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Math Methodology:
Instruction: Addressing Needs of Students with Math Difficulties

Sources of Math Difficulties

Students can experience math difficulties for a variety of reasons.  Teachers need to be able to identify the source of the problem.  Difficulties might stem from the nature of instruction itself, if for example the teacher relies too heavily on rote memorization or if instruction is different from that experienced in prior years.  The curricular materials themselves might not be spiraled to build conceptual understanding over time, or the content might not be appropriate for the student's ability level or experiences.  Words that have special meaning in math might confuse them.  Students might not have a growth mindset and believe their ability to learn math is not in their control.  They might not have developed adequate thinking skills to help them remember and recall previous learning.  They might be easily distracted and unable to focus on tasks with several steps and procedures.  Students might also have a learning disability, which is a life-long condition that manifests itself "by significant difficulties in acquisition and use of listening, speaking, reading, writing, reasoning, or mathematical abilities, or of social skills" (Kenyon, 2000, Definition section).

According to Brodesky, Parker, Murray, and Katzman, students' success in mathematics will depend on their strengths and needs related to cognitive processing, language, visual-spatial processing, organization, memory, attention, psycho-social, and fine-motor skills (2002). For elementary and middle schools, Gersten, Beckmann, Clarke, Foegen, Marsh, Star, and Witzel (2009) recommended that all students be screened to identify those at risk for potential mathematics difficulties and that interventions be provided to students identified as at risk (p. 6).

Parents also can become aware of signs indicating potential trouble with math.  Some problems result from physical, cognitive, sensory, and learning disabilities in general, which have been diagnosed by professional staff and relayed to the teacher so that appropriate accommodations and/or assistive technologies can be used. Other problems might not have been diagnosed and the teacher observes those after working with students for a period of time.

Teachers might be alerted to potential math or learning disabilities from the following examples provided by Rochelle Kenyon (2000) and at Misunderstood Minds where you can also experience the difficulties yourself with the examples provided:

• Inability to recall basic number facts, or easily forgetting rules, procedures, formulas, or where they are or what they are doing when solving problems.

• Computational weaknesses. These might also arise because students are not writing numerals clearly, are misreading operation signs in a problem. They might be writing numbers backwards. They might have difficulty keeping score in a game.

• Inability to connect abstract or conceptual representations with concrete representations or reality.

• Inability to make connections of math to real life experiences. For example, they might know a number but not see its relation to an actual quantity. They might have difficulty telling time.

• Difficulty with the language, such as with math terms that do not fit their everyday language, or following directions, or reading the math textbook.

• Difficulty comprehending the visual-spatial and perceptual aspects of math (e.g., perceptions of changes when objects are moved from one place to another, or working with 2-D representations of 3-D geometric objects).

• Problems with organization, such as when working with multi-step problems, identifying relevant information in word problems, losing sight of the final goal in problem solving, appreciating the reasonableness of a solution, inability to copy problems correctly, or overload when too many problems are presented at one time on a page to solve. (Kenyon, 2000)

Silver, Strong, and Perini, authors of The strategic teacher: Selecting the right research-based strategy for every lesson (2007), indicated lack of attention to learning styles (mastery, understanding, interpersonal, and self-expressive) also may lead to math difficulties, and these might be overcome by varying and using multiple instructional strategies. Mastery learners like drills, lectures, demonstrations, and practice. They "may experience difficulty when learning becomes too abstract or involves open-ended questions." Understanding learners appreciate logic, debate, and inquiry and value research projects and independent study and reading. They "may experience difficulty when there is a focus on the social environment of the classroom (e.g., cooperative learning)." Interpersonal learners would value the social environment with cooperative learning, group experiences, discussion, and role playing and may experience difficulty with "independent seat work or when learning lacks real world application."  Finally, self-expressive learners like creativity, "open-ended and nonroutine problems" and examining what ifs. For them, difficulties may arise with "drill and practice and rote problem solving" (Part One: Introduction section, Figure C). The key here is to strike a balance in a selecting instructional strategies, as students can work in all four styles.

Dyscalculia is the term applied to learning disabilities involving math.  Visual-spatial difficulties and language processing difficulties are major areas contributing to dyscalculia.  A math learning disability varies among those who have it and affects people differently at different stages of life.  Common characteristics include difficulty with counting, learning number facts, doing math calculations, measurements, telling time, counting money, estimating, mental math, and problem solving (Cortiella & Horowitz, 2014).

Consider the following books:

 

 

 

 

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Prevention and Intervention Principles

 

Lynn Fuchs and Douglas Fuchs (2001) said that prevention of math difficulties in this country is generally ineffective for all students, including the learning disabled (p. 85). Part of the problem might lie with textbooks used, which form the basis for the majority of instruction that takes place in classrooms. Texts might not adhere to important instructional principles that affect learning. For example, those principles include: “providing clear objectives, teaching 1 new concept or skill at a time, reviewing background knowledge, providing explicit explanations, structuring the use of instructional time efficiently, providing adequate practice, structuring appropriate review, and organizing effective feedback” (p. 85).

However, there is research on intervention providing evidence of methods to prevent and treat math difficulties. Fuchs and Fuchs (2001) discussed Principles for the Prevention and Intervention of Mathematics Difficulties at three levels. In essence, primary prevention focuses on universal design; secondary prevention (i.e., prereferral intervention) focuses on adaptations within the regular classroom; and tertiary prevention (i.e., intervention) focuses on highly individualized intensive and explicit contextualization of skill-based instruction.

According to the National Mathematics Advisory Panel (2008):

Explicit systematic instruction typically entails teachers explaining and demonstrating specific strategies and allowing students many opportunities to ask and answer questions and to think aloud about the decisions they make while solving problems. It also entails careful sequencing of problems by the teacher or through instructional materials to highlight critical features. (p. 48)

After its review of 26 high-quality studies related to teaching low achieving students and students with learning disabilities, mostly using randomized control designs, the National Mathematics Advisory Panel (2008) concluded that explicit methods of instruction are effective with both groups of students. In particular, "Explicit systematic instruction was found to improve the performance of students with learning disabilities in computation, solving word problems, and solving problems that require the application of mathematics to novel situations" (p. 48). Although the Panel recommended some explicit systematic instruction, "This kind of instruction should not comprise all the mathematics instruction these students receive" (p. 49).

Primary Prevention

Universal Design for Learning from CAST calls for students to have multiple means of expression, representation, and engagement in their learning. Instructional media should provide those elements and have scaffolds built in (Deubel, 2003). Within a universal design framework, Fuchs and Fuchs (2001, pp. 86-87) presented four principles of primary prevention that can be used with all students, including learning disabled:

1. Quick pace with varied instructional activities and high levels of engagement. Students benefit from active involvement (e.g., discussing, writing, computing, problem solving) within “a greater range of grouping arrangements” for carrying out activities.
2. Challenging standards for achievement. Motivating statements convey high expectations that everyone will learn, and convey more than just trying to convince students that activities will be fun and interesting.
3. Self-verbalization methods. Self-verbalization strategies for approaching and solving problems benefit students with learning disabilities, and low-, average-, and high-performing students. For example, problem solving performance has been shown to improve by memorizing and verbalizing seven cognitive steps: “read the problem, paraphrase, visualize with a picture or diagram, hypothesize a plan to solve the problem, estimate the answer, compute, and check” (p. 87).
4. Physical and visual representations of number concepts or problem-solving situations. The physical and visual representations help build conceptual understanding, facilitate application of procedural knowledge, and long term retention of procedural competence.

Secondary Prevention

There are three principles for secondary prevention of math difficulties within the classroom: adaptations cannot be disruptive to the target learner, must be unobtrusive for others in the class, and must be feasible for the teacher to implement within the normal classroom routine. At this stage, the teacher might benefit from additional structure and instructional strategies from special educators, school psychologists, collaboration with fellow teachers, or student-support groups (Fuchs & Fuchs, 2001). However, Lynn Fuchs (2008) indicated that six instructional principles must be incorporated at the secondary prevention level of a multi-tier prevention system:

1. Instructional explicitness
2. Instructional design that eases the learning challenge (e.g., via "precise explanations and with the use of carefully sequenced and integrated instruction," beginning with "teaching a set of foundational skills the student can apply across the entire program."
3. A strong conceptual basis for procedures that are taught
4. An emphasis on drill and practice
5. Cumulative review as part of drill and practice
6. Motivators to help students regulate their attention and behavior and to work hard. (para. 1, 4, 5)

Per the National Center on Intensive Intervention (2016), any implementation of explicit, systematic instruction should include six components: an advance organizer (i.e., lesson objective and its relevance to everyday life), assessment of background knowledge (i.e., prerequisite skills needed to be successful with the new concept), modeling, guided practice with the bulk of instruction occurring here, independent practice, and maintenance.  Maintenance involves distributed practice assessments on a specific skill, strategy, or concept at regularly scheduled intervals, and may include cumulative practice (pp. 3-4).

Secondary prevention strategies that might work at this level include goal setting, self-monitoring of task completion and work quality, computer-assisted instruction, concrete representations of numbers and number concepts, and reinforcement. However, unresponsive students might yet need the tertiary level of intervention (Fuchs & Fuchs, 2001).

Tertiary Prevention

Primary and secondary preventions have not been successful for the group of students needing tertiary prevention. This level, also known as intervention, is typically performed by special educators who employ a broader range of instructional strategies that might not be feasible within a regular classroom setting. Intervention is characterized by three principles (Fuchs & Fuchs, 2001, pp. 91-93):

1. A focus on the individual student as the unit of instructional decision making. Constructivist influences are found in instructional practices. When focusing on the individual student (individually referenced decision making), teachers do not prejudge the efficacy of a particular instructional method. Judgment can only be made after trying a method to see if it does or does not work for a learner.
2. Intensive instructional delivery. Intensive instruction includes, but is not limited to, one-to-one tutoring. Group lessons can also involve intensive instruction. Representative of a broader set of instructional features are “(1) high rates of active responding at appropriate levels, (2) careful matching of instruction with the individual student’s skill levels, (3) instructional cues, prompts, and fading to support approximations to correct responding, and (4) detailed task-focused feedback” (p. 92).
3. Explicit contextualization of skills-based instruction. Rather than teaching basic-skills in isolation, such skills are explicitly taught situated within a context of application. For example, students might be explicitly taught four ways that transfer occurs in mathematics: “problems can look different, can ask questions in a different way, can use different vocabulary, and can imbed skills within larger problem-solving contexts” (p. 92). Further, teachers would make “transparent the connections between knowledge acquisition and knowledge application, rather than leaving the student to discover those connections more incidentally” (p. 93).

 

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Assessing Mathematics Learning Needs and Associated Teaching Strategies

 

According to Kristine Augustyniak, Jacqueline Murphy, and Donna Phillips in Psychological Perspectives in Assessing Mathematics Learning Needs (2005), the current emphasis on targeted interventions for students makes it important for educators to refine their knowledge of the different learning disabilities and how they might be manifested in children. The federal government’s current classification system includes reading, language arts, and mathematics as three specific areas of deficit. The government presumes the disabilities are associated with a central nervous system dysfunction.

Factors in Learning Math

Research in developmental, cognitive, social, and neuro-psychology has shed light on factors related to learning mathematics and the nature of math learning disability (MLD). Typically, students with MLD require over-learning to retain skills required in math.

Developing numerical skills involves specialized arithmetic language, comprehension of quantity, reasoning, and an ability to convert words (verbal or written) and visual forms into symbols and vice-versa. A visual-spatial impairment “is often evidenced as problems in discriminating between similar letters, copying shapes and figures, using computerized answer sheets, making sense of graphs and charts, and lining up numbers in math problems.” Those with spatial acalculia might rotate or omit numbers, misread arithmetic signs, have difficulty with lining up numbers in columns and placing of decimals (Augustyniak, Murphy, & Phillips, 2005, p. 279).

Cognitive skill development relates to learners’ abilities to perceive, sustain attention, organize, remember, and monitor information such as distinguishing between essential and non-essential details. However, one should not assume that deficits can be attributed to a specific learning disability. There is great variability in normal development of those skills. Math performance might be impeded because the student’s higher order cognitive skills are just underdeveloped. Thus, an assessment of specific neuropsychological abilities is potentially unreliable. Yet when paired with assessments of academic skills, both can inform an intervention (Augustyniak, Murphy, & Phillips, 2005).  Development of cognitive skills in math is closely aligned with Jean Piaget's theory of cognitive development.  Readers might be interested in David Moursund's (2016) six-level, Piagetian-type, math cognitive development scale.  The scale examines math development from birth to becoming a true mathematician.  You can also learn more about math learning disorders.

As an intervention for developing cognitive skills, educators might consider BrainWare Safari.  This award-winning software program develops 41 cognitive skills in six areas: attention, memory, sensory integration, visual processing, auditory processing, and logic/reasoning.  It has an entertaining and motivating video-game format with a jungle theme. According to its developer, Brainware Learning Company (2017), "By improving students’ underlying mental processing skills, it enables them to be more successful across the curriculum, whether in reading, math or other subject matter.  BrainWare Safari benefits all students, not just those with special needs" (para. 1).

Social aspects of learning math are influenced by students’ beliefs about how math is learned (e.g., memorization, only one correct way to solve a problem, quick solutions), beliefs about oneself in relation to math, and beliefs about the social context of math learning and problem solving. Problems are manifested in emotions and behaviors such as frustration, lack of motivation, and poor problem solving strategies. A constructivist approach to teaching and learning is recommended that includes making math relevant to real-life situations, hands-on involvement, and exploration within a flexible learning environment. (Augustyniak, Murphy, & Phillips, 2005).

 

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Effective Strategies for Teaching Students with Difficulties in Math

Russell Gersten and Benjamin Clarke (2007) presented evidence-based practices that have been shown to be consistently effective in teaching students who have difficulties in mathematics, including special education students and other low-achievers.  From their review of studies, they also concluded that the "principles that emerged from the research seem appropriate for instruction in a variety of situations and possible settings."

• Visual and graphic depictions of problems: Effect size was 0.50 (moderate) for special education students.  " An interesting finding for the use of graphics and visual organizers was that the specificity of the visual representation determined the effectiveness of the intervention.  When teachers presented graphic depictions of problem-solving sets with multiple examples and had students practice using their own graphic organizers with specific guidance by the teacher on which visuals to select and why, the effects were much larger than when students did not have this practice or guidance" (p. 1).
• Systematic and explicit instruction: Effect size was 1.19 (large) for special education students and 0.58 (moderate to large) for low-achievers.  "In most studies, the emphasis was placed on providing highly explicit models of steps and procedures or questions to ask in solving problems. The degree of structure and specificity is atypical in conventional mathematics texts."  Gersten and Clarke noted "many students with learning disabilities in mathematics struggle with what are considered basic mathematical procedures. This, in turn, limits their ability to solve more-complex problem types in which basic procedures are embedded." (p. 2)
• Student Think-Alouds: Effect size was 0.98 (large) for special education students.  "The process of encouraging students to verbalize their thinking—by talking, writing, or drawing the steps they used in solving a problem— was consistently effective. In part, this procedure may be effective because the impulsive approach to solving problems taken by many students with mathematics difficulties was addressed" (p. 2).  In one set of studies, verbalization also helped to anchor learners behaviorally and mathematically.
• Use of structured peer-assisted learning activities involving heterogeneous ability groupings: Effect size was 0.42 (moderate) for special education students and 0.62 (large) for low-achievers.
• Formative Assessment Data provided to teachers and directly to students:  Effect sizes when such data was provided to teachers (0.31) of special education students and directly to special education students (0.33) were low to moderate; effect sizes for such data provided to teachers (0.51) of low-achieving students and directly to low-achieving students (0.57) was moderate.   "The use of ongoing formative assessment data invariably improved mathematics achievement of students with mathematics disability" (p. 2).

Witzel and Blackburn (2021) recommended 2 Key Math Strategies for Students with Disabilities: the concrete-visual-abstract sequence of instruction (CVA) and schema-based problem-solving instruction (SBI), both of which are research-supported.  They describe them as follows:

• CVA is a three-step model for developing computational proficiency.  It "has been shown effective for learning such mathematics concepts as number sense, whole and rational number computation, simplifying algebra expressions, solving algebra equations, and solving geometric principles."  At step 1, learners use a concrete manipulative to help solve a math problem, then at step 2 they solve similar problems using visuals of the concrete manipulatives, and at step 3 they solve problems using only the abstract notation.  Problems move from simple to complex.
• SBI is a four-step model that benefits learners when solving math word problems: problem identification (involves learning to analyze and categorize problems by different types), problem representation (involves learning to translate the problem from words into a graphic representation), problem set-up (involves applying appropriate mathematical operations based on the representation), and solve and check (involves computing the answer and determining if it makes sense by rereading the problem).

The IRIS Center at Vanderbilt University provides the steps in explicit, systematic instruction.

The National Institute for Direct Instruction includes a list of programs in multiple content areas that use direct instruction and research on this topic.  You'll also find an online tutorial: Implementing Direct Instruction Successfully.

Tiered Instruction

A tiered approach to teaching mathematics is most likely the most effective method to addressing the issues of math difficulties that exist among learners in the same classroom. 

According to David Suarez (2007), underperforming students might be bored or overwhelmed by a single approach to learning. "Through tiered instruction, students at different ends of the ability spectrum find success in math class" (p. 60).  His approach consists of thematic units.  Learners choose from green, blue, and black levels of difficulty in both instructional materials and assessments, and can vary their choices from unit to unit.  A green level designates foundational and meets grade level standards for proficiency, blue is intermediate, and black is advanced offering the greatest level of challenge sometimes requiring learners to tackle unfamiliar tasks.  Learners find choices motivational and provide experience taking charge of their own learning.  This tiered instruction has a theoretical foundation in the works of Lev Vygotsky's zone of proximal development, Mihaly Csikszentmihalyi's perspective on how to create joyful concentration, Eric Jensen's work on how stress affects learning, and William Glasser's choice theory.  Suarez maintains a blog, Challenge by Choice, on tiered instruction in math, where he elaborates on this method and offers videos, examples, and results from his implementation with a colleague at the Jakarta International School in Indonesia.

The Tiered Curriculum Project from the Indiana Department of Education further exemplifies this method for K-12.  This project includes examples of tiered lessons for mathematics, science, and language arts differentiated by readiness, interest, and learning styles.  For more on eight steps for creating a tiered lesson, read Tiered Lessons: One Way To Differentiate Mathematics Instruction by Rebecca L. Pierce and Cheryll M. Adams (2004).

Teaching Strategies for Hypothesized Primary Skill Deficits in Math

Augustyiak, Murphy, and Phillips (2005) proposed several teaching strategies that may prove helpful for learners with hypothesized primary skill deficits in mathematics. Their suggested strategies are summarized in Table 1.

 

As one examines Table 1 above, you observe that using drill and practice and related software is included among those recommendations, as is the use of manipulatives.  The National Mathematics Advisory Panel (2008) also "recommends that high-quality computer-assisted instruction (CAI) drill and practice, implemented with fidelity, be considered as a useful tool in developing students’ automaticity (i.e., fast, accurate, and effortless performance on computation), freeing working memory so that attention can be directed to the more complicated aspects of complex tasks" (p. 51). Further:

"Research has demonstrated that tutorials (i.e., CAI programs, often combined with drill and practice) that are well designed and implemented can has a positive impact on mathematics performance, particularly at the middle and high school levels. CAI tutorials have been used effectively to introduce and teach new subject-matter content. Research suggests that tutorials that are designed to help specific populations meet specific educational goals have a positive impact. However, these studies also suggest several important caveats. Care must be taken to ensure that there is evidence that the software to be used has been shown to increase learning in the specific domain and with students who are similar to those who will use the software. Educators should critically inspect individual software packages and the studies that evaluate them. Furthermore, the requisite support conditions to use the software effectively (sufficient hardware and software; technical support; adequate professional development, planning, and curriculum integration) should be in place, especially in large-scale implementations, to achieve optimal results." (p. 51)

In terms of using manipulatives, the National Center on Intensive Intervention (2016) reminded educators:

"It is important to note that although students may demonstrate proper use of a manipulative, this does not mean that they understand the concepts behind use of the manipulative. Explicit instruction and student verbalizations, such as explaining the concept or demonstrating use of the manipulative while they verbally describe the mathematical procedure, should accompany all manipulative use." (p. 5)

Gersten et al. (2009) made additional recommendations for elementary and middle school students who receive math interventions:

• Instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8. These materials should be selected by committee.

• Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.

• Interventions should include instruction on solving word problems that is based on common underlying structures.

• Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.

• Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts.

• Monitor the progress of students receiving supplemental instruction and other students who are at risk.

• Include motivational strategies in interventions. (p. 6)

In terms of frequent assessments, teachers and their school districts might consider adaptive testing software, which can be easily administered several times a school year to determine individual needs and to give a measure of class growth on state standards benchmarks.  The National Center on Intensive Intervention (NCII) has six tools charts addressing academics and behavior.  Academic charts include information about screening tools, progress monitoring tools (e.g. Acadience Math from Acadience Learning, ClassWorks Progress Monitoring from Curriculum Advantage, and STAR Math from Renaissance Learning, etc.) and intervention tools.  Per NCII, the charts are meant to "to assist educators and families in becoming informed consumers who can select academic and behavioral assessment tools and interventions that meet standards for technical rigor and address their specific needs."

 

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Response to Intervention / Multi-Tiered Systems of Support Resources

 

Response to Intervention (RTI) is typically a three-tiered method for early identification of students who may be at risk for learning disabilities or difficulties.  Briefly per MDRC (2017), Tier 1 instruction is provided generally to an entire class, Tier 2 to students requiring some additional help and might be in small groups for tutoring, and Tier 3 to students requiring the most help and individualized attention.

Note: The majority of states are now using the term Multi-Tiered Systems of Support (MTSS) rather than RTI to refer to a tiered system of support.  Tessie Rose Bailey (2019) provided possible rationales for the shift.  RTI needed rebranding as it "became synonomous with special education."  MTSS "integrates academic and behavior tiered models" and "is more comprehensive than RTI."  There is a "preference for MTSS in federal guidance and messaging."

Tutoring Programs

Evidence for ESSA includes research-based math programs for students that have been rated for their effectiveness for tutoring.  The following are among those and rated as "strong."

• ROOTS (gr. K)
• Galaxy Math (gr. 1)
• Number Rockets (gr. 1)
• FocusMATH (gr. 3-6)
• Pirate Math (gr. 3)
• Fraction Face-Off (gr. 4)
• Math Corps (gr. 4-8)
• Saga Math (gr. 9-10)

Books

 

Articles

Companies and Websites

The following will help you to learn more on this process and also provide you with some companies offering RTI, MTSS, and assessment software.

Acadience Learning: Acadience Math is an assessment used to measure the acquisition of basic math skills (numeracy, computation, problem solving) of K-6 learners. It "provides reliable and valid universal screening to identify students who may be at risk for mathematics difficulties. These measures also help identify the skills to target for instructional support. Acadience Math also provides progress monitoring measures for at-risk students while they receive additional, targeted instruction to close achievement gaps" (Why Use section).  It is also aligned to Common Core Math Standards.

Advocacy Institute includes A Parent's Guide to Response-to-Intervention among its resources.  The guide was written by the Advocacy Institute for the National Center for Learning Disabilities.

American Speech-Language-Hearing Association: What is Response to Intervention?

Ascend Math provides Tier 2/Tier 3 math intervention for learners principally in grades K-8, including progress monitoring.  It can also be used with special education learners and ELL/ESOL learners (it includes Spanish and English video based lessons), gifted/talented, and used for algebra readiness.  It supports Common Core and state standards.

Branching Minds provides a MTSS platform with multiple features.  It includes universal screeners and benchmarking exams to help identify struggling learners, and evidence-based interventions matched to a student's needs.  You can create collaborative intervention plans and track progress.  The site also offers an AI-powered meeting assistant and options for onsite or remote professional development.

Center on Multi-Tiered System of Supports at the American Institutes for Research supports implementation of the MTSS framework, which has "four essential components: screening, progress monitoring, multi-level prevention system, and data-based decision. Depending on state law, MTSS data may also support identification of students with learning or other disabilities."  The Center provides an Academic Screening Tools Chart among resources, which contains a list of products to assist educators and families in selecting a tool that meets individual needs.

Evidence for ESSA is a free website from the Center for Research and Reform in Education at Johns Hopkins University, which began in 2017.  It's purpose is to provide educators with the most up-to-date and reliable information regarding K-12 programs (e.g., in math and reading) that meet the strong, moderate, and promising evidence criteria per the Every Student Succeeds Act of 2015.  See Evidenced-Based Math Programs at the ESSA website.

FastBridge from Illuminate Education provides "Research-based universal screening and progress monitoring for academics and social-emotional behavior (SEB) with intervention recommendations" per its description.  FastBridge Math Assessments for K-12 "combine research-based Computer Adaptive Tests (CAT) for universal screening and highly sensitive Curriculum-Based Measures (CBM) for progress monitoring."

Intervention Central: RTI Resources Intervention Central "is committed to the goal of making quality Response-to-Intervention resources available to educators at no cost. The site was created in 2000 by Jim Wright, a school psychologist and school administrator in central New York State. Visit to check out newly posted academic and behavioral intervention strategies, download publications on effective teaching practices, and use tools that streamline classroom assessment and intervention."

National Center on Intensive Intervention supports "implementation of data-based individualization in reading, mathematics, and behavior for students with severe and persistent learning and/or behavioral needs" (About Us section).  The academic progress monitoring tools are of particular value to math educators.

Panorama includes an intervention management system.  It helps "Streamline your MTSS [Multi-Tiered System of Supports] or RTI process. Panorama makes it easy to identify students in need of intervention, manage and track tiered interventions, and understand whether interventions are working" (What is MTSS? section).

Pearson: aimswebPlus is a RTI solution, which provides universal screening, progress monitoring, and data management for K-12.  Per Pearson, it includes "assessments for fundamental reading, math, spelling, and writing skills for grades K-8, as well as norms for K-12."

Sourcewell Technology: Spring Math is a web-based K-8 math intervention program assessing approximately 130 skills in numeracy through pre-algebra.  It will also benefit high school learners to remedy skill gaps.  This MTSS (multi-tiered system of supports) solution includes tools for assessment, reporting, and intervention to help students get back on track and close gaps in math skills.  Per its description: "Spring Math aligns to and addresses student needs by pairing dynamically-generated screenings and robust progress monitoring to prescribed, customized, individual, and classwide interventions."

U.S. Department of Education, Office of Special Education Programs: IDEA website

Wrightslaw: What You Need to Know about IDEA 2004 Response to Intervention (RTI): New Ways to Identify Specific Learning Disabilities has numerous articles and links to other web sites on this topic.

 

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References

 

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See other Math Methodology pages:

Instruction--Resources, Assessment and Curriculum: Content and Mapping

 

 

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