Three-Tier Model for Elementary Mathematics

Three-Tier Model for Elementary Mathematics
Using RTI to Increase Student Achievement in the Early Grades Good afternoon and welcome to the Three-Tier Model for Elementary Mathematics webcast. West Virginia Department of Education

Lynn Baker, Office of Instruction Linda Palenchar, Office of Special Programs
I’m Linda and with me is Lynn Baker. If you have questions about the information we are going to share today, please type them into the box on the bottom of your screen. We will compile your questions and respond to them via an to all participants in today’s webcast. West Virginia Department of Education

West Virginia Department of Education
As you already know, the WV RTI process was first implemented for the area of reading. However, it also applies to mathematics and writing. During this overview, we will review the RTI framework and see how it is used to provide quality instruction to all students and research-based interventions for students who struggle in math. West Virginia Department of Education

RTI is the practice of Providing high-quality instruction and intervention matched to student needs and Using learning rate over time and level of performance to Make important educational decisions. (NASDSE, 2005) West Virginia’s working definition of Response to Intervention is shown on this slide and I would like to highlight a few phrases within this definition. First, High quality instruction is defined as “scientifically research-based.” This gives us confidence that it will be effective with a large majority of students. “Matched” refers to the fact that we are directly assessing student skills. “Results” allow us to match instruction directly to student need. “Level of performance” gives us a snapshot of how well a student is doing compared to other students (or district/state standards). “Rate of growth” gives us more of a motion picture as to how well our instruction is working for individual students or small groups of students. Finally, “Educational decisions” include: (1) How far behind is a student? (2) What resources are needed (both intensity and nature of resources should be considered)? (3) Is our instruction working? (4) If not, how do we need to change it? (5) If so, is the student catching up to his/her peers? RTI data can also constitute PART of the data needed for a full, individualized evaluation under IDEA. High-quality instruction/intervention defined as instruction or intervention matched to student need that has been demonstrated through scientific research and practice to produce high learning rates for most students. Individual response is assessed in RTI and modifications to instruction/intervention or goals are made depending on results with individual students. Learning rate and level of performance are the primary sources of information used in ongoing decision-making. Learning rate refers to a student’s growth in achievement or behavior competencies over time compared to prior levels of performance and peer growth rates. Progress monitoring is an essential component in determining learning rate and level of performance. Level of performance refers to a student’s relative standing on some dimension of achievement/performance compared to expected performance (either criterion or norm referenced). Decisions about the use of more or less intense interventions are made using information on learning rate and level. More intense interventions may occur in general education classrooms or pull-out programs supported by general, compensatory or special education funding. Important educational decisions about intensity and likely duration of interventions are based on individual student response to instruction across multiple tiers of intervention. Decisions about the necessity of more intense interventions, including eligibility for special education, exit from special education or other services, are informed by data on learning rate and level. West Virginia Department of Education

WV RTI Framework Components
Three Tier Instructional Model Universal Screening Progress Monitoring Teaming & Collaboration Data-based Decision Making Professional Development These are the six components of the WV RTI process and represent core principles. Each is essential to successful RTI implementation and together they comprise the RTI framework. The process is predicated on the importance of prevention and early intervention and applies to reading, mathematics, and written language. When these components are in place, a school can be assured that all students’ needs are being met and that a process for identifying and supporting students who struggle is established. West Virginia Department of Education

Lessons Learned from the RTI Reading Initiative
Interventions demand integrity Consistent monitoring is critical Professional development facilitates the change Hold fast to RTI guidelines Collaboration is essential RTI has been a work in progress in WV since the school year. We began with reading and have learned some valuable lessons along the way. Interventions must be delivered to struggling students as they were designed. The most important feature of an intervention is its explicitness. Research-based interventions have a high level of scaffolding, many opportunities for student practice, and a very systematic approach to skills instruction. “Tinkering” with a research-based intervention is most likely a recipe for its failure. As the saying goes, “what gets monitored, gets done”. We’ve learned that students must monitor their own progress. Teachers must monitor student achievement and effectiveness of instruction. Principals must monitor classroom instruction and how the RTI framework is actually being implemented. We have also learned that continuous and embedded professional development is needed for both teachers and principals. When teachers participate in book studies together, use other methods for learning new information, and most importantly, apply new techniques then discuss effectiveness, instructional practice changes. Holding fast to the RTI guidelines is critical. This refers to the 6 components discussed on Slide #4. All components are of equal value and importance and careful monitoring of them is essential. And last, but certainly not least, is the importance of strong and meaningful collaboration. RTI is a school wide process and impacts the work of all teachers and the principal. Frequent communication regarding each of the six components helps the system run smoothly. Everyone’s insight, dedication, and hard work is needed for successful RTI implementation. West Virginia Department of Education

A Three-Tier System for Mathematics
Key Research Findings & Features of the Model Now we’ll take a look at some of the research in terms of the RTI model and its use with the area of mathematics. West Virginia Department of Education

Why worry about math? 64% of US 4th graders are not proficient on National Assessment of Educational Progress (NAEP) measures. They lack facility in understanding whole numbers, fractions, and decimals. 70% of US 8th graders are not proficient on the NAEP measures of mathematics. They do not understand fractions, percents, decimals, and other basic arithmetic concepts needed to solve practical problems. So, why worry about mathematics? As the statistics on this slide indicate, there is a need to address mathematics achievement across the United States. Take a close look at the mathematics skills that are most often cited as in need of improvement. West Virginia Department of Education

WESTEST 2008 Mathematics Proficiency
All Students 3rd Grade 5th Grade 8th Grade 10th Grade 75.37% 80.79% 72.63% 67.98% Special Education 3rd Grade 5th Grade 8th Grade 10th Grade 55.82% 51.13% 31.36% 22.29% This slide shows the 2008 WESTEST proficiency rates in mathematics for selected grade levels. These data for West Virginia students are consistent with the NAEP information on the last slide. Low SES 3rd Grade 5th Grade 8th Grade 10th Grade 68.29% 74.59% 63.08% 57.02% West Virginia Department of Education

Key research findings indicate…
Most students fail to meet minimal mathematics proficiency standards by the end of high school (U.S. Department of Education, 2003). Existing instructional tools and textbooks often do a poor job of adhering to important instructional principles for learning mathematics (National Mathematics Advisory Panel, 2008). Early mathematics intervention can repair deficits and prevent future deficits (Fuchs, Fuchs, & Karns, 2001; Sophian, 2004). Here are some additional findings. Please note the second statement that refers to mathematics resources and tools. Mathematics curricula is determined by the WV CSOs and it’s important to remember that the mathematics textbook is one of many resources that supports instruction. West Virginia Department of Education

Key Research Findings Indicate…
Providing specific information on student performance to both teachers and students enhances mathematics achievement Using peers as tutors or guides improves low achievers’ computational skills and may improve problem-solving skills Providing specific feedback to parents on their students’ mathematics achievement is important Principles of direct or explicit instruction are useful in teaching mathematical concepts and procedures (Baker, Gersten & Lee, 2002) Here are some additional findings that we use to guide our thinking about designing core instruction for all students and intervention for those who struggle in mathematics. West Virginia Department of Education

We don’t have all the answers yet…
We don’t have all the answers yet, we’re just beginning our work in RTI for mathematics but West Virginia Department of Education

Together we will understand the processes and procedures needed for successful implementation of RTI for mathematics. Together we will understand the processes and procedures needed for successful implementation of RTI for mathematics. West Virginia Department of Education

Together we’ll move the research into practice…
West Virginia Department of Education

All Some RTI Continuum of Support for All Few Intensive Strategic
Universal So, what does the RTI model look like for mathematics? Just as in the reading model, we focus on a quality Tier 1 for all students, data-based targeted intervention for some students, and, for those few who struggle the most, intensive intervention. West Virginia Department of Education

Tier 1: Core Instruction
Definition Core instruction based on West Virginia CSOs Focus All students Program Standards-based mathematics instruction and curriculum Key Features of Instruction Active engagement; research-based mathematics practices; differentiated instruction Interventionist General education teacher Setting General education classroom Grouping Whole group and small group for differentiation Time Policy 2510 requirements Assessment Universal screening (fall, winter & spring) Let’s take a look at the characteristics of each tier. Tier 1 refers to core mathematics instruction based on WV CSOs. It is provided to all students by the general education teacher within a standards-based curriculum. Let’s look closely now at the key features of Tier 1 instruction for mathematics. Using a wide range of teaching strategies to teach mathematical concepts and skills helps ensure that all students make the necessary math connections. Strategies include: modeling with manipulatives, interacting with mathematical concepts through literature, engaging in discussion of math concepts, playing math games, and viewing and creating visual representations. Each of these strategies helps students strengthen and deepen their math knowledge, understanding, and skills. Also, grouping students within core instruction is essential for differentiation. Finally, the universal assessment piece of the RTI for Mathematics framework is currently under investigation. A place to begin is with your core math program which should include benchmark assessments. There are many commercial products as well and as schools in West Virginia begin to implement their RTI for mathematics processes, we will be able to share more information regarding effective universal screening tools. West Virginia Department of Education

Policy 2510 Requirements Chart II: Primary Elementary (K-2)
In k-2 classrooms, the given content areas are taught daily. It is required, in accordance with scientifically based reading research, that, at a minimum, a daily-uninterrupted 90 minute reading/English language arts block be scheduled during which students are actively engaged in learning through whole group, small group and reading center activities. A minimum of 60 minutes of daily mathematics instruction is required. It is important to keep State policy requirements in mind as you begin to plan for your mathematics implementation. In the primary grades, K-3, please note the section of the requirement in red – a minimum of 60 minutes of daily mathematics instruction is required. West Virginia Department of Education

Policy 2510 Requirements Chart III: Intermediate Elementary (3-4) Intermediate elementary students will be taught the given content areas. It is required, in accordance with scientifically based reading research, that, at a minimum, 90 minutes of reading and English language arts instruction be provided through whole group, small group and reading center activities as a block or throughout the school day. A minimum of 60 minutes of daily mathematics instruction is required. Sufficient emphasis must be placed on the following content areas to ensure that students master content knowledge and skills as specified in the 21st century content standards and objectives for each subject. The same time requirement is in place for intermediate grades 3 and 4. West Virginia Department of Education

Policy 2510 Requirements Chart IV: Middle Level Education (Grades 5-8) These required core courses shall be taught daily by a team of qualified teachers. An intervention component will ensure mastery of the rigorous content standards and objectives at each grade level. The core courses (Reading and English/Language Arts, Mathematics/Algebra I, Science and Social Studies) will be offered within a block of time no less than 180 minutes. The principal and a team of teachers will determine time allocations that provide adequate time to achieve mastery of the West Virginia content standards and objectives for each of the required courses and effectively address the academic needs of students who are below mastery in the basic skills of reading, writing and mathematics. For middle school, the time requirements are a bit different. Note that the principal and a team of teachers may use student achievement data to determine time allocations for core subjects, including mathematics. West Virginia Department of Education

The strength and quality of Tier 1 instruction determines the number of students who need Tier 2 intervention… The strength and quality of Tier 1 instruction determines the number of students who need Tier 2…This is an important concept within the RTI model. Improving general classroom instruction is the first and important aspect of implementing the RTI process. RTI practices are based on the assumption and belief that all children can learn. It is our responsibility, then, to identify the curricular, instructional and environmental conditions that enable learning for all. Differentiated instruction is a key factor in the delivery of quality general classroom instruction. Likewise, when teachers use research-based instructional strategies, including classroom assessments for and of learning, most students will benefit from the core program, only some will need Tier 2 (strategic support) and just a few will need the intensive supports of Tier 3. West Virginia Department of Education

Tier 2: Targeted Intervention
Definition Programs and procedures to support Tier 1 and target specific skills Focus Students identified with marked difficulties and insufficient response to Tier 1 Program Research-based interventions Key Features of Instruction Additional practice opportunities; explicit, scaffolded instruction; error correction; identification of misconceptions; peer interaction and collaboration Interventionist Personnel designated by school Setting Learning space designated by school Grouping Small groups with sufficient numbers of students to facilitate group interactions Time 20-30 minute sessions, 3 times/week Assessment Progress monitoring twice monthly on target skills Let’s move on to Tier II. This slide emphasizes the key features of Tier II intervention. The distinguishing characteristic of Tier II instruction is its explicit nature. Explicit instruction in mathematics includes: Teacher demonstrates and models how to solve problems or perform skills; Teacher guides students to understand and articulate relationships; Students are provided time for extensive practice and timely feedback’ Teachers encourage students to verbalize their thinking; and Teachers help students make connections between mathematics experiences and the concepts and skills Student interaction is critical. Time must be provided for students to explain their mathematics ideas to others. Interactions help students clarify and evaluate their own thinking processes. Mathematics is not just about getting the right answers. It’s also about how to get the answers. Practice must be meaningful and based on conceptual understanding, number sense, and connected to previously taught skills. Games, group activities, and computer software enhance student engagement for practice. Teaching vocabulary and the language of mathematics is another important aspect of instruction. Teaching students correct language gives them tools to articulate their mathematical thinking. Research shows that direct instruction of math vocabulary supports problem solving proficiency. Next, identifying and correcting students’ misconceptions about mathematics, both concepts and procedures, is an important intervention component. Students “own” their misconceptions and the teacher’s role is to listen to how students articulate mathematical concepts or watch them as they perform operations to identify where thinking goes awry. Once these misconceptions are identified, the teacher can help the student “unlearn” the incorrect concept and replace it with a legitimate one. Finally, group size is important. Research in this area indicates that larger group sizes facilitate the collaborative processes needed. As noted on this chart, you need small groups with sufficient numbers of students. When students can work in pairs or small groups to solve problems, articulate math concepts and procedures, play games, and complete projects together, learning is enhanced. Note the time for mathematics intervention. It is significantly less than the time recommended for early reading instruction. Again, the importance of effective Tier 1 is very important. When most students benefit from Tier 1, general classroom mathematics instruction that includes the components discussed earlier, fewer students will be in need of more intensive (Tier 2) support. West Virginia Department of Education

Key Features of Tier 2 Intervention
Additional practice opportunities Explicit, scaffolded instruction Error correction Identification of misconceptions Peer interaction and collaboration This slide is a snapshot of the key features of Tier II mathematics intervention. West Virginia Department of Education

Scaffolding We Do I DO You Do Model Independent Performance
Meaningful Practice We Do Independent Performance You Do Scaffolding the learner is a key component of intervention. It requires teachers to identify and sequence key concepts that are essential to what is being taught. Scaffolding involves careful organization and pacing of instruction to support student learning. Research shows that scaffolding content benefits all students, particularly those who struggle. Scaffolding is the systematic process of analyzing content and sectioning it into smaller manageable chunks for the purpose of planning and delivering instruction. This is a critical aspect of targeted intervention and is how the level of explicitness can be adjusted for struggling learners. As indicated on the slide, the first step in scaffolding is the “I do” piece wherein the teacher models the skill or procedure for students. This is followed by “we do” and the student and teacher work together. Finally, the “you do” part refers to placing the responsibility on the student to perform the skill. Throughout this process, the level of teacher support, by design, decreases over time. Scaffolding involves a purposeful release of the support and is accomplished through corrective feedback. West Virginia Department of Education

Six Instructional Principles for Tier 2 Intervention in Mathematics
Instructional explicitness Instructional design that eases the learning challenge A strong conceptual basis for procedures that are taught Sufficient, engaging, and meaningful practice Cumulative review Motivators to help students regulate their attention and behavior (Fuchs, 2008) As teachers establish Tier II interventions, it will be important to keep these instructional guidelines in mind. (Allow time to read slide.) West Virginia Department of Education

Tier 3: Intensive Intervention
Definition Customized instruction beyond Tiers 1 and 2 Focus Students with significant difficulties who have not responded to Tier 1 and Tier 2 Program Replacement program that provides intense intervention Key Features of Instruction More explicit and intense than Tier 2 Interventionist Personnel designated by school Setting Learning space designated by school Grouping Small groups with sufficient numbers of students to facilitate group interactions Time Sufficient to provide replacement program instruction Assessment Progress monitoring weekly on target skills to assess response to intervention Finally, this chart summarizes the components of Tier III. Notice the commonalities between Tiers 2 and 3. One of the distinguishing characteristics of Tier 3 is the possible use of a replacement program that addresses severe gaps in a student’s mathematics performance. These students are significantly below grade level and need to acquire skills not typically taught in their current grade placement. Please note the grouping recommendation – just as in Tier 2, sufficient numbers of students is a recommended practice. It supports the concept discussed earlier about the importance of peer interaction and collaborative learning in mathematics. West Virginia Department of Education

References Baker, S., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low achieving students. The Elementary School Journal, 103, Fuchs, L.S., Compton,D. L., Fuchs, D., Paulsen, K., Bryant, J. & Hamlett, C. L. (2005). Responsiveness to intervention: Preventing and identifying mathematics disability. Teaching Exceptional Children, Mar/Apr, VanDerHeyden, A. (2008). Using RTI to improve learning in mathematics. Retrieved August 16, 2008 from ent&task=view&id=325&pop This concludes the RTI overview section of our webcast. It is now my pleasure to welcome Lynn Baker as your presenter. West Virginia Department of Education

Quality Mathematics Instruction Tier 1

Quality Mathematics Instruction for Each Student
At the core of Response to Intervention, is the belief that each student has the right to quality mathematics instruction. It is not enough for the class to succeed as a whole. Each individual student should receive mathematics instruction that enables him to develop an understanding of grade level WV Content Standards and Objectives. West Virginia Department of Education

Questions to Think About
As we move forward with RTI in the context of mathematics there are a few questions for us to ponder. West Virginia Department of Education

What does it mean to be fluent in a language? Take a moment and discuss this question with your colleagues. What does it mean to fluent in a language? Allow time for discussion. As you discussed this question, you may have mentioned the following: When one is fluent in a language, he is able to communicate in the language. He is able to read, write and speak in the language. He is also thinks in the language. The individual does not translate the language into his native tongue. West Virginia Department of Education

What does it mean to be fluent in a language? What does it mean to be a fluent reader? Now, let’s discuss this question. What does it mean to be a fluent reader? Allow time for discussion. A fluent reader is one who reads and comprehends what she is reading quickly and with a minimum of effort. She is able to read a variety of texts, including fiction, nonfiction, newspapers and magazine articles, just to name a few. She is also able to communicate the meaning of the texts she is reading. West Virginia Department of Education

What does it mean to be fluent in a language? What does it mean to be a fluent reader? What does it mean to be fluent in mathematics? Finally, discuss: What does it mean to be fluent in mathematics? When one is fluent in math, he understands the concepts and procedures and is able to apply these concepts in the real-world. He is able to communicate his understanding of mathematical concepts. The quick recall of math facts is but one small component a student learns in order to become fluent in mathematics. Quality instruction in mathematics focuses on developing the conceptual understanding of the mathematics along side the teaching of procedures. One does not exist independently of the other. Quality mathematics instruction includes both. West Virginia Department of Education

NCTM-Intervention Lenses
As we move from mathematics for all to mathematics for every student, NCTM, The National Council of Teachers of Mathematics, has identified several lenses for us to look through as we design instruction within the RTI model. West Virginia Department of Education

Learning Significant Mathematics The first lens is Learning Significant Mathematics—all students are entitled to learn significant mathematics. What guarantees the learning of every student? What provides the mathematical power that every student should expect? This is the lens that determines the shape of the other lenses. West Virginia Department of Education

Learning Significant Mathematics Knowing the Mathematics Knowing the Mathematics- Teachers need a deep understanding of the mathematics they teach, its form and its structure, its developmental nature and its power in order to make informed decisions concerning the mathematics instruction of their students. Teachers make decisions daily as to the order concepts are taught, the scaffolding of concepts, instructional strategies used, which manipulatives or tools help students develop an understanding of the concepts, and when to incorporate technology to further a student’s understanding. West Virginia Department of Education

Learning Significant Mathematics Knowing the Mathematics Assessment and Data Gathering Assessment and Data Gathering—Data driven instruction. This is the heart of RTI. How do we know the mathematical understanding each student brings to the classroom? What information determines the goal setting? It is important for teachers to make informed instructional decisions. We want to collect important data. Which pieces of data will give us the needed information to make informed decisions about the instructional process. It is not a good use of time to simply collect data for the sake of collecting data. What are you going to do with the data once you have gathered it. If it is going to be compiled into a large box, just in case you may need it, your time would be better spent with another learning task. Data should also come from multiple sources including: summative tests (the WESTEST), benchmark tests, screening tools, informal assessment tasks, performance tasks, and teacher observation. Teachers should be constantly assessing the progress of their students. In relationship to RTI and mathematics, this is an area that is still emerging. In order to screen and monitor students’ progress, the tool must be aligned with the West Virginia Content Standards and Objectives. The coordinators at the West Virginia Department of Education are continuously reviewing material that is brought to our attention. As we find tools that support the West Virginia Content Standards and Objectives, we will share them with you. Your task will be to evaluate the appropriateness of the various tools and materials for your students. As we study this area, as a classroom teacher you will need to identify the resources you currently have available. This would include any materials that is available on the Teach 21 website or provided with your current text. Some texts provide an extensive assessment resource. Do not underestimate the importance of a teacher systematically recording her observations of student learning. West Virginia Department of Education

Learning Significant Mathematics Knowing the Mathematics Assessment and Data Gathering Quality Planning and Delivery Quality Planning and Delivery—Is the planning and delivery transparent? Are the plans flexible enough to address the needs of every student? This is often assumed, but it can fall into the “one-size-fits-all” category. Teachers should be using research-based strategies to deliver instruction to their students. West Virginia Department of Education

Learning Significant Mathematics Knowing the Mathematics Assessment and Data Gathering Quality Planning and Delivery Alignment The final lens is Alignment—1) chronology—intervention must be timely 2) curriculum—intervention materials need to compliment the materials used in the classroom [If classroom instruction centers around patterns the intervention should be supporting the classroom instruction. The intervention instruction should not be focusing on an unrelated concept.]3) pedagogy—strategies for intervention must be based on specific needs 4) standards and goals—intervention materials should reflect the nature and intent of the mathematical standards and goals. These lenses should be used not only to frame classroom instruction in Tier I, but should be used to impact all components of the RTI process. West Virginia Department of Education

Response to Intervention is a Process Not a Product
Before we move on, I want to take a moment and emphasize the following: Response to Intervention is a Process of using data to make instructional decisions. It is not a PRODUCT. I frequently receive s concerning products that are available for RTI in mathematics. I also believe this is an area where there will be an increase in product development. I want to CAUTION you at this point, to review all materials through the previously mentioned lenses. First, it is possible to provide quality instruction and intervention without commercial materials. As we proceed down this RTI path, we will be developing guidelines you should consider as you review materials. In the mean time BEWARE of promises and quick fixes. Teaching is demanding. Use your expertise as you design instruction for your students. With this being said, as material becomes available that supports mathematics instruction in our state, we will share this information with you.

First Steps West Virginia Department of Education
So the question is, “Where do we begin in the process of implementing RTI in the context of mathematics?” If RTI is to be successful we must systematically work to establish each of the components. While we may want to jump to the intervention components, we must begin by building a solid foundation. Beginning with quality instruction in Tier I. West Virginia Department of Education

Tier 1 Universal Instruction Quality Lesson Design
WV CSOs/Assessment Launch Explore Summarize As teachers begin planning daily lessons, there are several key components teachers need to consider: the purpose of the lesson, the assessment of the lesson, the launch the lesson, the exploration of the concept, and the summarization of the lesson. We will take a few minutes and explore each of these lesson components. West Virginia Department of Education

WV CSOs/Assessment We need to begin with the WV CSOs and the assessment of the lesson. This is supported by the work of Jay McTighe and Grant Wiggins in their work with Understanding By Design. We need to begin our planning with the end in mind. The WV CSOs drive our classroom instruction. When we speak of the CORE, we are referring to our Content Standards and Objectives not the textbook. The textbook is one of many resources we may use during our classroom instruction. With the revisions of our content standards, it is difficult if not impossible to develop a student’s understanding of the concepts of one objective within one lesson. There are multiple learning targets in each of our CSOs. Students’ mastery of an objective will take place throughout the year. Once you have determined the purpose of the lesson, you need to focus on the assessment. How will you know if the students achieved the goal you set for this lesson? What behaviors will you observe?, What type of discussions do you want to hear? Assessment will take different forms. This assessment will drive future instruction in mathematics. West Virginia Department of Education

WV CSOs/Assessment Launch -Review of student’s prior knowledge -A children’s literature storybook -A problem to solve Next our thoughts turn to the delivery of the lesson. The Launch is the introduction of the lesson. How will you get the students’ attention? This section may include a review of the students’ prior knowledge, a selection of children’s literature such as Spaghetti and Meatballs for All, by Marilyn Burns, or a problem to solve. The teacher wants to “hook” the students into wanting to learn more. The Launch is more than a “bell ringer or sponge.” It is the Velcro on which students attach new knowledge. William Bender, an authority on Differentiated Instruction in the area of mathematic, states “…instruction in math will be built almost entirely on prerequisite learned skills rather than on maturational-based knowledge.” What does this mean to a mathematics teacher? If a student does not have prior knowledge to attach the new concepts, the teacher must construct the this knowledge. West Virginia Department of Education

WV CSOs/Assessment Launch Explore Explore: This section of the lesson is the main section of the lesson. It is probably the longest of the three sections. This is where the students develop new knowledge and skills. Students should be actively engaged in doing mathematics instead of passively watching others do mathematics. This section may include: inquiry-based tasks, vocabulary development, research-based instructional strategies and collaborative learning experiences. West Virginia Department of Education

http://wvde.state.wv.us/teach21 West Virginia Department of Education
A multitude of research-based strategies are available on the Teach 21 site. The Strategy Bank is located under the Curriculum “button.” There are strategies to Activate Prior Knowledge, Vocabulary Development, Comprehension Strategies among others. Denise White compiled this information on the Teach 21 Site. She intentionally cited mathematical examples for many of the strategies. The Strategy Bank is constantly changing. You will want to frequently check the Strategy Bank for updates. West Virginia Department of Education

WV CSOs/Assessment Launch Explore Summarize Summarize: This section of the lesson design is a valuable component. It is frequently overlooked because teachers “run out of time.” Summarization is a research-based strategy that has been proven to be effective in classroom instruction. Classroom teachers need to monitor the flow of the instruction in order to allow time for summarization. This is the part of the lesson in which teachers insure that students have understood the mathematical concepts developed in the lesson. It is important to identify misconceptions early in the instructional process. Speaking of misconceptions. Misconceptions are created by the students. For example all rectangles have two long sides the same and two short sides the same with four right angles. This misconception may have been created by students because the examples of rectangles that were provided to the students always looked this way. Were examples of squares shown to the students as examples of rectangles. Misconceptions are difficult to “correct” because students have ownership of the them. They created them. So they will frequently create a new misconception in order to correct their old one. They do not want to give it up. Teachers need to always be watching for misconceptions. This will enable us to correct the students’ thinking early in the concept development process. West Virginia Department of Education

WV CSOs/Assessment Launch Explore Summarize Research-based Strategies Vocabulary Instruction Formative Assessment Differentiation Strategies As teachers plan their daily lesson, they should always be thinking about quality lesson design. Many of the National Science Foundation curricula follow this form. Within each of these sections we need to continually focus on research-based instructional strategies, vocabulary instruction should be a part of every lesson, formative assessment (Which problems will give you incite into students’ thinking?” and differentiate instruction strategies are a must?) We are designing lessons so that each student in our classrooms will have access to significant mathematics. West Virginia Department of Education

RESOURCES West Virginia Department of Education
As I mentioned earlier, there are numerous resources available to educators for RTI. New resources for mathematics come to our attention almost on a daily basis. During each webinar and PD session, we will take a few moments and share a few of these resources with you. West Virginia Department of Education

Informal Math Assessment
The West Virginia Informal Math Assessment is located on the Teach 21 site under Assessment. This site provides K-3 teachers with assessment prompts correlated to the “new” CSOs. These tasks are intended to be used throughout the school year to guide the teachers as they plan instruction for their students. You may notice that Inform is written in red. It may be said the goal of the IMA is to inform teachers about the progress of their students. There is also a student record sheet provided. Each CSO has multiple opportunities for the teacher record the students’ progress during the year. West Virginia Department of Education

Quantiles West Virginia Department of Education
Beginning with WESTEST2, students in the 3rd grade and above will also have a Quantile Score reported. The Quantile Framework for Mathematics takes the guesswork out of mathematics instruction. It uses a common, developmental scale to measure student mathematics achievement, the difficulty of mathematical skills and concepts, and the materials for teaching mathematics. Quantiles enable educators to predict which mathematical skills and concepts a student is ready to learn and those that will require additional instruction. With Quantiles, teachers have a proven measure of student mathematics achievement to target instruction, monitor student progress and forecast performance on high-stakes tests. During the past month the RTI specialists and the County Math Leadership Teams received training on the Quantile Framework. In the future, educators will be looking at Quantiles and the relationship between Quantiles and RTI. I’m sure the Quantile Framework will be a valuable tool for teachers to use as they plan instruction and interventions. West Virginia Department of Education

WV RTI Google Site This Google Site is a site where information is posted concerning RTI. You will find lists of resources, websites, presentations etc… This site is updated from time to time. You may access it from the WVDE WebTop under Google Sites. It has been shared with the world so you are able to access it without a WebTop. This PowerPoint presentation will also be posted on this site along with the notes for each slide. Participants will have access to this presentation for 90 days. A URL will be sent out to participants following this broadcast. West Virginia Department of Education

Next Steps School-level Planning West Virginia Department of Education
As a school begins to develop a plan for their implementation of the RTI model in mathematics, there are several questions they should consider? West Virginia Department of Education

Initiate Discussion about Mathematics Instruction in Your School
Based on your achievement data for mathematics, what are your goals for mathematics instruction? Do all students in your school have the opportunity to learn significant mathematics? How does your current mathematics instruction align with the description of quality Tier 1 instruction provided in this webinar? Within your school, which teachers provide leadership in mathematics? RTI Is a data driven decision making process. A school needs to begin the process, by looking at their achievement data for mathematics? Based on their needs, the school needs to set goals for mathematics instruction in their school. Do all students in your school have the opportunity to learn significant mathematics? Schools also need to assess the mathematics instruction in Tier I. What are the strengths of your current Tier 1 instruction? Teacher leaders can play an important role in the instructional process of your school. Who are the teacher leaders in your school in relationship to mathematics? West Virginia Department of Education

What resources are available? Personnel Instructional materials Time
Initiate Discussion about Mathematics Instruction at Your School (continued) What resources are available? Personnel Instructional materials Time Assessments Professional development Funding Each school has resources that are unique to their school. Each school needs to identify the resources that are available and match them to the instructional needs of the students. These include but are not limited to: personnel, instructional materials, time, assessments, professional development and funding. A discussion guide is available for downloading. A school may use this guide as they initiate their discussion about mathematics and RTI. West Virginia Department of Education

Lynn Baker, Coordinator Linda Palenchar, Coordinator
Contact Information Lynn Baker, Coordinator Office of Instruction Linda Palenchar, Coordinator Office of Special Programs Thank you for joining us today. If you have any questions about the information you heard today, please contact either or both of us at the addresses noted on the slide. Again, thank you and we look forward to sharing more information about RTI for mathematics in the future. West Virginia Department of Education

Three-Tier Model for Elementary Mathematics

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Three-Tier Model for Elementary Mathematics

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Presentation on theme: "Three-Tier Model for Elementary Mathematics"— Presentation transcript:

Similar presentations

About project

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