~Presented by~ Rick Pinchot and Angela Phillips Chets Creek Elementary, Jacksonville, Florida Math Navigator: Guide Your Students Back on Course

Welcome to Chets Creek Elementary School! An A+ America’s Choice National Model School We are a standards-based learning community committed to preparing students for success in a competitive, interdependent and global workplace. Sydney, a fifth grader at Chets Creek Elementary, shares the Vision of our school. Madison

We are a standards-based learning community committed to preparing students for success in a competitive, interdependent and global workplace.

Welcome to Chets Creek Elementary School! An A+ America’s Choice National Model School We are a standards-based learning community committed to preparing students for success in a competitive, interdependent and global workplace. Sydney, a fifth grader at Chets Creek Elementary, shares the Vision of our school.

We are a standards-based learning community committed to preparing students for success in a competitive, interdependent and global workplace.

Welcome to Chets Creek Elementary School! An A+ America’s Choice National Model School We are a standards-based learning community committed to preparing students for success in a competitive, interdependent and global workplace. Sydney, a fifth grader at Chets Creek Elementary, shares the Vision of our school.

We are a standards-based learning community committed to preparing students for success in a competitive, interdependent and global workplace.

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)

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)

A Systematic Approach to Math Intervention Special Course Intensive Instruction 2-3 Years Behind 4 Week Modules Extra Instruction Misconceptions from Previous Learning Tutoring Outside Help Not Doing Homework Help in Class Feedback Needs Help with Assignments None Regular Program Successful in Class Intervention Needs Student

Philosophy Behind Math Navigator: Builds on Prior Knowledge Targets and Surfaces Misconceptions

Builds on Prior Knowledge

Philosophy Behind Math Navigator: Targets Specific Concepts

Targets Specific Concepts

Philosophy Behind Math Navigator: Targets Specific Concepts Skills Concepts Problem Solving

Targets Specific Concepts

Philosophy Behind Math Navigator: Uses an Algebraic Approach with Properties of Equality 3 + 5 = 3 + = 8 + 5 = 8

Uses an Algebraic Approach with Properties of Equality

Philosophy Behind Math Navigator: Provides a Language Rich Environment addend minuend sum subtrahend difference

Provides a Language Rich Environment

Philosophy Behind Math Navigator: Teaches Students to be Better Learners of Mathematics

Teaches Students to be Better Learners of Mathematics

Philosophy Behind Math Navigator: Offers Instructional Support

Offers Instructional Support

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

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

Addressing Student Misconceptions

Skill Cards

What is a misconception? A misapplication of a rule or procedure An “over” or “under” generalization An alternative interpretation of a situation

A misapplication of a rule or procedure

An “over” or “under” generalization

An alternative interpretation of a situation

Looking at a “Lesson”

Lesson 14

Addressing Student Misconceptions

Meet Student 1…

Meet Student 2…

Meet Student 3…

Meet Student 4…

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

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

Misconceptions 36 - 19 10.2 4 + 5.5

36

- 19

10.2 4

+ 5.5

Misconceptions 27 - 19 -9 -10 _______________________ 8 17 27 19 - 27 -8 -19 _____________________________ -8 0 19

27 - 19

-9 -10

_______________________

8 17 27

19 - 27

-8 -19

_____________________________

-8 0 19

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.

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.

Diagnostic Teaching (Focus on Misconceptions) Goal is to surface and make students aware of their misconceptions Begin with a problem or activity that surfaces the various ways students may think about the math Engage in reflective discussion (challenging for teachers but research shows that it develops long-term learning) Reference: Bell, A. Principles for the Design of Teaching Educational Studies in Mathematics. 24: 5-34, 1993

Goal is to surface and make students aware of their misconceptions

Begin with a problem or activity that surfaces the various ways students may think about the math

Engage in reflective discussion (challenging for teachers but research shows that it develops long-term learning)

Reference:

Bell, A. Principles for the Design of Teaching Educational

Studies in Mathematics. 24: 5-34, 1993

The Lesson Skills Practice Introducing Today’s Lesson Presenting the Task Solo Work Partner Work Probing for Understanding Closing Lesson --Your thoughts

Skills Practice

Introducing Today’s Lesson

Presenting the Task

Solo Work

Partner Work

Probing for Understanding

Closing Lesson

--Your thoughts

Rituals and Routines

Implementation Model Jennifer Snead Teacher, Chets Creek Elementary

Jennifer Snead

Teacher, Chets Creek Elementary

Implementation Model

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.

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.

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.

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.

20-Day Module

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 Equations Generalizing from Patterns Exponents

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 Equations

Generalizing from Patterns

Exponents

Great Results , page 32

Special Education Students Make Dramatic Gains

Navigator Results- Chets Creek 17 9 Knowing Multiplication and Division 2006-2007 Kiara 19 11 Knowing Multiplication and Division 2006-2007 Courtney 20 11.5 Knowing Multiplication and Division 2006-2007 Nick 16 9 Knowing Multiplication and Division 2006-2007 Briana 17 9 Knowing Multiplication and Division 2006-2007 Kim 19 10 Knowing Multiplication and Division 2006-2007 Jay 15 10 Understanding Addition and Subtraction 2006-2007 Gorgi 14 8 Understanding Addition and Subtraction 2006-2007 Daija 14 8 Understanding Addition and Subtraction 2006-2007 Ryan 11 6 Understanding Addition and Subtraction 2006-2007 Mario 13 8 Understanding Addition and Subtraction 2006-2007 Michael 12 7 Understanding Addition and Subtraction 2006-2007 Ashley 13 10 Understanding Division 2006-2007 Levi 12 10 Understanding Division 2006-2007 Janai 9 8 Understanding Division 2006-2007 Kierstin 7 8 Understanding Division 2006-2007 Halie 11 7 Understanding Division 2006-2007 Lorenzo 12 8 Understanding Division 2006-2007 Hunter 12 6 Understanding Addition and Subtraction 2006-2007 Amber 10 8 Understanding Addition and Subtraction 2006-2007 Zenaida 14 8 Understanding Addition and Subtraction 2006-2007 Alyssa 12 8 Understanding Addition and Subtraction 2006-2007 Tristin 11 5 Understanding Addition and Subtraction 2006-2007 Somer 13 9 Understanding Multiplication 2005-2006 Miller 10 8 Understanding Multiplication 2005-2006 Alexis 7 5 Understanding Multiplication 2005-2006 Daija 12 7 Understanding Multiplication 2005-2006 Jennifer 8 7 Understanding Multiplication 2005-2006 Frank 11 8 Understanding Multiplication 2005-2006 Kali 12 9 Understanding Multiplication 2005-2006 Lauren 7 3 Understanding Multiplication 2005-2006 Susan Post-test Pre-test Course School Year Name