How to pick a math intervention "program."

1. Recent Advances in
Math Interventions:
Programs, Tactics, &
Strategies
Minnesota State
University
August 14, 2023
Robin S. Codding, Ph.D.
r.codding@northeastern.edu

2. What are you
hoping to 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. WHAT IS MATH
PROFICIENCY?

7. • understanding math concepts, 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…
Pitting procedural 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’ math success can
be promoted by ensuring
that students have the
foundational skills
necessary to engage in
advanced math topics as
they progress through
schooling

11. MATH MYTHS

12. WHAT MYTHS OPERATE IN
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 conceptual understanding & 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 We Get 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: ALL STUDENTS
PARTICIPATE IN AND CAN
ACCESS THE CORE CURRICULUM
75-Minute Block (45 Core + 30 Min of Tiered Supports)

16. Layered MTSS Model

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
seems only 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 Elementary Level 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
•COLLECTION of
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
Look For
(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
See with
Your
Screening
Data

25. Alternative Illustrations of Your
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
Foundational Skills
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 Math Facts & 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 THE CORE SKILL SEQUENCE
Achievethecore.org :: Instructional Content Nav -
Mathematics: Focus by Grade Level
Identify A Skill
Sequence

31. Benefits of
Peer-Assisted
Learning
Students working in 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 to ensure 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 basic facts
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 Practice Activity
• 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 Math Intervention 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 Recall of 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 Areas to 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 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)

41. Bucket 1
Whole Number Knowledge
Word
Problems
Number
Operations
Numeracy
National Mathematics Advisory Panel (2008)

42. 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)

43. Bucket 2
Rational Number Knowledge
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
Word Problem
Solving
Rational Number
Knowledge
Magnitude
Understanding
Number
Operations
Word Problem
Solving

46. Establishing Proficiency with Foundation 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 Precise Math 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 Not That
• “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 Examples and 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
Strip Diagrams
Number line
Abstract
Symbolic
3. USE REPRESENTATIONS

54. 4. Use Number Lines (& 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
Word Problems
• Organize problems on structural
features (e.g., additive  total,
difference, change) using
diagrams
• Use explicit modeling of problem-
solving steps
• Teach attack strategies

56. Word
Problem
Solving
Curricula

57. CULTURALLY RESPONSIVE
ADAPTATIONS
Include Culturally
Relevant Teaching
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 Timed Practice 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 STANDARD PROTOCOL
INTERVENTIONS
Effective Interventions
Interventions that
Work
Interventions with
Known Evidence
Based Practices

61. Standard
Protocol
Interventions
(Gresham, 2007)
Goal: Provide research
validated treatment protocols
Includes: Materials, protocols,
assessment tools, treatment
adherence forms
Advantages: Better quality
control of treatment delivery,
more feasible and usable

62. PLANNING
FOR
TIER 3
SUPPORTS

63. DATA-BASED
INDIVIDUALIZATION
https://intensiveintervention.org/intensive-intervention
Determine
the
Dimensions
of Intensity
Needed to
Individualize
the
Intervention

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
Unit Tests 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…
Changes in 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 et al., 2010; Peltier, 2021)
Find Students’ Stage
of Skill Development
& Match it to
Corresponding
Instructional
Strategies

70. Using the IH for 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
Establish Skill/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 of Practice 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
Retain Skill/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 of Practice for Fluency-Building
Drill
Practice
Skill in Isolation
• Flash Cards
• Incremental
Rehearsal
Combine Sets of
Problems

75. Instructional Goals
Transfer Across Tasks, 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 of Practice 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 is the 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 of Skills 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 of Education Sciences RtI Mathematics Practice Guides (Gersten et al., 2009)

80. LONGER TOTAL DURATION
Tendency to
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
Students with 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 &
Motivation Components 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 become aware 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
•Include Common 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
Set Size
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?
Fraction intervention 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 Individualize Math 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 Next Time
Linking Assessment to
Intervention
Creating Systems to Support
Data-Based Decision Making

92. Questions
&
What Do You Want
to Know More
About?

93. Robin S. Codding, Ph.D.
r.codding@northeastern.edu