The Math Learning Companion (MLC)
An Individualized Intervention for Students with
Math Learning Disabilities
Contents
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General Characteristics of Students with MLD and
participants in MLC research study
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What works with Students with MLD
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MLC Pedagogy
About Students with MLD
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Less understood than reading disabilities (RD)
Not achieving in the general ed curriculum
5-8% prevalence
Disability versus difficulty
 Persistent and sustained
 Cognitive not environmental
 No clear biological marker
Weak math automaticity
Co-occurrence with RD and ADHD
MLC Research Students (2009-2010)
Math Achievement Scores of Study Students
Grade Level Equivalent
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Broad Math GE
3.5
2.8
3.0
2.6
3.2
3.8
4.1
4.2
3.8
3.2
4.5
3.2
3.7
3.5
3.7
1.5
4.4
3.9
2.5
3.6
3.8
Brief Math GE
3.4
2.8
3.0
2.6
3.2
3.9
4.3
4.4
3.9
3.2
4.7
3.2
3.6
3.6
3.9
1.4
4.6
3.8
2.4
3.6
3.7
Math Calc GE
4.6
2.5
4.0
3.1
3.0
3.8
4.8
4.7
3.4
3.8
4.3
4.4
4.6
3.1
3.4
2.0
5.0
4.5
2.7
4.0
4.4
Applied Problems GE
2.5
3.2
2.2
2.2
3.5
3.9
3.5
3.7
4.4
2.7
4.6
2.2
2.8
3.9
4.1
0.0
3.7
3.3
2.3
3.3
3.3
Calculation GE
4.8
2.3
4.3
3.2
2.8
3.8
5.4
5.4
3.4
4.0
4.8
5.1
4.8
3.4
3.6
2.0
5.7
4.5
2.5
4.0
4.3
Math Fluency GE
4.0
3.1
2.9
2.6
3.6
3.6
3.3
3.1
3.2
2.9
3.1
2.6
4.0
2.4
2.9
2.0
3.4
4.3
3.6
3.5
4.5
Quantitative Concepts GE
4.7
3.0
3.4
3.4
5.3
4.3
3.9
4.3
3.7
3.6
2.6
2.6
4.3
4.3
4.3
0.0
2.3
5.0
2.3
2.5
3.7
Current Grade Level
6.6
6.6
6.6
6.6
6.6
6.6
6.6
6.6
6.9
6.9
6.9
6.9
6.9
6.9
6.9
7.9
7.9
7.9
7.9
7.9
7.9
MLC Research Students (2009-2010)
MLC Research Students (2009-2010)
About the Math Learning Companion
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Online intervention designed and developed specifically for students
with Math Learning Disabilities
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Comprehensive math content & skills development
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Interwoven language support, with read-aloud and audio
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Full alignment to CCS, NCTM, TX, CO and other state standards,
grades 3-8
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Standards-based assessments; pre and post diagnostic placement
assessments at each grade (hundreds of test items)
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Automatic placement and progression through curriculum
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Cognitively challenging with consistent feedback and review
MLC Pedagogy
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Emphasizes critical foundations and prerequisite concept knowledge &
skills
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Scaffolds the learning; makes math comprehensible without simplification
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Visual representation
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Synchronicity, visual contextual hints, modeling, guided practice, pacing,
sequencing tasks and practice, etc.
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Focuses on vocabulary & development of academic language Breaks
concepts into learning chunks
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Engaging and interactive: games, manipulatives, real world scenarios, with
explicit connections between concrete and abstract
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Universal Design for Learning: adaptive & flexible
Emphasis on Critical Foundations & Prior Knowledge
(Gersten & Chard, 1999; Marzano, 2004; National Math Advisory Panel,
2008)
• Provides embedded and active supports
• Universal Design for Learning: adaptive & flexible
• Breaks concepts into learning chunks (Miller, 1956)
Visual Representation
(Krashen, 1992, Gersten et al., 2009)
• Read-aloud throughout
• Synchronizing audio, visual, and text
to create a visual connection between
words, symbols, and meaning (e.g.,
corresponding vocabulary, symbols, or
pictures flash in sync with audio).
Scaffolding Math Concepts & Skills
(Jitendra et al., 2005, Vygotsky, 1978)
Emphasis on Critical Foundations and Number Sense
In order to achieve higher
levels of understanding
foundational emphasis is on
key math milestones,
including rational numbers,
fractions, decimals, ratios,
and pivotal concepts in
geometry and measurement
(National Mathematics
Advisory Panel, 2008).
Students use a number line
to help them visualize the
operation. Number lines are
an excellent tool for
developing students’ number
sense (Gersten et al. 2009).
Scaffolding Math Concepts & Skills
Reaching Grade Level
Explicit Instruction & Modeling
(Baker et al., 2002; Fuchs et al., 2008, Gersten et al., 2009)
Emphasizes Language & Vocabulary
(Marzano, 2004, Bull, 2007)
Engaging Games & Manipulatives
(Wright, 1996)
Explicit Connections between Concrete & Abstract
(Bull, 2007; Utall et al., 1997)
Real World Scenarios
Linking Prior Knowledge to Real Life (Lock, 1997)
Systematic and Specific Instructional Feedback
(Baker et al., 2002; Heward, 2009)
Using Technology to Pinpoint: Diagnostic AssessmentPrescriptive Intervention
2. Which ratios are equivalent?
A.7:2 and 2/7
B. 1/3 and 0.3
C. 2:4 and 4: 2
D. 2/3 and 0.6 [correct answer]
Grade 6: (6.1) Number, operation, and quantitative reasoning. The student represents and uses rational
numbers in a variety of equivalent forms. The student is expected to:
(B) generate equivalent forms of rational numbers including whole numbers, fractions, and decimals
Prescriptions:
NMS Lesson: 11 (Working with Rational Numbers) – define sets of rational numbers; describe
relationships between sets of rational numbers, including equivalency; compare and order rational numbers –
whole numbers, integers, fractions, and decimals
Math Foundations 3 Lesson: 4 (Number Line) – represent decimals on a number line; represent fractions
and mixed numbers on a number line; represent positive and negative integers on a number line.
Math Foundations 2 Lesson: 2 (Fractions & Decimals) – understand fractional equivalents using models;
understand fraction and decimal equivalents
Matching Student Need with Math Content
SKILL MISSED:
Number, operation, and quantitative reasoning.
The student adds, subtracts, multiplies, and divides to solve problems and justify solutions.
The student is expected to: use multiplication and division of whole numbers to solve problems including
situations involving equivalent ratios and rates.
BACKGROUND KNOWLEDGE MISSED:
Math Foundations 1 Lesson: 4 (Division) - Dividing a multi-digit number evenly by a one-digit divisor
Math Foundations 2 Lesson: 6 (Division) - Dividing multi-digit numbers by one-digit divisors using models
(Hundreds Chart with Skip Counting, Arrays, and Checking Long Division with Multiplication)
Math Foundations 3 Lesson: 6 (Division Skills) - Performing long division with multi-digit divisors, using
long division in problem solving situations, and checking quotients with multiplication and models
GRADE LEVEL LESSONS MISSED:
Numbers Make Sense Lesson: 1 (Positive & Negative Numbers)
Assign: Grade Level Lessons
Assign all: Background and Grade Level
MLC Features are Modifiable
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Diagnostic pretest and Individualized Student Pathway
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MLC features can be modified to fit individual student, group or class
needs
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Custom lessons: including a library of favorites
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Custom lessons: search by topic, select particular sections
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Custom curriculum: order lessons, set mastery levels, present content
from previous grades
Arrange lesson to allow students to progress through content in a
more linear or more constructive fashion
Turn on/off active features: calculator, key terms, certain sections,
translations
Contact Information
Lindy Crawford, Ph.D.
Ann Jones Endowed Chair in Special Education
Alice S. Neeley Special Education Institute
College of Education
Texas Christian University
817-257-4645
Barbara Freeman, Ed.D.
MLC Managing Director
970-704-1017
barbarafreeman1@comcast.net