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 cards Activity: 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 MotivationEfficiency Judy 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?

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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 Interest Math 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 MI, Sternberg, modality & array interaction surveys ACTIVITY Online MI with graphs global vs sequential Sternberg’s survey MI survey & others sensory modality personality assessment 4mat personality type – group dynamics

17 Multiple Intelligences Product 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 Theory

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 Differentiation Choices of books Homework options Use of working buddies Varied journal Prompts Orbitals Varied pacing with anchor options Student-teaching goal setting Work alone / together Whole-to-part and part-to-whole explorations Flexible seating Varied computer programs Design-A-Day Varied Supplementary materials Options for varied modes of expression Varying scaffolding Let’s Make a Deal projects Computer mentors Think-Pair-Share by readiness, interest, learning profile Use of collaboration, independence, and cooperation Open-ended activities Mini-workshops to reteach or extend skills Jigsaw Negotiated Criteria Explorations by interests Games to practice mastery of information Multiple levels of questions High-Prep Differentiation Tiered activities and labs Tiered products Independent studies Multiple texts Alternative assessments Learning contracts 4-MAT Multiple-intelligence options Compacting Spelling by readiness Entry Points Varying organizers Lectures coupled with graphic organizers Community mentorships Interest groups Tiered centers Interest centers Personal agendas Literature Circles Stations Complex Instruction Group Investigation Tape-recorded materials Teams, Games, and Tournaments Choice Boards Think-Tac-Toe Simulations Problem-Based Learning Graduated Rubrics Flexible reading formats Student-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

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24 Fair Game Dilemma Tiered 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 building a framework of understanding Think about your students/use assessments readiness range interests learning profile talents skills reading thinking information 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

28 Differentiation by Learning Style Math - 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 Readiness Math - Algebra Operations - Rainbow

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