Guided math power_point_by_the_author_of_guided_math

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4 2 5 1 0011 0010 1010 1101 0001 0100 1011 Guided Math A Framework for Math Instruction Laney Sammons

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Guided MathA Framework for Math Instruction

Laney Sammons

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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

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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.

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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?

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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?

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First Grade Second Grade

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2007

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2007 (New Standards)

2008 (Guided Math)

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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%

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Third Grade Fourth Grade Fifth Grade

2007

2008

2009

Why Implement the Guided Math Framework?

2008 (New Standards)

2009 (Guided Math)

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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.

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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

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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

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Why should we explore different ways to teach math?

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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

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How can we effectively teach mathwhen we have a classroom of students at many different levels of achievement?

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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.

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Guided Math Framework

Daily Components

• Classroom Environment of Numeracy

• Math Warm-up/Calendar Board

• Individual Conferences

• Ongoing Assessment

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Guided Math Framework

Choice Components

•Whole-Class Instruction

•Small-Group Instruction

•Math Workshop

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Use of Manipulatives

Creating a Classroom Environment of Numeracy

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Read literature that promotes exploration and application of math concepts

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Display a Mathematics Word Wall

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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

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Morning Math Warm-ups

• Mathematical Stretches

• Mathematical Current Events

• Math-Related Classroom

Responsibilities

• Calendar Board

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Mathematical Stretches

Data Collection and Analysis Tasks

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Mathematical Stretches

Data Collection and Analysis Tasks

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Mathematical Stretches

Data Collection and Analysis Tasks

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Mathematical Stretches

Number of the Day Stretch

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Mathematical Stretches

What’s Next? Stretch

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Mathematical Stretches

• How Did My Family Use Math Last Night? Stretch

• _______________ Makes Me Think of… Stretch

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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

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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

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Menu of Instruction

• Whole class instruction

• Small group guided instruction

• Math Workshop (independent work or work in cooperative groups)

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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.

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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

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Whole Class Instruction??

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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.

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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.

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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)

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Small Group Guided Instruction??

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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

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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

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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.

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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

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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.

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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)

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64Versatiles

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65Activboard

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Math Conferencing

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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

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Making a Choice

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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

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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

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Sample Guided Math Schedule

Day Activity Component

Friday Math Huddle

Create class chart to post in classroom for reference

Whole Class

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Assessment

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“…assessment is not an end goal, but a means to achieving instructional outcomes.” National Council of Teachers of Mathematics

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Balanced Assessment

Observation

Communication Product

Balanced assessment provides a “photo album” of student achievement rather than just a “snapshot.”

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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

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Ticket Out the Door

• How can you use these methods in your classroom?

• How can using Guided Math help you with your math instruction?

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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

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Join a Guided Math Group:

http://tech.groups.yahoo.com/group/guidedmath/

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Questions?

Laney [email protected]