We at the GaDOE are pleased to be able to offer Days 1-5 of our GPS High School Mathematics Training in an online format. Included in these materials you will find the following:

• this guide for using the materials,
• the Research and Resource Manual, and
• eleven video clips of the training sessions included in days 1-3.

This document gives suggestions and tips for the use of the materials based on what was learned in actual training sessions.

The Research and Resource Manual

The Research and Resource Manual contains two main types of information.

• Background information related to the development of the Standards (pages 4-30)
  
  This section includes a listing of the people involved in the writing and implementation of the curriculum, and articles containing some of the research upon which the curriculum is based. This material will be especially helpful in explaining to students, teachers, parents and other stakeholders why Georgia has chosen an integrated curriculum based on international benchmarks. We recommend that all of the articles in the manual be read by teachers and other educators involved in the effort to raise student achievement in mathematics. The articles address not only the research behind our curriculum but what we know about effective classroom practices. They are particularly useful when read and discussed in teacher meetings, study groups, and learning communities.
  
  
• Instructional Resources (pages 31-79)
  
  Pages 31-73 contain the actual tasks, articles, and other documents used in the video clips of the training sessions. Use of these materials is addressed in the discussion of video clips. An extensive bibliography of related resources that may be used throughout the school year is provided on pages 74-79.

Note: One copy of the Research and Resource Manual was provided to each teacher team that attended Days 1-3 of high school training. The hard copy of the manual includes the Grade-Level Instructional Frameworks for grades 6-8. Because these resources are already online at georgiastandards.org, they are not included in this online version of the manual.

Video Clips

Eleven video clips are currently posted on this website. They represent the sessions that comprise Days 1-3 of training. Additional video will be added as subsequent days of training are completed.

We suggest that the video clips be watched in order as the training was chronological in nature. On those clips where tasks are worked or articles read, it is most effective to follow this procedure:

• allow participants to watch the “set-up” for the task or article;
• pause the video while participants work the tasks or read the articles;
• allow participants to have their own presentations of tasks or discussions of articles;
• and finally, return to the video to view our trainers’ presentations and discussions.

In the delivery of this training, particular attention should be paid to the incremental development of mathematical concepts. The tasks are designed to enable students (and teachers) to build new understandings based upon prior knowledge. For this reason, it is not enough for the professional developers or the participants to simply read through the tasks. In order to understand this fundamentally different approach to learning mathematics, the tasks, and the mathematics they involve, must be experienced and contemplated. A reasonable amount of time for the working and presentation of a task in this training is approximately ninety minutes.

Before leading training sessions with teachers or other educators, professional developers should go through each clip following the steps suggested above, including the careful working of each task.

At the end of this guide there is a list of the documents from the Research and Resource Manual that should be used with each video clip. These materials will need to be downloaded and copied for each participant.

List of Materials and Tools

The following materials and tools were provided to each participant in Days 1-3 of high school training and will be needed for use with the video clips.

Rulers Protractors Compasses Spinners Color tiles Cuisenaire rods

Graph paper Markers Colored pencils Chart paper Graphing calculators Post-it Notes

List of Books Provided to Participants

This list contains the books that will be provided to each teacher attending Days 1-5 of high school training. In some cases, it is advantageous for each mathematics teacher in a school to have a copy of the resource. In other cases, one book per school or mathematics department is sufficient. That distinction has been made on the list.

1. Integrated Mathematics: Choices and Challenges
   McGraw, S. A., ed. (2003).Reston,VA
   The National Council of Teachers of Mathematics, Inc.
   ISBN 0- 87353-530-9
   (one per school)
   
   
2. Implementing Standards-based Mathematics Instruction.
   Stein, M. L., Smith, M. S., Henningsen, M. A. and Silver, E. A. (2000)
   New York, NY: Teachers College Press.
   ISBN 0-8077-3907-3
   (one per teacher)
   
   
3. Guidelines for Assessment and Instruction in Statistics Education
   Franklin, C.A., et al. 2007 ISBN 978-0-9791747-1-1
   May be downloaded at http://www.amstat.org/education/gaise
   (This book should be on the desk of every K-12 teacher who teachers mathematics in Georgia. The hardback copy can be bought for $15 or it can be downloaded free from the web.)
   
   
4. EDThoughts: What we know about mathematics teaching and learning.
   Sutton, J., & Krueger, A. (Eds.). (2002)
   Aurora, CO: Mid-continent Research for Education and Learning.
   ISBN-1-893476-02-2
   (one per teacher)
   
   

Documents and Videos Needed for High School Mathematics Training: Mathematics I, Algebra/Geometry/Statistics and Mathematics II: Geometry/Algebra II/Statistics

Mathematics I: Algebra/Geometry/Statistics

Session 1:  History and Overview
Book:   EdThoughts
Video:  Day 1, Session 1 "History and Overview"

Session 2:   Climbing the Algebra Ladder
Tasks:  “Puzzling Percentages” (GPS 6: Unit 9), “Analyzing Tables” (GPS 6: Unit 9), “Surprise Birthday Party” (GPS 7: Unit 6), “A Staircase” (GPS 8: Unit 5)
Video:  Day 1, Session 2 "Climbing the Algebra Ladder"

Session 3:   The Function Learning Task
Document:  The Algebra Ladder (cut into strips)
Tasks:  “The Function Learning Task” (Mathematics I: Unit 1)
Video:  Day 1, Session 3 "Function Learning Task"

Session 4:   Around the Garden
Task:  “Around the Garden Learning Task” (Mathematics I: Unit 1)
Video:  Day 1, Session 4 "Around the Garden Learning Task"

Session 5:   The Standards-based Mathematics Classroom
Article:  Never Say Anything a Kid Can Say
Video:  Day 2, Session 5 "The Standards-based Classroom"

Session 6:   Tiling Learning Task
Task:  “The Tiling Learning Task” (Mathematics I: Unit 2)
Document:  The Equalizer
Video:  Day 2, Session 6 "Tiling Learning Task"

Session 7:   Instructional Strategies to Support the Standards-based Classroom
Documents:  Co-teaching Models, Georgia Student Achievement Pyramid of Interventions
Article:  Tips and Strategies for Co-Teaching at the Secondary Level, Teaching Exceptional Children, Vol. 36, No. 5, pp. 52-58
Video:  Day 2, Session 7 "Instructional Strategies to Support the Standards-based Curriculum"

Session 8:   The Jogging Learning Task
Task:  “The Jogging Learning Task” (Mathematics I: Unit 2)
Video:  Day 2, Session 8 "Just Jogging Learning Task"

Session 9:   Spinner Learning Task 1
Task:  “Spinner Learning Task 1” (Mathematics I: Unit 4)
Video:  Day 3, Session 9 "Spinner Learning Task 1"

Session 10:   Spinner Learning Task 2
Task:  “Spinner Learning Task 2” (Mathematics I: Unit 4)
Video:  Day 3, Session 10 "Spinner Learning Task 2"

Session 11:   Resources to Support Mathematics GPS
Documents:  No documents required.
Note:  Internet access in order to examine resources on GSO or hard copies of Grade-level Instructional Frameworks for grades 6-8 suggested.
Video:  Day 3, Session 11 "Resources to Support GPS and Standards-based Mathematics Instruction"

Session 12:  A Geometry Learning Task
Tasks:  “Centers of Triangles Learning Task” (Mathematics I: Unit 3)
“Cell Tower Location Learning Task” (Mathematics I: Unit 3)
Video:  Day 4, Session 12 “A Geometry Learning Task”

Session 13:  Instruction in a Standards-Based Classroom
Task:  “Centers of Triangles Learning Task” (Mathematics I: Unit 3)
Book:  EdThoughts
Document:  Questioning Techniques
Video:  Day 4, Session 13 “Instruction in a Standards-Based Classroom”

Session 14:  Planning Instruction for a Student Focused Standards-Based Classroom
Tasks:  “Centers of Triangles Learning Task” (Mathematics I: Unit 3)
“Perplexing Task” (Mathematics I: Unit 3
Document:  Perplexing Task 1 – Teacher Version , Perplexing Task 2 – Teacher Version
Video:  Day 4, Session 14 “Planning Instruction for a Student Focused Standards-Based Classroom”

Session 15:  Assessing to Learn and Learning to Assess-Part 1
Document:  NAEP Q and A
NAEP Questions – Group A
NAEP Questions – Group B
NAEP Questions – Group C
NAEP Questions – Group D
NAEP Student Work – Group A
NAEP Student Work – Group B
NAEP Student Work – Group C
NAEP Student Work – Group D
Video:  Day 5, Session 15 “Assessing to Learn and Learning to Assess-Part 1”

Session 16:  Assessing to Learn and Learning to Assess-Part 2
Document:  NAEP Questions – Groups A-D, NAEP Student Work – Groups A-D
Article:  Changing Assessment Practices in an Algebra Class, or “Will This Be on the Test”, Vol.92, No.3, pp.247-249.
Video:  Day 5, Session 16 “Assessing to Learn and Learning to Assess-Part 2”

Session 17:  Assessing to Learn and Learning to Assess-Part 3
Task:  “Tiling Learning Task” (Mathematics I: Unit 2)
Document:  Assessment For and Of Learning Cards
Article:  Walking Around: Getting More from Informal Assessment, Vol.4, No.4, pp.224-227.
Video:  Day 5, Session 17 “Assessing to Learn and Learning to Assess-Part 3”

Session 18:  Assessing to Learn and Learning to Assess-Part 4
Video:  Day 5, Session 18 “Assessing to Learn and Learning to Assess-Part 4”

Mathematics I: Algebra/Geometry/Statistics Training
Assessing for Mathematics Success: Mathematics I EOCT

Session 1:  Big Ideas in Mathematics I: Algebra/Geometry/Statistics
Task:   “Video Game Learning Task” (Mathematics I: Unit 6)
Document:  Go Ahead, Teach to the Test!
Video:  Session 1 “Big Ideas in Mathematics I: Algebra/Geometry/Statistics”

Session 2:  The EOCT
Documents:   Math I AMS Assessment Set 1,Math I AMS Assessment Set 2, Test Development Cycle,DOK-Side 1, DOK-Side 2
Video:  Session 2 “The EOCT”

Session 3:  Instruction That Puts It All Together
Document:   Math I EOCT Formulas
Video:   Session 3 “Instruction That Puts It All Together

Mathematics II: Geometry/Algebra II/Statistics

Session 1:   The Big Picture of the New Curriculum
Document:  Why an Integrated Curriculum
Video:  Day 1, Session 1 “The Big Picture of the New Curriculum”

Session 2:  Climbing the Algebra Ladder-Part 1
Tasks :  “View Tube Experiment”(GPS 6: Unit 9), “Seesaw Nickels”(GPS 7: Unit 6), “Connecting Arithmetic Sequences and Arithmetic Functions” (GPS 8: Unit 4)
Document :  Algebra Ladder
Video :  Day 1, Session 2 “Climbing the Algebra Ladder-Part 1”

Session 3:  Climbing the Algebra Ladder-Part 2
Tasks :  “Exploring Functions with Fiona Learning Task” (Mathematics I: Unit 1)
Video :  Day 1, Session 3 “Climbing the Algebra Ladder-Part 2”

Session 4:  From Wonderland to Functionland
Tasks :  “Exploring Functions with Fiona Learning Task” (Mathematics I: Unit 1), “From Wonderland to Functionland Learning Task” (Mathematics I: Unit 1)
Video :  Day 1, Session 4 “From Wonderland to Functionland”

Session 5:  The Standards-Based Mathematics II Classroom
Video :  Day 2, Session 5 “The Standards-Based Mathematics II Classroom”

Session 6:  Quadratics in Mathematics I: Algebra/Geometry/Statistics
Tasks :  “Paula’s Peaches Learning Task” (Mathematics I: Unit 5)
Video :  Day 2, Session 6 “Quadratics in Mathematics I: Algebra/Geometry/Statistics”

Session 7:  Quadratics in Mathematics II: Geometry/Algebra II/Statistics
Tasks :  “Paula’s Peaches Revisited Learning Task” (Mathematics II: Unit 1)
Document :  The Equalizer
Video :  Day 2, Session 7 “Quadratics in Mathematics II: Geometry/Algebra II/Statistics”

Session 8:  We Are Teachers of All Students
Document :  Response to Intervention Graphic, Co-Teaching Models, Learners Needing Support, Mathematics I Support Strategies and Interventions, Six Step Process for Building Academic Vocabulary
Video :  Day 2, Session 8 “We Are Teachers of All Students” **in Math 2, Day 3 Folder

Session 9:  Georgia Department of Education Web Resources for Mathematics Teachers
Video :  Day 3, Session 9 “Georgia Department of Education Web Resources for Mathematics Teachers”

Session 10:  What We Know about Student Learning
Document:  EdThoughts
Video :  Day 3, Session 10 “What We Know about Student Learning”

Session 11:  Growing by Leaps and Bounds
Tasks :  “Growing by Leaps and Bounds Learning Task” (Mathematics II: Unit 5)
Video :  Day 3, Session 11 “Growing by Leaps and Bounds”

Session 12:  Assessment in a Standards-Based GPS Mathematics II Classroom-Part 1
Article :  Go Ahead, Teach to the Test!
Video :  Day 4, Session 12 “Assessment in a Standards-Based GPS Mathematics II Classroom-Part 1”

Session 13:   Assessment in a Standards-Based GPS Mathematics II Classroom-Part 2
Document :  Assessment Items
Video :  Day 4, Session 13 “Assessment in a Standards-Based GPS Mathematics II Classroom-Part 2”

Session 14:  Instruction in a Standards-Based GPS Mathematics II Classroom-Part 1
Tasks :  “The Protein Bar Toss, Part 2, Learning Task” (Mathematics II: Unit 1)
Video :  Day 5, Session 14 “Instruction in a Standards-Based GPS Mathematics II Classroom-Part 1”

Session :  Instruction in a Standards-Based GPS Mathematics II Classroom-Part 2
Tasks :  “The Protein Bar Toss, Part 2, Learning Task” (Mathematics II: Unit 1)
Video :  Day 5, Session 15 “Instruction in a Standards-Based GPS Mathematics II Classroom-Part 2”

Effective Mathematics Instruction for Students with Diverse Needs:
A Systematic and Explicit Approach Dr. Paul Riccomini

Session 1:   Overview
Document:  Who Struggles in Math: Handout # 3, Who Struggles in Math: Handout # 4, Sequence Activity: Multistep Problems, Arithmetic Activity: Using Basic Facts,
Video:  Session 1 “Overview”

Session 2:  Explicit and Systematic Instruction
Video:  Session 2 “Explicit and Systematic Instruction”

Session 3:   Instructional Scaffolding
Document:  Breakout Activity
Video:  Session 3 “Instructional Scaffolding”

Session 4:   Organizing Instruction and Study
Document:  Spaced Instructional Review Planning Sheet, Additional Information and Resources
Video:  Session 4 “Organizing Instruction and Study”