addressing the instructional needs of diverse learners
DESCRIPTION
Addressing the Instructional Needs of Diverse Learners. with Strategic Teaching Presented by Amy Scheuermann Bowling Green State University January 11, 2008. Everyday……. More than 3000 adolescents dropout of school……that’s 540,000+ per year!. Some Pressing Problems. - PowerPoint PPT PresentationTRANSCRIPT
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
Eq
uiv
alen
t S
core
s o
n D
ST:
R
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
LAST UNIT /Experience CURRENT UNIT NEXT UNIT /Experience
UN
IT S
EL
F-T
ES
TQ
UE
ST
ION
S
is about...
UN
ITR
EL
AT
ION
SH
IPS
UNIT SCHEDULE UNIT MAP
CURRENT UNIT1 32
4
5
6
7
8
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
1/29 Cooperative groups - over pp. 210-225
"Influential Personalities" project due
1/30 Quiz
2/2 Cooperative groups - over pp. 228-234
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
NE
W
UN
IT
SE
LF
-TE
ST
QU
ES
TIO
NS
Expanded Unit Map is about...
9
10
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
Always Present Sometimes Present Never Present
Examples: Nonexamples:
TIE DOWN A DEFINITION
EXPLORE EXAMPLES
Key Words
PRACTICE WITH NEW EXAMPLE
CONVEY CONCEPT
NOTE KEY WORDS
OFFER OVERALL CONCEPT
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
NAMEDATEThe Unit Organizer BIGGER PICTURE
LAST UNIT/Experience NEXT UNIT/Experience U
NIT
SE
LF
-TE
ST
Q
UE
ST
ION
S
is about...
UN
IT
RE
LA
TIO
NS
HIP
S
UNIT SCHEDULE UNIT MAP
CURRENT UNIT1 32
4
5
6
7
8
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
NAMEDATEThe Unit Organizer BIGGER PICTURE
LAST UNIT/Experience NEXT UNIT/Experience U
NIT
SE
LF
-TE
ST
Q
UE
ST
ION
S
is about...
UN
IT
RE
LA
TIO
NS
HIP
S
UNIT SCHEDULE UNIT MAP
CURRENT UNIT1 32
4
5
6
7
8
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
Problem and Solution
•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
NAMEDATEThe Unit Organizer
NE
W
UN
IT
SE
LF
-TE
ST
QU
ES
TIO
NS
Expanded Unit Map is about...
9
10
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
NAMEDATEThe Unit Organizer BIGGER PICTURE
LAST UNIT/Experience NEXT UNIT/Experience U
NIT
SE
LF
-TE
ST
Q
UE
ST
ION
S
is about...
UN
IT
RE
LA
TIO
NS
HIP
S
UNIT SCHEDULE UNIT MAP
CURRENT UNIT1 32
4
5
6
7
8
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
Problem and Solution
•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
NAMEDATEThe Unit Organizer
NE
W
UN
IT
SE
LF
-TE
ST
QU
ES
TIO
NS
Expanded Unit Map is about...
9
10
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
Always Present Sometimes Present Never Present
Examples: Nonexamples:
TIE DOWN A DEFINITION
EXPLORE EXAMPLES
Key Words
PRACTICE WITH NEW EXAMPLE
CONVEY CONCEPT
NOTE KEY WORDS
OFFER OVERALL CONCEPT
CLASSIFYCHARACTERISTICS
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
Always Present Sometimes Present Never Present
Examples: Nonexamples:
TIE DOWN A DEFINITION
EXPLORE EXAMPLES
Key Words
PRACTICE WITH NEW EXAMPLE
CONVEY CONCEPT
NOTE KEY WORDS
OFFER OVERALL CONCEPT
CLASSIFYCHARACTERISTICS
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
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
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.
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
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)
Height is the distance from the base to the top
Height is the distance from the base to the top
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
Height is the distance from the base to the top
B x h = pi x r2 x h
The FRAME RoutineKey Topic
Main idea
is about…
So What? (What’s important to understand about this?)
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.
The FRAME RoutineKey Topic
is about…
So What? (What’s important to understand about this?)
Main idea
Essential details Essential details
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