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A Different….iated Mathematics Classroom

Adapted from a presentation by:Dr. Laura Rader

May 14 &15, 2008

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Teachers modify – Content: the what …..examples?– Process: the how …..examples?– Product: the vehicle used to demonstrate

understanding …..examples?Activity: Create Scaffolded Question set of 15 questions on cardsActivity: Create A Jeopardy game using Jeopardy blank, Internet and resources

Students vary in– Readiness: what is my understanding now?– Interest: why should I want to do this?– Learning Profile: how do I best learn and

understand?

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Speak their language!

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Readiness

Growth

Interest Learning Style

Motivation EfficiencyJudy Rex presentation 2006

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Readiness

How do you get to know your learners?

How do you use this information?

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Are they Ready?

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Readiness

Know where you want students to be

Begin where the students are

Continually assess your students

Keep USEFUL records and data

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“Effective differentiated classrooms include many times in which whole-class, non-differentiated fare is the order of the day.

Discuss

Modify a curricular element only when (1) you see a student need and (2) you are convinced that modification increases the likelihood that the learner will understand important ideas and use important skills more thoroughly as a result” The differentiated Classroom, Tomlinson p11

Discuss: Reasonable?

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Ways to incorporate interest

Create interest within a lesson– Give choice within content– Give choice for the final product

Use general interests– Incorporate interests outside of school.

For example: sports, clubs, parents, history, news

Hook student interest through relevance– Applications, connections with other sections

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Differentiation by InterestMath

Sequence of Numbers –Real Number System Choice Board

Write a poem about the number groups or sequence of numbers

Sing a song/rap about the groups or sequence of numbers

Draw a picture that represents the grouping of numbers

Explain and describe the problem generated from a geometric representation of an irrational number using the Pythagorean Theorem

Construct a number line with only decimals and fractions with different denominators

Web search and report- if it’s not a Real Number, what is it?...how do we sequence non Real numbers

Write a paragraph about the importance of understanding the ordering of numbers in elation to Money/Finances and what number groups are associated with money

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Learning Style

What type of learner are you?

How do you know?

To what extent is your learning style reflected in your teaching style?

Rodney S… Trumpet

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“As we start a new school year, Mr. Smith, I just want you to know that I’m an Abstract-Sequential learner

and trust that you’ll conduct yourself accordingly!”

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“Have some respect for my learning style!”

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Learning Style

Conduct surveys to collect data– Multiple intelligences: musical, verbal/linguistic, logical

interpersonal, intrapersonal, kinesthetic, visual/spatial– Sternberg: creative, practical, analytical– Modality: visual, verbal, kinesthetic– Jung, 4MAT, Array: social interaction and personality

Use data to purposefully group students– Like grouping– Unlike grouping– Whole group

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Resources for learning profiles www.e2c2.com/fileupload.asp

MI, Sternberg, modality & array interaction surveys http://www.learning-styles-online.com/ ACTIVITY Online

MI with graphs http://www.engr.ncsu.edu/learningstyles/ilsweb.html

global vs sequential http://www.rrcc-online.com/~psych/LSInventory.html

Sternberg’s survey http://ttc.coe.uga.edu/surveys/

MI survey & others http://www.brookhavencollege.edu/learningstyle/modality_test.html

sensory modality http://www.humanmetrics.com/cgi-win/JTypes1.htm

personality assessment http://www.cse.fau.edu/~maria/COURSES/CAP5100-UI/LearningStyles.html

4mat personality type – group dynamics

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Multiple Intelligences Multiple Intelligences Product GridProduct Grid Categorizes different

products under separate headings

Many are listed in more than one column and may look different due to the approach taken

Howard Gardner’s Multiple-Intelligences Howard Gardner’s Multiple-Intelligences TheoryTheory

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Things to Remember

Know your learner; Use the information DI does not have to be a project You don’t have to use a specific DI tool You don’t have to do DI all the time

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Check for Understanding

Thumbs up?

Thumbs down?

Thumbs sideways?

Exit Slips

Homework

Error Analysis

and?

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Begin Slowly – Just Begin!

Low-Prep DifferentiationChoices of booksHomework optionsUse of working buddiesVaried journal PromptsOrbitalsVaried pacing with anchor optionsStudent-teaching goal settingWork alone / togetherWhole-to-part and part-to-whole explorationsFlexible seatingVaried computer programsDesign-A-DayVaried Supplementary materialsOptions for varied modes of expressionVarying scaffoldingLet’s Make a Deal projectsComputer mentorsThink-Pair-Share by readiness, interest, learning profileUse of collaboration, independence, and cooperationOpen-ended activitiesMini-workshops to reteach or extend skillsJigsawNegotiated CriteriaExplorations by interestsGames to practice mastery of informationMultiple levels of questions

High-Prep DifferentiationTiered activities and labsTiered productsIndependent studiesMultiple textsAlternative assessmentsLearning contracts4-MATMultiple-intelligence optionsCompactingSpelling by readinessEntry PointsVarying organizersLectures coupled with graphic organizersCommunity mentorshipsInterest groupsTiered centersInterest centersPersonal agendasLiterature CirclesStationsComplex InstructionGroup InvestigationTape-recorded materialsTeams, Games, and TournamentsChoice BoardsThink-Tac-ToeSimulationsProblem-Based LearningGraduated RubricsFlexible reading formatsStudent-centered writing formats

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Benefits of DI Decreases behavior problems

Stretches each student

Engages students for learning

Focuses on student rather than teacher

Creates variety

Offers choice

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Fair Game DilemmaTiered Math Assignment

Tier ?

A few students want me to play a game with them. They will give me a dime for each odd sum I roll with two die. I have to give them a dime for each even sum they roll with two die. I think I’m going to get cheated! I noticed that I can’t roll one of my odd numbers – 1! I only get a choice of 5 odd numbers (3, 5, 7, 9, 11) but they will get a choice of 6 even numbers (2, 4, 6, 8, 10, 12). Should I play this game with the students? Using as much mathematical language and representation as you can, show me that this is or is not a fair game.

Data Analysis and Probability Standard for Grades 6-8 (NCTM)

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Tiering Continued…..

Tier ?

A few students want me to play a game with them. They will give me a dime for each odd sum I roll with two die. I have to give them a dime for each even sum they roll with two die. I think I’m going to get cheated! Should I play this game with the students? Using as much mathematical language and representation as you can, show me that this is or is not a fair game.

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Tiering Continued……

Tier ?A few students want me to play a game with them. They will give me a dime for each odd sum I roll with two die. I have to give them a dime for each even sum they roll with two die. I think I’m going to get cheated! I noticed that I can’t roll one of my odd numbers – 1! I only get a choice of 5 odd numbers (3, 5, 7, 9, 11) but they will get a choice of 6 even numbers (2, 4, 6, 8, 10, 12). List all of the possible ways of getting each sum using the digits 1-6. Then determine the probability of getting an even and odd sum. Use the information to draw a conclusion, is this a fair game to play with the students?

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Developing a Tiered Activity

Select the activity organizer•concept•generalization

Essential to buildinga framework ofunderstanding

Think about your students/use assessments

• readiness range• interests• learning profile• talents

skillsreadingthinkinginformation

Create an activity that is• interesting• high level• causes students to use key skill(s) to understand a key idea

Chart the complexity of the activity

High skill/Complexity

Low skill/complexity

Clone the activity along the ladder as needed to ensure challenge and success for your students, in

• materials – basic to advanced• form of expression – from familiar to

unfamiliar• from personal experience to removed

from personal experience•equalizer

Match task to student based on student profile and task requirements

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Differentiation by Learning StyleMath - Exponential Equations

Global: (Whole to Parts)– Skim chapter to explore exponential equations– Show examples of when exponentials are used– Show connection to linear equations/compound interest– Begin defining parts of linear equations

Sequential: (Parts to Whole)– Define parts of linear equation– Show possible graphs– Define parts of exponential equation– Show possible graphs– Explain differences and similarities

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Differentiation by ReadinessMath - Algebra Operations - Rainbow

Red Orange Yellow Green Blue Purple

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3 ( 2 + 4 ) 5 1000 - 3 x 7 2 4 + 3 ( 7 + 9 ) 10 + 3 x 4 2 6 x 2 3 85 + 9 x 2

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10 + 20 Ö ( 2 + 3 6) 7 + 9 ( 2 + 3 ) 6 + 5 ( 4 2 ) 2 3 ( 4 3 - 2 ) 2 3 ( 2 + 4 ) 2 1000 - 3 x 7 2

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2[4+6(35-4)]-3(30-3) [ (3-1) 3 + (3-1) 4 ] 2 3 [2 + 4 ( 5 + 2 ) ] 10 + 20 Ö ( 2 + 3 6) 7 + 9 ( 2 + 3 )

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X4X + 3Y

Evaluate ifX = 10 and Y = 7

27 - 2R - REvaluate if R = 3

4 + 3PEvaluate if P = 7

3X + 9Evaluate if X= 5

2WEvaluate if W = 10

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X X

7% = 7 x 0.0119% = 19 x 0.01

4.2% = 4.2 x 0.01Find the pattern.

10 x 0 = 08.9 x 0 = 015/5 x 0 = 0

Find the pattern.

x + y = y + xGive one example.

x/x = 1Give one example.

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X X XWhat is the P(King) in a

deck of cards?What is the

P(rolling 1, 2, 5, or 6)?What is the probability of

flipping a heads?

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X X X XIf the P(A) = 1/4 and P(B) = 1/3, then which event is

more likely to occur?

If P(have a test) = 80%, then what is

P(not have a test)?

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X X X X XWhat does relative frequency mean?

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Differentiated Instruction (DI): a Definition

“Differentiated instruction is a teaching philosophy based on the premise that teachers should adapt instruction to student differences….Teachers should modify their instruction to meet students’ varying readiness levels, learning preferences, and interests.”– Carol Ann Tomlinson, Associate Professor

University of Virginia