Post on 27-Jan-2015
description
42510011 0010 1010 1101 0001 0100 1011
Guided MathA Framework for Math Instruction
Laney Sammons
4251
0011 0010 1010 1101 0001 0100 1011
Background Information
• My experience
• Lessons learned in kindergarten
• Differentiating to meet diverse needs
• Links to literacy instruction and the Guided Reading model
• Development of the Guided Math framework
4251
0011 0010 1010 1101 0001 0100 1011
What is Guided Math?Guided Math is a flexible instructional
framework that enables teachers to
promote the deep mathematical understanding
and computational fluency of their students by
determining their unique needs and then
prescriptively addressing those needs through a
combination of whole class instruction, small
group instruction, math workshop, and
conferences within a classroom environment
supportive of numeracy.
4251
0011 0010 1010 1101 0001 0100 1011
Samuel E. Hubbard Elementary SchoolForsyth, Georgia
• Small town in an area that has been predominately poor and rural, but is gradually becoming suburban.
• Pre-K through Fifth Grade• Title I School of Distinction for 10 years• 63% Free/Reduced Lunch• 34% Minority Students• 924 Students
Why Implement the Guided Math Framework?
Samuel E. Hubbard Elementary SchoolForsyth, Georgia
• Georgia implemented new, more rigorous math performance standards for Kindergarten through Second Grade in 2006-2007.
• Guided Math implemented in 2007-2008
Why Implement the Guided Math Framework?
50%
60%
70%
80%
90%
100%
First Grade Second Grade
2006
2007
2008
2009
2007 (New Standards)
2008 (Guided Math)
Samuel E. Hubbard Elementary SchoolForsyth, Georgia
• The new math performance standards were implemented in grades three to five in 2007-2008.
• Guided Math implemented in 2008-2009
50%
60%
70%
80%
90%
100%
Third Grade Fourth Grade Fifth Grade
2007
2008
2009
Why Implement the Guided Math Framework?
2008 (New Standards)
2009 (Guided Math)
Samuel E. Hubbard Elementary School• Students Exceeding Standards in Math
Why Implement the Guided Math Framework?
0%
20%
40%
60%
80%
100%
First Grade
Second Grade
Third Grade
Fourth Grade
Fifth Grade
2008
2009
First and second grades had experienced gains in the percentage of studentsexceeding in 2008 when they implemented Guided Math. In 2009, the percentageof students exceeding standards continued to increase.
4251
0011 0010 1010 1101 0001 0100 1011
8
The Traditional Approach to Teaching Math
• Large group instruction• All students work on the same level• Primarily instruction and practice
from text book• Emphasis on paper and pencil work• One correct answer• Individual work
4251
0011 0010 1010 1101 0001 0100 1011
9
Does this approach work?
• Successful for some students• Less successful for those who
quickly acquire mastery• Even less successful for struggling
students• Encourages emphasis on
computation skills• Little opportunity for communication• More emphasis on evaluation, rather
than assessment for learning
4251
0011 0010 1010 1101 0001 0100 1011
Why should we explore different ways to teach math?
4251
0011 0010 1010 1101 0001 0100 1011
11
To more effectively teach math, we must
• reach students at all levels of achievement
• provide diverse methods of learning• allow more opportunities for
observation and communication by students
• encourage active engagement by students
4251
0011 0010 1010 1101 0001 0100 1011
12
How can we effectively teach mathwhen we have a classroom of students at many different levels of achievement?
4251
0011 0010 1010 1101 0001 0100 1011
The Guided Math framework offers a daily menu of instruction from which teacherscan choose based on the needs of their students and upon the standards being taught.
4251
0011 0010 1010 1101 0001 0100 1011
Guided Math Framework
Daily Components
• Classroom Environment of Numeracy
• Math Warm-up/Calendar Board
• Individual Conferences
• Ongoing Assessment
4251
0011 0010 1010 1101 0001 0100 1011
Guided Math Framework
Choice Components
•Whole-Class Instruction
•Small-Group Instruction
•Math Workshop
4251
0011 0010 1010 1101 0001 0100 1011
18
Use of Manipulatives
Creating a Classroom Environment of Numeracy
4251
0011 0010 1010 1101 0001 0100 1011
19
Read literature that promotes exploration and application of math concepts
4251
0011 0010 1010 1101 0001 0100 1011
21
Display a Mathematics Word Wall
4251
0011 0010 1010 1101 0001 0100 1011
Math-Related ClassroomResponsibilities
• Attendance
• Lunch counts
• Fund raising
• Class elections
• Field Trip Collections – Total cost of the trip– Total amount collected– Percentage of total amount needed
4251
0011 0010 1010 1101 0001 0100 1011
27
4251
0011 0010 1010 1101 0001 0100 1011
34
Morning Math Warm-ups
• Mathematical Stretches
• Mathematical Current Events
• Math-Related Classroom
Responsibilities
• Calendar Board
4251
0011 0010 1010 1101 0001 0100 1011
Mathematical Stretches
Data Collection and Analysis Tasks
4251
0011 0010 1010 1101 0001 0100 1011
Mathematical Stretches
Data Collection and Analysis Tasks
4251
0011 0010 1010 1101 0001 0100 1011
Mathematical Stretches
Data Collection and Analysis Tasks
4251
0011 0010 1010 1101 0001 0100 1011
Mathematical Stretches
Number of the Day Stretch
4251
0011 0010 1010 1101 0001 0100 1011
Mathematical Stretches
What’s Next? Stretch
4251
0011 0010 1010 1101 0001 0100 1011
Mathematical Stretches
• How Did My Family Use Math Last Night? Stretch
• _______________ Makes Me Think of… Stretch
4251
0011 0010 1010 1101 0001 0100 1011
Math Current EventsTeacher or students bring in articles or
web sites with current events that have to do with math:
• Levels of precipitation
• Economic statistics
• Population
• Vote counts
4251
0011 0010 1010 1101 0001 0100 1011
45
4251
0011 0010 1010 1101 0001 0100 1011
46
Daily Calendar/Morning Work
• Problems of the Day
• Incredible Equations
• Daily Data Work
• Calendar Activities
• Preview new concepts and skills.
• Maintain previously mastered skills.
• Regular focus on difficult to master skills
4251
0011 0010 1010 1101 0001 0100 1011
50
Menu of Instruction
• Whole class instruction
• Small group guided instruction
• Math Workshop (independent work or work in cooperative groups)
4251
0011 0010 1010 1101 0001 0100 1011
51
National Mathematics Advisory Panel
• “All-encompassing recommendations that instruction should be entirely ‘student centered’ or ‘teacher directed’ are not supported by research.”
• Teachers must use their professional judgment to determine their methods of instruction.
4251
0011 0010 1010 1101 0001 0100 1011
Gradual Release of Responsibility
• Whole Group Instruction• Highest level of teacher support• Teacher modeling and think-alouds• Mini-lessons, direct instruction
• Small Group Guided Instruction• Moderate level of teacher support• Scaffolded instruction tailored to individual needs
of students
• Math Workshop• Lowest level of teacher support• Independent work by individuals or groups
4251
0011 0010 1010 1101 0001 0100 1011
53
Whole Class Instruction??
4251
0011 0010 1010 1101 0001 0100 1011
54
Whole Class Instruction
• Advantages– Captures everyone’s attention at once.– Quick way to present same information to
all.– Builds mathematical community by
creating common experiences.– More time can be devoted to the lesson.
4251
0011 0010 1010 1101 0001 0100 1011
55
Whole Class InstructionChallenges
– Often fails those at top and bottom of class.– Fails to target students’ varying levels of
competency– Difficult to maintain attention of all.– Communication opportunities limited.– Minimal descriptive feedback from the teacher or
peers.– Ongoing assessment is more difficult.– Students may engage in work based on a
misunderstanding and then practice incorrect methods.
4251
0011 0010 1010 1101 0001 0100 1011
56
Effective Uses of Whole Class Instruction
• When most students are on about the same instructional level for a math concept
• Introduction of a new series of lessons with an activating strategy to generate interest, enthusiasm, and curiosity
• Use of literature to teach a math concept• Review of previously taught and mastered
skills to ensure maintenance• Preparing a class for cooperative group work;
providing common knowledge about requirements
• Some assessments (timed math facts tests, for example)
4251
0011 0010 1010 1101 0001 0100 1011
57
Small Group Guided Instruction??
4251
0011 0010 1010 1101 0001 0100 1011
58
Small Group Guided Instruction
• Is similar to guided reading, but composition of the groups may be even more fluid
• Homogenous, flexible grouping by level of achievement
• Requires assessment to determine each student’s level
• Provides scaffolding to support the learning efforts of students
• Encourages exploration of math concepts in a risk-free learning environment
• Maximizes the benefit of co-teaching
4251
0011 0010 1010 1101 0001 0100 1011
59
Small Group Guided InstructionAdvantages:
– Students work at their appropriate levels.– Work may be differentiated in procedure, level
of difficulty, or by work product.– More time can be spent with struggling
students.– Enhanced communication– Students stay focused– Incorrect understanding easily detected and
corrected– Opportunities for ongoing assessment for
learning– Cooperation among students is encouraged “the social nature of learning”-Vygotsky
4251
0011 0010 1010 1101 0001 0100 1011
60
Small Group Guided Instruction
Challenges– More extensive planning required– Less direct instruction by teacher of each
student– Meaningful work must be provided for
students who are not in the small group– Time must be spent establishing and
teaching routines and procedures to ensure uninterrupted small groups.
4251
0011 0010 1010 1101 0001 0100 1011
61
Small Group Guided Instruction• Effective Uses:
– Introduction of new concepts– Practice of new skills– Instruction with manipulatives– Intensive instruction for students having
difficulty mastering concepts– Introduction of activities that will later become
independent work during math workshop– Informal assessment– Re-teaching based on results of formative
assessment
4251
0011 0010 1010 1101 0001 0100 1011
62
Math Workshop
• Students work independently, in pairs, or in groups.
• Procedures and routines must be established and practiced.
• Activities should provide opportunities for exploration or practice of mastered skills.
• The work need not be related to the work being done in small groups.
4251
0011 0010 1010 1101 0001 0100 1011
63
Math Workshop Activities• Follow-up work from small group lesson• Paper and pencil practice of previously
mastered skill for maintenance• Mathematical Investigations/ Problems of the
Week• Math games (for example Math 24)• Work with manipulatives• Math journals• Multidisciplinary Connections (where Language
Arts, Science or Social Studies relate to Math)
4251
0011 0010 1010 1101 0001 0100 1011
64Versatiles
4251
0011 0010 1010 1101 0001 0100 1011
65Activboard
4251
0011 0010 1010 1101 0001 0100 1011
66
4251
0011 0010 1010 1101 0001 0100 1011
69
4251
0011 0010 1010 1101 0001 0100 1011
71
4251
0011 0010 1010 1101 0001 0100 1011
75
Math Conferencing
4251
0011 0010 1010 1101 0001 0100 1011
76
Math Conferencing• Occurs throughout the day with
individual students in any of the components
• Sometimes used to “trouble shoot”• Prompts self-assessment by students• Assists teacher in monitoring
comprehension and identifying teaching points
• Increases communication• Provides descriptive feedback for
students
4251
0011 0010 1010 1101 0001 0100 1011
78
Making a Choice
4251
0011 0010 1010 1101 0001 0100 1011
Sample Guided Math ScheduleDay Activity Component
Monday Activating Strategy
Problem Solving
Think-Aloud
Prep for independent
work
Whole Class
Tuesday Read-aloud
Independent
work/conferencing
Guided Math Group 1
Whole Class
Workshop
Conferencing
Small Group
4251
0011 0010 1010 1101 0001 0100 1011
Sample Guided Math ScheduleDay Activity Component
Wednesday Problem challenge
minilesson
Independent
work/conferencing
Guided Math Group 2
Whole Class
Workshop
Conferencing
Small Group
Thursday Independent
work/conferencing
Guided Math Group 3
Guided Math Group 1
Workshop
Conferencing
Small Group
4251
0011 0010 1010 1101 0001 0100 1011
Sample Guided Math Schedule
Day Activity Component
Friday Math Huddle
Create class chart to post in classroom for reference
Whole Class
4251
0011 0010 1010 1101 0001 0100 1011
82
Assessment
4251
0011 0010 1010 1101 0001 0100 1011
83
“…assessment is not an end goal, but a means to achieving instructional outcomes.” National Council of Teachers of Mathematics
4251
0011 0010 1010 1101 0001 0100 1011
85
Balanced Assessment
Observation
Communication Product
Balanced assessment provides a “photo album” of student achievement rather than just a “snapshot.”
4251
0011 0010 1010 1101 0001 0100 1011
88
How can you assess students to determine grouping prior to and during instruction?• Observation of an assigned task• Small group discussion of problem solving
related to the concept to be studied• Written explanation of understanding by
students in their math journals• Paper and pencil pretest• Formative test results• Performance in earlier work on sequential
math concepts • Checklist • Conferencing
4251
0011 0010 1010 1101 0001 0100 1011
89
Ticket Out the Door
• How can you use these methods in your classroom?
• How can using Guided Math help you with your math instruction?
Resources
Guided Math: A Framework for Mathematics Instruction by Laney Sammons
Available online at http://www.teachercreatedmaterials.com/estore/product/50534
Or at other online book sites.
To be published in Spring 2010:Mathematical Stretches for Grades K-2
By Laney Sammons
4251
0011 0010 1010 1101 0001 0100 1011
Join a Guided Math Group:
http://tech.groups.yahoo.com/group/guidedmath/