Addressing the Instructional Needs of Diverse Learners

Addressing the Instructional Needs of Diverse Learners

with Strategic TeachingPresented by

Amy Scheuermann

Bowling Green State University

January 11, 2008

Everyday…….Everyday…….

More than 3000 adolescents dropout of school……that’s 540,000+ per year!

Some Pressing Problems

• Higher performance standards• Increased accountability• Greater academic & cultural diversity• Larger class sizes• Learning is difficult for many students• Unrealistic planning expectations• Greater sense of “disconnectedness”

Content Explosion Dilemma

The Performance Gap

Years in School

Demands/Skills

The “Gap”

NCLB 2013-2014

About the Center for Research on Learning

Founded in 1978, their mission is to ...dramatically improve the performance of students considered to be at-risk for school failure through research-based interventions.

Goal: Success Across HALO Levels

• High Achieving

• Average Achieving

• Low Achieving

• Other Achieving

(including students with Specific Learning Disabilities)

• Lion• Nissan• Orange• Saturn • Whale• Ford• Monkey• Banana• Apple• Toyota• Cherry• Dog• Lemon• Snake• Volvo

Non-Strategic Learners

• Do not use effective & efficient study procedures• Spend inordinate amounts of time on assignments• Have difficulty distinguishing the important from the

unimportant• Do not organize information appropriately for learning• Have difficulty setting and attaining goals• Often fail to take advantage of prior knowledge when facing

new problems• Use no systematic approach to solving problems

The Performance Gap

SkillsDemands

Years in School

/

Learning Strategies (∆ the student)

Learning & Applying

• Pretest• Describe

– Commitment (student & teacher)– Goals– High expectations

• Model• Practice and quality feedback

– Controlled and advanced• Posttest & reflect• Generalize, transfer, apply

The Word Identification Strategy

Discover the contextIsolate the beginningSeparate the endingSay the stemExamine the stemCheck with someoneTry the dictionary

5.1 5.0 5.0

6.5

9.1

6.9

7.9

10.1

0.0

2.0

4.0

6.0

8.0

10.0

12.0

1998-99 1999-00 2000-01 2001-02

Gra

de

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ST:

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PRE (Form A) POST (Form B)

Students with LD

Self-Questioning-2003 n= 133

0

10

20

30

40

50

60

comparison experimental

comparison

experimental

7th Grade Science Class: Growth Scores

Learning Strategies Curriculum

Acquisition Word

Identification

Paraphrasing

Self-Questioning

Visual Imagery

Interpreting Visuals

Multipass

Storage First-Letter Mnemonic

Paired Associates

Listening/Notetaking

LINCS Vocabulary

Expression of Competence

Sentences

Paragraphs

Error Monitoring

Themes

Assignment Completion

Test-Taking

But…..we learned that trying to “change” the students as learners wouldn’t be sufficient to close the performance gap. So…..

The most effective interventions for students with and without learning disabilities are …

• Graphic organizers

• Direct, intensive, systematic instruction in learning strategies

In order for transfer and maintenance of these skills to significantly increase instruction must occur across settings

While Research Findings told us

The Performance Gap

Years in School

SkillsDemands

/Content Enhancement (∆ the teacher)

Content Enhancement Routines(Creating “learner-friendly” classrooms)

• A way of teaching academically diverse classes in which

• The integrity of the content is maintained• Critical content is selected and transformed• Content is taught in an active partnership with

students

SMARTER PlanningKey Planning Principles

Teach truly critical content

Know what makes the critical content difficult

Use Teaching Routines that make critical content accessible

Teach strategies that will help students learn critical content

Share plans about how you will teach critical content

Know the critical content

Thinking About the Curriculum...

Knowledge

Thinking About the Curriculum... Knowledge

Course Critical Content

KnowledgeCourse Unit

Thinking About the Curriculum...

A UnitALL

MOST

SOME

Generalization & Problem Solving

Content Manipulation

Content: Facts, Concepts,

Definitions, Propositions

Content Enhancement

• A way of teaching an academically diverse group of students in which– Both group & individual needs are valued and meet– The integrity of the content is maintained– Critical features of the content are selected and transformed

in a manner that promotes student learning– Instruction is carried out in a partnership with students

A Powerful Teaching Device:

Is an instructional tool that:• is used under teacher guidance• focuses attention on important outcomes• identifies critical content features • prompts elaboration on critical points• helps make relationships concrete• is designed to enhance student...

...organization ...remembering ...understanding

...responses ...belief in the value of the content

Explicit Linking Steps

Guide the teacher in ways to:

• present the device effectively

• involve students in using the device

• elicit student prior knowledge

• focus student attention on learning

A Structured Cue-Do-ReviewSequence:

The overall instructional process that guides use of the Teaching Device and Linking Steps.

Cue– The teacher announces the Teaching Device and explains its

use.

Do– The teacher and class collaboratively interact with the device

using a set Linking Steps that “connect” the content to the needs and goals of students.

Review– Learning is reviewed and confirmed.

Content Enhancement Teaching Routines

Planning & Leading LearningCourse OrganizerUnit OrganizerLesson Organizer

Exploring Text, Topics, &

DetailsFraming RoutineSurvey RoutineClarifying Routine

Teaching ConceptsConcept Mastery RoutineConcept Anchoring RoutineConcept Comparison Routine

Increasing PerformanceQuality Assignment RoutineQuestion Exploration RoutineRecall Enhancement Routine

Concept Diagram

A mammal is a warm-blooded vertebrate that has hair and nurses its young.

CONCEPT DIAGRAM CONVEY CONCEPT

NOTE KEY WORDS

OFFER OVERALL CONCEPT

CLASSIFYCHARACTERISTICS:

21

Always Present Sometimes Present Never Present

Examples: Nonexamples:

PRACTICE WITH NEW EXAMPLE

TIE DOWNA DEFINITION

EXPLORE EXAMPLES

1

3

2

4

5

6

7

33 Key Words Mammal Vertebrate

warm-blooded

nurse their young

has hair

walks on 2 legs walks on 4 legs

cold-blooded

human snake

elephant

whale

+

+

+

duckbillplatypus

swims in water

alligator

shark

bird

elephant

human

warm-blooded

nurse their young

whale

bird

shark

walks on 4 legs

can fly

cold-blooded

bat

can fly

moves on the ground

O

9th Grade Physical Science (n-78)

62%

65%65%

71%

73% 73%

56%

58%

60%

62%

64%

66%

68%

70%

72%

74%

76%

Students w/ Disabilties (n=13) Students w/o Disabilities (n=65) Whole Group (n=78)

Av

era

ge

% S

co

re o

n U

nit

Te

sts

NON CE Units CE Units

How well does ContentEnhancement really work?

• Each routine has been studied in secondary content-area classes characterized by diversity.

• In each study, teachers learned the routine easily and student learning gains were observed by both teachers and researchers.

• In each study, students gained an average of at least 10 to 20 percentage points on tests or tasks that required students to demonstrate learning.

• In general, the greatest gains were seen in classes where teachers had the highest expectations for student learning and were consistent in their use of the routine over time.

Routine ADD RESSES RESEARCH D ATA

Unit Organizer Planning and Leading - structure and relationships of the content

+ of 10 to 20 percentage points on unit tests

Lesson Organizer Planning and Leading -- paraphrase the lesson, fit content together

+ of at least 10 to 20 percentage points on tests or tasks

Clarifying Routine Exploring - topic and details in context + 14 to 30 percentage points

Framing Routine Exploring - relationships between main ideas and details

+ 10 to 15 percentage points on tests or tasks

Survey Exploring - find key information and structure

+ of 10 to 15 percentage points on unit tests

Concept Anchoring

Teaching concepts - connects prior knowledge to key concepts

an average + of 7 to 27 percentage points on tests or tasks

Concept Mastery Teaching concepts - define concepts Both LD and NLD students made substantial increases on unit tests ( + 10 points)

Concept Comparison

Teaching concepts - compare and contrast concepts

LD and Low achievers + 15 to 24 percentage points

Recall Enhancement

Increased performance - focuses on critical information

LD + of 21 percentage points NLD + of 29 percentage points

Vocabulary LINCing

Increased performance - vocabulary knowledge

LD Pretest 53% Posttest 77% NLD Pretest 84% Posttest 92% Control Pretest 86% Posttest 85%

Research Statistics - Content Enhancement

But…..we’ve now learned that while individual interventions (or packages of interventions) are necessary to close the gap, they aren’t sufficient (AYP realities). So…..

Content Literacy Continuum

Students not making AYP in reading

1. Mastery of critical content

5. Intensive clinical

Intervention

3. Intensive strategies instruction

2. Weave strategies across classes

4. Intensive basic skill instruction

CLC- A Continuum of School Action

Level 1: Enhance content instruction (mastery of critical content for all regardless of literacy levels)

Level 2: Embedded strategy instruction (routinely weave strategies within and across classes using large group instructional methods)

Level 3: Intensive strategy instruction (mastery of specific strategies using 8-stage instructional sequence; individual Strategic Tutoring)

Level 4: Intensive basic skill instruction (mastery of entry level literacy skills at the 4th grade level)

Level 5: Therapeutic intervention (mastery of language underpinnings of curriculum content and learning strategies)

Tutoring: Strategic Tutoring (extending the instructional time “box” through before or after school tutoring)

LANGUAGE

SKILLS

STRATEGIES

SUBJECT MATTER

Building Blocks for Academic Competency

Teacher- Mediated Instruction

Student- Mediated Instruction

• Heavy Scaffolding

• Dependence

• Limited Scaffolding

• Independence

Instructional Continuum

Ebb and Flow

Level 1Presenting Critical Content for Mastery

Level 2Introducing Strategy

BuildingLevel 3

Intensive Strategy Instruction

Level 4Skill BuildingLevel 5

Therapeutic

Students and Instructional Focus

Significant gains occur when we……

• use well-designed interventions -- regularly, with fidelity, with intensity

• combine an ‘instructional core’ with key ‘infrastructure supports’ to create a critical mass of activity focused on student outcomes

The Performance Gap

Years in School

SkillsDemands

/

Instructional Core

ExistingSupport

Instructional Core

•Continuum of literacy instruction

•Direct/explicit instruction

•Engaging/diverse materials

•Motivation/management systems

•Formative/summative assessments

Learning Strategies Curriculum

Content Enhancement

Routines

Cooperative Thinking Strategies

Teaming & Problem Solving

Strategies

Community Building

Strategies Possible Selves

Learning Expressways

Self Advocacy Strategy

Engaging & Diverse Materials

• Below frustration level

• Responsive to wide range of abilities

• Broad array of engaging topics

• Relevant to student backgrounds (SES, culture, etc.)

Avoid Fragmentation

• Coordinated, sustained, targeted instruction across– Teachers– Classes– Grades– Schools

Teacher:

Time:

The

Course OrganizerStudent:

Course Dates:

This Course: FUSION Reading

Course Questions:

isabout

learning to apply ADVANCED reading strategies to a variety of text structures in order to improve reading comprehension

1. How does thinking about your hopes, expectations and fears change the way you approach learning?

2. How do you use reading comprehension strategies to help you understand and learn from what you read?

3. How can studying word structures and word meaning help you become an advanced level reader?

4. When reading text, why is it important to read fluently?

5. How and why do expert readers integrate and apply reading strategies?

Grading Procedures

Agenda & Warm-ups: 10%

Assignments : 70%

(in class/outside of class)

projects

practice activities

reading application

Tests & Quizzes: 20%

Classroom Expectations for: Learning Routines

Course Map This Course:

includes

Tasks/Activities

Student:

Critical Concepts

Learned in theseUnits

TeamworkRespectVoiceChoiceEffort

FUSION Reading

Intensive LearningClassroom ProceduresDaily Agenda/warm-upFeedback SessionsProgress Charting

QuizzesPeer TeamsDiscussionsProducts

Classroom Learning ProceduresFocus on What is PossibleExpert Reading Strategies

Supportive Learning ExperiencesExplicit Instruction

Classroom Learning Procedures

Possible Selves The Bridging Strategy

The Summarization Strategy

Advanced Phonics

Decoding Word Recognition

The Prediction Strategy

such as

such as

such as

Fluency

Launching

Thinking Reading

Book Study

Strategy Integration

Vocabulary

PASS the TestStrategies

LessonLessonStructureStructure

Lesson Two-at-a-Glance

Overview This lesson provides an overview of the Bridging Strategy and an introduction in how to apply the first step of TBS with words lists. Objectives: To become aware of the purpose of TBS To watch an expert model the how to apply TBS to difficult reading materials To learn and practice the first step of TBS

Time Topic Activity Materials

5 minutes Warm Up Advance Organizer

Guiding questions to recap The Bully Chapter 2

17 minutes Guided Reading

Student-led Reading Novel: The Bully

15 minutes

Introduction to The Bridging Strategy

Model expert use of TBS

Cue Cards 1 & 2 Tool Book

25 minutes

Vowels: short, long, VCe P step

Guided & Individual practice

Vowel Sound Chart Learning Sheet 1a Practice Sheet 1a

15 minutes

Vocabulary

Guided & Individual practice

Steno pads List Set 4

3 minutes

Post Organizer

Reminder: Book Study Due Date

Fusion Test Results

50556065707580859095

100

Pre Score Mean Post Score Means

ExperimentalControl

The Performance Gap

Years in School

SkillsDemands

/

Infrastructure Support

ExistingSupport

Instructional Core

Infrastructure Support

•Professional development

•Aligned instruction

•Extended time

•Role integrity

Key Principles of Professional Development

Professional Development Should be: • Focused. • Sustained.• Data driven. • Personalized.• Designed to create a learning community.• About systems change.

Professional Development Approaches

• Traditional– Inservice on inservice days

• Enlightened– Interviews, partnership learning, participant choice, in-

class modeling, ongoing

• Instructional Coaches– Enlightened + Onsite coaching and collaboration for

implementation

Implementation Rates

0

10

20

30

40

50

60

70

80

90

Implementation Rate

Traditional

Enlightened

InstructionalCollaborators

Effectiveness of Staff Development Activities

Knowledge Skill Classroom Acquisition Application

Present Information

Present + ModelPresent + Model +

Practice + FeedbackPresent + Model +

Practice + Feedback +

Coaching

40-80% 10% 5%

80-85% 10-40% 5-10%

80-85% 80% 10-15%

90% 90% 80-90%

National Staff Development Council, 1995; Fullan, 1991; Joyce & Showers, 1988; Mehring, 1999.

The University of Kansas Center for Research on Learning

Common Factors for Successful Implementation

• Strong administrative leadership• Strong instructional commitment• Support for ongoing support & learning• Financial support for new professional

developers and ongoing support• Strong ties to CRL

Improving Outcomes for Struggling Adolescent Learners

Instructional Core Infrastructure Support(administrative leadership)

Improved Outcomes+ =

•Continuum of literacy instruction

•Direct/explicit instruction

•Engaging/diverse materials

•Motivation/management systems

•Formative/summative assessments

•Professional development

•Aligned instruction

•Extended time

+ =Ability to apply what is learned to novel situations

•Role integrity

Content Enhancement Examples

Elida CordoraNAMEDATEThe Unit Organizer BIGGER PICTURE

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4

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The roots and consequences of civil unrest.

The Causes of the Civil WarGrowth of the Nation The Civil War

Sectionalism

pp. 201-236

1/22 Cooperative groups - over pp. 201-210

1/28 Quiz


"Influential Personalities" project due

1/30 Quiz


2/6 Review for test

2/7 Review for test

2/6 Test

Areas of the U.S.

Differences between the areas

Events in the U.S.

Leaders across the U.S.

was based on

emerged because of became greater with

was influenced by

descriptive

cause/effect

What was sectionalism as it existed in the U. S. of 1860?

How did the differences in the sections of the U.S. in 1860 contribute to the start of the Civil War?

compare/contrast

1/22

What examples of sectionalism exist in the world today?

NAMEDATEThe Unit Organizer

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How did national events and leaders pull the different sections of the U.S. apart?

The Causes of the Civil WarElida Cordora

1/22

Sectionalism

pp. 201-236

was based on the

developed because of

North

South

West

SocialDifferences

PoliticalDifferences

EconomicDifferences

Areas of the U.S.

Differences between the

areas

-Henry Clay-Stephen Douglas-Zachary Taylor-Harriet Beecher Stowe-Douglas Filmore-John Brown-Jefferson Davis

-Abraham Lincoln

such as

was influenced by

Leaders of change

became greater with

Events in the U.S.

such as

-1820 Missouri Compromise-1846 Mexican War

-1850 Compromise of 1850-1850 Fugitive Slave Law of 1850-1852 Uncle Tom's Cabin-1854 Kansas-Nebraska Act-1854 Republican Party formed-1854 Bleeding Kansas-1857 Dred Scott Case

-1858 Lincoln Douglas Debates -1859 John Brown's Raid-1860 Lincoln Elected -1860 South Carolina Secedes-1861 Confederacy formed

whic

h in

cluded t

he

whic

h in

cluded t

he

whic

h in

cluded

th

e

and includedand included and included

CONCEPT DIAGRAM



TIE DOWN A DEFINITION

EXPLORE EXAMPLES

Key Words


CONVEY CONCEPT

NOTE KEY WORDS


CLASSIFYCHARACTERISTICS

U.S. Civil War

Northern Ireland

citizens

one nation

Civil War armed conflict

groups of citizens

within a single nation

about distribution of power

economic

religious

ethnic

social

political

war between nations

United States war between states

Northern Ireland

1990's Crisis in the Balkans

World War I

A civil war is a type of armed conflict among groups of citizens of a single nation that is caused by concerns about distribution of power.

World War II

"Desert Storm"

in Kuwait

American Revolutionary

War

ethnic

many nations

social rights

"Desert Storm"in Kuwait

3 CollectKnown Information

4 HighlightCharacteristics ofKnown Concept

5 ObserveCharacteristics

of New Concept

6 RevealCharacteristics

Shared

7 StateUnderstanding of

New Concept

KnownInformation

Name: Date:Anchoring Table

2 NameKnown Concept

6Characteristics of Known Concept Characteristics of New ConceptCharacteristics Shared

Known Concept New Concept

1 Announcethe New Concept

ANCHORSLinkingSteps:

Understanding of the New Concept:

Unit:

12

4 5

3

7

Federalism in the U.S.A.

Decision makingin your school

Federalism in the U.S.A. is a form of government in which decisions are made by both

state and national govts. Rules to decide how power is divided are based on the Constitution. Some powers (e.g., make

war, coin money) belong to the national govt. Other powers (e.g., education, marriage, gambling) belong to the states.

Some powers (e.g., tax, punish crimes) belong to both.

administra-tors

penalties

teachers make assignments

administra-tors expel

rules

teachers

not sure if powers are written down

Decisions are made by state & national govts.

Rules, based on Constitution, tell how power is divided.

Some powers belong to national govt (war, money).

Some powers belong to states (education, marriage, gambling).

Some powers belong to both (tax, punish crimes).

Decisions are made by administrators & teachers.

Rules, written or understood, tell how power is divided.

Some powers belong to administrators (expel).

Some powers belong to teachers (give assignments).

Some powers belong to both (make rules, set penalties).

2 groups are involved.

Rules tell how power is divided.

Some powers belong to both groups.

Some powers belong to the other group.

Some powers belong to one group.

The Teaching Device: The Anchoring Table

To really create social change, many peoplehave to be organized, outspoken, and persistent!

Progressive Era

Unsafe food

Monopolies

Limited voting rights

Unsafe and unfairworking conditions

Muckrakers wroteabout problems

Bully pulpits forcednew laws

Demonstratorscreated public pressure

Activists organizedprotests

Meat Inspection Act

Anti- trust Act

Voting rightsexpanded

Commerce and LaborDepartments

Tools for Social Change Social Changes

The FRAME RoutineKey Topic

Main idea

is about…

So What? (What’s important to understand about this?)

Essential details

Main idea

Essential details Essential details

Main idea

a period of social change in the U. S.

Social Problems

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Filling and Wrapping (Area and Volume)

Building Boxes

Designing Packages

Volume of Boxes

•Check up 1*

Cylinders

*Test / Assessment*

Data Around Us Fractions

Using Mathematics

Describing the characteristics

(attributes) of 3-D shapes

Characteristics

Compare & Contrast

Steps

Problem and Solution

•How do we build boxes?

•How do I identify a box?

•How do I find volume and surface area?

•What is the relationship between length, width, height, volume, area, and perimeter?

•Can I compare a cylinder to a box? Why or Why not?

Building Boxes

by

Cylinders

Applied to

Volume of Boxes

by finding

Designing Packages

by



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Looking for Pythagoras (Rt triangles)

Locating Points

Finding Areas and Lengths

•Check up 1*

Pythagorean Theorem

Using the Theorem

*Test / Assessment*

Moving Straight Ahead (Linear Relationships)

Kaleidoscopes, Hubcaps, & Mirrors (symmetry)

Geometry

Finding and applying a secret relationship!

(Pythagorean Theorem)

Characteristics

Compare & Contrast

Steps


•How do I locate and graph points on the plane?

•How do I figure out areas of shapes using grid points?

•Do I see right triangles in situations and use them to my advantage?

•How do right triangles help me figure out unknown distances?

Locating Points

Begins with

Find unknowns

Used to

Right Triangles

Comes from

Area and Length

is rooted in


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Looking for Pythagoras (Rt triangles)

Finding and applying a secret relationship!

(Pythagorean Theorem)

Locating Points

Begins with

Find unknowns

Used to

Right Triangles

Comes from

Area and Length on a grid

is rooted in

Distance

To find

Geometric figures

To define

squares

By looking for

distance

using

√

Which leads to

And the relationship between

legs

hypotenuse

lenghts

angles

Such as



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Comparing and Scaling

Making Comparisons

Finding Percents

•Check up 1*

Using Ratios

Finding Rates

*Check up 2*

Estimating Populations

*Test / Assessment*

Stretching and Shrinking Samples and Populations

Number

Developing special ways of looking at

quantities to(proportional reasoning)

Comparisons

Compare & Contrast

Equivalence


•How can I represent the same data in different ways using percents, ratios, and rates?

•How do I know which comparison (percent, ration, or rate) to use?

•How can I make comparisons?

•How could you evaluate data?

Comparisons

make

Rates

find

Ratios

use

Percents

find

Populations / size

estimate


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X to Y

as X per Y

in tables

expressed

•When is it appropriate to use a ratio?

•How do you compare two or more related measures or counts?

Comparing and Scaling

Developing special ways of looking at quantities

(proportional reasoning)Comparisons

To make

Unit Rates

By finding

using

Percents

By finding

Populations / size

In order to estimate

Which is larger or smaller

How much larger or smaller

To describe

division

using

Ratios

Written as

rounding

X / Y

X:Y

Part to part

Part to whole

Which can be

Two different things

with rules (equations)

as straight lines

scalingusing

ratios

sampling

CONCEPT DIAGRAM




EXPLORE EXAMPLES

Key Words


CONVEY CONCEPT

NOTE KEY WORDS



Measurement Mathematics

In Mathematics, measurement is a about assigning a value to various attributes of an object using units with the same attribute.

Units

Object

Attributes

Value

Standardized Units

Nonstandard Units

Formulas

Treating the object as a whole

20 square feet of carpet

6 inches long

$100 desk

20 % green

Five gallons of paint

Blue carpet

The square box

The brown desk

Sixteen tiles

22 days until break

The tall book

The tall book

Units

Standardized

Whole

Attributes

Value

20 square feet of carpet

22 days until break

Blue carpet

Brown desk

Tall book

Objects

Non-standardized

Formulas

$100 desk

CONCEPT DIAGRAM




EXPLORE EXAMPLES

Key Words


CONVEY CONCEPT

NOTE KEY WORDS



Addition Operation

One operation is addition in which two or more values are combined to create a new value.

New value

combined

2 or more Values

Single digits

Multiple digits

Three values

groups

objects units

Taking away

Single value

2 + 3 = 5

** *** *****

Two cookies were added to a plate of three cookies leaving five cookies on the plate

20 green and 4 red blocks make 24 blocks

4 - 1 = 3

Sixteen tiles

16 school days and 3 weekends mean we have 22 days until break

Plus sign

Equal sign

2 + 3 = 5

4 - 1 = 3

Addition

Subtraction

Operations

Taking away

Combining

Single digits

Multiple digits

Units

Objects

Sixteen tiles

*** *****

Two cookies were taken off a plate of three cookies leaving one cookie on the plate


Main idea

is about…


Essential details

Main idea


Main idea

Square Root

Can be expressed mathematically

√9 = 3 because 3*3 = 9

A = s2 s = √A

Can be found using area of a square

Area of a square is the length of a side multiplied by itself

the length of the side of a square given the area of that square.

The square root of a number is a number that when multiplied by itself will give you the area of a square.


Main idea

is about…


Essential details

Main idea


Main idea

VolumeThe amount of space, or the capacity, of a three-dimensional shape

Rectangular Prism

Base is rectangular

Height is the distance from the base to the top

B x h = l x w x h

Cube

Base is a squareBase is a polygon (triangular, pentagonal, hexagonal)



B x h

where B = 1/2 l * w etc.B x h = l x w x h = s3

Prism (triangular, square, pentagonal, hexagonal)

By recognizing the formula for volume is B * h, I can calculate the volume of any regular prism by substituting the formula for the area of the appropriate shape for B.

Main idea

Essential details

Cylinder

Base is a circle


B x h = pi x r2 x h


Main idea

is about…


Essential details

Proportional Reasoning

The different ways to make comparisons

Ratio

People who preferred Bolda outnumbered those who preferred Nola by a ratio of 3 to 2.

X to Y; X : Y; X/Y

Main idea

Essential details

Rate

Comparison of two different units or objects

20 cookies for 5 children

4 cookies per child

Is a direct comparison of two sets or and average

Tells the scale between two quantities

Main idea

Essential details

Unit rates

X units per object

32 miles per gallon

1.9 children per family

Compares an amount to a single unit

X units per object

X units for Y object

Tells the value or cost for one item

Comparison of two quantities

Different relationships require different comparisons. Therefore, I need to match my comparison to the relationship that is being expressed.


is about…


Main idea


Main idea

Proportional Reasoning

The different ways to make comparisons

Difference

A - B = X

Compares number of parts to a whole

Students who prefer television outnumber those who prefer radio by 20.

3/5 of cola drinkers prefer Coke to Pepsi

X/Y

Tells how many you would have left if you pair them

Fractions

Different relationships require different comparisons. Therefore, I need to match my comparison to the relationship that is being expressed.

Main idea

Essential details

Percents

Compares a part to a whole

28% of people aged 12-17 go camping

Creates a common scale (part of 100) for two data sets

Compares two measures or counts

Tells you how many parts of the whole you have

X%

Time to Think and Ask Questions………..

How can SIM and the CLC help you and your district?

What are your immediate and long term needs?

Opportunities and Possibilities

• Classroom Teacher PD

• School-wide PD

• District -wide opportunity

• Just express your thoughts…….

Professional Development Plan

• Who: Upper Elementary Math Educators• What: Effective Math Instruction using

Content Enhancement Devices• Why: to increase the student performance

and understanding of math concepts related to rational numbers

Professional Development Plan

• How: – Two full days of PD on the purpose and development of the

Unit Organizer Routine and the Concept Mastery Routine, – the participants will implement the routines in their

classroom setting. – This implementation will be monitored and additional

assistance and support will be available in the form of follow up sessions to share struggles and triumphs, polish and refine devices, and support and encourage fellow colleagues in the implementation process.

• With: – Dr. Amy Scheuermann from Bowling Green State University

Objectives of the PD - Participants• Gain a deeper understanding of rational numbers for the purpose of

addressing the educational needs within their classroom.• Explore and examine critical math content and concepts for the purpose of

clarifying and explaining them to their students.• Be able to describe the research support and evidence for the

implementation of both routines.• Be able to identify and name the critical elements of the Unit Organizer

Routine and the Concept Mastery Routine.• Develop a minimum of two devices for each routine for their unique

classroom setting.• Implement a minimum of one device for each routine within their individual

classroom setting.• Be given the opportunity to participate in a research project on the

effectiveness of this professional development model.

Objectives of the PD - Presenter• Provide the background and content knowledge needed to lead and direct the

participants in their development of a deeper understanding of rational numbers.• Offer several resources to aid and assist the participants in their exploration and

examination of critical math content and concepts.• Communicate the research support and evidence of effectiveness for both routines• Convey the critical elements of the Unit Organizer Routine and the Concept Mastery • Offer support, encouragement, suggestions, and guidance during device creation.• Be available to model the routine implementation within each participants’ classroom.• Monitor implementation for the purpose of assessing fidelity (the consistent use of the

critical elements)• Organize an informal research project on the effectiveness of this professional

development model.

Thank You for your time.

Amy ScheuermannAssistant Professor

Bowling Green State University

And

Certified Professional Developer

Center for Research at University of Kansas

Documents

Addressing the Instructional Needs of Diverse Learners