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Bellringer: Type of Audience Member

Use adhesive dots to indicate which type of audience member you are currently. Please vote only once by placing dot on poster.

Real Learner

Vacationer

Prisoner

Differentiated Instruction in the Upper Elementary Math

ClassPresented by

Melissa Petrilak

Agenda

• Addressing diverse learners

• Identifying the Principles of Differentiated Instruction

• Applying brain research into

practice

• Identifying ways to assess

student learners

Magnetic Quotes

• Walk around the room and read the statements on the wall.

• Choose a statement that attracts you and stand near that statement.

• Why did you select this statement?

• How does this statement connect to what you know about differentiated instruction or what you think about differentiated instruction.

“Brain Dumps”

1. Summarize ideas up to now.

2. Make a connection to your current professional development plan.

3. Plan how to use the ideas presented in your current setting.

4. Name one important piece of information that you heard up to this point that made you think differently about differentiated instruction.

5. Name one important piece of information you heard so far that you can apply to your position immediately.

6. Name one thing we discussed up to now that you want to hear more about.

Processing Time

• Guidelines for direct instruction time:

• Grades: K to 2 5 to 7 minutes

3 to 7 8 to 12 minutes

8 to 12 12 to 15 minutes

3 Facts and a Fiction

Use index card in your folders!

Can you guess the fiction statement?

1. I rode a camel.

2. I met a famous actor in a grocery store.

3. I drove a golf cart in my prom gown.

4. I was part of a seventh-inning stretch ceremony at a Red Barons game.

What is Differentiated Instruction

What it is…. What it isn’t….• Use only the post-it notes at your table.

• Write your thoughts as to what

Differentiated Instruction is…

and what it isn’t….

• Post the notes on your table in

random order.

• You will visit another table and

sort your post-it notes according

to what Differentiated Instruction

is and isn’t.

As you know, students come to our classrooms with a variety of:

Summary Statements About LearningSummary Statements About Learning

1. People learn what is personally meaningful to them.

2. People learn when they accept challenging but achievable goals.

3. Learning is developmental.

4. Individuals learn differently.

5. People construct new knowledge by building on their current knowledge

6. Much learning occurs through social interaction.

7. People need feedback to learn.

8. Successful learning involves use of strategies--which themselves are learned.

9. A positive emotional climate strengthens learning.

10. Learning is influenced by the total environment.Powerful Learning by Ron Brandt

Let’s at strategies that get the most bang for the buck…

Use the handout provided within the packet to identify where the instructional strategies fall

within the Learning Pyramid.

Practice by doing

Demonstration

Teach another

Audio/Visuals

Discussion

Reading

Lecture

Rank the strategies on the right of the pyramid from LEAST effective (top of pyramid) to most effective (bottom).

Try to guess the percentage of information a “typical” student may retain for each.

Least

Effective

Most Effective

Effective Instructional Strategies

Effective Instructional Strategies

How’d you do?

Lecture 5%

Reading 10%

Audio/Visuals 20%

Demonstrations 30%

Discussion 50%

Practice by doing 75%

Teach others/immediate use of learning 95%

Placemat Activity

• The purpose of this activity is to reflect on our current professional practice.

• Answer the questions individually as presented on the following slides.

• Get together with your group and complete the “placemat.”

• Be sure to add all of your answers on the placemat and then determine the “big idea” or main focus of your findings in the middle of the placemat. Record your summary using

1 – 2 sentences in the center circle of your placemat.

Addressing Diverse Learner Needs

• List the 3 instructional practices you use most often in your math class.

1.

2.

3.

Self-reflection on Professional Practice


• Describe the unique learning needs of one of two of the students you have in your math class.



• How do you currently address the needs of students with diverse learning profiles?



Identify the factors that make it difficult for you to adapt your instruction and/or the

curriculum for diverse learners.


Differentiation of Instructionis a teacher’s response to learners’ needs

guided by general principles of differentiationsuch as:

respectful tasks flexible groupingongoing assessment

and adjustmentteachers can differentiate

Content Process Product

according to students’

Readiness Interests Learning Profile


Teachers Can Differentiate

Adapted from The Differentiated Classroom: Responding to the Needs of All Learners (Tomlinson, 1999)

ContentContent• What is Taught and Learned:

Relevant Helps students understand themselves and

their lives Authentic or “real” Can be used immediately

Differentiating by ContentWays to Differentiate Content

using Investigations’ Multiplication Compare, Unit 1, Sessions 2.3- 2.5

Games are a great way to differentiate content. Listed below are descriptions of suggested games dealing with using the same manipulatives, but adapting the goal of their intended use. The grade level expectation is to find the greater product

of 2 cards for each player.

Materials for Number Puzzles: Multiplication Compare Cards, 1 deck per pair, Resource Binder M44 - M45

Digit Cards, Resource Binder M48-M50, WILD CARDS removed Each pair of players needs Multiplication Compare Recording Sheet

Multiplication Compare, Resource Binder M46

On-Grade Level: Multiplication Compare with all Compare Cards Directions:

Each game has three rounds.

1. Divide the deck of cards evenly so that both players have the same number of cards. Place the cards facedown in a stack in front of the players.

2. Each player turns over the top two cards in his or own stack. 3. Determine which player has the greater product. Discuss why. 4. The player with the greater product takes all of the cards that have been turned over and places them at the

bottom of his/her stack of cards. 5. If both players have turned over cards that have equal products, each player turns over two new cards. The

player with the greater product takes all of the cards. 6. Play continues until one player has all of the cards or the player with more cards wins if given a set amount of

time to play game.

Above-Grade Level: Multiplication Compare with Digit Cards w/o 0 cards

Directions: Each game has three rounds.

1. Divide the deck of cards evenly so that both players have the same number of cards. Place the cards facedown

in a stack in front of the players. 2. Each player turns over the top four cards in his or own stack to create two 2-digit numbers. 3. Determine which player has the greater product. Discuss why. 4. The player with the greater product takes all of the cards that have been turned over and places them at the

bottom of his/her stack of cards. 5. If both players have turned over cards that have equal products, each player turns over four new cards. The

player with the greater product takes all of the cards. 6. Play continues until one player has all of the cards or the player with more cards wins if given a set amount of

time to play game.

Below-Grade Level: Multiplication Compare with Digit Cards w/ 0 cards Directions:

Each game has three rounds. 1. Divide the deck of cards evenly so that both players have the same number of cards. Place the cards

facedown in a stack in front of the players. 2. Each player turns over the top two cards in his or own stack. 3. Determine which player has the greater product. Discuss why. 4. The player with the greater product takes all of the cards that have been turned over and places them at the

bottom of his/her stack of cards. 5. If both players have turned over cards that have equal products, each player turns over two new cards.

The player with the greater product takes all of the cards. 6. Play continues until one player has all of the cards or the player with more cards wins if given a set amount

of time to play game.

ProcessProcess Blurred line between content and process

Often used as a synonym for “activities”

Begins when the student starts making personal sense out of information, ideas, and skills

Differentiating by Process Ways to Differentiate Process

using Investigations Games are also a great way to differentiate process. Listed below are descriptions of ways to differentiate the scoring of Close to 1,000. The materials for the game stay the same, but how the game is scored varies.

Scoring Variation 1: Write the score with a + or – sign to show the direction of your total from the target number. Goal is to get a total score for five rounds that is as close to 0. Scoring Variation 2: To play with 3-digit numbers, deal out 8 cards. Each player uses only 6 cards to make two numbers whose difference is as close to 0 as possible. For 4-digit numbers, deal out 10 cards and each player uses eight of them. Play five rounds, and the lowest total score wins. Scoring Variation 3: The rules of play remain the same; only the scoring is modified. If the player’s total is above 1,000, the score is recorded as positive. If the score is below 1,000, the score is recorded as negative. The player with the grand total closest to zero after five rounds is the winner.

ProductProduct Something students produce to exhibit major portions

of learning

Not pieces of work students produce during the course of a day

Vehicle through which a student shows what (s)he understands and can do as a result of learning over time

Differentiate by ProductWays to Differentiate Product

using Investigations

Game 1: Decimal Double Compare Materials: Decimal cards, set A (2 sets)

Mix the cards and deal them evenly so that each player has the same number of cards. Place the cards facedown in front of you.

Each player takes turns over the top two cards in his or her stack. Look at your two numbers and your partner’s two numbers. Decide which player

has the larger sum. Whoever has the larger sum takes all of the cards that have been turned over and

places them at the bottom of his or her stack. If both sums are the same, each player keeps his or her cards. Turn over the next

two cards. Play for a given amount of time or until one player has all of the cards. The player

with more cards wins,

Game 2: Decimals In Between Materials: Decimal cards, sets A and B

Find the three game cards labeled 0, ½, and 1. Place these cards on a playing table.

Mix the Decimal cards. Deal six to each player. Players take turns placing a card so that it touches another

card in one of these ways: o To the right of 0 o On either side of ½ o To the left of 1 o On top of any equivalent

As you play a card, read the decimal aloud. Cards must be placed in increasing order, from left to right.

A card may not be placed between two cards that are touching.

In the example above, the 0.025 card may not be placed between the 0 and 0.05

cards. It cannot be played in this round. Your goal is to place as many cards as you can. The round is over when neither

player can place any more cards. Your score is the number of cards left in your hand.

o At the end of the round, the table may look like this:

In this sample round, Player 1 could not play 0.25 or 0.6. Player 1 has a score of 2.

Player 2 could not play 0.025. Player 2 has a score of 1. At the end of five rounds, the player with the lower score wins.


According to Students’

Readiness InterestLearningProfile



What students learn How students learns How students show what they’ve learned











Knowledge, skills… What they like… How best they learn

Ways a class can be grouped

• Readiness

Student’s understanding, ability, and/or skill

of a given topic

• Interest

Student’s attraction and enthusiasm in relation to

a particular subject or skill

• Learning Style

Student’s particular approach to learning that is influenced by sensory, cognitive, and multiple

intelligence styles as well as gender and culture.

Flexible Grouping

Should be Purposeful: May be based on student interest, learning

profile, and/or readiness

May be based on needs observed during

learning times

Geared to accomplish curricular goals (K-U-D)

Implementation: Purposefully plan using information collected-interest surveys, learning profile inventories, exit cards,

quick writes, observations

List groups on an overhead or place in folders or mailboxes

“On the Fly” as invitational groups

Caution: Avoid turning groups into tracking situations

Provide opportunities for students to work within a variety of groups

Practice moving into group situations and assuming roles within the group

“Brain Dumps”







Break

Welcome Back

Find Someone Who…

When you find someone in the class who matches the description written in the box, have him/her sign their name in the box under the description. The first person to get five filled boxes across, down, or diagonal wins Bingo. You can only use a person’s name once. Good luck!

Can hum something by

Mozart (Music Smart)

Can do a simple dance step

(Body Smart)

Can recite four lines from a

poem (Word Smart)

FREE

Can briefly share a recent dream.

(Self-Smart)

Can draw a picture of a

horse (Picture Smart)

Can honestly say she is relaxed

and comfortable related to other people during this exercise.

(People Smart)

Can name five different types of birds (or trees)

that are found in the immediate

area. (Nature Smart)

Can explain why the sky is

blue. (Logic Smart)

FREE

FREE

Prefers to work in groups.

( People Smart) FREE

Loves to work with computers and calculators. (Logic Smart)

Keeps a diary or a daily journal. (Self- Smart)

Can name the book they are

reading now for pleasure.

(Word Smart)

Tells you what is on the picture of a jigsaw puzzle

they did recently. (Logic Smart)

Knows the words to a lot of songs. (Music Smart)

Takes photos where they go.

(Picture Smart)

Has a good imagination.

(Picture Smart)

Is designing a piece of jewelry. (Picture Smart)

FREE

Does a newsletter for

some organization.

(Word Smart)

Plays in a band. (Music Smart)

Loves to paint in their spare time. (Picture Smart)

Real LearnerVacationerPrisoner

Differentiation in Action Role Play

Close to 1,000 Close to 100 Close to 7,500

Teachers can differentiate: content, process, product

According to student: readiness, interest, learning profile

Based on the basic principles of differentiation:

Respectful Tasks

• On-going Assessment

• Flexible Grouping

“Silent Sort”

Sort the 9 cards describing the Guiding Principles of Differentiated Instruction according to :

• Flexible Grouping

• Ongoing Assessment

• Respectful Tasks

THE NINE PRINCIPLES

• 1. Learning experiences are based on student readiness, interest and learning style (profile).

• 2. Assessment of student needs is ongoing, and tasks are adjusted based on assessment data.

• 3. All students participate in respectful work.

THE NINE PRINCIPLES

• 4. The teacher is primarily a coordinator of time, space, and activities rather than a provider of information.

• 5. Students work in a variety of group configurations. Flexible grouping is evident.

• 6. Time use is flexible in response to student needs.

THE NINE PRINCIPLES

• 7. The teacher uses a variety of instructional strategies to help target instruction to student needs.

• 8. Clearly established criteria are used to help support student success.

• 9. Student strengths are emphasized.

Analyzing the Role of the Teacher in a Differentiated Classroom

Examples of differentiating for student interest, readiness or learning profile.

Characteristics of a Teacher in a

Differentiated Classroom

Examples of the basic principles of differentiation:Respectful TasksOn-going AssessmentFlexible Grouping

Examples of ways that the teacher pre-assesses his students.

School of Rock

After the Movie

Each person in your group take two pennies from the “Two Cents Worth” jar.

In your group discuss….

• Examples of differentiating for student interest, readiness or learning profile.

• Characteristics of a Teacher in a Differentiated Classroom

• Examples of the basic principles of differentiation:

• respectful tasks, on-going assessment, and flexible grouping

• Examples of ways that the teacher pre-assesses his students.

• As you share your thought, return one penny to the jar for each thought your share.

Brain-Based

Learning

See the Brain Quiz worksheetI can’t

believe I make 3000 nontrivial decisions each day!

“Keys” to Retention and Recall

• Say What?

• So What!

“It” has to make sense to you.

“It” has to be relevant to you.

• Gifted Students- take 8 repetitions before information is internalized

• Average Students - take 36 - 40 repetitions before information is internalized

• Special Education Students - take 70 - 250 repetitions before information is internalized

Why is repetition so important?

Physical Characteristics

Movement

• The oxygen link

• When to use itPrior to instructionDuring instructionAfter instruction

From A Celebration of Neurons, Robert Sylwester, 1995

“Neurons that fire together, survive together and wire together.”

(Siegel, 2000)

So, what are the barriers to working memory?

• Cocktail party effect:

• M Space:

DV DJF K FB IM TV

Sign you name as if signing a check. Now, cross your legs, rotate feet counter clockwise and sign your name.

Can you recall the letters?

• Short-term memory appears to develop with age.

• Adults’ working memory can hold 7 bits of information (plus or minus 2).

• A five-year old’s working memory can hold 2 bits of info (plus or minus 2)

DV DJF K FB IM TV

DVD JFK FBI MTV

Lost

Lost

Long

Term

Memory

Building

Networks

Networks Extended

How the Brain Processes Information

Senses Register

Information

Areas in the Brain

Filter Information

Emotion Meaning

Networks Strengthened

Time for a “Brain Dump”







Essential Skills for Differentiated Instruction

Know Your Students Thoroughly

Consistent Use of High Leverage Instructional

Strategies

Thorough Knowledge of the Curriculum

Effective

Management

Strategies

Strategies to Assess the Learners

• What Do I Assess? InterestsAbilitiesRate of learningWork/learning styles and strengthNeeds

Sternberg’s Three Intelligences

Creative Analytical

Practical

•We all have some of each of these intelligences, but are usually stronger in one or two areas than in others.

•We should strive to develop as fully each of these intelligences in students…

• …but also recognize where students’ strengths lie and teach through those intelligences as often as possible, particularly when introducing new ideas.

Sternberg Survey

Which “intelligence” am I if I like…

• Designing new things

• Coming up with ideas

• Using my imagination

• Playing make-believe and pretend games

• Thinking of alternative solutions

• Noticing things people usually tend to ignore

• Thinking in pictures and images

• Inventing (new recipes, words, games)

• Supposing that things were different

• Thinking about what would have happened if certain aspects of the world were different

• Composing (new songs, melodies)

• Acting and role playing

I AM CREATIVE!

Sternberg & Grigorenko, 2000


• Analyzing characters when I’m reading or listening to a story

• Comparing & contrasting points of view

• Criticizing my own & others’ work

• Thinking clearly & analytically

• Evaluating my & others’ points of view

• Appealing to logic

• Judging my & others’ behavior

• Explaining difficult problems to others

• Solving logical problems

• Making inferences & deriving conclusions

• Sorting & classifying

• Thinking about things

I AM ANALYTICAL!



• Taking things apart and fixing them

• Learning through hands on activities

• Making and maintaining friends

• Understanding and respecting others

• Putting into practice things I learned

• Resolving conflicts

• Advising my friends on their problems

• Convincing someone to do something

• Learning by interacting with others

• Applying my knowledge

• Working and being with others

• Adapting to new situations

I AM PRACTICAL!


Why Do This?

• It helps you get to know your students

• It helps you and your students know their learning styles

• Planning and teaching become more “efficient”

• It is more proactive than waiting for students’ strengths to emerge

• Because “interest” is connected to “motivation!” And motivation is essential to learning!

Math Style

Self-Expressive

Style

Mastery Style

Understanding

Style

Interpersonal

Style

Gardner’s Multiple Intelligences

Verbal/Linguistic Musical/Rhythmic

Logical/Mathematical Interpersonal

Visual/Spatial Intrapersonal

Body/Kinesthetic Naturalist

Learner Profile Card

Auditory, Visual, Kinesthetic

Modality

Multiple Intelligence Preference

Gardner

Analytical, Creative, Practical

Sternberg

Student’s Interests

Math Style

Gender Stripe

Nanci Smith,Scottsdale,AZ

Grouping using Sternberg’s Intelligences

• AnalyticalYour friend needs a really clear step-by-step

explanation of how to count money. Please create one.

• PracticalShow how someone at school, home, or in our

town how to count money. Help us see how and why this person needs to know how to count money.

• CreativeCreate a brand new money system and tell about

the names of the coins and the value of each.

•Show the parts of _____________ and howthey work.

•Explain why _____________ works the wayit does.

•Diagram how _________ affects ________.•Identify the key parts of _______________.•Present a step-by-step approach to _____.

For ANALYTICAL Thinkers

Analytical = Linear – Schoolhouse Smart -- Sequential

•Demonstrate how someone uses ________ in their life or work.•Show how we could apply ______ to solve this real life problem: _________________.•Based on your own experience, explain how _________________ can be used.•Here’s a problem at school, ________.•Using your knowledge of __________, develop a plan to address the problem

For PRACTICAL Thinkers

Practical = Street Smart – Contextual – Focus on Use

•Find a new way to show _____________.•Use unusual materials to explain ___________.•Use humor to show ____________________.•Explain (show) a new and better way to ______.•Make connections between _____ and _____ to help us understand ____________.•Become a _____________ and use your “new” perspective to help us think about __________.

For CREATIVE Thinkers

Creative = Innovator – Outside the Box – “What if?” – Improver

Applying Differentiation Instruction

Differentiated Instruction Application

How could I apply this to my classroom?

DI Strategy

1. 2. 3.

1. 2. 3.

1. 2. 3.

1. 2. 3.

Magnetic Quotes

Cooperative Learning (Placemat)

Preassessment (Brain Quiz)

3 Facts and a Fiction

Differentiated Instruction Application

How could I apply this to my classroom?

DI Strategy

1. 2. 3.

1. 2. 3.

1. 2. 3.

1. 2. 3.

Brain Dump

Dot Voting

Learner Profile Cards Learner Profile Card

Gender Stripe

Auditory, Visual, Kinesthetic

Multiple Intelligence Preference

Student’s Interests

Favorite Subject

NOTE: Put the student’s name on the back of the card so decisions can initially be made without knowing the particular student.

Favorite Color

3

Exit Card

Planning into Action

Differentiated Instruction using

Investigations Putting Planning into Action

My Class Currently

Please use the space provided to describe what instructional strategies you have used with your class.

“Knowledge is of little value unless it is passed on to someone.

It has been said that if we do not share the knowledge with a week, it will, more likely, become obsolete.”

Author unknown

Session 1 What I plan to do prior to session 2 with my students

What did I implement? What were the successes? What would I try differently?

Listed below are some suggestions

Create a math style survey for your grade level based on the information from the handout.

Create a Sternberg Intelligence survey for your grade level. Create a “Fantastic, Way Cool” graph based on concept mastery for one math

unit. Create several more brain processing strategies for use with your students. Create activities that are differentiated either by content, process, or product. Create a lesson by grouping students by readiness, interest, or learning

profile.

Name _______________________________ Grade Level ________________ School __________________________________________________________

Time for a “Brain Dump”







Documents

Bellringer: Type of Audience Member Use adhesive dots to indicate which type of audience member you are currently. Please vote only once by placing dot