RTI Framework for Success: Research-Based Math Instruction  Intervention

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RTI Framework for Success: Research-Based Math Instruction Intervention

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1. RTI Framework for Success: Research-Based Math Instruction & Intervention C. Lee Goss, Psy.D. Attention & Learning Pathways School Psychology Services

2. © C. Lee Goss, 2008 2 Acknowledgments Rachel Brown-Chidsey, Ph.D. Mark Steege, Ph.D. Marcia Davidson, Ph.D. RTI & research-based reading instruction is built on a foundation of years of research, professional expertise, and leadership: Ed Daly, Ph.D., Stan Deno, Ph.D., Barbara Foorman, Ph.D., Doug Fuchs, Ph.D., Lynn Fuchs, Ph.D., Laurice Joseph, Ph.D., Dan Reschly, Ph.D., Ed Shapiro, Ph.D., Mark Shinn, Ph.D., David Tilly, Ph.D., Joseph Torgeson, Ph.D., & Sharon Vaughn, Ph.D., Amanda VanDerHeyden, Ph.D., Joseph Witt, Ph.D.

3. © C. Lee Goss, 2008 3 Status of Research-Based Math Instruction Research-Based Math Instruction is in it’s infancy compared to the current research available for reading & behavior Current research in RTI for math is consistent with RTI in reading—the premise is the same Focus on the importance and benefits of screening to detect students at-risk for difficulty in math achievement Focus on formative assessment or progress monitoring data to inform instruction and intervention at all 3-Tiers

4. © C. Lee Goss, 2008 4 Benefits of Research-Based Math Instruction Provide all students with effective instruction and needed intervention that is supported by high quality peer-reviewed research studies Early intervention and prevention methods to prevent poor math achievement or the need for identification for special education services. Instruction is the one thing we can “control” on a daily basis to develop mastery of needed skills

5. © C. Lee Goss, 2008 5 Math Research Status U.S. National Research Council (NRC) conducted a review of math instruction research A panel of researchers with expertise in math instruction reviewed the preceding 30 years of math instruction research and summarized findings in Adding it Up: Helping Children Learn Mathematics (2001)

6. © C. Lee Goss, 2008 6 Adding It Up: 5 Essential Strands 1) Conceptual Understanding 2) Procedural Fluency 3) Strategic Competence 4) Adaptive Reasoning 5) Productive Disposition

9. © C. Lee Goss, 2008 9 Sample Skills Related to the Strands, Cont’d Note: Samples identified in the table are examples and do not represent all math skills Key Point identified in Adding It Up: All students need to be able to master all of the strands and skills identified in the table to develop proficiency in math

10. © C. Lee Goss, 2008 10 Adding It Up: 5 Essential Strands, Cont’d All 5 components or strands are interdependent All 5 strands are identified as essential for all students All 5 strands must be included in math instruction at all grade levels The 5 strands provide a way to organize the math instruction All strands can be matched with specific student instructional skills

11. © C. Lee Goss, 2008 11 National Mathematics Advisory Panel (NMAP) U.S. DOE appointed a National Mathematics Advisory Panel (NMAP) in 2006 Panel included researchers with strong expertise in mathematics and mathematics instruction Panel charged with reviewing all available research about math instruction and summarizing findings Final Report: Foundations for Success, 2008

12. © C. Lee Goss, 2008 12 NRC Report: Math Proficiency of U.S. Students International comparisons Low fractions of proficiency on NAEP Falling proficiency at higher grades Heavy remedial demand upon entry into college Achievement gap Algebra as a gateway (NMAP Report, 2008)

13. © C. Lee Goss, 2008 13 NRC Report: Math Proficiency of U.S. Students, Cont’d American students achievement in mathematics is mediocre compared to international peers 32% of our students are at or above the “proficient” level in Grade 8, but only 23% are proficient at Grade 12. Consistent with these findings is the vast and growing demand for remedial mathematics education among arriving students in 4-year colleges and community colleges across the nation. On the TIMSS (Trends in International Mathematics and Science Study), U.S. students do less well in Grade 8 than grade 4. The performance is still poorer in Grade 12. In the PISA (Programme for International Student Assessment), U.S. 15-year-olds ranked 25th among 30 developed nations in math literacy and problem solving. Even in elementary school, only 7% of U.S. 4th-graders scored at the advanced level in TIMSS, compared to 38% of 4th-graders in Singapore, a world leader in mathematics achievement (NMAP Report, 2008)

14. © C. Lee Goss, 2008 14 Basis of the Panel’s work Review of 16,000 research studies and related documents. Public testimony gathered from 110 individuals. Review of written commentary from 160 organizations and individuals 12 public meetings held around the country Analysis of survey results from 743 Algebra I teachers

15. © C. Lee Goss, 2008 15 NRC Effective Math Instruction Research Findings Core Conclusions: All U.S. children must develop math proficiency for successful academic achievement Math skills must be viewed as important for all children to learn Identified 5 Essential Components termed “Strands” of Effective Math Instruction

16. © C. Lee Goss, 2008 16 National Math Advisory Panel Report Fact Sheet Small Group Discussions by Grade Levels/Schools Read and discuss NMAP Fact Sheet findings Identify potential current math curricula strengths and weaknesses to share with the group Any Surprises?

17. © C. Lee Goss, 2008 17 NMAP Final Report Findings NMAP Report identified 6 main steps needed to improve math achievement: Pre-K to 8th grade math curriculum should be streamlined to emphasize a narrower set of the most critical skills and topics Implementation of best practice instruction methods and knowledge of how children learn with a focus on the benefits and importance of: Early Intervention Conceptual Understanding Fluency Automaticity Effort

18. © C. Lee Goss, 2008 18 NMAP Final Report Findings, Cont’d 3) Elementary grade teachers must have strong math skills in order to teach math well 4) Math instruction should not be purely ‘student-centered’ or “teacher centered” but must be an integration of both perspectives based on the findings of research 5) National assessments such as National Assessment of Educational Progress (NAEP) should be strengthened to include emphasis on the most critical math knowledge and skills 6) There is a need for more rigorous research about math instruction and the findings of such research must be used to improve teaching practices

19. © C. Lee Goss, 2008 19 NMAP Final Report Findings, Cont’d Key NMAP Conclusion Importance of early student mastery of basic math skills such as computation fluency NMAP Conclusion coincides with other recent research findings about math instruction (Baker, Gerston, & Lee, 2002)

20. © C. Lee Goss, 2008 20 Research Findings on Effective Math Instruction Effective math instruction includes a focus on: Basic Skills Teaching explicitly and systematically Frequent progress monitoring data to inform instruction and student progress (Baker, Gerston, & Lee, 2002)

21. © C. Lee Goss, 2008 21 Research Informs Federal Policies NCLB, IDEIA 2004, NMAP Report, ME Regs & ME RTI Guidelines highlight the importance of research-based instruction and research based interventions before a referral to special education is made. CBMs meet extensive research criteria for benchmark and progress assessments to measure student response to research-based instruction

22. © C. Lee Goss, 2008 22 RTI: Prevention & Early Intervention Scientifically-based math curriculum that incorporates effective instruction techniques Importance of early mastery of number values and math calculation fluency Not unusual for students to develop some math skills better than others (e.g. struggle w/ subtraction but master multiplication easily).

23. © C. Lee Goss, 2008 23 RTI: Prevention & Early Intervention, Cont’d RTI methods of prevention are a very helpful and effective way to reduce the number of students needing remediation Research demonstrates that many children experiencing difficulty respond to early intervention and explicit research-based instruction techniques

24. © C. Lee Goss, 2008 24 RTI is a Well-Child Prevention Model Prevention efforts to foster educational success for all students in school Incorporates regular screening of ALL children to determine who is at risk for developing academic and/or behavioral problems Provides strategic interventions for children determined at-risk in the early stages of a problem Acknowledges that some children will have serious and persistent problems that will require intensive support

25. © C. Lee Goss, 2008 25 RTI and Identification of LD Copious studies have shown the inaccuracy of IQ score-achievement test discrepancy scores for documenting the presence of a specific learning disability (SLD) Evidence of high risk for both false positive (over identification) and false negative (under identification) results Research evidence that math calculation fluency is highly correlated with future math achievement Response to Intervention/Early Intervention Models are recommended instead of IQ Discrepancy “Wait to Fail” Model Identification of the need for research based math interventions can be identified with CBM Benchmarks

26. © C. Lee Goss, 2008 26 Locating Research-Based Math Curricula Information about the efficacy of specific curricula can be found in peer-reviewed research journals and specific internet resources: ERIC is a federally-sponsored database of research in education http://www.eric.ed.gov/ National Math Advisory Panel Report www.nationalmathpanel.org What Works Clearing House is a new initiative of the Institute of Education Sciences developed to share information about effective programs http://ies.ed.gov/ncee/wwc/

27. © C. Lee Goss, 2008 27 FAQ: Where is the List for RBIs? There is not a list of research-based instruction or interventions There are credible research resources RBI Goal: research studies (scientific evidence) that document efficacy of instruction or intervention in multiple peer-reviewed journals Although more research is needed to inform effective math instruction, current research is consistent with NMAP findings

28. © C. Lee Goss, 2008 28 Caveat Emptor Buyer beware! Not all programs or curricula advertised as scientifically-based will actually have adequate data to support their use There is no “list” of approved programs so teachers and other educational personnel must be informed consumers and determine whether materials meet the standards of effective research-based curricula

29. © C. Lee Goss, 2008 29 Systematic & Explicit Math Instruction Strategic Skill Lesson Review (Activate Prior Knowledge) Introduce New Skill Best Practice Instruction I do it, We do it, You do it, Immediate Feedback Application to Controlled Skill Practice Teach to Mastery Generalization of Skill

30. © C. Lee Goss, 2008 30

31. © C. Lee Goss, 2008 31 Calculators: However, the Panel’s survey of the nation’s algebra teachers indicated that the use of calculators in prior grades was one of their concerns. The Panel cautions that to the degree that calculators impede the development of automaticity, fluency in computation will be adversely affected. Calculators: However, the Panel’s survey of the nation’s algebra teachers indicated that the use of calculators in prior grades was one of their concerns. The Panel cautions that to the degree that calculators impede the development of automaticity, fluency in computation will be adversely affected.

32. © C. Lee Goss, 2008 32 RTI: Math @ Secondary Level RTI: Mathematics is not as advanced as reading Challenges at secondary level: Math becomes much more specialized in terms of content Graduation requirements and state assessments are aligned to particular math courses (e.g., Algebra 1, Geometry 1, etc.) - Application of RTI in mathematics at the secondary level is in the development stage

33. © C. Lee Goss, 2008 33 RTI: Math @ Secondary Level, Cont’d RTI IS happening at the secondary level Exs: Minnesota, Colorado Systematically applied and evaluated models are in the emerging stage Exs: Minnesota Example The Good News: There is a research base to apply the RTI tiered model of instruction in math

34. © C. Lee Goss, 2008 34 Core Components of Math Instruction Core components essential to mathematics skill development Number/number sense appears to be most critical for K-12 math success Math Calculation Fluency Math Calculation Fluency is highly correlated with mathematics achievement and success in Algebra Lack of number sense and math calculation fluency seems to be a consistent issue for students who fail Algebra at the secondary level

35. © C. Lee Goss, 2008 35 How Math Calculation Fluency Impacts Comprehension Fluency allows the mind to concentrate on comprehension Automatic math calculation fluency leaves working memory free to think about application and problem solving strategies

36. © C. Lee Goss, 2008 36 Research-based Instructional Practices Explicit systematic instruction within authentic contexts Teaching strategies for learning and doing mathematics including use of graphic organizers Grounding abstract concepts within concrete experiences (concrete-representational-abstract sequence of instruction)

37. © C. Lee Goss, 2008 37 Research-Based Instructional Practices, Cont’d 4) Providing multiple opportunities for students to apply their mathematical understanding with immediate corrective feedback Newly learned concepts and Maintenance/Judicious Review of previously learned concepts 5) Continuous progress monitoring/instructional decision-making Key Point: These practices can be applied in the general education classroom in whole class, small group, and one-to-one situations.

38. © C. Lee Goss, 2008 38 Research on Effective Mathematics Instruction Research synthesis on effective mathematics instruction for students with mathematics difficulties: Gersten, Baker, & Chard (2006). Effective instructional practices for students with difficulties in mathematics: Findings from a research synthesis. Center on Instruction www.centeroninstruction.org

39. © C. Lee Goss, 2008 39 Best Practice Instruction Process Explicit, Sequential, Scaffolded Instruction Model: I do it Rehearsal: We do it together Practice: You do it (class/peer support) w/ multiple opportunities for repetition & practice when learning skills w/ immediate corrective feedback Mastery: Evidence that you can perform the skill w/ automaticity on your own Generalization: Evidence that you can perform the skill w/ automaticity in different contexts/environments Judicious review of prior skills taught to mastery

40. © C. Lee Goss, 2008 40 Importance of Immediate Corrective Feedback Error correction is a key feature of effective instruction Error correction is crucial to effective and efficient learning If errors are identified and corrected immediately in the learning sequence, students master skills more quickly with less frustration

41. © C. Lee Goss, 2008 41 Tier 1: Research-Based Math Instruction What Works Clearinghouse (WWC) http://ies.ed.gov/ncee/wwc/ Elementary School Math Middle School Math Notice the nonexistent research reviews available to date at the high school level Goal of website to locate and summarize information about instructional methods and materials for teachers Includes Summary Tables of findings about curricula and instruction for many subject areas A common table legend indicates the trend of evidence for each program Click on the title of the program for detailed information about each program reviewed

42. © C. Lee Goss, 2008 42 Tier 1: Small Group Research Activity Break into small groups by grade level/current math curricula Log on to What Works Clearinghouse (WWC) http://ies.ed.gov/ncee/wwc/ Identify your current math curricula or pick a curricula to review Review & Summarize research evidence to share w/ the group Click on the title of the program to summarize the research for specific grade levels and current effectiveness ratings

43. © C. Lee Goss, 2008 43 Tier 1: Core Class Instruction

44. © C. Lee Goss, 2008 44 Tier 2: Supplemental Math Interventions Tier 2 = Tier 1 + Tier 2 Small Group Additional Instruction 3-5 students (homogeneous skill groups) identifed for targeted skill instruction matched to student needs 2-5 days/week based on individual student needs and progress monitoring data

45. © C. Lee Goss, 2008 45 Tier 2: Math Intervention Researh Evidence Baker, S., Gerston, R., & Lee, D.S. (2002). Elementary School Journal. Baker, et. al. reviewed all available studies (15) which investigated the effects of math interventions for low-achieving students that were NOT receiving special education services. Key feature of this research is that it included students in need of Tier 2 interventions. On-going math research is still needed; however, results from previous research offer a great entry point for planning Tier 2 interventions.

46. © C. Lee Goss, 2008 46 Tier 2: Math Intervention 6 Key Principles Math interventions at Tier 2 level must incorporate 6 instructional principles: Instructional Explicitness Instructional design that eases the learning challenge A strong conceptual basis for procedures that are taught An emphasis on drill and practice Cumulative review as part of drill and practice Motivators to help students regulate their attention and behavior and to work hard (Lynn Fuchs, Vanderbilt University)

47. © C. Lee Goss, 2008 47 1) Instructional Explicitness Typicially developing children profit from Tier 1 instruction even though it may require inductive reasoning. Students at-risk for serious mathematics difficulties, however, fail to profit from inductive instructional methods in a way that produces understanding of the structure, meaning, and operational requirements of mathematics. (Fuchs & Fuchs, Vanderbilt University)

48. © C. Lee Goss, 2008 48 Instructional Explicitness, Cont’d A meta-analysis of 58 math studies (Kroesbergen & Van Luit, 2003) revealed that students with math disability benefit more from explicit instruction than from discovery-oriented methods. Tier 2 application: Effective intervention in Tier 2 requires an explicit, didactic form of instruction where the teacher directly shares the information the students need to learn. (Fuchs & Fuchs, 2008)

49. © C. Lee Goss, 2008 49 Explicit Instruction Research shows that when additional highly explicit and sequenced math instruction was provided for Tier 2 at-risk students, they made significant gains in math skills (Baker et. al., 2002) Ex: Student who has struggled to master the steps in solving word problems needs additional instruction and practice in how to “translate” words into numerical equations

50. © C. Lee Goss, 2008 50 2) Instructional Design Explicitness is critical but not enough Effective instruction also requires careful organization and design Goal: To anticipate and eliminate misunderstandings through precise explanations and carefully sequenced and integrated instruction Tier 2 application: To close the achievement gap as quickly as possible

51. © C. Lee Goss, 2008 51 Instructional Design, Cont’d Tier 2 application: To close the achievement gap as quickly as possible Key for Mathematics due to the many branches and strands with distinct conceptual and procedural demands Instructional efficiency is critical

52. © C. Lee Goss, 2008 52 Instructional Design, Cont’d Careful instructional design begins by teaching a set of foundational skills the student can apply across the entire program: Multi-digit calculations Solving algebraic equations Checking Work Such foundational skills can be taught as intact instructional targets and then applied efficiently across subsequent units along with word problem instruction. Overall goal: To purposely conceptualize, organize and teach students to recognize problem types so student can recognize novel problems as familiar vs. random

53. © C. Lee Goss, 2008 53 Instructional Design Goals To purposely conceptualize, organize and teach students to recognize problem types so student can recognize novel problems as familiar vs. random Generalization within problem type structure so the student can dismiss irrelevant information, find missing information (e.g., solve equations), and find relevant information in charts and graphs with efficiency and predictability

54. © C. Lee Goss, 2008 54 3) Conceptual Basis for Procedures Taught Effective instruction requires a strong conceptual basis for the procedures that are taught—Why? Neglect in emphasis on the concepts for mathematical procedures can result in confusion, learning gaps, and a failure to maintain and integrate previously mastered content

55. © C. Lee Goss, 2008 55 4) Emphasis on Drill and Practice Drill and Practice should include: Practice in sorting problems into problem types Mixing problem types within the daily lesson Daily Review

56. © C. Lee Goss, 2008 56 5) Cumulative Review Practice should be rich in cumulative review Cumulative Review includes: Continual reliance and practice of foundational math skills Use of mixed problem types Sorting practice Paper & Pencil Review

57. © C. Lee Goss, 2008 57 6) Motivation Motivators help students regulate their attention and behavior Motivators help students continue to work hard on difficult tasks Students at-risk for poor math achievement often display attention, motivation, and self-regulation difficulties that may adversely affect their behavior and learning (Fuchs et. al., 2006; Montague, 2007)

58. © C. Lee Goss, 2008 58 Motivation, Cont’d Tier 2 application: At-Risk students have often experienced failure in mathematics achievement, particularly at the secondary level, which may contribute to a lack of motivation or avoidance behaviors Learning may be adversely impacted for fear of failure For effective instruction, Tier 2 interventions must incorporate systematic self-regulation and motivators, and for many students tangible reinforces are required (Fuchs et. al., 2003)

59. © C. Lee Goss, 2008 59 Intervention Central Math Practice Worksheet Generator Go to the following website: www.interventioncentral.org In the section labeled “Online Tools” click on “Math Worksheet Generator” on the right hand side of the page. When the new math page loads, click on the button labeled “mixed skills”. Click on the specific skill(s) you want included in your practice worksheet.

60. © C. Lee Goss, 2008 60 Intervention Central: Math Practice Worksheet Generator, Cont’d At the bottom of the page choose how many columns, rows, and what size font you want students to use. Click on “Single Skill Computation Probe.” Once you click on the button to create the probe, your browser should create and load a new tab or page with the teacher (answer) key first. Once this page is loaded, click on the text at the very top of the page which says “click for student worksheet.” Another new tab or page will load. This is the one you want to print for the students. Either print as many copies as you need for the students, or print one copy and then make enough photocopies. Print a copy of the answer sheet onto an overhead transparency. (Brown-Chidsey, Bronaugh, & McGraw, 2008)

61. © C. Lee Goss, 2008 61 “Interspersing Easy and Hard Math Problems” Purpose: To provide practice opportunities solving known and new problems Research: McDonald & Ardoin, 2007 Ingredients: Easy and difficult math problems Prep Time: 5-10 minutes Activity time: 10 minutes per worksheet

62. © C. Lee Goss, 2008 62 Intervention Central: Mixed Skill Math Practice Worksheet Generator Identify what computation skills students have mastered and what ones the students need to practice in order to master (e.g., addition with re-grouping, subtraction without re-grouping). Go to the following website: www.interventioncentral.org In the section labeled “Online Tools” click on “Math Worksheet Generator” on the right hand side of the page. When the new math page loads, click on the button labeled “mixed skills”. Click on the specific skill(s) you want included in your practice worksheet.

63. © C. Lee Goss, 2008 63 Intervention Central: Mixed Skill Math Practice Worksheet Generator, Cont’d At the bottom of the page choose how many columns, rows, and what size font you want students to use. Click on “Single Skill Computation Probe.” Once you click on the button to create the probe, your browser should create and load a new tab or page with the teacher (answer) key first. Once this page is loaded, click on the text at the very top of the page which says “click for student worksheet.” Another new tab or page will load. This is the one you want to print for the students. Either print as many copies as you need for the students, or print one copy and then make enough photocopies. Print a copy of the answer sheet onto an overhead transparency

64. © C. Lee Goss, 2008 64 Timed Practice, Practice, Practice Purpose: To help students build fluency with basic computation skills Research: The National Mathematics Advisory Panel, 2008 Ingredients: Computation problems matched to students’ independent practice level Timer or stopwatch Graph on which students can enter the number of correct answers (attached) Prep Time: 5-10 minutes Activity Time: 2 minutes per worksheet

65. © C. Lee Goss, 2008 65 Timed Practice, Practice, Practice Preparation: Identify what computation skill students most need to practice for the purpose of developing fluency (i.e., accuracy plus speed). Go to the following website: www.interventioncentral.org In the section labeled “Online Tools” click on “Math Worksheet Generator” on the right hand side of the page. When the new math page loads, click on the computation skill(s) you want students to practice (e.g., addition, subtraction, multiplication, division, mixed skills). Click on the specific skill(s) you want included in your practice worksheet.

66. © C. Lee Goss, 2008 66 Timed Practice, Practice, Practice, Cont’d At the bottom of the page choose 4 columns, 5 rows, and medium size font. For the timed version of this activity, it is important that the same number of items be used for each timed session. Click on “Single Skill Computation Probe.” Once you click on the button to create the probe, your browser should create and load a new tab or page with the teacher (answer) key first. Once this page is loaded, click on the text at the very top of the page which says “click for student worksheet.” Another new tab or page will load. This is the one you want to print for the students. Either print as many copies as you need for the students, or print one copy and then make enough photocopies. Print a copy of the answer sheet onto an overhead transparency (optional).

67. © C. Lee Goss, 2008 67 Timed Practice Activity Instructions Say to students: “TODAY WE ARE GOING TO PRACTICE _____________. I WANT YOU TO DO THE PROBLEMS AS ACCURATELY AND AS FAST AS YOU CAN. YOU WILL HAVE 2 MINUTES TO FINISH THE PAPER I AM HANDING OUT. Hand out worksheet and say to students: “DO NOT START UNTILI SAY BEGIN.” Once all students have their worksheets, say: “BEGIN.” Begin your timer and give students 2 minutes to work on the problems. At the end of 2 minutes, say to students: “STOP. PASS YOU WORKSHEET TO A CLASSMATE. I WILL PUT THE CORRECT ANSWERS ON THE OVERHEAD – or – READ THEM OUT LOUD. MARK YOUR CLASSMATES’ ANSWER CORRECT OR INCORRECT. WRITE THE NUMBER OF CORRECT ANSWERS ON THE TOP OF THE PAGE.”

68. © C. Lee Goss, 2008 68 Timed Practice Activity Instructions, Cont’d When finished correcting answers say to students: “PASS THE WORK SHEET BACK TO ITS OWNER. TAKE OUT YOUR MATH GRAPH AND FILL IN THE NUMBER CORRECT FOR TODAY. BE SURE TO WRITE TODAY’S DATE AT THE BOTTOM OF THE GRAPH. WHEN YOU ARE DONE, PUT YOUR GRAPH AWAY.” Say: “NOW, LOOK AT YOUR CORRECT AND INCORRECT ANSWERS. FIX THE ONES YOU GOT WRONG.” Collect student worksheets and graphs.

69. © C. Lee Goss, 2008 69 Tier 2: Small Group Instruction/Intervention

70. © C. Lee Goss, 2008 70 Tier 3: Individualized Math Interventions Flashcards Flashcards w/ Folding in New Items Cover, Copy, Compare Great Leaps/Computer Practice More research is needed Presently, Tier 3 interventions typically involve more intensive versions of methods used at Tier 2.

71. © C. Lee Goss, 2008 71 Flashcards Purpose: To build student fluency with computation facts Research: Cates, 2005; Shapiro, 2004 Ingredients: Blank 3” x 5” flashcards Sets of math computation problems Marker Prep Time: 20 minutes Activity Time: 10 minutes

72. © C. Lee Goss, 2008 72 Flashcards, Cont’d Preparation: Identify sets of 10 math computation problems that the student needs to master Write one math problem on one side of each card. Write the answer to each problem on the other side of the cards.

73. © C. Lee Goss, 2008 73 Flashcards w/ Folding in New Items Purpose: To build and maintain students’ fluency with computation facts Research Base: Shapiro, 2004 Ingredients: Blank 3” x 5” flashcards Sets of known and new math computation problems Marker Prep Time: 20 minutes Activity time: 10 minutes

74. © C. Lee Goss, 2008 74 Flashcards w/ Folding in New Items, Cont’d Preparation: See Flashcards Once the student has mastered all of the items in a set of 10 problems, create an additional set of flashcards with new math problems. Write one new math problem on one side of each card; write the answer to each new problem on the other side of the cards. Shuffle the set of mastered problems and remove 2 randomly selected cards; replace the removed cards with 2 of the new (unknown) problem cards.

75. © C. Lee Goss, 2008 75 Cover, Copy, Compare Purpose: To provide students with errorless practice of computation skills Research base: Shapiro, 2004 Ingredients: Computation problems matched to students’ instructional learning level Pencil Prep Time: 5-10 minutes Activity Time: 5 minutes per worksheet

76. © C. Lee Goss, 2008 76 Cover, Copy, Compare, Cont’d Preparation: Identify what computation skill students most need to learn (e.g., addition with grouping, multiplication, etc.) Go to the following website: www.interventioncentral.org In the section labeled “Online Tools” click on “Math Worksheet Generator” on the right hand side of the page. When the new math page loads, click on the computation skill you want students to practice. Click on the specific skill you want included in your cover-copy-compare worksheet. At the bottom of the page select the number of columns, rows, and font size appropriate for the student. Click on “Cover-Copy-Compare Worksheet.” Once you click on the button to create the probe, your browser should create and load a new tab or page with the student worksheet. Either print as many copies as you need for students, or print one copy and then make enough photocopies. Print a copy of the answer sheet.

77. © C. Lee Goss, 2008 77 Tier 3: Intensive Instruction/Intervention

78. © C. Lee Goss, 2008 78 Research-Based Math: RTI 3-Tier Model RTI model allows for use of standard assessment practices as well as individual problem-solving. RTI helps to build a bridge between general and special education Focus is on exit as much as entrance. Matches our belief about education for all children.

79. © C. Lee Goss, 2008 79

80. © C. Lee Goss, 2008 80 RTI 3-Tier Model Process

81. Example of Tier Level Interventions

82. © C. Lee Goss, 2008 82 Minnesota Example of RTI: Mathematics Break into small groups by schools/grade levels Review Example of RTI: Mathematics at the high school level in Minnesota Identify RTI methods for screening, instruction/intervention, and continuous progress monitoring Identify existing or similar implementation opportunities at your school Identify challenges for implementation at your school Summarize Lessons Learned

83. © C. Lee Goss, 2008 83 Tier 1: Core Research-Based Class Instruction Critical Elements Universal Benchmark Screening and identification of skill level and at-risk students Direct and Explicit instruction and in-class support matched to student skill levels Incorporates current research findings (e.g., Adding it Up: 5 strands and NMAP, 2008 research-based instruction components) Treatment Integrity On-going professional development

84. © C. Lee Goss, 2008 84 Strategic Intervention Highly strategic/targeted interventions vs. comprehensive (everything) “All paths lead to nowhere” Time is critical Focus on identified priority skills

85. © C. Lee Goss, 2008 85 Strategic Intervention Outcomes At-risk students have heterogeneous skills Screening and frequent progress monitoring benefits and informs skill groups and instruction Gains are specific to skill match to instruction Evidence of increased outcomes when students monitor their academic progress, set goals, and chart results toward benchmark goals

86. © C. Lee Goss, 2008 86 Treatment Integrity Treatment Integrity is critical to determination of response to intervention Fidelity means adherence to the parts of the curriculum/program and procedures Fidelity increases the likelihood the curriculum/program will be successful Fidelity and Creativity are NOT mutually exclusive. Treatment Integrity should be documented Teacher Self-Report Check Lists & Teacher Logs of Instruction/Intervention Components and Student Response

87. © C. Lee Goss, 2008 87 What Math CBMs Offer CBMs in Math provide data about student proficiency with math calculation skills that have been shown to be predictive of later math achievement Other math instruction elements are also important and should also be monitored

88. © C. Lee Goss, 2008 88 Math CBM Resources @ Secondary Level System to Enhance Educational Performance (K-12): www.isteep.com Intervention Central (Free): www.interventioncentral.org AIMSweb (K-8): www.aimsweb.com www.studentprogress.org

89. © C. Lee Goss, 2008 89 Interpreting CBM Scores Each CBM activity generates a score specific to an important math skill Allows teachers to identify the instructional area(s) needed Progress monitoring allows review of whether the instruction is working

90. © C. Lee Goss, 2008 90 What Fluency Measures Fluency = Timed Fluency = Speed + Accuracy Research has shown that BOTH rate of speed and accuracy of math calculations are important for successful math achievement Each CBM task is a fluency measure because it allows for comparisons between students over time of skill automaticity Requires standardized administrations for each student for meaningful data and progress monitoring

91. © C. Lee Goss, 2008 91 Advantages of Charting CBM Progress Data Small gains are visible Steady growth over time is visible Student is motivated by visible progress If progress is not occurring teacher can respond quickly to modify instruction A clear benchmark goal is in sight

92. © C. Lee Goss, 2008 92 Benefits of CBMs Reliability and validity are established. Tests are efficient and economical. Scoring interpretation and record-keeping can be done by computer. Repeated assessments do not spoil the results. Subtest content is research-supported. End-of-year achievement predicted by CBM score. Instructional goals for each grade are established. Decision making for individual children is facilitated. Progress Monitoring possible w/ programs and curriculum

93. © C. Lee Goss, 2008 93 Progress Monitoring All interventions should be evaluated with regular progress monitoring Weekly assessments should be done with CBMs related to the skill of greatest concern to check progress Performance should be graphed to show whether student is improving If no progress, change instruction

94. © C. Lee Goss, 2008 94 Components of Instruction The instruction should match the student’s area(s) of learning needs Some interventions will cover more than one skill, but others are more targeted If a student moves forward in one area but not another, provide instruction in the area of greatest need

95. © C. Lee Goss, 2008 95 Changing Instruction/Intervention If a student does not show progress, a different instructional method or intervention is needed Changes can include changing the intensity, duration, or frequency of instruction An entirely different intervention may be needed

96. © C. Lee Goss, 2008 96 Potential Benefits of RTI Research has shown that students performing below grade level in reading, writing or mathematics benefit from the increased attention to instructional interventions and progress monitoring Students who have LD that have gone undetected in elementary school stand a better chance of being identified for special education services. RTI takes the focus off individual student deficits and refocuses attention on the interaction between teaching and learning. RTI has the potential to reduce the number of students incorrectly identified as having LD when they may be struggling due to cultural differences or poor instruction (Cortiella, 2005).

97. © C. Lee Goss, 2008 97 Longitudinal Intervention Research

98. © C. Lee Goss, 2008 98 Longitudinal Intervention Research: Best-Practice Grouping students for instruction based on student skill Monitoring their progress over small periods of time Adjusting instruction based on the data And providing students feedback on their performance is one of the most powerful sets of educational practices that exists. (Reschly & Tilly, 2006)

99. © C. Lee Goss, 2008 99 Big Ideas to Take Home Although there is less research about math interventions, there are studies which indicate specific interventions can be effective for most students. Tier 1, direct instruction has been found to be very effective. For some students, Tier 1 alone is not enough, and many students can benefit from Tier 2 interventions. Three main Tier 2 math intervention components have been shown to be most effective: 1) peer-teaching 2) explicit instruction 3) formative assessment and feedback for students and teachers

100. © C. Lee Goss, 2008 100 Big Ideas to Take Home, Cont’d Current research evidence that computation fluency is an important aspect of overall math skill development. For students who still struggle after participating in Tier 2 instruction, diagnostic teaching and evaluation at Tier 3 can be a way to identify the specific nature of their math difficulties. Match specific interventions to student skill levels and needs

101. © C. Lee Goss, 2008 101 Big Ideas to Take Home, Cont’d CBM benchmarks can be used to identify which students are at risk for math problems CBMs are fast and effective for identifying student’s math skills Instruction/Intervention should be matched to student current skill level Early intervention for at-risk population is critical

102. © C. Lee Goss, 2008 102 Big Ideas to Take Home, Cont’d Select interventions on the basis of student’s CBM performance confirmed with other data CBMs can be used to monitor a student’s progress with implemented math intervention Progress data that shows little or no improvement means that a new, or more intensive, intervention is needed

103. © C. Lee Goss, 2008 103 Website Resources for Math Instruction Designing Effective Mathematics Instruction: A Direct Instruction Approach by: Marcy Stein, Diane Kinder, Jerry Silbert, and Douglas W. Carnine. Website: http://www.prenhall.com/stein/ Intervention Central Website: http://www.interventioncentral.org National Center on Student Progress Monitoring: http://www.studentprogress.org/ National Math Advisory Panel Website: http://www.ed.gov/about/bdscomm/list/mathpanel/index.html RTI Action Network Website: http://www.rtinetwork.org/ System to Enhance Educational Performance Website: http://www.isteep.com/ What Works Clearinghouse (WWC) Website: http://ies.ed.gov/ncee/wwc/

104. © C. Lee Goss, 2008 104 References Baker, Scott, Gerston, Russ, & Lee, D. S. A synthesis of empirical research on teaching mathematics to low-achieving students. Elementary School Journal, 103, 51-73, 2002. Brown-Chidsey, Rachel, Bronaugh, Louise, & McGraw, Kelly. RTI in the classroom: Guidelines and recipes for success. New York: Guilford Press, 2008. Carnine, Doug. Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130-141,1997. Cates, Gary L. Effects of peer versus computer-assisted drill on mathematics response rates. Psychology in the Schools, 42, 637-646, 2005. Intervention Central. Math worksheet generator. Retrieved 4 August 2008 from: http://www.interventioncentral.org/htmdocs/tools/mathprobe/addsing.php, 2008. Kilpatrick, Jeremy, Swafford, Jane, & Findell, Bradford (Eds.). Adding it Up: Helping Children Learn Mathematics. Washington, DC: National Research Council, 2001.

105. © C. Lee Goss, 2008 105 References, Cont’d McDonald, Elizabeth, & Ardoin, Scott. Interspersing easy math problems among challenging problems: detection of interspersal effects in whole-class applications. Journal of Behavioral Education, 16, 342-354, 2007. National Mathematics Advisory Panel. Foundations for success [Final report]. Washington, DC: U.S. Department of Education, 2008. Peer Assisted Learning Strategies. [Website]. Retrieved 4 August 2008 from: http://kc.vanderbilt.edu/pals/, 2008. Shapiro, Edward S. Academic skills problems: Direct assessment and intervention (3rd. Ed.). New York: Guilford, 2004. Simon, Rebecca, & Hanrahan, James. An evaluation of the Touch Math method for teaching addition to students with learning disabilities in mathematics. European Journal of Special Needs Education, 19, 191-209, 2004. Stein, Marcy, Kinder, Diane, Silbert, Jerry, Carnine, Doug. W. Designing Effective Mathematics Instruction: A Direct Instruction Approach (4th Ed.). Upper Saddle River, NJ: Pearson-Prentice Hall, 2006.

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