Transcript LPLC - Idaho Training Clearinghouse

LPLC
Tier 3 Math
Lee Pesky Learning Center
Dr. Evelyn Johnson, Cristianne Lane, M.Ed
[email protected]
[email protected]
Introductions
Logistics for the Day
Your Materials
About Our Center
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Agenda – Day 1
• Factors that impact math performance
• Complex learner profile
• Teaching principles for working with
students with disabilities
• Number and Operations within Base 10
• Multiplication and Division
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Agenda – Day 2
• Rational Numbers:
– fractions, decimals, ratios, percentages
•
•
•
•
Study Skills
Algebra Resources
Progress Monitoring
Action Plan
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YOU ARE
HERE
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What Impacts Math Performance?
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Executive Functions
Attention/
Organization
Behavior/
Activity Level
Flexibility &
SelfRegulation
Emotions
Social
Interaction
Information Processing
Information Processing
Short-term memory
Immediate memory (Phonological
loop, Visual spatial sketchpad
Working memory
Long-term memory
– includes retrieval
Visual-motor production
Language
Visual-spatial thinking
Fluid reasoning
Crystallized knowledge
Information Processing
Executive Functions
Language
Short-term
memory
Immediate
memory
Working
memory
Visual-spatial thinking
Fluid reasoning
Crystallized knowledge
Long-term memory (LTM)
Visual-motor
production
Long-term
retrieval
Subtypes of Math Disability
Retrieval
Short-term Memory (Verbal)
Short-Term Memory
(Visual)
Processing Speed
Semantic
Memory
Working Memory
Fluid Reasoning
Language
Visual-Spatial Thinking
Magnitude/Quotity
Retrieval
Visual-Spatial Thinking
Procedural
Number Sense
Executive Function
Source: Geary, Hoard & Bailey (2010). How SLD Manifests in Mathematics.
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Teaching Principles
• Provide opportunities for success
• Use multisensory instruction
• Provide scaffolded, guided practice through
structured task analysis – CRA progression
• Practice and review with “relentless
consistency” to achieve automaticity
• Provide models – CRA progression
• Include students in the learning process –
opportunities to verbalize reasoning
• Teach diagnostically
rti
C-R-A Progression
Abstract
Representational
Concrete
Concrete- Representational-Abstract
(Remember the Lizzie problem from your MTI class)
Formal Equation
6x + 4y= 36
Tables and other methods to
organize information
Symbols and numbers
that represent the
pictures ( L= lizards)
Pictures that
represent objects
Concrete objects
and manipulatives
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What Impacts Math Performance?
Targeted Assessments
• Handout, page 1
• Video of student assessments
– Hiding Assessment by K. Richardson
– Making Tens by K. Richardson (Place Value)
– Math Reasoning Inventories by M. Burns
• Whole Numbers
• Fractions
• Decimals
Where is the breakdown in
understanding?
K
1
2
3
4
5
6
7
8
HS
Counting &
Cardinality
Number and Operations in Base Ten
Number and Operations –
Fractions
Ratios and Proportional
Relationships
Number &
Quantity
The Number System
Expressions and Equations
Algebra
Operations and Algebraic Thinking
Functions
Geometry
Measurement and Data
Functions
Geometry
Statistics and Probability
Statistics &
Probability
Chris Woodin, Landmark School
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Number Sense & Operations in Base 10
• Key Concepts
• Creating durable, consistent images to
represent numbers 1 – 10
– Consistent images address deficits in
working memory, visual-spatial thinking,
retrieval
– Create a foundational system for all other
operations
Source: Woodin, C. (2000)
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Number Sense & Operations in Base 10
Source: Woodin, C. (2000)
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Number Sense & Operations in Base 10
Source: Woodin, C. (2000)
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Number Sense & Operations in Base 10
• Activity: Teaching and Making Icons
• Handout, pages 2-7
Source: Woodin, C. (2012)
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Teaching and Making Icons – Base Five
Source: Woodin, C. (2012)
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Number Sense & Operations in Base 10
• Page 2 Tracking automaticity of icon
recognition
• Video Clip #1: Building to 5
– YouTube: “LBLD Math: Icon Card Addition
• Page 3: Moving to the X, writing
equations for numbers greater than 5
• Page 4: Missing addends (prerequisite
for regrouping with subtraction)
Source: Woodin, C. (2012)
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Preparing for Regrouping
• Page 5-7: adding 5 (horizontal, vertical)
• Video Clip #2
– YouTube: “Kinesthetic Learning: Doing Math
with Semiconcrete Diagrams”
Two Questions:
Are both numbers at least 5?
Which number is bigger?
Source: Woodin, C. (2012)
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Contextualized Problem Solving
• Where do you begin with contextualized
problems? “Hiding Assessment” video
• Problem Types
– Common Core Learning Progressions
document (handout page 8)
• Story Mats
– Contextualized problems
– “There are _________. Then __________”
Remember the math posters from Gildo Rey…
(refer to “Tier 2 training)
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Teaching Principles
• Provide opportunities for success
• Use multisensory instruction
• Provide scaffolded, guided practice through
structured task analysis – CRA progression
• Practice and review with “relentless
consistency” to achieve automaticity
• Provide models – CRA progression
• Include students in the learning process –
opportunities to verbalize reasoning
• Teach diagnostically
Let’s Try It!
5
+ 3
8
+ 5
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Place Value
• Develop place value concepts through
counting collections
– “Skip Counting with Counting Collections”
video clip from the Teaching Channel
(https://www.teachingchannel.org/videos/skipcounting-with-kindergarteners)
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Place Value
• Developing conceptual understanding
– Pattern of 0-9 repeating (Scrolling)
– Building a hundreds chart
– Number lines
• These activities allow students to ‘see’
numbers and patterns
• 10 x 10 blocks – connect to 100’s and 10’s
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Place Value - CRA
Source: http://moodle.rockyview.ab.ca
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Place Value
Hundreds
Tens
Source: http://moodle.rockyview.ab.ca
Ones
Regrouping: Two Examples
• Video: Chris Woodin (see next slide)
• Making Math Real
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Multi-Digit Subtraction Involving
Regrouping
• Page 9
• Page 9b
Making tens sticks and “X’s”
Displaying the place value
objects in icon formation
• Page 11:
prerequisite activities
• Video clip #3: “diagramming” subtraction
• Page 12-15: practice pages
Let’s Try It!
10
- 3
-
12
5
We do….then you do!
17
+24
26
+ 34
28
+ 17
Subtracting with regrouping
27
- 14
32
- 18
Regrouping: Two Examples
• Video: Chris Woodin (see next slide)
– YouTube: “Kinesthetic Learning: Subtraction
Math Using Diagrams”
• Making Math Real
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Teaching Principles
• Provide opportunities for success
• Use multisensory instruction
• Provide scaffolded, guided practice through
structured task analysis – CRA progression
• Practice and review with “relentless
consistency” to achieve automaticity
• Provide models – CRA progression
• Include students in the learning process –
opportunities to verbalize reasoning
• Teach diagnostically
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Operations: Multiplication & Division
• Whole to part, then part to whole fact
models
• Developing fluency with math facts
• Integration of division and multiplication
• Please note that slides are from Woodin,
C. L. (2012) Multiplication and Division
Facts for the Whole-to-Part, Visual
Learner (used here with permission
from the author)
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Create the Reference
Source: Woodin, C. (2012)
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Move to Establish Part to Whole
Source: Woodin, C. (2012)
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Create the Reference
Source: Woodin, C. (2012)
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Part to Whole Multiplication
2
Source: Woodin, C. (2012)
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Moving to the next step: Area Models
Source: Woodin, C. (2012)
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Moving to the next step: Area Models
Source: Woodin, C. (2012)
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Moving to the next step: Area Models
Source: Woodin, C. (2012)
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Moving to the next step: Area Models
Source: Woodin, C. (2012)
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Moving to the next step: Area Models
Source: Woodin, C. (2012)
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Moving to the next step: Area Models
Source: Woodin, C. (2012)
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Area Models to Matrix Diagrams
Source: Woodin, C. (2012)
Resource for Practice Activities…and More!
(O’Connell and SanGiovanni)
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Integrating Division
Source: Woodin, C. (2012)
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Integrating Division
Source: Woodin, C. (2012)
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Integrating Division
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
Images (Woodin… and Van de Walle too)
•
•
•
•
•
2’s= anything in pairs (shoes)
3’s= tricycles
4’s= legs
5’s= fingers on one hand
6’s= 6 pack
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Extending the 10 facts
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Developing Fluency
Source: Woodin, C. (2012)
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Moving on to multidigit multiplication
Distributive Property
Source: Woodin, C. (2012)
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Define multidigit factors with expanded notation.
1
x
3
2
= 10
+ 3
81
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Define the problem using a compound matrix.
The bottom factor defines the width,
the top factor defines the height.
1
x
2
3
2
10
+
Source: Woodin, C. (2012)
3
82
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Define the composite areas.
2
1
x
3
2
10
2 0
+
Source: Woodin, C. (2012)
3
6
83
The multiplication problem is solved procedurally by the
teacher.
1
x
2
3
2
6
2
10
2 0
+
Source: Woodin, C. (2012)
3
6
2 6
2
6
2 6
10
2 0
3
6
2x3=6
3x2=6
2 685
Organize the matrix so that the width is
defined by the bottom factor.
10
9
Source: Woodin, C. (2012)
86
Compute the composite areas.
10
9
300
270
20
18
Source: Woodin, C. (2012)
87
Solve the problem procedurally.
Compare the 1st row and right column.
10
2 8
9
8
300
270
20
18
288√
88
Solve the problem procedurally.
Compare the 2nd row and left column.
10
9
2 8
8
3
2 0
300
270
20
18
320√
89
Add Subproducts.
10
2 8
3
9
8
2 0
6 08
Source: Woodin, C. (2012)
300
270
20
18
90
Templated single step division
Matching procedure
done in parallel:
2
2
6
Put 6 Shoes on a
rectangular desk:
Source: Woodin, C. (2012)
91
Templated single step division
How many whole pairs
of shoes? 3.
It takes 2
to make
1 whole.
2
Source: Woodin, C. (2012)
Matching procedure
done in parallel:
2
3
6
92
Templated single step division
2
2
How many shoes are in
3 pair? 6.
3
6
6
3x2=6
Source: Woodin, C. (2012)
93
Templated single step division
2
2
After the 3 pair or 6
shoes are taken away
and boxed, how many
are left? (subtract 6).
Source: Woodin, C. (2012)
3
6
6
0
94
Templated single step division
Matching procedure
done in parallel:
2
2
7
Put 7 Shoes on a
rectangular desk:
Source: Woodin, C. (2012)
95
Templated single step division
How many whole pairs
of shoes ? 3.
It takes 2
to make
1 whole.
2
Source: Woodin, C. (2012)
Matching procedure
done in parallel:
2
3
7
96
Templated single step division
2
2
How many shoes are in
3 pair? 6.
Source: Woodin, C. (2012)
3
7
6
97
Templated single step division
2
2
After the 3 pair or 6
shoes are taken away
and boxed, how many
are left? (subtract 6).
Source: Woodin, C. (2012)
1 shoe is left on the
rectangular table.
3
7
6
1
98
Templated single step division
2
2
After the 3 pair or 6
shoes are taken away
and boxed, how many
are left? (subtract 6).
Source: Woodin, C. (2012)
Box the 1 shoe
remaining on
rectangular table.
3
7
6
1
99
Templated single step division
1
2
2
There is one shoe remaining.
It takes 2 to make 1 whole pair
Source: Woodin, C. (2012)
Record the
remainder as a
fraction.
3
7
6
1
100
2
Templated single step division
Write four related facts
Source: Woodin, C. (2012)
101
• Define each step.
Compare
Divide
Multiply
Subtract
Check Subtraction
Bring down
• Execute each step using gross
motor /kinesthetic processing – if
needed.
• Verbalize each step
to integrate language with each
production step.
103
Video Example:
YouTube: LBLD Math - Kinesthetic
Learning: Long Division
Check subtraction by adding UP.
0 +2= 2
2
6
2 4
2 4
0
0 +4= 4
105
5 x 9 = 45
45 ÷ 9 = 5
9 x 5 = 45
45 ÷ 5 = 9
9
4 5
0
106
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Agenda – Day 2
• Rational Numbers:
– Fractions, Decimals, Ratios, Percentages
•
•
•
•
Study Skills
Algebra Resources
Progress Monitoring
Action Plan
LPLC
YOU ARE
HERE
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Rational Numbers: Fractions
• “Big Ideas”
– handout, page 1
• Developing Effective Fractions Instruction
for Kindergarten Through 8th Grade
– IES Practice Guide (September 2010)
– Handout of 5 Recommendations, page 2
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Recommendation #1
“Build on students’ informal understanding
of sharing and proportionality to develop
initial fraction concepts.”
• Problem type sort
– page 3
It is the day after Halloween. A friend gives
you and your best friend 12 of her candies
to split equally.
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Recommendation #2
• “Cover Up” from MTI (handout, pages 4-5)
– Ordering basic unit fractions
– Writing equations that equal 1
– Equivalency activities
=
• Making a chart to order fractions (reference tool)
– Fraction War
– V Math example, page 6
• Equivalence activity (“simplifying fractions”)
– Ratio tables to show equivalency (recipes, etc.)
• Using number lines
– Measuring with strips
– Using tenths to link to decimals, page 7
– Hundreds charts (decimals, percentages, fractions page 8
Use of number lines to teach equivalence of
fractions in a Japanese curriculum
LPLC
Teaching Principles
• Provide opportunities for success
• Use multisensory instruction
• Provide scaffolded, guided practice through
structured task analysis – CRA progression
• Practice and review with “relentless
consistency” to achieve automaticity
• Provide models – CRA progression
• Include students in the learning process –
opportunities to verbalize reasoning
• Teach diagnostically
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Recommendations #3- #4
• Math Vids
– Using a number line to understand why procedures
work (next slide)
• Ratios the Landmark Way
– page 9
• Sorts for practice (Jennifer Sauriol)
– page 10
• Two column notes (study skills)
– page 11
• “Flapper cards” (study skills)
– pages 12a-c
MathVids.com
Why do we invert and multiply?
Use the number line to explain to your
partner why we invert and multiply?
Example: 2 ÷ 1/3
Close up of “flapper cards”
LPLC
Teaching Principles
• Provide opportunities for success
• Use multisensory instruction
• Provide scaffolded, guided practice through
structured task analysis – CRA progression
• Practice and review with “relentless
consistency” to achieve automaticity
• Provide models – CRA progression
• Include students in the learning process –
opportunities to verbalize reasoning
• Teach diagnostically
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Algebra Resources
• DMT website (MTI)
• MathVids
• Solving Equations: An Algebra Intervention
by Brad Witzel and Paul Ricommini
– handout, page 13 - 16
• KUTA software
– handout, page 17
• Jennifer Sauriol from Landmark
– Algebra “make it and take it” activities
LPLC
Teaching Principles
• Provide opportunities for success
• Use multisensory instruction
• Provide scaffolded, guided practice through
structured task analysis – CRA progression
• Practice and review with “relentless
consistency” to achieve automaticity
• Provide models – CRA progression
• Include students in the learning process –
opportunities to verbalize reasoning
• Teach diagnostically
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Error Analysis
• Handout page 18
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Progress Monitoring
• For students with disabilities, we want a
General Outcome Measure to gauge
progress relative to grade level
performance standards
• However, we also want individualized
progress monitoring tools to determine
growth in the taught skill.
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Progress Monitoring
GOM and Mastery Measures
• Handout page 1
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Progress Monitoring – Mastery
Measures
• Mastery Measures tell us whether
students are learning the skills we are
teaching them
• They are generally not norm referenced
or standardized
• Important to set MASTERY targets –
remember, we want kids to ‘overlearn’ a
skill
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Developing and Charting Mastery
Measures
• Ensure you have sufficient number of
problems reflecting current skill
• Typically mastery measures are not timed
• Establish baseline
• Review performance to inform teaching
• Compare performance on skill to GOM
measures
• Over time, you may want to create ‘mixed
skill’ measures to determine retention of
performance on specific concepts
Two Free Tools
• Intervention Central
– Math Worksheet Generator
• CBM Focus (PM Focus)
Progress Monitoring Focus
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Improving the lives of people who learn differently through
prevention, evaluation, treatment, and research.
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208-333-0008
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