RTI for Elementary Mathematics

1. Decision-Making for Intervention April 30, 2009 Webcast RTI for Elementary Mathematics Welcome to the second webcast in a series devoted to RTI for elementary mathematics. Schools across the state have been working diligently. They are analyzing mathematics data and taking critical looks at their Tier I or core mathematics instruction. Districts and schools are also recognizing the various professional development needs of teachers and addressing them through long-term planning. Today�s presentation will be archived for 90 days following the session. You will receive an e-mail containing the URL. The PowerPoint will also be posted on both the Teach 21 website and the OSPs RTI site.Welcome to the second webcast in a series devoted to RTI for elementary mathematics. Schools across the state have been working diligently. They are analyzing mathematics data and taking critical looks at their Tier I or core mathematics instruction. Districts and schools are also recognizing the various professional development needs of teachers and addressing them through long-term planning. Today�s presentation will be archived for 90 days following the session. You will receive an e-mail containing the URL. The PowerPoint will also be posted on both the Teach 21 website and the OSPs RTI site.

2. Today�s Presenters West Virginia Department of Education Lynn Baker MSP Coordinator Office of Instruction John Ford, Mathematics Coordinator, Title 1 Linda Palenchar, RTI Coordinator, Office of Special Programs Introduce speakers. 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 email to all participants in today�s webcast.Introduce speakers. 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 email to all participants in today�s webcast.

3. RTI is the practice of West Virginia Department of Education 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) Let�s take a moment to review West Virginia�s definition of RTI. 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. Let�s take a moment to review West Virginia�s definition of RTI. 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.

4. WV RTI Framework Components Three Tier Instructional Model Universal Screening Progress Monitoring Teaming & Collaboration Data-based Decision Making Professional Development West Virginia Department of Education These are the six components of the WV RTI process and represent core principles. Today we will focus on data-based decision-making and intervention within the context of the three-tier instructional model. Keep in mind the RTI framework or process applies to reading, writing and mathematics. While math implementation may look a bit different from your reading implementation, these core components are non-negotiables that preserve the integrity of the RTI process and provide consistency across West Virginia.These are the six components of the WV RTI process and represent core principles. Today we will focus on data-based decision-making and intervention within the context of the three-tier instructional model. Keep in mind the RTI framework or process applies to reading, writing and mathematics. While math implementation may look a bit different from your reading implementation, these core components are non-negotiables that preserve the integrity of the RTI process and provide consistency across West Virginia.

5. Revised Timelines for Implementation West Virginia Department of Education 2009 In February of 2009, the WVDE revised the timelines for implementing RTI for mathematics at the elementary level. Elementary schools will establish their frameworks for mathematics by July 1, 2010. The 2009-2010 school year will be a time for working together to build a strong Tier I mathematics program across all grades, making decisions about universal screening and progress monitoring tools, staffing for mathematics intervention and thinking about intervention lesson design. Each of these topics will be addressed in today�s presentation.In February of 2009, the WVDE revised the timelines for implementing RTI for mathematics at the elementary level. Elementary schools will establish their frameworks for mathematics by July 1, 2010. The 2009-2010 school year will be a time for working together to build a strong Tier I mathematics program across all grades, making decisions about universal screening and progress monitoring tools, staffing for mathematics intervention and thinking about intervention lesson design. Each of these topics will be addressed in today�s presentation.

6. Where is West Virginia with RTI for Mathematics? West Virginia Department of Education West Virginia elementary schools are: Using Acuity for benchmarking at grade 3 and beyond Using the WVDE Informal Math Assessment (IMA) to develop specific tasks for determining grade-level skills mastery Using mCLASS Math and AIMSWeb as benchmark and progress monitoring tools Refining their core mathematics instruction Exploring various mathematics intervention programs Facilitating book studies to learn more about mathematics instruction and intervention Over the past year, elementary schools across the state have been planning for and researching implementation of RTI for mathematics. This slide captures some of the ongoing activities at the elementary level. We�ll provide some information later in this presentation about assessment as well as how to select intervention materials and programs.Over the past year, elementary schools across the state have been planning for and researching implementation of RTI for mathematics. This slide captures some of the ongoing activities at the elementary level. We�ll provide some information later in this presentation about assessment as well as how to select intervention materials and programs.

7. Research-Base for RTI in Mathematics West Virginia Department of Education The field of math disabilities has a long history of research and several effective components of math intervention are clear.The field of math disabilities has a long history of research and several effective components of math intervention are clear.

8. National Mathematics Advisory Panel Effective Mathematics Instructional Practices West Virginia Department of Education Cooperative learning Formative assessment �real world� contexts The National Mathematics Advisory Panel Report offers findings and recommendations for evidence-based mathematics instructional practices. Cooperative learning practices improve computation skills. Use of the Team Assisted Individualization strategy can assist with conceptual understanding and problem solving Formative assessment improves student leaning, especially when teachers have additional guidance on using the assessment to design and individualize instruction. Use of �real world� contexts to introduce math ideas is another effective practice that engages students in authentic learning. The National Mathematics Advisory Panel Report offers findings and recommendations for evidence-based mathematics instructional practices. Cooperative learning practices improve computation skills. Use of the Team Assisted Individualization strategy can assist with conceptual understanding and problem solving Formative assessment improves student leaning, especially when teachers have additional guidance on using the assessment to design and individualize instruction. Use of �real world� contexts to introduce math ideas is another effective practice that engages students in authentic learning.

9. National Mathematics Advisory Panel West Virginia Department of Education Explicit instruction Clear models for problem solving Extensive meaningful practice of newly learned strategies and skills Opportunities to �think aloud� Extensive descriptive feedback Effective Mathematics Instructional Practices Finally, the National Panel noted that for students with mathematical difficulties, word problems and computation can be improved through explicit instruction. Explicit instruction includes clear models for problem solving using many examples, extensive practice in use of newly learned strategies and skills, opportunities to �think aloud� such as talking through a problem and elaborating on the decisions made, and extensive descriptive feedback that helps students understand concepts, avoid the same error in the future and improve their work. Finally, the National Panel noted that for students with mathematical difficulties, word problems and computation can be improved through explicit instruction. Explicit instruction includes clear models for problem solving using many examples, extensive practice in use of newly learned strategies and skills, opportunities to �think aloud� such as talking through a problem and elaborating on the decisions made, and extensive descriptive feedback that helps students understand concepts, avoid the same error in the future and improve their work.

10. The research is beginning to expand� West Virginia Department of Education Six instructional strategies have emerged as beneficial for students with math difficulties: Visual and graphic depictions Systematic and explicit instruction Student think-alouds Peer-assisted learning Formative assessment/progress monitoring data for teacher use Formative assessment/progress monitoring data for student use Each of the strategies listed on this slide show strong or moderate evidence in improving mathematics outcomes for students. Take a minute to review them and begin to think about how they can be incorporated into your school�s mathematics instruction.Each of the strategies listed on this slide show strong or moderate evidence in improving mathematics outcomes for students. Take a minute to review them and begin to think about how they can be incorporated into your school�s mathematics instruction.

11. Expanding research� West Virginia Department of Education Mathematics textbooks have little impact on student achievement on standardized tests � it�s the quality of instruction that makes a difference Studies on Computer Assisted Instruction (CAI) indicate positive achievement outcomes Instructional process strategies such as cooperative learning, peer assisted learning and small group tutoring have the strongest positive effects (Best Evidence Encyclopedia � BEE) It�s always important to remember that the West Virginia CSOs are the curriculum in any content area. Textbooks represent one tool that teachers utilize in facilitating student learning in a particular area. You also see that strategies that require students to work together to understand and apply mathematics skills are important ones to consider as you plan for improving mathematics at your school.It�s always important to remember that the West Virginia CSOs are the curriculum in any content area. Textbooks represent one tool that teachers utilize in facilitating student learning in a particular area. You also see that strategies that require students to work together to understand and apply mathematics skills are important ones to consider as you plan for improving mathematics at your school.

12. Expanding research� West Virginia Department of Education Language and nonverbal reasoning are key predictors for math disability (Fuchs, Compton & Fuchs, 2007) Experience, background knowledge, and entry skills of students are important (Ketterlin-Geller, chard & Fien, 2008) Math interventions for students who struggle can involve reteaching fundamental math concepts and/or providing extended time in the core mathematics program (Ma, 1999) Some final research concepts to consider as you plan for addressing the needs of students who struggle in mathematics are listed on this slide. A slide with full references is included at the end of this presentation. Some final research concepts to consider as you plan for addressing the needs of students who struggle in mathematics are listed on this slide. A slide with full references is included at the end of this presentation.

13. West Virginia Department of Education School teams need to analyze instruction, intervention methods, resources and the available research-based evidence supporting their use�

14. http://www.bestevidence.org/math/elem/top.htm West Virginia Department of Education Today we�ll talk about two websites designed to assist teachers with the task of selecting evidence-based intervention programs. First, the Best Evidence Encyclopedia is a free web site created by the Johns Hopkins University School of Education's Center for Data-Driven Reform in Education (CDDRE) under funding from the Institute of Education Sciences, U.S. Department of Education. It is intended to give educators and researchers fair and useful information about the strength of the evidence supporting a variety of programs available for students in grades K-12. The Best Evidence Encyclopedia provides summaries of scientific reviews produced by many authors and organizations, as well as links to the full texts of each review. Visit the BEE at the URL on the slide. Today we�ll talk about two websites designed to assist teachers with the task of selecting evidence-based intervention programs. First, the Best Evidence Encyclopedia is a free web site created by the Johns Hopkins University School of Education's Center for Data-Driven Reform in Education (CDDRE) under funding from the Institute of Education Sciences, U.S. Department of Education. It is intended to give educators and researchers fair and useful information about the strength of the evidence supporting a variety of programs available for students in grades K-12. The Best Evidence Encyclopedia provides summaries of scientific reviews produced by many authors and organizations, as well as links to the full texts of each review. Visit the BEE at the URL on the slide.

15. http://ies.ed.gov/ncee/wwc/Reports/Topic.aspx?tid=04 West Virginia Department of Education Another widely used website is the What Works Clearinghouse. The WWC is a US Department of Education Institute of Education Sciences initiative and offers a range of publications that evaluate elementary school math interventions and instructional strategies for students in grades K-5, which are designed to increase student outcomes related to mathematics achievement. The WWC assesses the rigor of research evidence on the effectiveness of interventions (programs, products, practices, and policies), giving educators the tools to make informed decisions. Intervention will be a focus during the upcoming year on the WWC so be sure to periodically check the site for updates.Another widely used website is the What Works Clearinghouse. The WWC is a US Department of Education Institute of Education Sciences initiative and offers a range of publications that evaluate elementary school math interventions and instructional strategies for students in grades K-5, which are designed to increase student outcomes related to mathematics achievement. The WWC assesses the rigor of research evidence on the effectiveness of interventions (programs, products, practices, and policies), giving educators the tools to make informed decisions. Intervention will be a focus during the upcoming year on the WWC so be sure to periodically check the site for updates.

16. http://www.iriscenter.com/resources.html West Virginia Department of Education Finally, the Iris Center, is a wonderful teacher resource. As this slide shows, it has a variety of resources to help general and special education teachers provide research-based instruction and intervention to students who struggle in mathematics.Finally, the Iris Center, is a wonderful teacher resource. As this slide shows, it has a variety of resources to help general and special education teachers provide research-based instruction and intervention to students who struggle in mathematics.

17. Key Features of Intervention West Virginia Department of Education If you participated in our December 2008 webcast, you have seen this information on the key features of Tier II mathematics intervention. As you analyze your student achievement data and begin to form intervention groups, these instructional elements help guide intervention lesson planning. If you participated in our December 2008 webcast, you have seen this information on the key features of Tier II mathematics intervention. As you analyze your student achievement data and begin to form intervention groups, these instructional elements help guide intervention lesson planning.

18. Tier 1: Core Instruction West Virginia Department of Education Let�s quickly review the main components of the 3-tier instruction model as they relate to mathematics. Tier 1 is considered the standards-based, differentiated general classroom.Let�s quickly review the main components of the 3-tier instruction model as they relate to mathematics. Tier 1 is considered the standards-based, differentiated general classroom.

19. Tier 2: Targeted Intervention West Virginia Department of Education Let�s revisit the important elements of Tier 2 mathematics instruction. 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, meaningful 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 intentional 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. Let�s revisit the important elements of Tier 2 mathematics instruction. 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, meaningful 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 intentional 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.

20. Tier 3: Intensive Intervention West Virginia Department of Education Finally, this chart summarizes the components of Tier 3. Notice the commonalities between Tiers 2 and 3. Distinguishing characteristics of Tier 3 include instruction 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 curriculum. 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.Finally, this chart summarizes the components of Tier 3. Notice the commonalities between Tiers 2 and 3. Distinguishing characteristics of Tier 3 include instruction 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 curriculum. 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.

21. Update from Washington, D.C. Last week, I (Lynn) had the opportunity to attend the Association of State Supervisors of Mathematics Conference and the National Council of Supervisors of Mathematics Conference. Some of you may have also attended NCSM or NCTM. West Virginia was well represented by a number of coaches and teachers. As I listened to leading experts in the field, I reflected on West Virginia�s journey with respect to implementation of RTI in the area of mathematics. Response to Intervention was a topic that was widely discussed. I was able to connect with various experts in the field. The steps we have taken thus far are in line with the recommendations from the mathematics experts. We are looking at quality Tier 1 instruction, data driven instruction, and Tier 2 instruction. This is an emerging area of study. A vast number of resources will become available over the next year especially in the area of assessing a student�s understanding of mathematics. In fact a document from the Institute of Education Sciences was released this past Friday. I am currently studying this extensive document for recommendations. So what did I take from away from D.C.? We need to take a deep breath and reflect on our journey thus far. It is not necessary for us to rush ahead. We need to reflect on our teaching practice, use the data we have to identify student�s understanding of mathematics and examine new resources as to their appropriateness for our students. Last week, I (Lynn) had the opportunity to attend the Association of State Supervisors of Mathematics Conference and the National Council of Supervisors of Mathematics Conference. Some of you may have also attended NCSM or NCTM. West Virginia was well represented by a number of coaches and teachers. As I listened to leading experts in the field, I reflected on West Virginia�s journey with respect to implementation of RTI in the area of mathematics. Response to Intervention was a topic that was widely discussed. I was able to connect with various experts in the field. The steps we have taken thus far are in line with the recommendations from the mathematics experts. We are looking at quality Tier 1 instruction, data driven instruction, and Tier 2 instruction. This is an emerging area of study. A vast number of resources will become available over the next year especially in the area of assessing a student�s understanding of mathematics. In fact a document from the Institute of Education Sciences was released this past Friday. I am currently studying this extensive document for recommendations. So what did I take from away from D.C.? We need to take a deep breath and reflect on our journey thus far. It is not necessary for us to rush ahead. We need to reflect on our teaching practice, use the data we have to identify student�s understanding of mathematics and examine new resources as to their appropriateness for our students.

22. How does a teacher assess a student�s mathematical understanding? West Virginia Department of Education Almost every session I attended focused on using formative assessment to guide our classroom instruction. We frequently will use this term for an assessment we may give our students to determine their mastery of a concept. These assessments are frequently completed by the class using paper and pencil. In the mathematics, these assessments may give an indication of learning that may well be an �illusion of learning.� Students may answer the questions correctly; however, they do not have an understanding of the mathematics. They were simply able to get the correct answer. So let�s take a few moments and discuss some assessment strategies that will help us as teachers to identify a student�s deep mathematical understanding.Almost every session I attended focused on using formative assessment to guide our classroom instruction. We frequently will use this term for an assessment we may give our students to determine their mastery of a concept. These assessments are frequently completed by the class using paper and pencil. In the mathematics, these assessments may give an indication of learning that may well be an �illusion of learning.� Students may answer the questions correctly; however, they do not have an understanding of the mathematics. They were simply able to get the correct answer. So let�s take a few moments and discuss some assessment strategies that will help us as teachers to identify a student�s deep mathematical understanding.

23. How does a teacher assess a student�s mathematical understanding? West Virginia Department of Education Observe students As teachers, we need to constantly be observing and listening to our students. Our focus should be on how they are solving problems, their math discourse and the challenges they face. It is more than, are the students following directions and did they complete the task? You may want to focus on a small group of students each day or a particular concept. It is not necessary to observe everything about every student every day. Be intentional with your observations!As teachers, we need to constantly be observing and listening to our students. Our focus should be on how they are solving problems, their math discourse and the challenges they face. It is more than, are the students following directions and did they complete the task? You may want to focus on a small group of students each day or a particular concept. It is not necessary to observe everything about every student every day. Be intentional with your observations!

24. How does a teacher assess a student�s mathematical understanding? West Virginia Department of Education Observe students Examine student work Encourage students to record their mathematical thinking as they complete the learning tasks. As you review the student work, think about what you are learning about their understanding of the mathematics concept in addition to the correctness of their solution. Encourage students to record their mathematical thinking as they complete the learning tasks. As you review the student work, think about what you are learning about their understanding of the mathematics concept in addition to the correctness of their solution.

25. How does a teacher assess a student�s mathematical understanding? West Virginia Department of Education Observe students Examine student work Conduct individual assessments Then there are times when it is necessary to conduct individual assessments. This will take the form of a diagnostic interview. After speaking with various experts in elementary mathematics, I feel the diagnostic interview is essential in assessing a student�s understanding of mathematical concepts. This gives the teacher the opportunity to explore a student�s thinking. Do they simply use procedures or do they understand the foundational mathematics of a given concept? Let�s take a moment and look at the following problem.Then there are times when it is necessary to conduct individual assessments. This will take the form of a diagnostic interview. After speaking with various experts in elementary mathematics, I feel the diagnostic interview is essential in assessing a student�s understanding of mathematical concepts. This gives the teacher the opportunity to explore a student�s thinking. Do they simply use procedures or do they understand the foundational mathematics of a given concept? Let�s take a moment and look at the following problem.

26. West Virginia Department of Education 32 + 26 27 - 14 Adding and subtracting two-digit number. Take a moment and discuss what a student would need to know in order to solve these problems correctly.Adding and subtracting two-digit number. Take a moment and discuss what a student would need to know in order to solve these problems correctly.

27. West Virginia Department of Education 32 + 26 27 - 14 If this were a student�s work what could you tell me about their understanding of adding and subtracting two-digit numbers. How is this different from the following?If this were a student�s work what could you tell me about their understanding of adding and subtracting two-digit numbers. How is this different from the following?

28. West Virginia Department of Education Procedurally a student may be able to complete these problems. But do they have an understanding of our number system. A student is able to solve these problems as if they were individual basic facts. Do they understand our number system? I cannot determine a student�s level of understanding by the correctness of an answer on a paper and pencil test. I hesitate to think about the number of times I said, �two plus six equals eight and three plus two equals five.� Over the years, I have learned how important it is for a teacher to choose his/her words carefully. A structured diagnostic interview would give the teacher insight into a student�s thinking. This will be an area that we explore during the upcoming year.Procedurally a student may be able to complete these problems. But do they have an understanding of our number system. A student is able to solve these problems as if they were individual basic facts. Do they understand our number system? I cannot determine a student�s level of understanding by the correctness of an answer on a paper and pencil test. I hesitate to think about the number of times I said, �two plus six equals eight and three plus two equals five.� Over the years, I have learned how important it is for a teacher to choose his/her words carefully. A structured diagnostic interview would give the teacher insight into a student�s thinking. This will be an area that we explore during the upcoming year.

29. How does a teacher assess a student�s mathematical understanding? West Virginia Department of Education Observe students Examine student work Conduct individual assessments Each of these assessment strategies will provide teachers will valuable �data� on a student�s level of mathematical understanding. This information is then used to inform instruction within the Tiered Instructional Model for RTI.Each of these assessment strategies will provide teachers will valuable �data� on a student�s level of mathematical understanding. This information is then used to inform instruction within the Tiered Instructional Model for RTI.

30. Key Components of Quality Intervention Lessons West Virginia Department of Education Mathematics Goal/Related WV CSOs/Assessment�Each lesson in Tier 2 is designed according to specific goals related to the West Virginia Content Standards and Objectives.� Formative assessment within the lesson provides the teacher with needed data to make informed instructional decisions. Introduction/Concept Development�The lesson begins with a task or problem enabling the teacher to assess the student�s understanding of the concept.� The teacher guides the student through learning tasks developing the identified concept. Practice/Application�The student is provided the opportunity to practice or apply the concept in meaningful tasks. Reflection�Students are provide time to reflect upon their learning for the session.� This may include responding to a prompt in a math journal, small group discussion or the completion of a performance task. Here are the essential components of mathematics intervention. Skills are related to critical grade-level curriculum and instruction is designed to accelerate student learning on those key skills. This information can be accessed on the Teach 21 website under �RTI�. Intervention lessons are developed to support student learning. It is imperative that students at each level of intervention are actively engaged in doing important mathematics. It is not possible to describe in detail the components of Tier 2 instruction within the context of the webcast. This will be an area of focus in the upcoming months as well as defining Tier 3 instruction.Here are the essential components of mathematics intervention. Skills are related to critical grade-level curriculum and instruction is designed to accelerate student learning on those key skills. This information can be accessed on the Teach 21 website under �RTI�. Intervention lessons are developed to support student learning. It is imperative that students at each level of intervention are actively engaged in doing important mathematics. It is not possible to describe in detail the components of Tier 2 instruction within the context of the webcast. This will be an area of focus in the upcoming months as well as defining Tier 3 instruction.

31. Considerations for Intervention West Virginia Department of Education Explicit vocabulary instruction should be a part of the learning plan for Tier 2 instruction. Students often understand mathematical concepts without understanding the wording of assessment and instruction questions (ASCD, 2008). Academic vocabulary instruction benefits a variety of learners and common language helps address students� mathematical misconceptions Vocabulary word banks, student-friendly definitions, illustrations and non-examples are effective strategies for embedding mathematics vocabulary in the classroom instruction This slide summarizes some considerations for designing and delivering Tier II intervention. Again, the relentless attention to the vocabulary of mathematics is a critical component of quality mathematics instruction and intervention. Students need to interact with the vocabulary on a daily basis. As a side note�Looking the word up in the glossary is not a research based strategy for learning vocabulary. The interactive CSOs on the Teach 21 Site will soon be identifying key vocabulary for the objective along with a research-based instructional strategy. Look for the �V� button along side the magnifying glass. Another resource for vocabulary instruction within Tier 2, would be the resources provided for the English Language Learner. I attended a session in D.C. on this topic. The strategies used would be valuable to a wide variety of students.This slide summarizes some considerations for designing and delivering Tier II intervention. Again, the relentless attention to the vocabulary of mathematics is a critical component of quality mathematics instruction and intervention. Students need to interact with the vocabulary on a daily basis. As a side note�Looking the word up in the glossary is not a research based strategy for learning vocabulary. The interactive CSOs on the Teach 21 Site will soon be identifying key vocabulary for the objective along with a research-based instructional strategy. Look for the �V� button along side the magnifying glass. Another resource for vocabulary instruction within Tier 2, would be the resources provided for the English Language Learner. I attended a session in D.C. on this topic. The strategies used would be valuable to a wide variety of students.

32. Considerations for Intervention West Virginia Department of Education Assessment data informs grouping decisions. Students move in and out of Tier 2 depending on their individual progress toward the identified learning goals.� As instructional goals change throughout the course of the year, some students may continue in Tier 2 while others receive additional support for only a brief time.� Take a moment and review this slide. I looked the term data up in the dictionary. The definition given was: individual facts, statistics, or items of information. Assessment data comes in various forms. It is the scrapbook of data that we have described in previous professional development sessions. Data only becomes important when we use it to inform instruction.Take a moment and review this slide. I looked the term data up in the dictionary. The definition given was: individual facts, statistics, or items of information. Assessment data comes in various forms. It is the scrapbook of data that we have described in previous professional development sessions. Data only becomes important when we use it to inform instruction.

33. Considerations for Intervention West Virginia Department of Education Teach 21 is a valuable resource for teachers planning instruction and intervention. Information on RTI is found on the WVDE Teach 21 site. There is a link on the first page of this site. If you have not explored these resources please take the time to review or revisit the site. Additional information will be placed on this site in the future.Information on RTI is found on the WVDE Teach 21 site. There is a link on the first page of this site. If you have not explored these resources please take the time to review or revisit the site. Additional information will be placed on this site in the future.

34. West Virginia Department of Education This page will provide you a link to the various other pages with important information. The slides and notes for this webcast will also be posted on this site. Organizational structures will provide you with information on scheduling and questions to consider as you implement RTI in your elementary schools. Assessment/Data Analysis will provide you sample charts to use as you document student achievement. Assessment and Data information will be added to this page as it become available. Finally, Instruction/Intervention will provide a description of Tier 1 and Tier 2 instruction. These pages will be revised as additional information becomes available. We will also be adding a page that defines the terms used within the RTI framework.This page will provide you a link to the various other pages with important information. The slides and notes for this webcast will also be posted on this site. Organizational structures will provide you with information on scheduling and questions to consider as you implement RTI in your elementary schools. Assessment/Data Analysis will provide you sample charts to use as you document student achievement. Assessment and Data information will be added to this page as it become available. Finally, Instruction/Intervention will provide a description of Tier 1 and Tier 2 instruction. These pages will be revised as additional information becomes available. We will also be adding a page that defines the terms used within the RTI framework.

35. Data-Based Decision-Making Using Assessment to Inform Instruction West Virginia Department of Education In addition to using data to make instructional decisions for students, school staffs may reflect on the data to make decisions concerning the instructional program within their schools.In addition to using data to make instructional decisions for students, school staffs may reflect on the data to make decisions concerning the instructional program within their schools.

36. Asking the right questions is critical. West Virginia Department of Education How many of our students are below grade level in mathematics? What do 3rd grade and beyond WESTEST scores indicate for our school? Which CSOs are particularly problematic for our students who are struggling? Here are some additional questions that a staff may use to reflect on the practice.Here are some additional questions that a staff may use to reflect on the practice.

37. Asking the right questions is critical. West Virginia Department of Education How do students compare with other students in the district? Across same grades in our school? What are we currently doing to address at-risk students in mathematics? Is it working? How do we know if it�s working?

38. West Virginia Department of Education Remember that the assessment information comes from a wide variety of sources. One type of data will not give you a true picture of student learning.Remember that the assessment information comes from a wide variety of sources. One type of data will not give you a true picture of student learning.

39. Currently Available Data Sources Let�s take just a few moments and identify some of the data sources that you currently have available.Let�s take just a few moments and identify some of the data sources that you currently have available.

40. K-3 Informal Math Assessment IMA supports standards-based assessment in three critical areas: Conceptual Understanding Procedural Skills Problem Solving West Virginia Department of Education Let�s begin our discussion of assessment with the West Virginia K-3 Informal Mathematics Assessment (IMA). The IMA helps teachers and schools to stimulate, nurture, and monitor students� mathematical progress and knowledge in three cognitive categories:� Conceptual Understanding, Procedural Skills, and Problem-Solving.� The IMA provides teachers with tasks correlated to the West Virginia 21st Century Content Standards and Objectives.� These tasks support Classroom Assessment for Learning as they are intended to provide the teacher with information on student understanding and learning of mathematical concepts.� The IMA supports standards-based assessment and should drive standards-based instruction in the classroom. Remember these tasks are formative in nature. They should be completed throughout the entire school year. It is not a recommended practice to assemble all of the tasks into one assessment. The IMA is intended to be a process not an event! Let�s begin our discussion of assessment with the West Virginia K-3 Informal Mathematics Assessment (IMA). The IMA helps teachers and schools to stimulate, nurture, and monitor students� mathematical progress and knowledge in three cognitive categories:� Conceptual Understanding, Procedural Skills, and Problem-Solving.� The IMA provides teachers with tasks correlated to the West Virginia 21st Century Content Standards and Objectives.� These tasks support Classroom Assessment for Learning as they are intended to provide the teacher with information on student understanding and learning of mathematical concepts.� The IMA supports standards-based assessment and should drive standards-based instruction in the classroom. Remember these tasks are formative in nature. They should be completed throughout the entire school year. It is not a recommended practice to assemble all of the tasks into one assessment. The IMA is intended to be a process not an event!

41. K-3 Informal Math Assessment West Virginia Department of Education Provides teachers with tasks correlated to the West Virginia 21st Century Content Standards and Objectives.� Supports Classroom Assessment for Learning and provide teachers with information on student understanding and learning of mathematical concepts.� Supports standards-based assessment and should guide standards-based mathematics instruction in the K-3 classroom. This slide provides a description of the purpose of the IMA.This slide provides a description of the purpose of the IMA.

42. 2nd Grade GeometryInformal Assessment Tasks West Virginia Department of Education M.O.2.3.1 Indentify and describe the following geometric solids according to the number of faces and edges: rectangular solid cube cylinder cone pyramid Students at the above mastery level in second grade mathematics will Identify and analyze geometric solids �Students at the distinguished level in second grade mathematics will Identify and analyze geometric solids. They communicate their reasoning in a clear and concise manner. Let�s look at one of the informal assessment tasks for grade 2 geometry. The CSO and student performance levels are stated.Let�s look at one of the informal assessment tasks for grade 2 geometry. The CSO and student performance levels are stated.

43. Academic Prompt: 2nd Grade Geometry West Virginia Department of Education Mission � Solids You are from the planet Geo-met-ric. You are part of a crew of Geometricians who are studying solids from other planets. Your mission is to land your spaceship on the planet earth and find some interesting solids. You will need to work with your fellow crew members to inform your leader about these strange new solids. Each crew member will need to draw, find a picture, or make a model of the solids you discover. Next, you will need to decide a way to display your solids and their descriptions. Be sure to use some words that the earthlings use, like faces and edges when describing your solids. Finally, share your findings with your fellow Geometricans and your Geo-met-ric leader. Here�s an academic prompt for the aforementioned geometry CSO. Since the words are small, I want to take a moment and read the prompt for you. [Read the prompt] A rubric to assess student performance is also provided in the IMA. Additionally, five tasks that help the teacher determine students� levels of mastery are included. Some of the tasks are for individual completion while others are done in a group format. For more information, look at the IMA on Teach 21. It is located under the assessment link. Here�s an academic prompt for the aforementioned geometry CSO. Since the words are small, I want to take a moment and read the prompt for you. [Read the prompt] A rubric to assess student performance is also provided in the IMA. Additionally, five tasks that help the teacher determine students� levels of mastery are included. Some of the tasks are for individual completion while others are done in a group format. For more information, look at the IMA on Teach 21. It is located under the assessment link.

44. Using Acuity for RTI West Virginia Department of Education 2009 Another option for assessing and monitoring students� mathematical progress is Acuity. Many West Virginia schools are using the Acuity platform for benchmark assessment purposes. Acuity� is a formative assessment system that helps educators improve student achievement: classroom-friendly assessments, insightful reports, and engaging instruction. Acuity helps educators target instruction by: delivering detailed insight on student strengths and weaknesses providing an easily integrated and useful formative assessment tool assigning personalized instructional activities based on assessment results. Another option for assessing and monitoring students� mathematical progress is Acuity. Many West Virginia schools are using the Acuity platform for benchmark assessment purposes. Acuity� is a formative assessment system that helps educators improve student achievement: classroom-friendly assessments, insightful reports, and engaging instruction. Acuity helps educators target instruction by: delivering detailed insight on student strengths and weaknesses providing an easily integrated and useful formative assessment tool assigning personalized instructional activities based on assessment results.

45. Using Acuity for RTI West Virginia Department of Education 2009 Acuity is an online/paper-pencil platform for grades 3-11 for Mathematics, Reading/Language Arts, Science and Social Studies Acuity includes: WVDE authored benchmark tests aligned with WESTEST2 Custom test capability using 25,000 items aligned with WV 21st Century CSOs Instructional resources to target instruction Immediate reporting capabilities In addition to the capabilities for assessment, Acuity features Instructional Resources that are tied to WV 21st Century CSOs and can be assigned by skill or by content standard. In essence, they are mini lessons that are divided into three parts: introduction of a topic, guided practice and a mini summative assessment. Teachers can access reports that show student progress on assigned Instructional Resources.In addition to the capabilities for assessment, Acuity features Instructional Resources that are tied to WV 21st Century CSOs and can be assigned by skill or by content standard. In essence, they are mini lessons that are divided into three parts: introduction of a topic, guided practice and a mini summative assessment. Teachers can access reports that show student progress on assigned Instructional Resources.

46. Using Acuity for RTI West Virginia Department of Education 2009 Guidance for teachers on using Acuity within the context of RTI will be developed by the WVDE. The potential for using Acuity for progress monitoring within the 3-tier model for mathematics is promising. Stay tuned for more information on upcoming WVDE information and guidance. Additional resources will be identified as they become available. There are several resources on the horizon. As mentioned earlier RTI in mathematics is an emerging field of study.The potential for using Acuity for progress monitoring within the 3-tier model for mathematics is promising. Stay tuned for more information on upcoming WVDE information and guidance. Additional resources will be identified as they become available. There are several resources on the horizon. As mentioned earlier RTI in mathematics is an emerging field of study.

47. Managing the Data and Documenting RTI West Virginia Department of Education As mentioned earlier you will need data from multiple sources. How will you assemble the data to make instructional decisions?As mentioned earlier you will need data from multiple sources. How will you assemble the data to make instructional decisions?

48. http://wvde.state.wv.us/teach21/StudentDocumentationForms.html West Virginia Department of Education Documenting a student�s response to intervention is an important component of implementing RTI. Information pertaining to how well and at what rate a student is learning once intervention is provided is a critical This documentation will become a component of the RTI process for students eventually suspected of having learning disabilities in the area of mathematics. The information will first be used by the Student Assistance Team (SAT) when considering a referral for evaluation for special education. Later, the Eligibility Committee will use the information along with other assessments to help determine if a student does indeed have a SLD. The RTI for Mathematics section of Teach 21 includes examples of student documentation forms for various grade levels. These forms have been developed by elementary school teachers and are used to document the provision of Tier 2. Documenting a student�s response to intervention is an important component of implementing RTI. Information pertaining to how well and at what rate a student is learning once intervention is provided is a critical This documentation will become a component of the RTI process for students eventually suspected of having learning disabilities in the area of mathematics. The information will first be used by the Student Assistance Team (SAT) when considering a referral for evaluation for special education. Later, the Eligibility Committee will use the information along with other assessments to help determine if a student does indeed have a SLD. The RTI for Mathematics section of Teach 21 includes examples of student documentation forms for various grade levels. These forms have been developed by elementary school teachers and are used to document the provision of Tier 2.

49. Documenting RTI West Virginia Department of Education Documenting RTI is important and schools are encouraged to develop systems that are efficient as well as useful. In terms of the 3-tier instruction model, general education lesson plans serve as the documentation of the provision of differentiated classroom instruction. At Tier II and III, classroom teachers and/or interventionists begin to document the nature, frequency and duration of interventions that are provided. There is no universal State documentation form and schools and districts are encouraged to create systems that meet their needs and provided the necessary documentation for students who eventually are referred for special education under the SLD category.Documenting RTI is important and schools are encouraged to develop systems that are efficient as well as useful. In terms of the 3-tier instruction model, general education lesson plans serve as the documentation of the provision of differentiated classroom instruction. At Tier II and III, classroom teachers and/or interventionists begin to document the nature, frequency and duration of interventions that are provided. There is no universal State documentation form and schools and districts are encouraged to create systems that meet their needs and provided the necessary documentation for students who eventually are referred for special education under the SLD category.

50. I want to share one additional resource with you this afternoon. The NCTM website has a wealth of information on RTI and mathematics. After my discussion with Dr. Hank Kepner NCTM�s president, I�m confident additional information will be added to this site over the next year.I want to share one additional resource with you this afternoon. The NCTM website has a wealth of information on RTI and mathematics. After my discussion with Dr. Hank Kepner NCTM�s president, I�m confident additional information will be added to this site over the next year.

51. Topics for Discussion West Virginia Department of Education Use the Elementary Discussion Guide to reflect on mathematics instruction in your school. Additional information on RTI and mathematics will become available during the next year. The a waiver for the implementation deadline has provided schools with the opportunity to reflect on mathematics instruction in each elementary school. Schools need to take this time to identify strengths, challenges, and professional development needs. We have also included topics for future webcasts. We encourage you to send topics that your school would like addressed. If your school sees this topics as a need, I�m sure other schools will have the same need. They may be included in future webcasts or the information may be placed on the RTI page of Teach 21. Through the next year our steps need to be thoughtful and intentional. We need to remember that our focus should always be on helping students further their understanding of mathematics.Additional information on RTI and mathematics will become available during the next year. The a waiver for the implementation deadline has provided schools with the opportunity to reflect on mathematics instruction in each elementary school. Schools need to take this time to identify strengths, challenges, and professional development needs. We have also included topics for future webcasts. We encourage you to send topics that your school would like addressed. If your school sees this topics as a need, I�m sure other schools will have the same need. They may be included in future webcasts or the information may be placed on the RTI page of Teach 21. Through the next year our steps need to be thoughtful and intentional. We need to remember that our focus should always be on helping students further their understanding of mathematics.

52. West Virginia Department of Education In closing, I want to share a statement that was made by Dr. Jim Rubillo last week in Washington, D.C. Jim Rubillo, the executive director of NCTM, provided us with the following caution: We should remember that students are human beings not data points. This is a powerful statement. We may be tempted to focus on the data. As professionals we need to focus on the students. In closing, I want to share a statement that was made by Dr. Jim Rubillo last week in Washington, D.C. Jim Rubillo, the executive director of NCTM, provided us with the following caution: We should remember that students are human beings not data points. This is a powerful statement. We may be tempted to focus on the data. As professionals we need to focus on the students.

53. Contact Information West Virginia Department of Education John Ford � Title 1 Jford@access.k12.wv.us Lynn Baker � Office of Instruction lhbaker@access.k12.wv.us Linda Palenchar � Office of Special Programs lpalench@access.k12.wv.us For more information or the opportunity to share your RTI for Mathematics ideas, please contact John, Lynn or Linda.For more information or the opportunity to share your RTI for Mathematics ideas, please contact John, Lynn or Linda.

54. West Virginia Department of Education We�re glad you joined us this afternoon�Please feel free to share your RTI for mathematics work with us. We will continue to work together and improve the math achievement of all students in West Virginia.We�re glad you joined us this afternoon�Please feel free to share your RTI for mathematics work with us. We will continue to work together and improve the math achievement of all students in West Virginia.