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![CRITICAL
FOUNDATIONS
FOR
(Gersten et al., 2009; National Mathematics Advisory Panel [NMAP], 2008; USDOE, 2008)
Algebra
Whole Number
Proficiency
Fluency with
Fractions
Key Aspects of
Geometry
Key Aspects of
Measurement](https://image.slidesharecdn.com/recentadvancesinmathinterventions-231219195805-3fd82def/75/Recent-Advances-in-Math-Interventions-Programs-Tactics-Strategies-Handouts-pdf-9-2048.jpg)
![Key Content Targets for Mastery (K-5)
Algebra
Whole Number
Proficiency
Fluency with
Fractions
Key Aspects of
Geometry
Strategic
Counting
Magnitude
Comparison
Composition
Decomposition
Fluency w/ Simple
Number
Operations
Fluency w/
Complex
Number
Operations
Word
Problems
(Gersten et al., 2009; National Mathematics Advisory Panel [NMAP], 2008; USDOE, 2008)](https://image.slidesharecdn.com/recentadvancesinmathinterventions-231219195805-3fd82def/75/Recent-Advances-in-Math-Interventions-Programs-Tactics-Strategies-Handouts-pdf-40-2048.jpg)
![Key Content Targets for Mastery (4-8)
Algebra
Whole Number
Proficiency
Fluency with
Fractions
Key Aspects of
Geometry
Magnitude
Comparison
Operations
Word
Problems
(Gersten et al., 2009; National Mathematics Advisory Panel [NMAP], 2008; USDOE, 2008)](https://image.slidesharecdn.com/recentadvancesinmathinterventions-231219195805-3fd82def/75/Recent-Advances-in-Math-Interventions-Programs-Tactics-Strategies-Handouts-pdf-42-2048.jpg)
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Recent Advances in Math Interventions. Programs Tactics Strategies.Handouts.pdf
- 1. Recent Advances in MathInterventions: Programs, Tactics, & Strategies Minnesota State University August 14, 2023 Robin S. Codding, Ph.D. [email protected]
- 2. What are you hopingto learn today?
- 4. Overview 1. Math Proficiency 2.Math Myths 3. Tier 1 Strategies,Tactics, Interventions 4. Tier 2 Strategies,Tactics, Interventions 5. Tier 3 Strategies,Tactics, Interventions
- 6.
- 7. • understanding mathconcepts, laws, principles, and relations. Concepts • algorithms, mnemonics, mental math, and automatic recall of basic facts. Procedures • formulating, representing, and solving math problems. Strategies • explaining, reflecting, and justifying math problems and their solutions. Reasoning • beliefs about the value of math as useful, sensible, and worthwhile. Disposition
- 8. What the Science Says… Pittingprocedural fluency against conceptual understanding creates a FALSE DICHOTOMY (NCR, 2001, p. 100) Conceptual understanding and procedural fluency (including quick & effortless recall of facts) are MUTUALLY BENEFICIAL (NMAP, 2008, p. 11) Empirical studies have shown a bidirectional relationship between concepts and procedures (Canobi, 2009; Hectht & Vagi, 2010; Rittle-Johnson & Koedinger, 2009; Rittle-Johnson et al., 2001, 2015; Schneider et al., 2011)
- 9. CRITICAL FOUNDATIONS FOR (Gersten et al.,2009; National Mathematics Advisory Panel [NMAP], 2008; USDOE, 2008) Algebra Whole Number Proficiency Fluency with Fractions Key Aspects of Geometry Key Aspects of Measurement
- 10. KEY IDEA Students’ mathsuccess can be promoted by ensuring that students have the foundational skills necessary to engage in advanced math topics as they progress through schooling
- 11.
- 12. WHAT MYTHS OPERATEIN YOUR SCHOOL/DISTRICT? 1. Teach Conceptual Knowledge 1st 2. Standard Algorithms are Harmful 3. Productive Struggle Leads to Deeper Learning 4. Explicit Instruction is Only Helpful for Some Students 5. All Standards Are Created Equal 6. Executive Functioning Training Matters 7. Growth Mindset Increases Math Achievement 8. Timed tests & Tasks Cause Math Anxiety 9. Fact Fluency Doesn’t Matter
- 13. • Interleave conceptualunderstanding & procedural knowledge in every lesson 1 • Teach the standard algorithm 2 • Challenge students with novel problems ONLY AFTER they are accurate and fluent with key skills & concepts 3 • Use explicit & systematic instruction everyday & at all tiers (including core instruction) 4 • For mastery of key foundational skills required for students to engage in advanced math 5 • Remediate learning challenges by improving students’ accuracy, fluency, and generalization of critical MATH skills 6 • Show students how to engage in their own learning 7 • Once of the most effective practices for building fluency is timed practice activities 8 • Facts are the building blocks in math 9
- 14. How Did WeGet Here? Pseudoscience is Seductive Reform Efforts Left Behind Proven Practices Limited tSOM Examples Included in Textbooks Overload of information on the internet and via social media Implementation Challenges
- 15. TIER 1: ALLSTUDENTS PARTICIPATE IN AND CAN ACCESS THE CORE CURRICULUM 75-Minute Block (45 Core + 30 Min of Tiered Supports)
- 16.
- 17. Strengthening Core Instructional Practices… •the number of students who will require additional supports to be successful Reduces • resources to provide those students with or at- risk for learning disabilities the services and supports that they need Frees • the accuracy with which we identify students that need specialized intervention supports Increases • in BETTER OUTCOMES for students receiving specialized intervention supports Results Targeted Interventions Individualized Interventions High-quality Core Instruction Provided In The General Education Classroom (Barrett & VanDerHeyden, 2020; Fuchs et al., 2008; VanDerHeyden et al., 2021)
- 18. Procedural vs. Conceptual Debate seemsonly to apply to U.S. Other countries recognize practice with procedures as a route to understanding U.S. students cannot solve basic facts as quickly or efficiently as their international peers Neither textbooks nor instruction provide enough opportunities for practice with procedural knowledge U.S. Curricula Gaps in BOTH Conceptual & Procedural Knowledge (Codding et al., 2017; NCR, 2001;NMAP, 2008 )
- 19. Access Problem Nearly 30%of surveyed 4th and 8th grade math teachers reported that a lack of adequate math instructional materials and supplies was a moderate or serious problem (NAEP, 2019)
- 21. Review of ElementaryLevel Curricula Inconsistent Use of Explicit & Systematic Instruction Lack of Dedicated Time for Opportunities to Practice Limited Iterative Sequencing of Conceptual Understanding & Procedural Knowledge Little Guidance to Teachers for Providing Student Feedback Minimal Guidance on Using Assessment for Instructional Decision Making (Bryant et al., 2008; Doabler et al., 2012; Jitendra et al., 2005; Sood & Jitendra, 2007)
- 22. Evidence-Based PRACTICES •Skills, Techniques, or Strategies Evidence-Based PROGRAMS •COLLECTIONof practices https://iris.peabody.vanderbilt.edu/module/math/cresource/q1/p03/#content …that experimental research studies or large-scale research field studies have proven effective
- 23. Evaluating Curricula: 8 Instructional Practices to LookFor (Doabler et al., 2012; Hughes et al., 2016; Riccomini et al., 2015) Prerequisite Skills Teach Key Math Vocabulary Explicit & Systematic Instruction Instructional Examples Use of Math Models Opportunities to Practice & Cumulative Review Procedures for Providing Student Feedback Formative Assessment
- 24. What You Hope to Seewith Your Screening Data
- 25. Alternative Illustrations ofYour Actual Pyramid
- 26. Tertiary • Smaller Group& Individualized Supports • Monitor Weekly Secondary • Small Group Intervention (homogeneous skills) • Monitor Bi-Weekly/Weekly Class-Wide Supplements • Address Foundational Skill Gaps with Whole Class • Monitor Weekly Core Instruction • Universal Grade Level Instruction to All Students • Monitor 2-3 times Per Year Tier 1.5
- 27. Classwide Intervention • Fluency with FoundationalSkills Build • Average Classroom Performance • Beliefs & Attitudes @ Math Improve • Into Naturally Occurring Routines Embed (Codding et al., 2009; Kilpatrick et al., 2001; NMAP, 2008; Slavin & Lake, 2008; 2009)
- 28. Class-Wide Intervention Class Median <25th Percentile on Universal Screener Address Critical Skill Gaps (50%+ of the class are missing) Provide Brief (10- to 15-Min) Interventions Increase Opportunities to Practice Skills & Concepts Increase Amount & Type of Feedback Provided
- 29. Focus on MathFacts & Complex Computation 390 Math Facts 109 +62 | 317 – 25 25 x 50 | 6,598/18 Determine Equivalent Fractions | Compare & Order Fractions | Estimate Sums of 2 Fractions (Dehaene, 2011; DeSmedt et al., 2011; Gersten et al., 2009; Hasselbring et al., 1988; Jordan et al., 2009; O’Connell & SanGiovanni, 2011; Powell & Fuchs 2013; Price et al., 2013; Stickney et al., 2012)
- 30. ADD ACHIEVE THECORE SKILL SEQUENCE Achievethecore.org :: Instructional Content Nav - Mathematics: Focus by Grade Level Identify A Skill Sequence
- 31. Benefits of Peer-Assisted Learning Students workingin PAIRS or SMALL GROUPS daily scored higher on the NAEP (2017) than their peers Benefits students from low income, minoritized backgrounds in urban schools as well as English learners Better when students monitor own outcomes, set goals, & evaluate own performance More evidence supporting benefits for whole- number concepts (Bowman-Perrott et al., 2013; Ginsburg-Block et al., 2006; Greenwood et al. 1993; Kunsch et al., 2007; NCES, 2018; Robinson et al., 2005)
- 32. Peer-Assisted Learning Steps 1.Select Activity & Set Time (10-15 min) 2. Pair Students 3. Provide background + review key concepts & procedures 4. Identify Rules for Working Together 5. Create Team Score Card 6. Have Pairs Select Daily or Weekly Goals 7. Assign Student to Begin as Tutor/Coach 8. Use Timer to Signal Role Switching 9. Wrap-Up: Evaluate Teamwork & Goals
- 33. Cover-Copy-Compare • Model toensure accurate responding • Easy to use when differentiating skills or different set sizes among students Pros • Number of opportunities to respond are slowed by the study-cover-copy-compare process Cons
- 34. Detect-Practice-Repair DETECT: Powerpoint slide with basicfacts scheduled to change every 3 seconds (1- min). Students have worksheet to write answers & later score. PRACTICE: Select 5 incorrect problems from the detect phase & build own Cover- Copy-Compare worksheet REPAIR: Redo Detect Phase with second worksheet (e.g., Poncy et al. 2010)
- 35. Explicit Timing Timed PracticeActivity • Students need to accurately & independently complete the activity • Teacher provides finite time for task (1-min, 2-min, 4-min) • Student either works problems for the time allocated or stops at 30 second intervals Pros and Cons • PROS: Easy to incorporate in classroom routines, low cost, efficient & effective • CONS: Need to match the student to the appropriate skill & know when to move to a new skill
- 36. TIER 2 MATH STRATEGIES,INTERVENTIONS, & TACTICS
- 37. Logistics of MathIntervention Delivery Daily (@ least 4 days per week) Small Groups of • 2 (higher quality teacher-student interactions & more OTPs) • 5 (more opportunities for peer discourse) 30-Minutes Per Session (minimum) Progress Monitor Outcomes 2 Ways • Grade Level CBM • Subskill Mastery Measures
- 38. Behaviors of Students with Math Problems Poor Recallof Number Combinations (Facts) Not Understanding Commutative Property Ineffective Counting Strategies Regrouping Errors Misaligns Numbers Trouble with Meaning of Symbols (+, -, <, %) Difficulty Solving Word Problems Problems Implementing a Plan to Solve Word Problems Trouble Identifying Tangential Information Not Understanding the ? Asked Math Language Failing to Check Work (Bryant, Bryant, & Hammill, 2000)
- 39. Key Content Areasto Target Kindergarten to Grade 5 • Strategic Counting • Magnitude Comparison • Number Composition & Decomposition • Basic Whole Number Operations • Place Value • Explicit Teaching of Word Problems Grades 4-8 • Operations (fractions, decimals, ratios, percentages) • Complex Operations (e.g., long division) • Explicit Teaching of Word Problems (Gersten et al., 2009) In Depth Knowledge of Rational Numbers In Depth Knowledge of Whole Numbers
- 40. Key Content Targetsfor Mastery (K-5) Algebra Whole Number Proficiency Fluency with Fractions Key Aspects of Geometry Strategic Counting Magnitude Comparison Composition Decomposition Fluency w/ Simple Number Operations Fluency w/ Complex Number Operations Word Problems (Gersten et al., 2009; National Mathematics Advisory Panel [NMAP], 2008; USDOE, 2008)
- 41. Bucket 1 Whole NumberKnowledge Word Problems Number Operations Numeracy National Mathematics Advisory Panel (2008)
- 42. Key Content Targetsfor Mastery (4-8) Algebra Whole Number Proficiency Fluency with Fractions Key Aspects of Geometry Magnitude Comparison Operations Word Problems (Gersten et al., 2009; National Mathematics Advisory Panel [NMAP], 2008; USDOE, 2008)
- 43. Bucket 2 Rational NumberKnowledge Word Problem Solving Magnitude Number Operations
- 44. Relationship Between Whole & Rational# Knowledge Whole Number Magnitude Representations Calculation Fluency Fraction Knowledge (Hansen, et al., 2017; Numkung et al., 2018;Resnick et al 2018; Ye et al., 2016) Students without whole number proficiency wereMORE LIKELY to have TROUBLE with fraction understanding than students with whole number proficiency
- 45. Best Practices K-8: Teach Foundational Skills 1st Screening Whole Number Knowledge Numeracy Number Operations WordProblem Solving Rational Number Knowledge Magnitude Understanding Number Operations Word Problem Solving
- 46. Establishing Proficiency withFoundation Skills within Common Core Standards: Climbing a Mountain 3.OAA: REPRESENT AND SOLVE PROBLEMS INVOLVING MULTIPLICATION & DIVISION Interpret 5 x7 as 5 groups of 7 objects Interpret 35/7 35 objects partitioned into equal shares of 7 objects each Use x and / within 100 to solve word problems Determine unknown number in 5 x ? = 35 •A Common Core cluster is at the top of the mountain. •Standards fall below the cluster, when these foundational skills are integrated they lead to mastery of the cluster. Powell et al. (2013, p. 43)
- 48. 1. EXPLICIT INSTRUCTION… (ROSENSHINE,2010) Sets the Stage For Learning Presents clear explanation of what to do Modeling & Demonstration Guided Practice Independent Practice Lesson Closure & Assessment
- 49. Evidence Students with math difficulties& disabilities BENEFIT MORE from explicit instruction than discovery-oriented methods (Kroesbergen & Van Luit, 2003) 0 0.25 0.5 0.75 1 1.25 Gresham et al. (2009) Swanson (2009) Baker et al. (2002) Effect Size Moderate Large
- 50. 2. Include PreciseMath Language 105 Novel Math Terms by the End of 1st Grade 325+ Novel Math Terms by the End of 5th Grade Teaching language that is mathematically correct can help children generalize across concepts and is necessary for understanding math in oral and written forms (Ernst-Slavit & Mason, 2011; Hughes et al., 2016; Riccomini et al., 2015)
- 51. Say This NotThat • “Let’s start counting with 1” • “Three hundred twenty-four” • “Compose” or “Decompose” • “Greater than” or “Less than” • “regroup” • “Numerator” and “Denominator” • “Equivalent fraction in simplest form” • 5.4 is “five and four tenths” • “Cube has 6 faces” • Transformations: “Reflection, translation, rotation” • “1 is the first number” • “Three hundred and twenty-four” • “Make” or “Break Apart” • “Bigger” or “Smaller” • “borrow” • “Top Number” and “Bottom Number” • “Reduce” • 5.4 is “five point four” • “Cube has 6 sides” • Transformations: “flips, slides, turns”
- 52. Vocabulary Pre-View Provide Examplesand Non- Examples Illustrate with a Visual or Picture Use Simple, Direct Language Pre-teach Key Vocabulary Terms for Unit/Lesson
- 53. Concrete Counters Chips Blocks Semi-Concrete Pictures of Objects Tallies StripDiagrams Number line Abstract Symbolic 3. USE REPRESENTATIONS
- 54. 4. Use NumberLines (& Other Math Models) • Students who use accurate visual representations are 6 times more likely to correctly solve mathematics problems than are students who do not. • Students with math disabilities and difficulties often DO NOT USE or CREATE accurate visual representations (Boonen et al., 2014; Chard, Gellar, & Powell, 2017; van Garderen et al., 2012; van Garderen et al., 2014) Number Lines Strip Diagrams Pictures Graphs/Charts Graphic Organizers
- 55. 5. Explicitly Teach WordProblems • Organize problems on structural features (e.g., additive total, difference, change) using diagrams • Use explicit modeling of problem- solving steps • Teach attack strategies
- 56.
- 57. CULTURALLY RESPONSIVE ADAPTATIONS Include Culturally RelevantTeaching Examples Encourage Students to Create their Own Examples & Word Problems based on Their Lived Experiences Encourage Bilingual & Multilingual Students to Use Their Preferred Language When Using “Math Talk” Preview & Review Math Vocabulary in Students’ Preferred Language (Driver & Powell, 2017; Freeman-Green et al., 2021; Luevano & Collins, 2021)
- 58. 6. Use TimedPractice To Build Fluency (Codding et al., 2019; Doabler et al., 2019, Fuchs et al., 2021) Deliberate, Productive Opportunities To Practice Are Required For All Types Of Learning (e.g., sports, music, math) Promote Active Engagement with Math Content Provide High Levels of Feedback & Support Timed Practice Opportunities that Promote Efficient & Accurate Performance Improve Student Outcomes
- 59. Guided Practice Timed Practice Cumulative Review Teacher-Led (Accuracy) • Demonstration& Modeling • Think Aloud While Solving • Worked & Partially Worked Examples Student-Led (Fluency) • Flash Cards • Worksheets • Peer-Mediated or Team Based • Technology Integrate Previously Learned Skills & Concepts (Generalization) • Games • Challenge Problems • Interleaved Practice Establishing Retaining & Maintaining Enduring & Applying
- 60. BEGIN WITH STANDARDPROTOCOL INTERVENTIONS Effective Interventions Interventions that Work Interventions with Known Evidence Based Practices
- 61. Standard Protocol Interventions (Gresham, 2007) Goal: Provideresearch validated treatment protocols Includes: Materials, protocols, assessment tools, treatment adherence forms Advantages: Better quality control of treatment delivery, more feasible and usable
- 62.
- 63.
- 64. Individualize Instruction by (Gresham,2007) Clearly DEFINE the Learning Challenge Collecting DATA Generating REASONS for the Learning Challenge Linking Reasons to Instructional Intervention PLANS
- 65. Diagnostic Data Student & Teacher Interviews Curriculum- Based Measures UnitTests Observations Fact & CRA Assessments Task Analysis Measures & Other Data that Provide Detailed & Specific Information on What Students Know & Don’t Know (Hosp & Ardoin, 2008)
- 66. Students in Need of Intensive Individualized Support Require… Changesin frequency and duration of instruction Increased motivation & sustained engagement Smaller slices of the curricula (More focused and specific goals) Consider cognitive load, working memory, and retention of learners (e.g., Fuchs et al., 2012; Lemons et al., 2018; Mellard et al., , 2010;Vaughn et al., 2010)
- 67. REASONS FOR STUDENTS’ACADEMIC DIFFICULTIES Academic Challenges Don’t Want To Not Enough Practice Need More Help Its Too Hard Haven’t Done it That Way (Daly et al., 1997) Motivation Increase Support Evaluate Pre- Requisite Skills More OTPs Generalization Daly et al. (1996)
- 68. Instructional Hierarchy Adaptation APPLYING: Skills &Concepts are Integrated and Applied to Novel Problems Generalization ENDURING: Skills & Concepts Transfer Across Academic Tasks & Situations Fluency REMEMBERING & RETAINING Skills & Concepts: Building Efficiency | Automaticity| Fluency + Accuracy Acquisition ESTABLISHING Skills & Concepts: Building Accuracy (Burns et al., 2010; Codding et al., 2017; Haring et al., 1978)
- 69. Instructional Hierarchy (Burns etal., 2010; Peltier, 2021) Find Students’ Stage of Skill Development & Match it to Corresponding Instructional Strategies
- 70. Using the IHfor Diagnosis & Intervention Slow + Inaccurate • Implement explicit instruction with modeling, guided practice, immediate and corrective feedback Slow + Accurate • Develop fluency with opportunities for productive practice Fast + Accurate; No Transfer • Help student generalize their skills across time and tasks Fast + Accurate + Transfer • Provide novel and challenging problems that require skill integration ADAPTATION FLUENCY ACQUISITION GENERALIZATION
- 71. Instructional Goal Build Accuracy EstablishSkill/Concept Deliver Small Slices of Curriculum Make Learning Errorless & Concrete Instructional Strategies Modeling Present example of a skill (e.g., look at this…) Demonstration Active performance of a skill (e.g., watch me, I will show you how to…) Prompting & Cueing Providing a cue to perform a response (e.g., remember to…) Immediate Feedback Provide praise for correct responses & correct misconceptions Acquisition A student is in the ACQUISITION STAGE when: They perform a skill slowly & inaccurately
- 72. Best Forms ofPractice For Acquisition Guided Practice Drill Worked Examples Teacher-Led • Demonstration & Modeling • Think Aloud While Solving Skill in Isolation • Flash Cards • Incremental Rehearsal Worked Examples • Completed • Partially Completed
- 73. Instructional Goal Build Efficiency/Fluency RetainSkill/Concept Provide Lots of Opportunities for Brief & Frequent Practice Instructional Strategies Timed & Peer Practice Delayed Feedback Feedback on Fluent Performance Self-Monitoring, Reflection & Graphing Progress Fluency A student is in the FLUENCY STAGE when: They perform a skill slowly & accurately
- 74. Best Forms ofPractice for Fluency-Building Drill Practice Skill in Isolation • Flash Cards • Incremental Rehearsal Combine Sets of Problems
- 75. Instructional Goals Transfer AcrossTasks, Activities, Problems Consistency Across Time & Settings Application of Skills Combine Previous & Recently Learned Skills and Concepts Instructional Strategies Solve Problems Multiple Ways Team-based Activities Math Games Generalization A student is in the GENERALIZATION STAGE when: They perform a skill fast & accurate but without transfer
- 76. Best Forms ofPractice for Generalization Interleaved Practice Cumulative Review Interleaved Practice • Tasks & Activities that Integrate Skills Integrate Previously Learned Skills & Concepts • Games, Advanced Problems
- 77. Interleaving Problems • Interleaving isthe process of mixing up the skills practiced rather than focusing on a single topic or skill • Consecutive problems cannot be solved with the same strategy • Students need to learn to choose the most efficient strategy • Cognitive psychologists believe that interleaving improves the brain’s ability to differentiate, or discriminate, between concepts and strengthens memory associations. (Rohrer, Dedrick, & Agarwal, 2017, pp. 3-4) (Rohrer, Dedrick, & Agarwal, 2017, p. 8)
- 78. Instructional Goals Application ofSkills and Concepts Integration of a Variety of Skills & Concepts Instructional Strategies Simulations Novel & Challenging Problem Solving Adaptation A student is in the ADAPTATION STAGE when a skill or concept is mastered: They perform a skill quickly, accurately with transfer
- 79. DOSE Session Length Frequency per Week Total Duration Institute ofEducation Sciences RtI Mathematics Practice Guides (Gersten et al., 2009)
- 80. LONGER TOTAL DURATION Tendencyto hold onto the idea we can address student learning needs in a fixed period of time (8-12 weeks) Total Duration Initial Scores Matter • Met criterion after 10, 20, 30 weeks (Vaughn & Linan-Thompson, 2003) More Total Weeks • Secondary students = 2 years of Support (Vaughn et al., 2011) Fading 100 min/day to 50-min • 40% of students could transition out of special education (Torgersen et al., 2001)
- 81. MOTIVATION & ENGAGEMENT Studentswith math learning difficulties have trouble beginning and persisting with problem solving tasks Student attention is one of the most persistent child-level predictors of responsiveness to whole number interventions (Gersten, Beckmann et al., 2009; NMAP, 2008; Powell et al., 2015, 2017)
- 82. Improve Student Beliefs& Attitudes About Math Teamwork & Motivation • Facilitate teamwork, mutual assistance, encouragement, and commitment to pro- social goals. • Math achievement is improved by enhancing motivation and making students active learners. Token Economy Group Contingency Behavior Contract Mystery Motivator (Gersten et al., 2009; NMAP, 2008; Powell et al., 2015, 2017, Pellegrini et al, 2021)
- 83. ADD AMOUNT &SALIENCE OF FEEDBACK Praise Self-Scoring Self-Charting Choice Goal Reflection Ticket Out: 3 Things I Learned
- 84. Layer Self-Regulation & MotivationComponents Into Skill-building • Praise Effort & Persistence • Establish Short-Term Learning Goals • Offer Opportunities for Reflection • Teach Students to Monitor Their Own Progress Toward Individualized Learning Goals • Show Students How to Record Learning Accomplishments • Encourage Students to Check their Work (Park et al., 2016)
- 85. SELF- REGULATION Help students becomeaware of how they think when problem solving Use of Heuristics & Mnemonics & Verbalization to teach students how to PLAN, MONITOR, & MODIFY their work Metacognitive strategies IMPROVE math problem solving of students with mathematics learning difficulties and disabilities (Montague, Enders, & Dietz, 2011; Pfannenstiel, Bryant, Bryant, & Porterfield, 2015)
- 86. SELF-MONITORING CHECKLIST Creating A Checklist: •Individualize •IncludeCommon Errors •List Appropriate Step for Error Prevention
- 87. Teaching Heuristics (Zrebiec Uberti,,Mastropieri & Scruggs, 2004) Understand the Problem Restate In Own Words; Break It Down Into Smaller Parts; Draw A Picture; Act It Out; Use Manipulatives Or Visuals Devise a Plan Make a table Draw a diagram Translate into an equation Carry out the Plan Look Back (check results) Put Results In Words Does The Answer Address The Question?
- 88. REDUCE SET SIZE SetSize Number of Items Targeted As SET SIZE increases, magnitude of intervention effect decreases Example: Set Size 2 Facts ~50% Retention 4 Facts ~75% Retention 8 Facts ~33% Retention ( Burns et al., 2016; Poncy et al., 2015 )
- 89. What about Individual Differences? Fractionintervention with either fluency or conceptual practice activities Students with very poor working memory scores did better with the conceptual practice version Students with better working memory scores did better with fluency practice version Number knowledge intervention with fluency building or conceptual knowledge activities Regardless of cognitive reasoning skills (weak or strong) improvement occurred with fluency building version For students with weak reasoning ability, the conceptual activity version led to poorer outcomes than students with stronger reasoning ability Bottom Line: the way the math activities were constructed was altered to address individual cognitive differences (Fuchs et al., 2013; Fuchs et al, 2014)
- 90. Best Practices To IndividualizeMath Interventions • Minimize cognitive load on working memory and reasoning by • including explicit instruction & breaking down problems into smaller more manageable parts • Minimize excessive language load by • using visual and concrete representations and providing fluency practice • Increase repetition and opportunities to practice (especially if carryover from one day to next doesn’t happen) The most effective way to address math skill deficits is to DIRECTLY remediate math skills
- 91. Preview for NextTime Linking Assessment to Intervention Creating Systems to Support Data-Based Decision Making
- 92. Questions & What Do YouWant to Know More About?
- 93.