1 A Different….iated Mathematics Classroom Adapted from a presentation by: Dr. Laura Rader May 14...
-
Upload
valentine-booth -
Category
Documents
-
view
217 -
download
2
Transcript of 1 A Different….iated Mathematics Classroom Adapted from a presentation by: Dr. Laura Rader May 14...
1
A Different….iated Mathematics Classroom
Adapted from a presentation by:Dr. Laura Rader
May 14 &15, 2008
2
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?
3
Speak their language!
4
Readiness
Growth
Interest Learning Style
Motivation EfficiencyJudy Rex presentation 2006
5
Readiness
How do you get to know your learners?
How do you use this information?
6
Are they Ready?
7
Readiness
Know where you want students to be
Begin where the students are
Continually assess your students
Keep USEFUL records and data
8
“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?
9
10
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
11
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
12
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
13
“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!”
14
“Have some respect for my learning style!”
15
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
16
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
17
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
18
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
19
Check for Understanding
Thumbs up?
Thumbs down?
Thumbs sideways?
Exit Slips
Homework
Error Analysis
and?
20
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
21
Benefits of DI Decreases behavior problems
Stretches each student
Engages students for learning
Focuses on student rather than teacher
Creates variety
Offers choice
22
23
24
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)
25
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.
26
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?
27
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
1
3
5
2
4
6
28
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
29
Differentiation by ReadinessMath - Algebra Operations - Rainbow
Red Orange Yellow Green Blue Purple
1
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
2
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
3
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 )
4
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
5
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.
6
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?
7
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)?
8
X X X X XWhat does relative frequency mean?
30
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