. Students learn to model teacher questions while teachers provide feedback as the learner explores the meaning of reading material.
Resource programs: one of the options within the continuum of services in which students are "pulled out" of the general education classroom for small group instruction for a specified of time and for a specified academic subject.
Response cost: a punishment strategy in which performance of an inappropriate behavior results in the loss of something deemed desirable by the student (e.g., loss of a token for inappropriate classroom behavior).
Scaffolding: mediation (usually by a teacher) of the student's language and/or learning process to support the student in developing a new skill or enhancing proficiency. The concept was adopted from the image of a scaffold in building construction.
School-wide management systems: efforts to establish behavior change programs across classrooms in order to set up a consistent strategy for enhancing student behavior.
Self-correction strategies: students learn to correct specific errors immediately after being assessed (e.g., letter-by-letter proofreading in spelling).
Self-determination: a central concept of empowerment, which involves students' ability to make choices, become advocates for themselves, and exercise control over their lives. It refers to an individual's awareness of personal strengths and weaknesses, and the ability to interact with others in a socially competent manner.
Self-management: a set of procedures used to regulate or guide a person's behavior so that goals can be accomplished. Examples of self-management include self-instruction and self-monitoring.
Self-monitoring: a sub-skill of self-management which involves an individual's development of the skills to monitor their attention or performance.
Semantic mapping: a strategy to aid in reading comprehension based on the development of maps or webs to organize information.
Semantics: the study of how meaning is expressed within a language.
Sentence combining: a step in sentence development that expands simple sentences into more complex ones, and that can be an effective way to increase syntactic maturity and improve the overall quality of writing.
Shaping: a strategy in which successive approximations toward the specific academic or behavioral goal are reinforced. It requires the shifting of the performance criterion to reinforce gradual increments in performance.
Sight words: a whole word approach through which students learn to automatically recognize important, high-frequency words without decoding.
Social competence: a person's overall ability to achieve his or her goals and desires in the personal and social aspects of life.
Social problem solving: the sequence of behaviors that are developed to ameliorate a particular social interaction problem.
Social skills: the complex ability both to emit behaviors which are reinforced and not to emit behaviors that are punished or extinguished by others. These behaviors may include overt behaviors (e.g., turn-taking) and covert behaviors (e.g., ability to empathize with another person and discriminate social cues).
Speech: the use of oral motor articulators to express the forms, content, and uses of language.
SQ3R: a systematic approach to improve reading comprehension through study skills, which includes the following steps: Survey, Question, Read, Recite, and Review.
Standards-based education: the development and implementation of curriculum based on federal and state standards for school achievement and the assessment of student success via high-stakes testing.
Story grammar strategy: a method that facilitates story writing in which students learn to focus on a series of specific story elements: setting of the story, main and supporting characters, identification of the problem and plan to solve it, and the ending or resolution.
Structural analysis: students use larger segments of words for decoding cues. The recognition of root words, compound words, prefixes, suffixes, contractions, and plurals allow students to use clusters of words for reading a new word.
Student-directed learning: the type of learning through which students become independent learners and subsequently become able to direct their own behavior in ways that assist in maximizing learning.
Student-directed questioning: approaches that are based on the development of a student's ability to read, pose a question to him/herself, answer the question, and continue reading as a basis for enhanced understanding (e.g., metacomprehension).
Subsequent environments: the future school, work, and/or community environment of a student. Special education is intended to be outcomes-focused toward students' successful transitions to these future environments.
Supported education: an alternative term to inclusive education in which the emphasis is on the assurance that appropriate supports are in place to promote the success of students with disabilities in general education.
Syntax: the study of grammar, or structure, within a language.
Task analysis: an assessment approach in which the specific task to be learned is broken down into its component steps as a basis for instruction to acquire the sub-skills within the task.
Teacher assistance teams (TAT): a common, generic term used to refer to child study teams that operate on a prereferral basis to identify the needs of students in general education classrooms, develop strategies, and monitor progress, prior to the consideration of comprehensive assessment procedures and possible eligibility for special education.
Teacher-directed questioning: approaches (such as DRTA) that rely on teachers to work with students in establishing a foundation for what they are about to read, predicting what they will learn, and reviewing what has been read.
Text generation: the transfer of ideas into representation in language, which is commonly referred to as written expression.
Time management: the process of using time effectively to complete daily assignments and carry out responsibilities. It includes allocating time and organizing the environment.
Time out: a strategy in which a form of punishment is used by requiring students to receive time out from positive reinforcement (e.g., removal to a non-reinforcing location in the classroom).
Token economy: a strategy in which tokens are used as representation of positive reinforcers to structure a learning and/or living environment to promote the development of appropriate behaviors and important skills.
TOWER: a structure for completing initial and final drafts of written reports. It includes the following steps: Think, Order ideas, Write, Edit, and Rewrite.
Transcription: the translation of language representations most commonly via handwriting (or keyboarding) and spelling.
Transition Planning Inventory: an assessment tool for adolescents and young adults that focuses on adult-relevant domains.
Turn-taking: taking turns in conversational interactions.
Unison reading: an approach in which students read along with teachers (usually with a brief delay) in order to increase fluency. The approach has often been referred to as the neurological impress method.
Unit teaching: an approach based on integrating academic instruction around and within thematic units that serve as the organizing principle for the curriculum.
Universal design for learning (UDL): a basis for conceptualizing access to the general curriculum, in which curricular goals contain adequate challenge and materials and methods are flexible, challenging, and provide supports. The concept of UDL is adopted from the architectural term and serves as the basis for the inclusion of persons with disabilities in varied living and learning environments.
Vertical transitions: transitions that are based on chronological age and reflect the process of moving, for example, from preschool programs into primary grades programs or from high school into postsecondary environments.
Whole language: a holistic approach that focuses on the meaningfulness of language, stresses the importance of language as a bridge to literacy, and includes speaking, listening, and expressive writing as integral parts of literacy development.
Writing stage: the translation of thoughts into written words that involves the two processes of text generation and transcription.

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