©2007 America’s Choice
~Presented by~
Rick Pinchot and Angela PhillipsChets Creek Elementary, Jacksonville, Florida
Math Navigator: Guide Your Students Back on Course
©2007 America’s Choice
Welcome to Chets Creek Elementary School! An A+ America’s Choice National Model School
Sydney, a fifth grader at Sydney, a fifth grader at Chets Creek Elementary, Chets Creek Elementary,
shares the Vision shares the Vision of our school.of our school.
We are a standards-based learning community
committed to preparing students for success in a
competitive, interdependent and global
workplace.
MadisoMadisonn
©2007 America’s Choice
Welcome to Chets Creek Elementary School! An A+ America’s Choice National Model School
Sydney, a fifth grader at Sydney, a fifth grader at Chets Creek Elementary, Chets Creek Elementary,
shares the Vision shares the Vision of our school.of our school.
We are a standards-based learning community
committed to preparing students for success in a
competitive, interdependent and global
workplace.
©2007 America’s Choice
Welcome to Chets Creek Elementary School! An A+ America’s Choice National Model School
Sydney, a fifth grader at Sydney, a fifth grader at Chets Creek Elementary, Chets Creek Elementary,
shares the Vision shares the Vision of our school.of our school.
We are a standards-based learning community
committed to preparing students for success in a
competitive, interdependent and global
workplace.
©2007 America’s Choice
Our “High-Stakes Assessment” Mathematics Story
Florida Comprehensive Assessment Test
(Proficiency Level- 3 or above)
Year Percent of Students scoring > Level 3
1998- 21%
1999- 52%
2000- 70%
2001- 80% (75% w/ ESE)
2002- 83% (78% w/ ESE)
2003- 84% (76% w/ ESE)
2004- 88% (83% w/ ESE)
2005- 89% (84% w/ ESE)
2006- 93% (84% w/ ESE)
2007- 94% (88% w/ ESE)
Phil Daro ©2007 America’s Choice
A Systematic Approach to Math Intervention
Student Needs InterventionSuccessful
in ClassRegular
ProgramNone
Needs Help with Assignments
Feedback Help in Class
Not Doing Homework
Outside Help
Tutoring
Misconceptions from Previous
Learning
Extra Instruction
4 Week Modules
2-3 Years Behind
Intensive Instruction
Special Course
Phil Daro ©2007 America’s Choice
Philosophy Behind Math Navigator:
Targets and Surfaces
Misconceptions
Builds on Prior Knowledge
Phil Daro ©2007 America’s Choice
Philosophy Behind Math Navigator:
Targets Specific Concepts
Phil Daro ©2007 America’s Choice
Philosophy Behind Math Navigator:
Targets Specific Concepts
SkillsSkills
Concepts Concepts
Problem Problem Solving Solving
Phil Daro ©2007 America’s Choice
Philosophy Behind Math Navigator:
Uses an Algebraic Approach with Properties of Equality
3 + 5 = 3 + 5 =
3 + = 83 + = 8
+ 5 = 8+ 5 = 8
Phil Daro ©2007 America’s Choice
Philosophy Behind Math Navigator:
Provides a Language Rich Environment
Phil Daro ©2007 America’s Choice
Philosophy Behind Math Navigator:
Teaches Students to be Better Learners of Mathematics
Phil Daro ©2007 America’s Choice
Philosophy Behind Math Navigator:
Offers Instructional Support
©2007 America’s Choice
Professional Development
Teachers learn how to identify and remedy misconceptions
Teachers learn how to teach for conceptual understanding
Teachers learn how to develop and nurture a problem solving and collaborative environment
Teachers develop their pedagogy about mathematics
©2007 America’s Choice
Addressing Student Misconceptions
©2007 America’s Choice
Skill Cards
James Williams ©2007 America’s Choice
What is a misconception?
A misapplication of a rule or procedure
An “over” or “under” generalization
An alternative interpretation of a situation
©2007 America’s Choice
Looking at a “Lesson”
©2007 America’s Choice
Lesson 14
©2007 America’s Choice
Addressing Student Misconceptions
©2007 America’s Choice
Meet Student 1…
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Meet Student 2…
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Meet Student 3…
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Meet Student 4…
James Williams ©2007 America’s Choice
Common Misconceptions
You can’t subtract a larger number from a smaller one
The number is larger than any other number that has fewer digits
You add numbers by lining them up on the right
Multiplication makes a number bigger
A fraction is larger than any other fraction with a bigger denominator
Subtracting numerators and denominators when subtracting fractions
Multiplying fractions by inverting and multiplying
And the list goes on
©2007 America’s Choice
Misconceptions
36
- 19
10.2 4
+ 5.5
©2007 America’s Choice
Misconceptions
27 - 19
-9 -10
_______________________
8 17 27
19 - 27
-8 -19
_____________________________
-8 0 19
James Williams ©2007 America’s Choice
Misconceptions
Many result from procedural instruction.
Misconceptions are also caused by the lack of meaningful discussions in the classroom.
May result from lack of teacher pedagogy.
©2007 America’s Choice
Diagnostic Teaching (Focus on Misconceptions)
• Goal is to surface and make students aware of Goal is to surface and make students aware of their misconceptionstheir misconceptions
•Begin with a problem or activity that surfaces Begin with a problem or activity that surfaces the various ways students may think about the the various ways students may think about the mathmath
•Engage in reflective discussion (challenging for Engage in reflective discussion (challenging for teachers but research shows that it develops teachers but research shows that it develops long-term learning)long-term learning)
Reference: Reference:
Bell, A. Principles for the Design of Teaching Educational Bell, A. Principles for the Design of Teaching Educational
Studies in Mathematics. 24: 5-34, 1993Studies in Mathematics. 24: 5-34, 1993
©2007 America’s Choice
The Lesson
Skills Practice
Introducing Today’s Lesson
Presenting the Task
Solo Work
Partner Work
Probing for Understanding
Closing Lesson
--Your thoughts
©2007 America’s Choice
Rituals and Routines
©2007 America’s Choice
Implementation Model
Jennifer SneadTeacher, Chets Creek Elementary
©2007 America’s Choice
Implementation Model
QuickTime™ and aDV/DVCPRO - NTSC decompressor
are needed to see this picture.
Suzanne Shall ©2007 America’s Choice
Special Education Challenge
Special education students share the same characteristics as struggling students.
Intervention for special education students also have the following challenges.– Teachers are typically Literacy Specialists.
– Some students have difficulty reading and comprehending text.
– Perception among many teachers that success for students require sacrifice of rigor.
Suzanne Shall ©2007 America’s Choice
Navigator and Special Education Intervention
Modular approach to remediation allows for a focused and coherent presentation of mathematics. This is extremely beneficial to special education students in that it minimizes confusion and distractions by other unrelated content.
Intervention outside of regular class allows students to remain in inclusion setting and still receive additional assistance.
Present students with a simple approach to what can often be complex and confusing mathematics content.
©2007 America’s Choice
20-Day Module
Post -Test and CheckpointRegular sessionRegular sessionRegular sessionRegular session
Regular sessionRegular sessionRegular sessionCheckpointRegular session
Regular sessionRegular sessionRegular sessionRegular sessionCheckpoint
Regular sessionRegular sessionRegular sessionRegular sessionPre-Test and Regular session
Post -Test and CheckpointRegular sessionRegular sessionRegular sessionRegular session
Regular sessionRegular sessionRegular sessionCheckpointRegular session
Regular sessionRegular sessionRegular sessionRegular sessionCheckpoint
Regular sessionRegular sessionRegular sessionRegular sessionPre-Test and Regular session
©2007 America’s Choice
Navigator Modules
Series 1 (2nd grade and up) Beginning Place Value Knowing Addition and Subtraction Facts Knowing Multiplication and Division Facts Understanding: Addition and Subtraction Understanding: Multiplication Understanding: Division
Series 2 (4th grade and up) Knowing Fractions
Understanding Fractions
Understanding and Reading Word Problems
Measurement
Place Value from Decimals to Billions
Multiplying Multidigit Whole Numbers
Series 3 (6th grade and up) Decimals and Powers of 10 Rational Numbers Percents Operations and Word Problems
Series 4 (8th grade and up)
Functions and Graphs Expressions and EquationsGeneralizing from PatternsExponents
©2007 America’s Choice
Great Results, page 32
©2007 America’s Choice
Special Education Students Make Dramatic Gains
©2007 America’s Choice
Navigator Results- Chets Creek Name School Year Course Pre-test Post-test
Susan 2005-2006 Understanding Multiplication 3 7Lauren 2005-2006 Understanding Multiplication 9 12Kali 2005-2006 Understanding Multiplication 8 11Frank 2005-2006 Understanding Multiplication 7 8Jennifer 2005-2006 Understanding Multiplication 7 12Daija 2005-2006 Understanding Multiplication 5 7Alexis 2005-2006 Understanding Multiplication 8 10Miller 2005-2006 Understanding Multiplication 9 13Somer 2006-2007 Understanding Addition and Subtraction 5 11Tristin 2006-2007 Understanding Addition and Subtraction 8 12Alyssa 2006-2007 Understanding Addition and Subtraction 8 14Zenaida 2006-2007 Understanding Addition and Subtraction 8 10Amber 2006-2007 Understanding Addition and Subtraction 6 12Hunter 2006-2007 Understanding Division 8 12Lorenzo 2006-2007 Understanding Division 7 11Halie 2006-2007 Understanding Division 8 7Kierstin 2006-2007 Understanding Division 8 9Janai 2006-2007 Understanding Division 10 12Levi 2006-2007 Understanding Division 10 13Ashley 2006-2007 Understanding Addition and Subtraction 7 12Michael 2006-2007 Understanding Addition and Subtraction 8 13Mario 2006-2007 Understanding Addition and Subtraction 6 11Ryan 2006-2007 Understanding Addition and Subtraction 8 14Daija 2006-2007 Understanding Addition and Subtraction 8 14Gorgi 2006-2007 Understanding Addition and Subtraction 10 15Jay 2006-2007 Knowing Multiplication and Division 10 19Kim 2006-2007 Knowing Multiplication and Division 9 17Briana 2006-2007 Knowing Multiplication and Division 9 16Nick 2006-2007 Knowing Multiplication and Division 11.5 20Courtney 2006-2007 Knowing Multiplication and Division 11 19Kiara 2006-2007 Knowing Multiplication and Division 9 17
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