Concrete - Representational - Abstract:  Sequence of Instruction

The purpose of teaching through a concrete-to-representational-to-abstract sequence of instruction is to ensure students truly have a thorough understanding of the math concepts/skills they are learning. When students who have math learning problems are allowed to first develop a concrete understanding of the math concept/skill, then they are much more likely to perform that math skill and truly understand math concepts at the abstract level.

What is it?

• Each math concept/skill is first modeled with concrete materials (e.g. chips, unifix cubes, base ten blocks, beans and bean sticks, pattern blocks).
• Students are provided many opportunities to practice and demonstrate mastery using concrete materials
• The math concept/skill is next modeled at the representational (semi-concrete) level which involves drawing pictures that represent the concrete objects previously used (e.g. tallies, dots, circles, stamps that imprint pictures for counting)
• Students are provided many opportunities to practice and demonstrate mastery by drawing solutions
• The math concept/skill is finally modeled at the abstract level (using only numbers and mathematical symbols)
• Students are provided many opportunities to practice and demonstrate mastery at the abstract level before moving to a new math concept/skill.

As a teacher moves through a concrete-to-representational-to-abstract sequence of instruction, the abstract numbers and/or symbols should be used in conjunction with the concrete materials and representational drawings (promotes association of abstract symbols with concrete & representational understanding)

What are the critical elements of this strategy?

• Use appropriate concrete objects to teach particular math concept/skill (see Concrete Level of Understanding/Understanding Manipulatives-Examples of manipulatives by math concept area). Teach concrete understanding first.
• Use appropriate drawing techniques or appropriate picture representations of concrete objects (see Representational Level of Understanding/Examples of drawing solutions by math concept area). Teach representational understanding second.
• Use appropriate strategies for assisting students to move to the abstract level of understanding for a particular math concept/skill (see Abstract Level of Understanding/Potential barriers to abstract understanding for students who have learning problems and how to manage these barriers).

How do I implement the strategy?

When initially teaching a math concept/skill, describe & model it using concrete objects (concrete level of understanding).

• Provide students many practice opportunities using concrete objects.
• When students demonstrate mastery of skill by using concrete objects, describe & model how to perform the skill by drawing or with pictures that represent concrete objects (representational level of understanding).
• Provide many practice opportunities where students draw their solutions or use pictures to problem-solve.
• When students demonstrate mastery drawing solutions, describe and model how to perform the skill using only numbers and math symbols (abstract level of understanding).
• Provide many opportunities for students to practice performing the skill using only numbers and symbols.

After students master performing the skill at the abstract level of understanding, ensure students maintain their skill level by providing periodic practice opportunities for the math skills.

How Does This Instructional Strategy Positively Impact Students Who Have Learning Problems?

• Helps passive learner to make meaningful connections
• Teaches conceptual understanding by connecting concrete understanding to abstract math process
• By linking learning experiences from concrete-to-representational-to-abstract levels of understanding, the teacher provides a graduated framework for students to make meaningful connections.
• Blends conceptual and procedural understanding in structured way

Concrete

What is it?

The concrete level of understanding is the most basic level of mathematical understanding. It is also the most crucial level for developing conceptual understanding of math concepts/skills. Concrete learning occurs when students have ample opportunities to manipulate concrete objects to problem-solve. For students who have math learning problems, explicit teacher modeling of the use of specific concrete objects to solve specific math problems is needed.

Understanding manipulatives (concrete objects)

To use math manipulatives effectively, it is important that you understand several basic characteristics of different types of math manipulatives and how these specific characteristics impact students who have learning problems. As you read about the different types of manipulatives, click on the numbers beside each description to view pictures of these different types of manipulatives.

General types of math manipulatives:

Discrete - those materials that can be counted (e.g. cookies, children, counting blocks, toy cars, etc.).

Continuous - materials that are not used for counting but are used for measurement (e.g. ruler, measuring cup, weight scale, trundle wheel). See example - 1
Suggestions for using Discrete & Continuous materials with students who have learning problems:

Students who have learning problems need to have abundant experiences using discrete materials before they will benefit from the use of continuous materials. This is because discrete materials have defining characteristics that students can easily discriminate through sight and touch. As students master an understanding of specific readiness concepts for specific measurement concepts/skills through the use of discrete materials (e.g. counting skills), then continuous materials can be used.

Types of manipulatives used to teach the Base-10 System/place-value (Smith, 1997):

Proportional - show relationships by size (e.g. ten counting blocks grouped together is ten times the size of one counting block; a beanstick with ten beans glued to a popsicle stick is ten times bigger than one bean).

Non-linked proportional - single units are independent of each other, but can be "bundled together (e.g. popsicle sticks can be "bundled together in groups of 'tens' with rubber bands; individual unifix cubes can be attached in rows of ten unifix cubes each).

Linked proportional - comes in single units as well as "already bundled" tens units, hundreds units, & thousands units (e.g. base ten cubes/blocks; beans & beansticks).

Non-proportional - use units where size is not indicative of value while other characteristics indicate value (e.g. money, where one dime is worth ten times the value of one penny; poker chips where color indicates value of chip; an abacus where location of the row indicates value). A specified number of units representing one value are exchanged for one unit of greater value (e.g. ten pennies for one dime; ten white poker chips for one blue poker chip, ten beads in the first row of an abacus for one bead in the second row). See example - 1
Suggestions for using proportional and non-proportional manipulatives with students who have learning problems:

Students who have learning problems are more likely to learn place value when using proportional manipulatives because differences between ones units, tens units, & hundreds units are easy to see and feel. Due to the very nature of non-proportional manipulatives, students who have learning problems have more difficulty seeing and feeling the differences in unit values.

Examples of manipulatives (concrete objects)

Suggested manipulatives are listed according to math concept/skill area. Descriptions of manipulatives are provided as appropriate. A brief description of how each set of manipulatives may be used to teach the math concept/skill is provided at the bottom of the list for each math concept area. Picture examples of some of the manipulatives for each math concept area can be accessed by clicking on the numbers found underneath the title of each math concept area. This is not meant to be an exhaustive list, but this list does include a variety of common manipulatives. The list includes examples of "teacher-made" manipulatives as well "commercially-made" ones.

Counting/Basic Addition & Subtraction Pictures

Colored chips
Beans
Unifix cubes
Golf tees
Skittles or other candy pieces
Packaging popcorn
Popsicle sticks/tongue depressors

Description of use: Students can use these concrete materials to count, to add, and to subtract. Students can count by pointing to objects and counting aloud. Students can add by counting objects, putting them in one group and then counting the total. Students can subtract by removing objects from a group and then counting how many are left.

Place Value Pictures

Base 10 cubes/blocks
Beans and bean sticks
Popsicle sticks & rubber bands for bundling
Unifix cubes (individual cubes can be combined to represent "tens")
Place value mat (a piece of tag board or other surface that has columns representing the "ones," "tens," and "hundreds" place values)

Description of use: Students are first taught to represent 1-9 objects in the "ones" column. They are then taught to represent "10" by trading in ten single counting objects for one object that contains the ten counting objects on it (e.g. ten separate beans are traded in for one "beanstick" - a popsicle stick with ten beans glued on one side. Students then begin representing different values 1-99. At this point, students repeat the same trading process for "hundreds."

Multiplication/Division Pictures

Containers & counting objects (paper dessert plates & beans, paper or plastic cups and candy pieces, playing cards & chips, cutout tag board circles & golf tees, etc.). Containers represent the "groups" and counting objects represent the number of objects in each group. (e.g. 2 x 4 = 8: two containers with four counting objects on each container)
Counting objects arranged in arrays (arranged in rows and columns). Color-code the "outside" vertical column and horizontal row helps emphasize the multipliers
.
Positive & Negative Integers Pictures

Counting objects, one set light colored and one set dark colored (e.g. light & dark colored beans; yellow & blue counting chips; circles cut out of tag board with one side colored, etc.).

Description of use: Light colored objects represent positive integers and dark colored objects represent negative integers. When adding positive and negative integers, the student matches pairs of dark and light colored objects. The color and number of objects remaining represent the solution.

Fractions Pictures

Fraction pieces (circles, half-circles, quarter-circles, etc.)
Fraction strips (strips of tag board one foot in length and one inch wide, divided into wholes, ½'s, 1/3's, ¼'s, etc.
Fraction blocks or stacks. Blocks/cubes that represent fractional parts by proportion (e.g. a "1/2" block is twice the height as a "1/4" block).

Description of use: Teacher models how to compare fractional parts using one type of manipulative. Students then compare fractional parts. As students gain understanding of fractional parts and their relationships with a variety of manipulatives, teacher models and then students begin to add, subtract, multiply, and divide using fraction pieces.

Geometry Pictures

Geoboards (square platforms that have raised notches or rods that are formed in a array). Rubber bands or string can be used to form various shapes around the raised notches or rods.

Description of use: Concepts such as area and perimeter can be demonstrated by counting the number of notch or rod "units" inside the shape or around the perimeter of the shape.

Beginning Algebra Pictures

Containers (representing the variable of "unknown") and counting objects (representing integers) -e.g. paper dessert plates & beans, small clear plastic beverage cups 7 counting chips, playing cards & candy pieces, etc.
Description of use: The algebraic expression, "4x = 8," can be represented with four plates ("4x"). Eight beans can be distributed evenly among the four plates. The number of beans on one plate represent the solution ("x" = 2).

Suggestions for using manipulatives:

• Talk with your students about how manipulatives help to learn math.
• Set ground rules for using manipulatives.
• Develop a system for storing manipulatives.
• Allow time for your students to explore manipulatives before beginning instruction.
• Encourage students to learn names of the manipulatives they use.
• Provide students time to describe the manipulatives they use orally or in writing. Model this as appropriate.
• Introduce manipulatives to parents

Representational

What is it?

At the representational level of understanding, students learn to problem-solve by drawing pictures. The pictures students draw represent the concrete objects students manipulated when problem-solving at the concrete level. It is appropriate for students to begin drawing solutions to problems as soon as they demonstrate they have mastered a particular math concept/skill at the concrete level. While not all students need to draw solutions to problems before moving from a concrete level of understanding to an abstract level of understanding, students who have learning problems in particular typically need practice solving problems through drawing. When they learn to draw solutions, students are provided an intermediate step where they begin transferring their concrete understanding toward an abstract level of understanding. When students learn to draw solutions, they gain the ability to solve problems independently. Through multiple independent problem-solving practice opportunities, students gain confidence as they experience success. Multiple practice opportunities also assist students to begin to "internalize" the particular problem-solving process. Additionally, students' concrete understanding of the concept/skill is reinforced because of the similarity of their drawings to the manipulatives they used previously at the concrete level.

Drawing is not a "crutch" for students that they will use forever. It simply provides students an effective way to practice problem solving independently until they develop fluency at the abstract level.

Examples of drawing solutions by math concept level

The following drawing examples are categorized by the type of drawings ("Lines, Tallies, & Circles," or "Circles/Boxes"). In each category there are a variety of examples demonstrating how to use these drawings to solve different types of computation problems. Click on the numbers below to view these examples.

Abstract

What is it?

A student who problem-solves at the abstract level, does so without the use of concrete objects or without drawing pictures. Understanding math concepts and performing math skills at the abstract level requires students to do this with numbers and math symbols only. Abstract understanding is often referred to as, "doing math in your head." Completing math problems where math problems are written and students solve these problems using paper and pencil is a common example of abstract level problem solving.

Potential barriers to abstract understanding for students who have learning problems and how to manage these barriers

Students who are not successful solving problems at the abstract level may:

• Not understand the concept behind the skill

Suggestions:

Re-teach the concept/skill at the concrete level using appropriate concrete objects (see Concrete Level of Understanding).
Re-teach concept/skill at representational level and provide opportunities for student to practice concept/skill by drawing solutions (see Representational Level of Understanding).
Provide opportunities for students to use language to explain their solutions and how they got them (see instructional strategy Structured Language Experiences).

- Have difficulty with basic facts/memory problems

Suggestions:

• Regularly provide student with a variety of practice activities focusing on basic facts. Facilitate independent practice by encouraging students to draw solutions when needed (see the student practice strategies Instructional Games, Self-correcting Materials, Structured Cooperative Learning Groups, and Structured Peer Tutoring).
• Conduct regular one-minute timings and chart student performance. Set goals with student and frequently review chart with student to emphasize progress. Focus on particular fact families that are most problematic first, then slowly incorporate a variety of facts as the student demonstrates competence (see evaluation strategy Continuous Monitoring & Charting of Student Performance).
• Teach student regular patterns that occur throughout addition, subtraction, multiplication, & division facts (e.g. "doubles" in multiplication, 9's rule - add 10 & subtract one, etc.)
• Provide student a calculator or table when they are solving multiple-step problems.

Repeat procedural mistakes

Suggestions:

• Provide fewer #'s of problems per page.
• Provide fewer numbers of problems when assigning paper & pencil practice/homework.
• Provide ample space for student writing, cueing, & drawing.
• Provide problems that are already written on learning sheets rather than requiring students to copy problems from board or textbook.
• Provide structure: turn lined paper sideways to create straight columns; allow student to use dry-erase boards/lap chalkboards that allow mistakes to be wiped away cleanly; color cue symbols; for multi-step problems, draw color-cued lines that signal students where to write and what operation to use; provide boxes that represent where numerals should be placed; provide visual directional cues in a sample problem; provide a sample problem, completed step by step at top of learning sheet.
• Provide strategy cue cards that student can use to recall the correct procedure for solving problem.
• Provide a variety of practice activities that require modes of expression other than only writing

The Big Idea

Student learning & mastery greatly depends on the number of opportunities a student has to respond!! The more opportunities for successful practice that you provide (i.e. practice that doesn't negatively impact student learning characteristics), the more likely it is that your student will develop mastery of that skill.

It's funny as teachers we build culture in our classroom and it becomes "the way things are done." We hard to build it so that everyone soon becomes a family. We never give a second thought to what our School Building Culture is. We may think we know what it is such as warm and welcoming; everyone shares ideas; everyone has an open door. But is it really.? I think about School Culture the same way I do in my class.

I would like to offer here an approach to learning where the locus of classroom standards is centered neither in the teacher nor the individual student, but rather in a classroom culture, imbedded in a consonant school culture. This classroom culture contains the teacher and each individual student, the peer groups of students, but also transcends them: it is a framework which governs the learning and social interaction of all classroom members, and builds norms for a new peer culture.

Culture is a powerful concept. It goes deeper than what is spoken, deeper, even, than what is consciously understood Students in my classroom probably couldn't articulate exactly why they try so hard at their work and probably haven't even stopped to fully analyze it. Similarly, as members of a larger culture, we rarely stop to think about how many of our personal attitudes and actions are simply reflections of cultural norms. Culture defines how people function, and to some extent, even how they think. If a notion of high standards is not simply included in classroom culture but is actually at the core of this culture, then high standards become the norm.

This is all fine in the abstract, but a picture and understanding of how this culture looks in practice is needed. Painting this picture is, for me, a difficult task. A visit to my classroom in action, where I can often leave the room for twenty minutes and students don't even notice, as they are gripped in project work, would be much more compelling and persuasive than my words here could hope to be. Even this, however, would be inadequate, as it would fail to disclose how the environment was built, and what unspoken norms define its social structure.

Schools can sometimes take on the feel of a production shop, students cranking out an endless flow of final products without much personal investment or care. The emphasis is on keeping up with production, not falling behind in classwork or homework, rather than in producing something of lasting value. Like a fast food restaurant, the products are neither creative nor memorable. Teachers create and fuel this situation, despite the fact that we grow tired of repetitive, trivial assignments, and dread correcting piles of such work.

Turning in final drafts of work every day, often many times in one day, even the most ambitious of students must compromise standards continually simply to keep up with the pace. Internalized high standards are no defense against a system which demands final draft work at this rate. If an adult writer, scientist, historian, visual artist, was asked to turn in a finished piece of work every day, two or three finished pieces on some days, how much care could he or she put into each?

An alternative is a project-centered approach. In this structure, students still work hard every day, but their work is instead a small part of a long-range, significant project. Daily work entails the creation or revision of early drafts of a piece, the continued research of a topic or management of an experiment, or the perfection of one component of a large piece of work. Final drafts or presentations of completed projects are no longer trivial events occurring every day, but are special events, moments of individual and class pride and celebration.

Universal success does not mean uniformity. Though the structure which braces and guides student progress is common to every project, each student's project is unique. The structure provides a frame for common learning and critique, as well as appraisal of progress, but it also has room for significant creative expression and direction by individual students. If every student in a classroom prepares a guidebook to a different local building, the steps and skills involved may be somewhat prescribed: conducting interviews, researching local history, consulting city records, trying to obtain blueprints, doing sketches, taking photographs, preparing diagrams, writing and proofreading drafts of text, preparing illustrations, composing book layout, and learning book binding. Within this frame though, individual students have substantial latitude for artistic choices: the choice of building, the choice of whom to interview, the use of research and interviews, the nature of text and illustrations, the balance of text and illustrations, the use of photographs or diagrams, the tone of presentation, and the layout of the finished book.

My comments thus far may have raised a lot of questions. What about "untalented" students? Or teachers, for that matter. People who feel incompetent in particular academic or artistic areas. What about students with pronounced disabilities in perception, memory, or motor skills? If high standards are applied to the work of everyone, won't it just emphasize the painful weaknesses of some?
What about assessment? If so much of project work is creative and individualized, and even deadlines and requirements often differ from student to student, how can fair and constructive assessment take place?
What about a sense of community? If you work to dissolve the boundaries between school and outside life, don't you destroy the precious asylum of school which provides safety and security to children?
What about the cultivation of positive personal qualities in students: politeness, thoughtfulness, cooperation, initiative, self confidence, equanimity. Environments of "high standards" are often high-stress; a high standards classroom often means fighting for teacher recognition.

I'd like to say that I, and my school, have found the definitive answers to all these questions. Of course, we haven't. We are forever confused with trying to fashion a schoolwide assessment system which fits our teaching approach and documents student progress for the community or district in a real way. We are just now undertaking an effort to begin using student portfolios as archives of individual projects and achievement, as many schools have already done. And we are continually trying to restructure our school resources and community traditions to make the school more supportive for students with disabilities, insecurities, or other factors which make them "marginal".

Nevertheless, I think there is much going on in my classroom and school that addresses these questions in powerful ways. Despite having a full range of "academic abilities" in my students, and even students of real special needs, visitors to the classroom are often bemused and skeptical that this is a "regular" group of students. The work on display looks too impressive, the focus, cooperation, investment, and friendly ease of children too good to be true. The answer, I believe, is that students in my classroom are deeply and genuinely supported in countless ways to do their best and act their best, and have been so since Kindergarten. To a great extent, this is due to the ways in which the school culture deals with issues of assistance and assessment for students, and also for teachers.

People often say to me that this learning approach works in my classroom because I am a strong teacher, or works in the school because the school has strong teachers. In fact, they say, it's importance is trivial, because it can only work with strong teachers. Your school has strong teachers, but you don't know the teachers at my school. I would never contend that this approach is easy to use, nor that my colleagues are not full of talent.

First, it is suspiciously similar to that of teachers who visit my room and tell me: "Oh, but your kids are all bright (or artists, or interested, or well-behaved), you should see my kids. This would never work with my class." Now the kids in my class are no special group, but somehow they seem to shine. Is it because they're inherently strong , as the school's teachers are described, or is it because the structure and culture inspires them to do their best? Granted, children are more malleable and open than adults, particularly schoolteachers (we tend to be a defensive and protective bunch). I would argue, though, that the school culture where I teach inspires teachers to do their best (though this is an argument which might generate some laughter at times in my staff room). In addition to searching for strong teachers, school cultures can be building strong teachers. Perhaps more accurately, school cultures can inspire and reward teachers for displaying their strengths more fully, by taking risks, working together, and assuming substantially more decision-making power. I would guess that children too good to be true. The answer, I believe there are more "strong" teachers than people realize, teachers whose strengths are hidden by isolation, lack of power, and lack of inspiration. The talent and spark in these teachers can be fueled with the same approach used with students in the classroom. If teachers are expected and supported to design curriculum and projects, to take risks, be original, to work together in critique and learning, teachers can often blossom just as "weak" students do. I don't mean to trivialize the difficulty in effecting teacher change, but I think it's crucial to emphasize that standards for teaching are as much a product of school culture as standards for student learning: teachers, like students, tend to settle into surrounding expectations, standards and norms.

Second, on a classroom level, saying that this approach needs a strong teacher may be true, but it doesn't begin to reveal why the approach works. The power in the approach it is that it is based in a classroom community which shares a culture. The assessment, encouragement, accountability and teaching which goes on in the classroom is vastly wider than that which emanates from me, as teacher it is a continual and ubiquitous process among students. When I think of a particular student I had last year, a painfully shy girl who was new to town, I would be crazy to take credit for her astonishing emotional and academic growth-- I could hardly get her to speak to me during the year. I take credit only for managing a classroom where countless students took time to tutor her, support her, welcome her, and guide her success.

Again, where do student standards originate? Partly from me as the teacher, but very much from watching each other. Students did quality work, treated each other well, because that is what their friends did, it was the "cool" way to be, it was what the culture supported. How do students decide what is "good enough" as work, what is good enough behavior? Teacher standards only define the minimum standards allowed, they can't define the upper limit of care. Students in my classroom look to each other, help each other, critique each other's work, most of all, push each other to achieve their best. For all of my teacher power, the power in this total culture is infinitely greater.

The culture is rooted in a class community in which the first priority is supporting everyone. The responsibility for each person's emotional well-being and success is shared by everyone; the teacher bears more of this responsibility, but each student is encouraged and expected to help his or her peers. As a teacher, this means setting up a classroom structure which allows time and space for peer collaboration and tutoring; it means complimenting students, rather than complaining, when they abandon their own work at times to assist others. Supporting others means emotional support and care as much as it means academic support and care. In this team concept, the hope is that no student will be left out, left behind, allowed to fail or feel like a failure. It's everybody's job to look out for others.

For me, a culture of high standards means high standards for kindness and cooperation as much as for academic work. In the same way that careful quality in work is stressed over fast production, careful attention to treating all students fairly and thoughtfully is stressed over efficiency and speed in school logistics. "Simple" classroom decisions, such as which students should make a presentation or attend a limited event, often take a long time as they are discussed carefully with students to insure that all feelings are considered. Events and honors which are exclusionary or individualistic, displays of the "best" work or awards for the "best" students or athletes, are avoided in favor of whole-class, whole-school pride. When visitors to my classroom are impressed with student work, it is often due not to specific outstanding examples but rather to the absence of careless work, the uniform commitment to quality. This is a testament to the degree of cultural pride and peer support in the classroom.

 My teachers in elementary school often instructed us to try to do your best". This isn't a bad motto; I'd use it with my class today, and most schools would embrace it without a thought. There's a big step between teachers saying this to students, and students actually doing it. Not too many schools seriously look at what aspects of their structure and culture support and compel students to do their best, to act their best, and what aspects undermine this spirit. Rather than searching for individual teachers or principals who they hope can demand high standards, I feel that schools should be looking at how they can create a spirit of high standards, a school culture of high standards.

What's your building culture like? Have a great week! Say cool:)

I took a huge leap of faith in May and decided not to return to my previous school and district. I spent the summer working on finding a new home. At the beginning of the week (after a driving though a thunderstorm which caused my interview to be in the dark) I started in a rural school district about an hours drive from my home. I'm still working K-5 special education but I'm leaving behind mild/moderate with inclusion for working with everything under the sun plus inclusion.

What Are the Essential Components of RTI?

• ·         High quality, research-based instruction and behavioral support in general education.
• ·         Universal (school-wide or district-wide) screening of academics and behavior in order to determine which students need closer monitoring or additional interventions.
• ·         Multiple tiers of increasingly intense scientific, research-based interventions that are matched to student need.
• ·         Use of a collaborative approach by school staff for development, implementation, and monitoring of the intervention process.
• ·         Continuous monitoring of student progress during the interventions, using objective information to determine if students are meeting goals. (Progress monitoring like DIBELS Next)
• ·         Follow-up measures providing information that the intervention was implemented as intended and with appropriate consistency.
• ·         Documentation of parent involvement throughout the process.
• ·         Documentation that the special education evaluation timelines specified in IDEA 2004 and in the state regulations are followed unless both the parents and the school team agree to an extension.
• 
  
• What Are the Key Terms?

• Response to Intervention (RTI) is an array of procedures that can be used to determine if and how students respond to specific changes in instruction. RTI provides an improved process and structure for school teams in designing, implementing, and evaluating educational interventions.
• Universal Screening is a step taken by school personnel early in the school year to determine which students are “at risk” for not meeting grade level standards. Universal screening can be accomplished by reviewing recent results of state tests, or by administering an academic screening test to all children in a given grade level. Those students whose test scores fall below a certain cut-off are identified as needing more specialized academic interventions.
• Student Progress Monitoring is a scientifically based practice that is used to frequently assess students' academic performance and evaluate the effectiveness of instruction. Progress monitoring procedures can be used with individual students or an entire class.
• Scientific, Research-Based Instruction refers to specific curriculum and educational interventions that have been proven to be effective –that is, the research has been reported in scientific, peer-reviewed journals.

What Role Does RTI Play in Special Education Eligibility?

How Can Parents Be Involved in the RTI Process?

• ·         Does our school use an RTI process? (Be aware that your child's school may call their procedures a “problem solving process,” or may have a unique title for their procedures, e.g., Instructional Support Team, and not use the specific RTI terminology.)
• ·         Are there written materials for parents explaining the RTI process? How can parents be involved in the various phases of the RTI process?
• ·         What interventions are being used, and are these scientifically based as supported by research?
• ·         What length of time is recommended for an intervention before determining if the student is making adequate progress?
• ·         How do school personnel check to be sure that the interventions were carried out as planned?
• ·         What techniques are being used to monitor student progress and the effectiveness of the interventions? Does the school provide parents with regular progress monitoring reports?
• ·         At what point in the RTI process are parents informed of their due process rights under IDEA 2004, including the right to request an evaluation for special education eligibility?
• ·         When is informed parental consent obtained and when do the special education evaluation timelines officially commence under the district's RTI plan?

What Are the Potential Benefits of RTI?

Like many schools, mine has a growing ELL population. In many ways they are more challenging then my LD students but here are a couple ideas that might help you while working with these students. I have found changing up my instruction and adding a couple of different ideas work for ALL students.

English language learners (ELLs) face academic challenges as they work to acquire conversational language skills, as well as the more formal academic language they need to learn content in English. When teaching ELL students, it is important to remember that just like native speakers, ELL students bring a wealth of background experiences into your classroom and have a range of learning style preferences and cultural backgrounds, all of which should be considered when planning their reading instruction.

Who Are ELL Students?

Are trying to acquire English language proficiency, while in English-speaking classrooms. My goal is to help them master the English language, while enabling them to maintain their native language and culture. Students are trying to gain knowledge and experiences in the four domains of language learning:  listening, speaking, reading, and writing.

• Will learn to use English in social interactions, both formally and informally. In this context, students need abundant opportunities to interact with proficient English speakers in a range of settings. By facilitating these interactions around meaningful topics, you will help students gain exposure to a wide vocabulary and a range of topics they might not come across naturally.
• Need to learn, and practice using, content-specific language so they can successfully learn, communicate, and extend academic content-area learning. 
• Benefit from lessons rich with visual aids and non=linguistic cues. Picture books (especially nonfiction picture books) 
• Benefit from model readings and hearing the English language read with fluency. Modeling is a great way for students to hear the English language read fluently while they follow along, viewing both the text and art.
• Model fluent reading. While listening to a story being read aloud, readers can track each word as it is highlighted. In this way, students make sound-symbol correlations between the words and audio pronunciations.
• Utilize graphic organizers. After listening to a book, students can draw pictures illustrating the beginning, middle, and end of the book on a graphic organizer. 
• Students can further build their vocabulary using the infer-and-define strategy in which students infer the meaning of an unknown word and then clarify it by using a student made dictionary.  Students can add their newly acquired words into their personal dictionaries.  
• Use guided reading.  As you work with your ELL students to teach and model reading strategies.
• Use conferencing, explicit modeling, and think-alouds to guide ELL students in thinking critically about the texts they read. 
• Use inferential questions in the notes section of your students' text to encourage critical thinking about the text. Seeing these preview questions before they read will provide students with a reading focus and will require them to analyze the text and synthesize information as they read.   
• Encourage evaluation. Students are working toward synthesizing and evaluating information and responding to reading through writing.  Use this time to guide students in evaluating their own opinions based on the text.  

Phonological and Phonemic Awareness

Phonological awareness is a broad skill that includes identifying and manipulating units of oral language – parts such as words, syllables, and onsets and rimes. Children who have phonological awareness are able to identify and make oral rhymes, can clap out the number of syllables in a word, and can recognize words with the same initial sounds like 'money' and 'mother.'

Phonemic awareness refers to the specific ability to focus on and manipulate individual sounds (phonemes) in spoken words. Phonemes are the smallest units comprising spoken language. Phon
emes combine to form syllables and words. For example, the word 'mat' has three phonemes: /m/ /a/ /t/. There are 44 phonemes in the English language, including sounds represented by letter combinations such as /th/. Acquiring phonemic awareness is important because it is
the foundation for spelling and word recognition skills. Phonemic awareness is one of the best predictors of how well children will learn to read during the first two years of school instruction.

Students at risk for reading difficulty often have lower levels of phonological awareness and phonemic awareness than do their classmates. The good news is that phonemic awareness and phonological awareness can be developed through a number of activities.

What the problem looks like:

A kid's perspective: What this feels like to me

• Children will usually express their frustration and difficulties in a general way, with statements like "I hate reading!" or "This is stupid!". But if they could, this is how kids might describe how difficulties with phonological or phonemic awareness affect their reading:
• I don't know any words that rhyme with cat.
• What do you mean when you say, "What sounds are in the word brush?"
• I'm not sure how many syllables are in my name.
• I don't know what sounds are the same in bit and hit.

A parent's perspective: What I see at home

Here are some clues for parents that a child may have problems with phonological or phonemic awareness:

• She has difficulty thinking of rhyming words for a simple word like cat (such as rat or bat).
• She doesn't show interest in language play, word games, or rhyming.
• Click here to find out what parents can do to help a child at home.
• A teacher's perspective: What I see in the classroom
• Here are some clues for teachers that a student may have problems with phonological or phonemic awareness:
• She doesn't correctly complete blending activities; for example, put together sounds /k/ /i/ /ck/ to make the word kick.
• He doesn't correctly complete phoneme substitution activities; for example, change the /m/ in mate to /cr/ in order to make crate.
• He has a hard time telling how many syllables there are in the word paper.
• He has difficulty with rhyming, syllabication, or spelling a new word by its sound.

How to help

With the help of parents and teachers, kids can learn strategies to cope with phonological and/or phonemic awareness problems that affect his or her reading. Below are some tips and specific things to do.

What kids can do to help themselves

• Be willing to play word and sounds games with parents or teachers.
• Be patient with learning new information related to words and sounds. Giving the ears a workout is difficult!
• Practice hearing the individual sounds in words. It may help to use a plastic chip as a counter for each sound you hear in a word.
• Be willing to practice writing. This will give you a chance to match sounds with letters.
• What parents can do to help at home
• Check with your child's teacher or principal to make sure the school's reading program teaches phonological, phonemic awareness, and phonics skills.
• If your child is past the ages at which phonemic awareness and phonological skills are taught class-wide (usually kindergarten to first or second grade), make sure he or she is receiving one-on-one or small group instruction in these skills.
• Do activities to help your child build sound skills (make sure they are short and fun; avoid allowing your child to get frustrated):
• Help your child think of a number of words that start with the /m/ or /ch/ sound, or other beginning sounds.
• Make up silly sentences with words that begin with the same sound, such as "Nobody was nice to Nancy's neighbor".
• Play simple rhyming or blending games with your child, such as taking turns coming up with words that rhyme (go – no) or blending simple words (/d/, /o/, /g/ = dog).
• Read books with rhymes. Teach your child rhymes, short poems, and songs.
• Practice the alphabet by pointing out letters wherever you see them and by reading alphabet books.
• Consider using computer software that focuses on developing phonological and phonemic awareness skills. Many of these programs use colorful graphics and animation that keep young children engaged and motivated.

What teachers or parents can do to help at school?

• Learn all about phonemes (there are more than 40 speech sounds that may not be obvious to fluent readers and speakers).
• Make sure the school's reading program and other materials include skill-building in phonemes, especially in kindergarten and first grade (these skills do not come naturally, but must be taught).
• If children are past the age at which phonemic awareness and phonological skill-building are addressed (typically kindergarten through first or second grade), attend to these skills one-on-one or in a small group. Ask your school's reading specialist for help finding a research-based supplemental or intervention program for students in need.
• Identify the precise phoneme awareness task on which you wish to focus and select developmentally appropriate activities for engaging children in the task. Activities should be fun and exciting – play with sounds, don't drill them.
• Make sure your school's reading program and other materials include systematic instruction in phonics.
• Consider teaching phonological and phonemic skills in small groups since students will likely be at different levels of expertise. Remember that some students may need more reinforcement or instruction if they are past the grades at which phonics is addressed by a reading program (first through third grade).

I hope these ideas help and answer some questions for parents. Have a great week.

What Do Speech Therapists Help With?

• articulation disorders: This when a kid has trouble saying certain sounds or saying words correctly. "Run" might come out as "won." Or "say" may sound like "thay." Lisps are considered articulation disorders.
• fluency disorders: If a kid repeats certain sounds and has trouble saying the complete word, he or she may have fluency disorder. For example, a kid trying to say "story" might get stuck on the "st" and say "st-st-st-story." Or he or she might draw out certain sounds and say "ssssssstory." A stutter is a fluency disorder
• voice disorders: A kid might have a voice disorder if people have trouble understanding him or her. The kids might start a sentence loud and clear, but it's quiet and mumbling by the end. Sometimes these kids sound like they have a cold or like they're talking through their noses.
• language disorders: A kid who has trouble understanding people or has trouble putting words together to express thoughts might have a language disorder.

Who Needs Speech Therapy?

• hearing impairment
• weak muscles around the mouth
• cleft lip or palate
• vocal nodules/ hoarseness
• autism
• breathing disorder
• swallowing disorder

What's It Like?

How Long Will Treatment Last?

Another area of development to encourage this year is fine motor skills -- or use of the hands. Just as gross motor skills enable your child to perform important everyday tasks, such as getting out of bed and going downstairs for breakfast, fine motor abilities allow for increasing independence in smaller but equally significant matters: opening doors, zipping zippers, brushing teeth, washing hands, and so on.

When combined with increasing hand-eye coordination, fine motor skills also open new doors to exploration, learning, and creative expression. In fact, research shows that emphasis on purely intellectual activities -- memorization of letters and numbers, for instance -- is far less useful at this stage than pursuits that encourage fine motor abilities and hand-eye coordination. These skills -- rather than counting or reciting the alphabet -- lay the foundation for academic learning in later years. In order to learn to write or draw, for example, a child's hand must be strong and coordinated enough to hold a pencil steady for a long period of time; in order to participate in school sports, games, and projects, dexterity and coordination must be up to par.

Among the fine motor skills your child will perfect in the preschool years are the abilities to:

• paste things onto paper
• lap hands
• touch fingers
• button and unbutton
• work a zipper
• build a tower of 10 blocks
• complete puzzles with five or more pieces
• manipulate pencils and crayons well enough to color and draw
• copy a circle or cross onto a piece of paper
• cut out simple shapes with safety scissors

The best way for you to help promote these and other hand-related skills is to provide your child with a wide range of materials to manipulate as her imagination dictates. Good choices include blocks (especially the interlocking types like magnetic blocks, Legos, bristle blocks, Tinker Toys, and construction straws), crayons, nontoxic and washable markers and paints, paste, glue, modeling clay, an easel, construction paper, safety scissors, a smock to guard against stained clothing, coloring books, and simple sewing cards. This is also a prime time for puzzles, sand and water toys, and musical instruments.

Encourage Your Child's Creativity

Once you've provided your child with the tools that inspire creativity, stand back and let him loose, even if things are likely to get rather messy. Preschoolers tend to focus more on process than on product. They throw themselves into exploring the properties and possibilities of materials like paint, mud, sand, water, and glue without worrying about the results. In fact, when your 3-year-old proudly displays his latest masterpiece, you should try not to ask, "What is it?" That question may have never even occurred to him.
Instead, admire the work for what it is: "That's really wonderful! Tell me just how you did it." Then, encourage him to explain to you in his own words how he felt and what he was thinking about while he was making it.

The less control you try to impose over your child's creativity, the better. This advice especially holds true when it comes to the hand your child favors. One of the milestones of this age is becoming right-handed or left-handed. In fact, handedness is an important sign of increasing brain organization. By age 4, some 90 percent of children have become clearly right-handed, while the rest have become dedicated southpaws.
The main determinant of handedness is heredity, so it's best not to tamper with your child's genetic predisposition. Left-handers are no less socially acceptable than righties. And when pressure from parents or preschool teachers induces a child to switch, doing so usually takes a long-term toll in emotional upset and poor coordination.

So let your child lead the way. And don't be alarmed if her fine motor skills progress more slowly than her gross motor development. Fine motor skills develop more slowly because the kinds of delicate movements that enable children to manipulate objects (stacking and nesting blocks or putting together puzzle pieces, for example) can be learned only over time with a lot of practice. Unfortunately, while most 3-year-olds will run happily for hours on a playground, few really have the patience to sit and copy a drawing of a circle or a cross over and over. And keep in mind that the smaller muscles of the body (like those in the hands and fingers) tire out more easily than the larger muscles in the arms and legs, so endurance and strength must be built up gradually before your child's dexterity can improve.

There's one more reason why your child's fine motor skills progress more slowly: They are closely linked to cognitive development. In order to build a fort with blocks, for instance, a child must be able to think in a three-dimensional manner. Adding limbs, hair, or facial features to an incomplete picture of a person means that your child is capable of understanding that two-dimensional drawings can symbolize real people. Your child must mentally compare the picture with stored images of what people look like to figure out what's missing from the drawing, and he must be able to manipulate a pencil or crayon well enough to fill in the absent features.

The thought process involved in such acts is far more complicated than that for figuring out how to climb a ladder, chase a ball, or walk out a door. So it's important for you to be patient, encouraging, and supportive of your child's efforts. Whatever he masters today will stand him in good stead once he starts more formal learning in kindergarten and beyond.

Summer Ideas: Check our Imagination Tree

What are Gross motor skills?

Gross motor skills are the abilities required in order to control the large muscles of the body for walking, running, sitting, crawling, and other activities.

Motor skills are actions that involve the movement of muscles in the body. They are divided into two groups: gross motor skills, which are the larger movements of arms, legs, feet, or the entire body (crawling, running, and jumping); and fine motor skills , which are smaller actions, such as grasping an object between the thumb and a finger or using the lips and tongue to taste objects. Motor skills usually develop together since many activities depend on the coordination of gross and fine motor skills. Gross motor skills develop over a relatively short period of time. Most development occurs during childhood. However, soldiers, some athletes, and others who engage in activities requiring high degrees of endurance may spend years improving their level of muscle and body coordination and gross motor skills.

Encouraging gross motor skills requires a safe, open play space, peers to interact with, and some adult supervision. Promoting the development of gross motor abilities is considerably less complicated than developing fine motor skills. Helping a child succeed in gross motor tasks requires patience and opportunities for a child to practice desired skills. Children reach developmental milestones at different rates. Pushing a child to perform a task that is impossible due to development status promotes frustration and disappointment. Children should be allowed to acquire motor skills at their own paces.

There are a number of activities parents can have children do to help develop gross motor skills. These include:
• playing hopscotch and jumping rope; activities that help children learn balance
• hitting, catching, kicking, or throwing a ball, such as a baseball, football, or soccer ball; activities that help develop hand-eye or foot-eye coordination
• kangaroo hop, in which children hold something, such as a small ball or orange, between their knees and then jump with their feet together frontward, backwards, and sideways
• playing wheelbarrow, in which someone holds the children's legs while they walk on their hands along a specific route
• walking on a narrow bar or curb, while holding a bulky object in one hand, then the other hand, and then repeating the activity walking backwards and sideways
• toss and catch, in which children toss an object, such as a baseball, in the air and then catch it, while sitting or lying down and also while using alternate hands

Infancy
The first gross motor skill infants learn usually is to lift their heads and shoulders before they can sit up, which, in turn, precedes standing and walking. Lifting the head is usually followed by head control. Although they are born with virtually no head or neck control, most infants can lift their heads to a 45-degree angle by the age of four to six weeks, and they can lift both their head and chest at an average age of eight weeks. Most infants can turn their heads to both sides within 16 to 20 weeks and lift their heads while lying on their backs within 24 to 28 weeks. By about nine to 10 months, most infants can sit up unassisted for substantial periods of time with both hands free for playing.

One of the major tasks in gross motor development is locomotion, the ability to move from one place to another. Infants progress gradually from rolling (eight to 10 weeks) to creeping on their stomachs and dragging their legs behind them (six to nine months) to actual crawling (seven to 12 months). While infants are learning these temporary means of locomotion, they are gradually becoming able to support increasing amounts of weight while in a standing position. In the second half-year of life, babies begin pulling themselves up on furniture and other stationary objects. By the ages of 28 to 54 weeks, on average, they begin navigating a room in an upright position by holding on to the furniture to keep their balance. Eventually, they are able to walk while holding on to an adult with both hands and then with only one. They usually take their first uncertain steps alone between the ages of 36 and 64 weeks and are competent walkers by the ages of 12 to 18 months.

Toddlerhood
Toddlers are usually very active physically. By the age of two years, children have begun to develop a variety of gross motor skills. They can run fairly well and negotiate stairs holding on to a banister with one hand and putting both feet on each step before going on to the next one. Most infants this age climb (some very actively) and have a rudimentary ability to kick and throw a ball. By the age of three, children walk with good posture and without watching their feet. They can also walk backwards and run with enough control for sudden stops or changes of direction. They can hop, stand on one foot, and negotiate the rungs of a jungle gym. They can walk up stairs alternating feet but usually still walk down putting both feet on each step. Other achievements include riding a tricycle and throwing a ball, although they have trouble catching it because they hold their arms out in front of their bodies no matter what direction the ball comes from.

Preschool
Four-year-olds can typically balance or hop on one foot, jump forward and backward over objects, and climb and descend stairs alternating feet. They can bounce and catch balls and throw accurately. Some four-year-olds can also skip. Children this age have gained an increased degree of self-consciousness about their motor activities that leads to increased feelings of pride and success when they master a new skill. However, it can also create feelings of inadequacy when they think they have failed. This concern with success can also lead them to try daring activities beyond their abilities, so they need to be monitored especially carefully.

School age
School-age children, who are not going through the rapid, unsettling growth spurts of early childhood or adolescence , are quite skilled at controlling their bodies and are generally good at a wide variety of physical activities, although the ability varies according to the level of maturation and the physique of a child. Motor skills are mostly equal in boys and girls at this stage, except that boys have more forearm strength and girls have greater flexibility. Five-year-olds can skip, jump rope, catch a bounced ball, walk on their tiptoes, balance on one foot for over eight seconds, and engage in beginning acrobatics. Many can even ride a small two-wheel bicycle. Eight- and nine-year-olds typically can ride a bicycle, swim, roller skate, ice skate, jump rope, scale fences, use a saw, hammer, and garden tools, and play a variety of sports . However, many of the sports prized by adults, often scaled down for play by children, require higher levels of distance judgment and hand-eye coordination , as well as quicker reaction times, than are reasonable for middle childhood. Games that are well suited to the motor skills of elementary school-age children include kick ball, dodge ball, and team relay races.

In adolescence, children develop increasing coordination and motor ability. They also gain greater physical strength and prolonged endurance. Adolescents are able to develop better distance judgment and hand-eye coordination than their younger counterparts. With practice, they can master the skills necessary for adult sports.

Common problems

There are a range of diseases and disorders that affect gross motor skill development and skills. Among young persons, developmental problems such as genetic disorders, muscular dystrophy , cerebral palsy , and some neurological conditions adversely impact gross motor skill development.

Gross motor skills can become impaired in a variety of ways, including injury, illness, stroke , and congenital deformities. Developmental coordination disorder affects motor skills. A person with this disorder has a hard time with skills such as riding a bike, holding a pencil, and throwing a ball. People with this disorder are often called clumsy. Their movements are slow and awkward. People with developmental coordination disorder may also have a hard time completing tasks that involve movement of muscle groups in sequence. For example, such a person might be unable to do the following in order: open a closet door, get out a jacket, and put it on. It is thought that up to 6 percent of children may have developmental coordination disorder, according to the 2002 issue of the annual journal Clinical Reference Systems . The symptoms usually go unnoticed until the early years of elementary school; the disorder is usually diagnosed in children who are between five and 11 years old.

Children with any one or combination of developmental coordination disorder symptoms should be seen by a pediatrician who specializes in motor skills development delays. There are many ways to address gross motor skills impairment, such as physical therapy. This type of therapy can include treating the underlying cause, strengthening muscles, and teaching ways to compensate for impaired movements.

When to Worry?
Parents, teachers, and primary caregivers need to have a clear understanding of how young children develop gross motor skills and the timetable for development of the skills. The Lincoln-Oseretsky Motor Development Scale is an individually administered test that assesses the development of motor skills in children and adults. Areas covered include fine and gross motor skills, finger dexterity and speed, and hand-eye coordination. The test consists of 36 tasks arranged in order of increasing difficulty. These include walking backwards, standing on one foot, touching one's nose, jumping over a rope, throwing and catching a ball, putting coins in a box, jumping and clapping, balancing on tiptoe while opening and closing one's hands, and balancing a rod vertically. Norms have been established for each part of the test for children aged six to 14. When in doubt ask. There is never anything worry in asking questions.

Have a great weekend!

There is never enough practice in math for money. I have no memory for learning money or coin value growing up, I just know that I'm asked all the time how to help and build those money skills. I think in many times our math move faster than many kids are ready to move. Some need more practice other need that practice that always be part of their day as review.

For me, money practice can from my weekly allowance--sometimes I would try it get it twice week but there were times when the bank would have to owe me as well. (That didn't work out so well.) Summer is a great time for kids to work with coins plus gain some responsibility.

In class, I have set up a classroom bank and charged students for everything from borrowing pencils to renting the chair they are sitting in.

Ok some ground rules.

In either event, before they get an allowance, a child should be old enough to count money. The key to a successful allowance is structuring it right from the outset.

Make it clear to your children what kinds of expenditures the money is for, and that they are expected to save some of it. Younger children - ages 7 to 10 - shouldn't be held accountable for items like school lunch money as part of their allowances, but it's not a bad idea for older kids and has the added benefit of fewer payments changing hands.

Some experts think parents should not link the allowance money to household chores. Children should be expected to help out around the house and in the yard because they are members of the family, not because they are paid. That's your call, obviously, not mine. When my family moved, my sister and I were slave labor and charged riding the lard of weeds at 5 cents a pop--we were rich in no time.

Yet with children over 8 or 9 years old, giving an allowance doesn't preclude paying them for specific chores, especially the occasional type that you might otherwise pay outsiders to perform, such as shoveling the sidewalk or washing the car. Why not keep the money in the family?

So instead of grimacing when your children hit you up for a raise, decide when the time is right and then engage them in fruitful negotiations. How long since the last raise? Will new expenditures be covered? What amount of the raise will be saved long-term for expenditures requiring your approval?

The most vexing decision on allowances is how much - a decision affected by personal values, family income and common sense. Don't let your children influence the amount by saying what their friends are getting: Any normal child will bring in high figures.

Many parents like to give their children the equivalent in today's dollars of the allowance they received at the same age. Assuming that these parents have more or less the same means as their parents did, this can be a comfortable solution.

Something to think about trying. It seems easier than running a classroom bank. My freebie is designed to help you teach and reenforce learning the value of coins. Without knowing those, kids are sunk. Print it off and use it to reteach coin values and to help you in the class and at home.

It seems only like yesterday when the year started. I always wonder where it went but I'm glad the year the year is almost over--it's been a year and then some but the pile of reading I want to get done over the summer.

My plan this summer is to continue to build my Common Core depth of knowledge and ways to shift the cognitive load to my students. My district has been pulling curriculum from just about every other district but ones in Colorado. (New York and Georgia--have great math units)

Book 1 & 2) Both of Eric Jenson's Students with Poverty books. Many of our RTI conversations seem to come back to this basic issue. Poverty impacts student learning more than most realize.

Book 3) Academic Conversations--the rubric I'm evaluated on looks at the basic of teacher to student talk and how much of that is high order thinking that students are doing without my help. Yes, without me. You would be amazed its really not super hard to get them to do that. Just lots of guided practice.

Book 4) Learning in the Fast Lane--I'm always on the look out for high impact, researched based instructional approaches that are easy to do.





Anyone have a pile of books you are planing to get through this summer? Share them below.

Have a great last couple weeks of school before summer starts.