session 2 tier 2 – category of the problem 1. © amanda vanderheyden, do not reproduce without...
TRANSCRIPT
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Session 2
Tier 2 – Category of the Problem
1
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How-To Classwide Math
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Intervention Plan- 15 Min per Day• Protocol-based classwide peer tutoring,
randomized integrity checks by direct observation
• Model, Guide Practice, Independent Timed Practice with delayed error correction
• Group performance contingency• Teachers encouraged to
– Scan papers for high error rates– Do 5-min re-teach for those with high-error rates– Provide applied practice using mastery-level
computational skill
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• Usually the higher-performing student, goes (models) first.• Rotating high performers helps maintain motivation
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Measurement Plan
• Weekly probe of Intervention skill• Weekly probe of Retention of previously
mastered computational skills• Monthly probe using GOM approach to
monitor progress toward year-end computational goals
• To this you might add an application measure
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Sample Sequence
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Sample Sequence
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Sample Sequence
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Kindergarten, 1st Semester
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Kindergarten, 2nd Semester
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Intervention Plan
• Class Median reaches mastery range for skill, next skill is introduced
• Following promising results at one site in 2002-2003, lead to implementation district-wide grades 1-8 for all children by 2004-2005.
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Instructional Criteria• MATH
– K: • 0-7 Count Objects, Circle Number• 0-5 Count Objects, Write Number• 0-4 Identify Number, Draw Circles• 0-5 Rapid Discrimination (sorting)
– Grades 1-3• 0-19 dc/2 min Frustration• 20-39 dc/2 min Instructional• 40+ dc/2 min Mastery
– Grades 4-6• 0-39 dc/2 min Frustration• 40-79 dc/2 min Instructional• 80+ dc/2 min Mastery
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Instructional Hierarchy: Stages of Learning
Acquisition Proficiency Generalization Adaption
Learning Hierarchy
Instructional Hierarchy
Slow and inaccurate
ModelingExplicit instructionImmediate corrective feedback
Accurate but slow
Novel practice opportunitiesIndependent practiceTimingsImmediate feedback
Can apply to novel setting
Discrimination trainingDifferentiation training
Can use information to solve problems
Problem solvingSimulations
Haring, N. G., & Eaton, M. D. (1978). Systematic instructional procedures: An instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.) The fourth R: Research in the classroom (pp. 23-40). Columbus, OH: Charles E. Merrill.
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Acquisition
Fluency
Generalization
Instructional Hierarchy
To gain the steepest growth, introduction of new skills should happen here– Core Instruction- Not manipulated
But fluency building should happen here with an instructional level skill– Intervention Focus was here
Finally, problem-solving/ application practice should occur here with a mastery level skill– Core Instruction- Not Manipulated but could be
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Class-wide Math Intervention
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Decision making
• Review data to make decisions:
DATA OUTCOME 1: Class median is below mastery range and most students gaining digits correct per week.
ACTION: Consider implementing intervention for an additional week and then review progress again.
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Decision making DATA OUTCOME 2: Class median is below
mastery range and most students are not gaining digits correct per week:
ACTION: Check Integrity first and address with training if needed. Consider implementing intervention for an additional week with incentives or easier task and then review progress again.
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Decision making
DATA OUTCOME 3: If the class median is above mastery range then consider:
ACTION: Increasing task difficulty and continuing classwide intervention.
ACTION: For students performing 1 SD below the class mean, consider Tier 3.
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Results
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Tier 1 Screening Indicates Class-wide Problem
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Tier 2: Class-wide Intervention
Teacher F Mult 0-12
0
20
40
60
80
100
120
10/2
4/20
03
10/3
1/20
03
11/7
/200
3
11/1
4/20
03
11/1
8/20
03
Weeks
Dig
its
Co
rrec
t Tw
o M
inu
tes
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Increased Difficulty- Intervention Continues
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Contextually-Relevant Comparisons and Use of Trend Data
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5th Grade Math Intervention
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Instructional range
Frustrational range
Pre-post changes to performance detected by CBM
Each bar is a student’s performance
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Fourth Grade
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Computation Gains Generalized to High Stakes TestImprovements
(Gains within Multiple Baselineshown as pre-post data)
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Gains within Multiple Baseline (shown as pre-post data)
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District-Wide RCT 4th & 5th Graders
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treatment
control
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treatment
control
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• Effects on year-end scores significant at fourth grade. Effects strongest for students who were lowest performing on the prior year’s test score.
• CBMS showed strong effects, both grades.
• Integrity varied by class and variations explained effects
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Overall
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For Vulnerable Students
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For Vulnerable Students
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Conclusions
• Low-performing students more prone to have week(s) of missing data.
• Probability of failure was reduced at a greater rate for students who receive free and reduced lunch, students receiving special education, and for African American students.
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And Ed Shapiro was right, but these data are preliminary
• New decision rule to select students in need of Tier 2 or 3 intervention
• Class Median= Mastery, Any child in frustration range at any point during intervention– Sens: .46; Spec = .91
• Class Median= Mastery, Any child 1SD below class mean– Sens: .73; Spec= .66
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How to Tier 2
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Kindergarten, 1st Semester
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Kindergarten, 2nd Semester
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1st Grade
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2nd Grade
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3rd Grade
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4th Grade
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5th Grade
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6th Grade
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7th Grade
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8th Grade
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Count Objects- Write Number
• Two forms available. Easier form has answers from 1-10. More challenging form has answers from 1-20.
• Classwide or Individual Administration• 1 minute• Scored as correctly written numbers per
minute
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Count Objects- Write Number
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Tier 2 Assessment
• Evaluate effects of– Incentives on performance (can’t do/won’t do
assessment)– Brief instructional trials on performance– GOAL- identify intervention that will improve
performance and can be delivered efficiently (e.g., small groups)
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Tier 2 Intervention
• Identify instructional-level task– Develop logical hierarchy (VanDerHeyden, 2005)– Identify difficulty level for which child responding is
accurate most of the time
• Emphasize multiple opportunities to respond– Use response cards– Use choral responding
• Provide Immediate Corrective Feedback• Provide rewards for skill gains each session
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Counts in order to 10
Accurate Number Names to 5
Fluent Number Names to 5
Accuate Number Names to 10
Fluent Number Names to 10
Identifies Number of Objects in a Set to 10
Define the Behaviors/skills
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Response Card Intervention
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Not at Risk
screening
incentives
intervention
At Risk
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Let’s Talk about Another Pitfall
• Overemphasizing intervention selection and under-emphasizing intervention management
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Integrity Failures are Sentinel Events
• Untreated integrity problems become student learning deficits, schoolwide learning problems, and false positive decision errors
• Integ problems affect dose and quality of the treatment (an intervention implemented with fidelity is a functionally different intervention than one implemented inconsistently
• Integ positively correlated with student learning gains, amount of intervention covered
• Even veteran sites require monitoring and follow-up
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Sometimes it’s the Simple Things• Proximity to trainer• Child availability for intervention sessions• Intervention error (e.g., modeling too
rapidly, failing to give feedback)• Materials available• No one’s watching• Tracking and troubleshooting
implementation failures• Remember, intervention failures should be
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Just like your mama told you: INTEGRITY MATTERS
59% Integ 96% Integrity
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64VanDerHeyden, McLaughlin, Algina, Snyder (in press). AERJ
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TIER 3
What is the causal variable?
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Components of Tier III
• Precise measurement on a frequent basis
• Individualized and intensive interventions
• Meaningful multi-disciplinary collaboration regarding individual kids
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Materials
• Assessment materials (basic skill builders)• Digital timer• Treasure Chest• Excel for Graphs• Criteria for Decision Making• Intervention Materials
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Instructional Criteria• MATH
– K: • 0-7 Count Objects, Circle Number• 0-5 Count Objects, Write Number• 0-4 Identify Number, Draw Circles• 0-5 Rapid Discrimination (sorting)
– Grades 1-3• 0-19 dc/2 min Frustration• 20-39 dc/2 min Instructional• 40+ dc/2 min Mastery
– Grades 4-6• 0-39 dc/2 min Frustration• 40-79 dc/2 min Instructional• 80+ dc/2 min Mastery
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Instructional Criteria- Updated
• Grades 2-3– 28-61 dc/2 min
• Grades 4-5– 48-98 dc/2 min
– Burns, VanDerHeyden, & Jiban (2006)
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Within-child Variables
•Temperament
•Ability/biology
•Early deficits or insults
•Learned Coping Strategies
Environmental Variables
• Task demands
•Quality of Instruction
• Learning opportunities
• Motivation
Child-Environment Fit
CHILD PERFORMANCE/SUCCESS/ADAPTATION
Largely Unalterable Alterable
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• Acquisition Interventions– Designed to establish correct responding– Cover, copy, compare; modeling; immediate
corrective feedback/guided practice; prompt hierarchies; Incremental Rehearsal
• Instructional Skill Interventions– Designed to build fluency– Timed trials with reinforcement; goal setting; rapid
advancement of task content; delayed feedback/error correction; Task interspersal
• Mastery Level Interventions– Designed to teach generalization– Guided practice applying learned skill; variation of
materials during intervention
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Functional Assessment
• Consider logical sequence of skills• Identify target skills
– Watch the child do the task– Ask the child to “think out loud”– Ask the child to teach you how to do it
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• Examine effect of reduced task difficulty, use of incentives, and brief instruction (modeling and guided practice)
• Two key questions-– Does child understand concept?– Can child complete problem-solving steps?
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Instructional Hierarchy: Stages of Learning
Acquisition Proficiency Generalization Adaption
Learning Hierarchy
Instructional Hierarchy
Slow and inaccurate
ModelingExplicit instructionImmediate corrective feedback
Accurate but slow
Novel practice opportunitiesIndependent practiceTimingsImmediate feedback
Can apply to novel setting
Discrimination trainingDifferentiation training
Can use information to solve problems
Problem solvingSimulations
Haring, N. G., & Eaton, M. D. (1978). Systematic instructional procedures: An instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.) The fourth R: Research in the classroom (pp. 23-40). Columbus, OH: Charles E. Merrill.
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Instructional Hierarchy for Conceptual KnowledgePhase of Learning
Acquisition Proficiency Generalization Adaption
Examples of appropriate instructional activities
Explicit Instruction in basic principles and concepts
Modeling with math manipulatives
Immediate corrective feedback
Independent practice with manipulatives
Immediate feedback on the speed of responding, but delayed feedback on the accuracy.
Contingent reinforcement for speed of response.
Instructional games with different stimuli
Provide word problems for the concepts
Use concepts to solve applied problems
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Instructional Hierarchy for Procedural KnowledgePhase of Learning Acquisition Proficiency Generalization Adaption
Examples of appropriate instructional activities
Explicit instruction in task steps
Modeling with written problems
Immediate feedback on the accuracy of the work.
Independent practice with written skill
Immediate feedback on the speed of the response, but delayed feedback on the accuracy.
Contingent reinforcement
Apply number operations to applied problems
Complete real and contrived number problems in the classroom
Use numbers to solve problems in the classroom
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Phase of Learning for Math
ConceptualAcquisition Proficiency Generalization Adaption
ProceduralAcquisition Proficiency Generalization Adaption
© Matthew Burns, Do Not Reproduce Without Permission
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© Amanda VanDerHeyden, Do Not Reproduce Without Permission
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• Step 1: Build conceptual understanding• Step 2: Build procedural fluency• Check acquisition (accuracy),
independence (fluency), and application
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Assessing Conceptual KnowledgeConcept Oriented CBM
• Monitoring Basic Skills Progress-Math Concepts and Applications (Fuchs, Hamlett, & Fuchs, 1999).
• Focal Point Assessments (Witt, 2008) isteep.com
• Math Applications (Connell, 2008).
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Assessing Conceptual KnowledgeConcept Oriented CBM
• Monitoring Basic Skills Progress-Math Concepts and Applications (Fuchs, Hamlett, & Fuchs, 1999).
• 18 or more problems that assess mastery of concepts and applications
• 6 to 8 minutes to complete
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Conceptual Assessment
• Ask students to judge if items are correct– 10% of 5-year-old children who correctly
counted did not identify counting errors in others (Briars & Siegler, 1984).
• Provide three examples of the same equation and asking them to circle the correct one
• Provide a list of randomly ordered correct and incorrect equations and ask them to write or circle “true” or “false” (Beatty & Moss, 2007).
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Conceptual Assessment
Problem 1Please use a picture to solve the problem
3 x 4 = ___
Problem 2Please use a picture to solve the problem
5 x 6 =___
Next 4 slides from Burns 2010
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To Establish the Skill
• Use manipulatives to demonstrate• Ask child to explain what it means• Vary answer format • Ask equivalence, more-less, and true/false
questions• Add a within-stimulus prompt or cue• Once accurate, begin procedural fluency
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Common Procedural Errors
• Not attending to operation, wrong operation
• Regrouping errors in addition, subtraction, and multiplication
• Dysfluency in basic computations• Misalignment of columns- place value
errors (e.g., long division)
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Strategies
• Model, guided practice
• Provide Cues (e.g., use graph paper for column alignment, use highlighter to highlight operation)
• Use cover, copy, compare intervention
• Use within-stimulus prompt
• Build fluency on component skills
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Cover-Copy-Compare
Match?
= 3
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An Interpreted Example…
3
5
2
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An Interpreted Example…
35
2
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An Interpreted Example…
35
2
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Interspersal
• Mix challenging with easier tasks (1:1, 1:3, 1:5)
• Effects for completion of challenging problems and preference
3
+ 1 2
+ 2
6
+ 3
1
+ 2
3
+ 2
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Incremental Rehearsal
• Drill “unknown” item mixed in with “known” items
• Present 9 known flashcard problems to 1 unknown in 1:1 rotation.
• When an unknown is correct 9 times in session, it becomes a known
• When a known is missed three times, it becomes an unknown again
• Good effects for retention
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Unknown
• 16 x 8 = 128
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2 x 3
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16 x 8
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2 x 3
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1 x 5
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16 x 8
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2 x 3
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1 x 5
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10 x 5
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16 x 8
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2 x 3
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1 x 5
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10 x 5
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2 x 10
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16 x 8
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Unknown
Known 1
Unknown
Known 1
Known 2
Unknown
Known 1
Known 2
Known 3
Unknown
Known 1
Known 2
Known 3
Known 4
Unknown
Known 1
Known 2
Known 3
Known 4
Known 5 © Amanda VanDerHeyden, Do Not Reproduce Without Permission
Unknown correct 5 times = KnownNext Session, Unknown becomes Known 1
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Amanda’s Show and Tell
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Some Lessons Learned• We often measure too much and too much
of the wrong things.• We do not begin with a plan in mind of
what the most critical “big ideas” are and make these explicit for students.
• Students are not provided with adequate time to practice to mastery.
• We do not connect instructional strategies to student proficiency.
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Lessons Learned• We fail to attend to the basics
– Adequate time, intention, systematic advancement of content based on mastery of prior content, explicit connection of computations to conceptual understandings past and future, providing sufficient demonstrations and checking for student understanding
• We de-value fluency in computational skills and bigger ideas like quantity discriminations with proportions
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• We think of “application” as only word problems
• If we graph expectations for mathematical learning across years of school, it is not a linear upward trend. We expect too little at the lower grades and try to make up for lost time later on.
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For More Information• Amanda VanDerHeyden
– [email protected]– 251-300-0690
• www.isteep.com and www.gosbr.net • www.rtinetwork.org• www.nasdse.org (blueprints)• Keeping RTI on Track: How to Identify, Repair and Prevent
Mistakes That Derail Implementation• http://www.shoplrp.com/product/p-300620.html• Or 1-800-341-7874• http://www.jeabjaba.org/abstracts/JabaAbstracts/26/26-597.Htm
(Fixsen & Blasé, 1993)• Hattie (2009). Visible Learning.
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