rti in math - the conference exchange · 2014-04-14 · differentiating practice: peer tutoring...
TRANSCRIPT
![Page 1: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/1.jpg)
RTI in Math:
Evidence-Based Interventions for Struggling Students
NCTM 2014
New Orleans
![Page 2: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/2.jpg)
Dr. Linda Forbringer
Associate Professor
Dept. of Special Education & Communication Disorders
Southern Illinois University Edwardsville
![Page 3: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/3.jpg)
What evidence-based interventions support learners who struggle with
mathematics?
http://ies.ed.gov/ncee/wwc/publications/practice
guides/
Assisting Students Struggling with
Mathematics: RtI for Elementary and Middle Schools
(2009)
What Works Clearinghouse Practice Guide:
![Page 4: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/4.jpg)
![Page 5: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/5.jpg)
WWC Recommendations
1. Universal Screening
Tiered, Targeted Interventions
2. Monitor Progress & Adjust Interventions
3. Include Motivational Support
4. Focus on Foundational Skills
(whole numbers & rational numbers)
![Page 6: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/6.jpg)
WWC Recommendations
5. Develop Fluency with Basic Facts
6. Use Visual Representations
7. Use Underlying Structures
to Teach Problem Solving
8. Use Explicit Instruction
During Interventions
![Page 7: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/7.jpg)
5. What Works Clearinghouse
Recommends
Develop Fluency with Basic Facts
Interventions at all grade levels
should devote about 10 minutes each session
to building fluent retrieval of basic arithmetic facts.
![Page 8: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/8.jpg)
To build fluency –
How many unfamiliar facts should
students practice at one time?
![Page 9: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/9.jpg)
Memorize the following numbers:
7 4 3 8 5 9 2
![Page 10: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/10.jpg)
How many did you remember?
7 4 3 8 5 9 2
![Page 11: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/11.jpg)
The number of items
that the average adult
can hold in working memory
is about
Miller, 1956
7 ± 2
![Page 12: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/12.jpg)
Capacity increases with age:
Age # of Items
15 7 + 2
13 6 + 2
11 5 + 2
9 4 + 2
7 3 + 2
5 2 + 2
Pascual-Leon, 1970
![Page 13: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/13.jpg)
Research Findings
Students who
struggle with mathematics typically have
deficits in working memory.
![Page 14: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/14.jpg)
What happens when the pace of instruction
exceeds the learner’s capacity?
Memorize this list of numbers:
6 3 1 5 2 7 4 2 1 9 4
![Page 15: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/15.jpg)
How well did you do?
6 3 1 5 2 7 4 2 1 9 4
![Page 16: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/16.jpg)
When the task
exceeds the child’s capacity,
little learning occurs!
![Page 17: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/17.jpg)
Limit the number of new facts students practice at one time!
WWC suggests
2 new facts,
plus review
![Page 18: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/18.jpg)
Potential Roadblock
• Commercial materials often practice too many facts at a time.
![Page 19: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/19.jpg)
Differentiating Practice: Peer Tutoring
Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS) • Etc. Process: • Pre-assess. Create flashcards for facts that the student
will learn first and a bank of facts for later practice.
• Partner Practice Partners take turns practicing the facts on 5 of their
cards. • Reward Improvement www.promisingpractices.net/program.asp?programid=99
![Page 20: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/20.jpg)
Differentiating
Practice
![Page 21: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/21.jpg)
6. WWC Recommendation:
Use Visual Representations
• Ten Frames
• Mathline
• Base Ten Blocks
• DigiBlocks
![Page 22: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/22.jpg)
Concrete Representational Abstract
Manipulatives
Act it out
Pictures
Drawings
Diagrams
Numberlines
Tally marks
Words
Symbols
2 + 3
a + b
5²
one half
![Page 23: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/23.jpg)
Concrete – Representational – Abstract Explicitly link CRA!
//
//
//
//
4 x 2 = 8
![Page 24: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/24.jpg)
Dividing Fractions
5th grade:
4 ÷ ½
5th grade: ½ ÷ 4
6th grade:
½ ÷ ¼
![Page 25: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/25.jpg)
Dividing Fractions
“Division by fractions, the most complicated operation with the most complex numbers, can be considered
as a topic at the summit of arithmetic.”
Liping Ma, 1999
![Page 26: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/26.jpg)
Solve: 1¾ ÷ ½
U.S. Teachers: 39% could solve 4% could represent Chinese Teachers: 100% could solve 90% could represent
Represent 1¾ ÷ ½
![Page 27: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/27.jpg)
Modeling Division of Fractions
Review:
Dividing Whole Numbers- 6 ÷ 2 = 3 If I have 6 items, how many groups of 2 can I make?
Dividing Fractions: If I have 1 ¾ items, how many groups of
½ can I make?
1 ¾ ÷ ½ = 3 ½
![Page 28: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/28.jpg)
Fractions: Percentage of Problems
Using Each Representation
Representation
CMP Thematics Glencoe
Concrete:
Manipulatives
2.86% 5.12% 0.25%
Representational:
Pictures
27.31% 7.28% 7.36%
Abstract:
Written language
31.94% 7.28% 6.38%
Abstract:
Symbols
58.15% 88.95% 95.71%
Fraction Representation: The Not-So-Common Denominator among Textbooks Mathematics Teaching in the Middle School 14(2), 78-84. NCTM (2008)
![Page 29: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/29.jpg)
Effective Visuals: Ten Frames
![Page 30: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/30.jpg)
![Page 31: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/31.jpg)
Ten Frames
dot_card_and_ten_frame_package2005.pdf
• 497303/dot_card_and_ten_frame_packag
e2http://sbmathwebsites.pbworks.com/w/fil
e/50497303/dot_card_and_ten_frame_pac
kage2005.pdf005.pdf
![Page 32: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/32.jpg)
Concrete Visual Abstract Representation:
Number lines
![Page 34: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/34.jpg)
![Page 35: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/35.jpg)
3 x 246 = 738
![Page 36: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/36.jpg)
The Low Stress or Partial Products Algorithms: Representing Multiplication
with Arrays and Area Models
12 x 3 = 36
3
12
12
x 3
30
6
36
![Page 37: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/37.jpg)
The representation should
match the abstract process.
3 x 246 = 738
![Page 38: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/38.jpg)
Modeling Multiplication
The Standard Algorithm
14
X 3
tens ones
Multiply ones.
Regroup and Record.
Multiply tens.
Add regrouped tens.
Record.
![Page 39: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/39.jpg)
Modeling Multiplication
The Standard Algorithm
14
X 3
tens ones
Multiply ones.
Regroup and Record.
Multiply tens.
Add regrouped tens.
Record.
![Page 40: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/40.jpg)
Modeling Multiplication
The Standard Algorithm
14
X 3
2
tens ones
Multiply ones.
Regroup and Record.
Multiply tens.
Add regrouped tens.
Record.
![Page 41: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/41.jpg)
Modeling Multiplication
The Standard Algorithm
14
X 3
2
tens ones
Multiply ones.
Regroup and Record.
Multiply tens.
Add regrouped tens.
Record.
![Page 42: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/42.jpg)
Modeling Multiplication
The Standard Algorithm
14
X 3
4 2
tens ones
Multiply ones.
Regroup and Record.
Multiply tens.
Add regrouped tens.
Record.
![Page 43: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/43.jpg)
Effective Visuals: Digi-blocks
• http://www.digi-block.com/
![Page 44: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/44.jpg)
Research Findings
Concrete: 3 lessons
Representational: 3 lessons
Abstract
Hudson, Peterson, Mercer & McLeod, 1988; Peterson, Mercer & O’Shea,
1988; Butler, Miller, Crehan, Babbitt & Pierce, 2003; Harris, Miller & Mercer,
1995; Mercer & Miller, 1992; Miller, Harris, Strawser, Jones & Mercer, 1998;
MMiller, Mercer & Dillon, 1992
![Page 45: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/45.jpg)
Concrete – Representational – Abstract
3 concrete 3 pictorial abstract
//
//
//
3 x 2 = 6
![Page 46: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/46.jpg)
Potential Roadblock
• Commercial materials
–Often fail to provide any
concrete or visual representation
–Move too quickly to abstract words and symbols
–Do not provide a clear link from concrete to representational to abstract presentations
![Page 47: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/47.jpg)
7. WWC
Recommendation: Problem Solving
• Interventions should include instruction on solving word problems that is based on common underlying structures. - What Works Clearinghouse 2009
Schema-based Instruction
![Page 48: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/48.jpg)
Addition & Subtraction
3 Basic Structures:
• Group (Part-Whole)
• Change
• Compare
![Page 49: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/49.jpg)
Group Problem
Whole
Part Part
![Page 50: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/50.jpg)
Group Problem
I have 7 M&Ms.
4 of them are pink.
3 of them are red.
7 M&Ms
4 pink 3 red
![Page 51: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/51.jpg)
Group Problem
Whole
Part Part
Part + Part = Whole
Whole – Part = Part
![Page 52: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/52.jpg)
Representing Group Problems
4 2 6
Singapore Math
Jitendra
part part
whole
Everyday Math
![Page 53: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/53.jpg)
‘Change’ Problems
5 3 2
![Page 54: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/54.jpg)
‘Compare’ Problems
2 ?
3
![Page 55: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/55.jpg)
Potential Roadblock
Commercial materials seldom
organize problems by underlying structures.
![Page 56: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/56.jpg)
Resources 1. Solving Math Word Problems:
http://www.proedinc.com/customer/productView.aspx?ID=4145
2. Go Solve Computer Program
http://www.tomsnyder.com/products/product.asp?SKU=GOSGOS
![Page 57: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/57.jpg)
Resources
http://www.mathplayground.com/wordproble
ms.html
4.
Step-by Step Model Drawing Char Forsten (Singapore Math)
3.
![Page 58: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/58.jpg)
Resources
5. Pirate Math Fuchs – Vanderbilt University
www.kc.vanderbilt.edu/pals
![Page 59: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/59.jpg)
8. WWC Recommendation:
Students requiring math interventions
learn best with explicit
instruction.
![Page 60: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/60.jpg)
Frequently have deficits in:
– Language
– Memory
– Executive Functioning
– Motivation & Attention
Allsop et al., 2010; Geary, 2004; Hallahan et al., 2005;
Mabbott & Bisanz, 2008; Morzzacco, 2007; Swanson, Jerman & Zheng, 2009
Characteristics of Learners Requiring Math Interventions
![Page 61: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/61.jpg)
How does explicit instruction differ from the inquiry model?
Example: Counting Coins
![Page 62: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/62.jpg)
1. Review Prerequisite Skills
– Identify coins and coin values
– Count by 1’s, 5’s, 10’s
– Count on
![Page 63: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/63.jpg)
111
2. Model Explicit Strategies
Counting Coins 1. Group like coins. 2. Order from largest value to smallest
value. 3. Total the largest coins. 4. Move to the next largest coins. Count
on (by skip counting) to find the new total.
5. Repeat step 3 until you have counted all the coins.
1 11 11 5 10
![Page 64: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/64.jpg)
3. Guided Practice • Students demonstrate understanding
before working independently.
• Teachers provide scaffolded support and feedback, monitor understanding, and gradually fade support.
![Page 65: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/65.jpg)
4. Independent Practice
Only when students can practice successfully!
Successful practice =
90-100% accuracy
![Page 66: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/66.jpg)
Summary 1. Universal Screening
Tiered, Targeted Interventions
2. Monitor Progress & Adjust Interventions
3. Include Motivational Support
4. Focus on Foundational Skills (whole numbers & rational numbers) 5. Develop Fluency with Basic Facts
6. Use Visual Representations
7. Use Underlying Structures for Problem Solving
8. Use Explicit Instruction During Interventions
![Page 67: RTI in Math - the Conference Exchange · 2014-04-14 · Differentiating Practice: Peer Tutoring Examples: • Classwide Peer Tutoring (CWP) • Peer Assisted Learning Strategies (PALS)](https://reader035.vdocuments.us/reader035/viewer/2022062920/5f0229d37e708231d402e2ba/html5/thumbnails/67.jpg)
Thank you!