The Math Learning Companion (MLC) by 8iyctnC3

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									The Math Learning Companion (MLC)




An Individualized Intervention for Students with
           Math Learning Disabilities
Contents

   General Characteristics of Students with MLD and
    participants in MLC research study
   What works with Students with MLD
   MLC Pedagogy
About Students with MLD
   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
                               9.0
      Grade Level Equivalent



                               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
   Online intervention designed and developed specifically for students
    with Math Learning Disabilities
   Comprehensive math content & skills development
   Interwoven language support, with read-aloud and audio
   Full alignment to CCS, NCTM, TX, CO and other state standards,
    grades 3-8
   Standards-based assessments; pre and post diagnostic placement
    assessments at each grade (hundreds of test items)
   Automatic placement and progression through curriculum
   Cognitively challenging with consistent feedback and review
MLC Pedagogy
     Emphasizes critical foundations and prerequisite concept knowledge &
      skills
     Scaffolds the learning; makes math comprehensible without simplification
     Visual representation
     Synchronicity, visual contextual hints, modeling, guided practice, pacing,
      sequencing tasks and practice, etc.
     Focuses on vocabulary & development of academic language Breaks
      concepts into learning chunks
     Engaging and interactive: games, manipulatives, real world scenarios, with
      explicit connections between concrete and abstract
     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 Assessment-
Prescriptive 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

    Diagnostic pretest and Individualized Student Pathway
    MLC features can be modified to fit individual student, group or class
     needs
         Custom lessons: including a library of favorites
         Custom lessons: search by topic, select particular sections
         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

								
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