teaching math for each and every student! - e2c2.come2c2.com/files/hs di math...

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H E M P F I E L D A R E A S C H O O L D I S T R I C T

H I G H S C H O O L M A T H T E A C H E R SN O V E M B E R 1 0 , 2 0 1 7

N A N C I S M I T H , P H . D .N A N C I @ E 2 C 2 . C O M

@ D O C N A N C I

Teaching Math For Each and Every Student!

Our Agenda:

1. Some Set Up and Big Ideas …2. Engaging Students: Quick Ideas3. Differentiating Mathematics:

1. Readiness2. Interest3. Learning Profile

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Our goal..We must change our students from being “problem

performers” to “problem solvers!”Problem Performers Problem solvers

Do it just like the teacher did.

Think before you start.

Write your numbers straight.

Draw a picture to understand the problem.

Don’t talk when you work. That’s cheating.

Explain how you solved it, using math vocabulary.

Find an answer and move on.

Check your work. Do it a different way.

The Big Picture: Standards for Mathematical Practice1. Make sense of complex problems and persevere

in solving them. 2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning.

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“In times of change, the learners inherit the future while the learned find themselves beautifully equipped to deal with a world thatno longer exists.”

Eric Hoffer

The most basic idea in the learning of mathematics is

Mathematics makes sense! John Van de Walle

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MyAppointmentClock

Round the Clock Learning Buddies

Makeanappointmentwith12differentpeople– oneforeachhourontheclock.Besureyoubothrecordtheappointmentonyourclocks.Onlymaketheappointmentifthereisanopenslotatthathouronbothofyourclocks.

Tapethispaperinsideanotebook,ortosomethingthatyouwillbringtoclasseachday.

Suggestions for the Clock

� About the third week of school, pass out the clocks. Students make “appointments” by asking a friend if (s)he will be a 12:00 appt. Students write each other’s name on the appropriate line on the clock.

� Let students choose 12:00, 4:00 and 8:00.� Collect the clocks.� Assign appointments at 2:00, 6:00 and 10:00 as

follows:¡ 2:00 Like learning profile aspect (MI, Sternberg, Modality,

etc.)¡ 6:00 Similar readiness¡ 10:00 a different way of thinking.

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Using the Clock

� If the activity you have planned will be the same for all students, use their choice of partner at 12:00, 4:00 or 8:00. Randomly rotate these.

� If the activity is differentiated by learning profile, use 2:00 partners.

� If the activity is differentiated by readiness, use 6:00 partners (important for games!).

� If the problem is open ended or complex, use 10:00 partners.

Our Agenda:

1. Some Set Up and Big Ideas …2. Engaging Students: Quick Ideas3. Differentiating Mathematics:

1. Readiness2. Interest3. Learning Profile

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Using each of the digits 1 through 9 only once, find two 3-digit numbers whose sum uses the remaining three digits.

STARTER PROBLEM

Engaging Students12

When I die, I hope it’s during a lecture;

the difference betweenlife and death will be so small,

that I won’t notice it!(Anonymous Student)

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Engaging Students: Activities

Quick Ideas:� Turn and Talk� Analogies� Headlines� Find the Error� Agree/Disagree� White Boards (Back to

Back)� On A Roll� Exit Cards� Journal Entries� Hands and Brain

(Reciprocal teaching; Sage and Scribe)

Ideas Needing More Planning:� Stations� Build-A-Problem� Four In A Row� Algebra Tiles� MARS tasks� Think Dots� Learning Profile Prompts� Inside / Outside Circles� Concept Attainment� Manipulatives� Card Games

HandsandBrain

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Concept Attainment Model

1. Select and Define a Concept2. Select the Attributes3. Develop Positive and Negative Examples4. Introduce the Process to the Students5. Present the Examples and List the Attributes6. Have Students write Their Own Concept

Definition7. Give Additional Examples8. Discuss the Process with the Class

These Are These Are Not

Polygons

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Send-a-Problem1. Each team member writes a high consensus (short answer)

question on an index card.2. Each team member checks the validity of the question and

answer with the team.3. If the team agrees on the answer, it is written on the back of the

card at the top.4. Repeat for each team member.5. At the signal, teams gather cards together and pass them to the

next team.6. Questions are dealt out--one to a person. Each question is read

aloud in turn; an answer is agreed upon; if different, it is written below the original response. Rules for game: No spelling correction! No writing on the question side of the card.

7. Cards are passed form team to team until they return to the group who authored them.

8. Questions with alternate responses are reviewed. Disputes are resolved.

Send-a-Problem Game Rules

� Stack and pass cards at the teacher’s direction.� Deal cards out, one to a person.� Decide who will read the first question.� Read question; count to three before anyone

answers.� Check your answer with the answer on the back of

the card. If you agree, do nothing. If you disagree, write what you think is the correct answer on the answer side of the card.

� Wait until the instructor says, “Stack ‘em and pass” to pass the cards to the next team.

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Inside Outside Circles

1. The teacher discusses the topic and distributes the index cards. You can have students generate questions or just answer problems on the cards.

2. Students answer their question on scratch paper, then after checking their answer, write it on the back of the card.

3. Taking their questions with them, half of the class forms a circle. Once the circle is formed they turn around. This is the “Inside” circle.

4. The second half of the class forms an “Outside” circle by matching up with individuals on the inside.

5. The students on the inside read their questions to their partners; partners answers the question.

6. The students on the outside read their questions to their partners; partner answers the question.

7. Cards are exchanged.8. At the direction of the teacher one of the circles rotate.9. Repeat beginning at step 5.

On A Roll� Each table rolls a number cube� Students at the table answer the question

that corresponds to the number rolled� Can be used for several days over the course

of a topic of study

Please use this strategy to discuss what you have learned so far…

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If you roll a:

1. Write a question someone should be able to answer after hearing this lesson.

2. Explain the most important idea in the lesson in a way a first-grader could understand.

3. Draw a picture that represents the main idea of the lesson.

4. Tell which part you found to be the most confusing.

5. If you were going to learn more about this topic, what would you choose to investigate.

6. Write a headline for a newspaper article about today’s lesson.

Our Agenda:

1. Some Set Up and Big Ideas …2. Teaching in a Block: Dos and Don’ts3. Differentiating in the

Mathematics Block:1. Readiness2. Interest3. Learning Profile

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The numbers at the end of each row and column give a total value of the fruit in the row or column. Determine the

value of the ?

Differentiation is NOT…

ONE SIZE FITS ALL…

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Differentiation is NOT…

Individualized instruction with separate lesson plans for each student

Good Differentiated Instruction is NOT…

…like the “Bowling Theory” – Shoot straight down the middle and hit as many

as you can.

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Good Differentiated Instruction is NOT…

…a passing fad that will go away if we just “wait it out” long enough.

Good Differentiated Instruction is NOT……dividing students into “high” and “low” ability

groups and using the same groups everyday.

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Differentiation IS…

Recognizing that students are different and responding to those differences in a thoughtful way.

Guiding Principle:

�Differentiation is a PHILOSOPHY, not a “Bag of Tricks.”

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Fairness is noteveryone getting the same

thing.It is everyone getting

what they need.

Embracing Differences

� “Differentiation is distinct from the above approaches (those that try to “handle” diversity) in that it embraces the diversity inherent in classrooms rather than masking it or regarding it as an inconvenience to be avoided at all costs” (Doubet & Hockett, 2015, p. 176).

� But how can we do this?

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Acknowledges that students have different motivational factors. Interest differentiation can be connecting students’ interests with content, but also by giving students voice and choice.

Interest

Activities can be designed to access different ways for making sense. Some structures will be more natural for learning than others for students, and this can change based on topic and circumstances.

Learning Profile

ReadinessAcknowledges a student’s entry point into learning. Factors are prior knowledge, speed of learning new concepts, independence and home factors.

How Do You Differentiate?

DI in a nutshell

Ways to think about learning differences:uReadiness

u Starting Pointsu Appropriate Challengeu Prior Knowledge

uInterestu Motivationu Voice and Choice

uLearning Profileu MIu Creative, Analytical, Practical (Sternberg Triarchic Theory)u Visual, Auditory, Kinesthetic

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Differentiation is not about individualization…But it is about individuals.

Our Agenda:



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ReadinessAcknowledges a student’s entry point into learning. Factors are prior knowledge, speed of learning new concepts, independence and home factors.


BRAIN RESEARCHReticular Activating System

RAS = “Toggle Switch”

HIGH MIDDLE LOWHot (EEG) Mild (EEG) Cold (EEG – sleeplike)

Limbic aroused Cortical arousal Brain StemFlight / Fight Problem Solving Sleep / Relaxation

(depression)Out of Control In Control Off DutyCarbohydrates Proteins Carbohydrates/Dairy

Burnout Achievement DepressionExtreme Challenge Moderate Challenge No Challenge

Only one of these three states is activated (aroused) at a time:

“Certain motivational states which interfere with learning condition are especially dangerous: anxiety and boredom. Anxiety occurs primarily when teachers expect too much from students; boredom occurs when teachers expect too little.” – Howard Gardner

Learning only happens when the toggle switch is in the middle position

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Differentiation does NOT mean “dumbing down”

Rather than a vice that keeps kids down, differentiation is meant to be a stool that gives students a “boost.”

Watch ItSolving Equations

� http://players.brightcove.net/268012963001/default_default/index.html?videoId=5309969878001

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A Few Routes to READINESS DIFFERENTIATION

� Varied texts by reading level� Varied supplementary materials� Varied scaffolding

• reading• writing• research• technology

� Tiered tasks and procedures� Flexible time use� Small group instruction� Homework options� Tiered or scaffolded assessment� Compacting� Mentorships� Negotiated criteria for quality� Varied graphic organizers

Double Entry Journal

Your TurnModel

2x + 3 = 15- 3 - 3

2x = 12

2 2

x = 6

3x – 1 = 17

Step1. Gather variables to one side of the equal sign (if needed).

2. Isolate the variable. Use an inverse operation, addition or subtraction.3. Solve for one of the variable – use inverse operation again, multiplication or division.

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Make Card Games!

Triplets

© ThinkDOTSA Versatile Strategy for Differentiation

© Kay Brimijoin, 2003

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Level1:1. a,b,canddeachrepresentadifferentvalue.Ifa=2,find

b,c,andd.a+b=ca– c=da+b=5

2. Explainthemathematicalreasoninginvolvedinsolvingcard1.

3. Explaininwordswhattheequation2x+4=10means.Solvetheproblem.

4. Createaninterestingwordproblemthatismodeledby8x– 2=7x.

5. Diagramhowtosolve2x=8.6. Explainwhatchangingthe“3” in3x=9toa“2” doesto

thevalueofx.Whyisthistrue?Nanci Smith

Level2:1. a,b,canddeachrepresentadifferentvalue.Ifa=-1,find

b,c, andd.a+b=cb+b=dc– a=-a

2. Explainthemathematicalreasoninginvolvedinsolvingcard1.

3. Explainhowavariableisusedtosolvewordproblems.4. Createaninterestingwordproblemthatismodeledby

2x+4=4x– 10.Solvetheproblem.5. Diagramhowtosolve3x+1=10.6. Explainwhyx=4in2x=8,butx=16in½x=8.Why

doesthismakesense?Nanci Smith

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7513 +£- xx

Level3:1. a,b,canddeachrepresentadifferentvalue.Ifa=4,find b,c,andd.

a+c=bb- a=ccd=-dd+d=a

2. Explainthemathematicalreasoninginvolvedinsolvingcard1.3. Explaintheroleofavariableinmathematics.Giveexamples.4. Createaninterestingwordproblemthatismodeledby

. Solvetheproblem.5. Diagramhowtosolve3x+4=x+12.6. Givenax =15,explainhowx ischangedifa isgreaterora is

lesserinvalue.

Nanci Smith

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 understanda 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

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Information,Ideas,Materials,Applications

Representations,Ideas,Applications,Materials

Resources,Research,Issues,Problems,Skills,Goals

Directions,Problems,Application,Solutions,Approaches,DisciplinaryConnections

Application,Insight,Transfer

Solutions,Decisions,Approaches

Planning,Designing,Monitoring

PaceofStudy,PaceofThought

TheEqualizer

1. Foundational Transformational

2. Concrete Abstract

3. Simple Complex

4. SingleFacet MultipleFacets

5. SmallLeap GreatLeap

6. MoreStructured MoreOpen

7. LessIndependence GreaterIndependence

8. Slow Quick

Quadrilateral Review Tiered Activity

All Groups play “Guess the Quadrilateral” in pairs or quads.1. One person thinks of a quadrilateral.2. The remaining members of the group (or partner) ask yes / no questions about the properties of the quadrilateral.3. The group tries to guess the quadrilateral based on the answers to the question in less than ___ questions. (You can vary the number allowed.)

� Average Group:¡ Play the game as stated above.

� Struggling Group:¡ A list of quadrilaterals and basic properties is provided for

reference. The degree of completeness of the list can be determined by the teacher.

� Advanced Group:¡ After guessing the quadrilateral, the group sketches the

quadrilateral and lists all properties that belong to it.

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Your Task…

Look at one of the End Behaviors tiered lesson.Use the equalizer to determine which task is for which tier of students.

After the group work, groups presented their findings to the class which became the lesson notes.

An alternative way to conclude the lesson was to form new groups with one of each of the four tasks represented. They teach each other their learning, and then complete sketches of functions based on the collaborative learning.

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Build – A – Square

� Build-a-square is based on the “Crazy” puzzles where 9 tiles are placed in a 3X3 square arrangement with all edges matching.

� Create 9 tiles with math problems and answers along the edges.

� The puzzle is designed so that the correct formation has all questions and answers matched on the edges.

� Tips: Design the answers for the edges first, then write the specific problems.

� Use more or less squares to tier.� Add distractors to outside edges and “letter” pieces at the end.

m=3

b=6 -2/3

Nanci Smith

Our Agenda:



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Acknowledges that students have different motivation factors. This differentiation can be connecting students’ interests with content, but also by giving students voice and choice.

Interest


Interest

� Motivation leads to greater willingness, retention, and persistence (Meaning).

� High interest is intrinsically motivating (which leads to higher achievement levels than extrinsic motivation).

� Open ended questions that are student-centered can keep them interested if they receive encouragement for expressing their ideas.

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Personal vs. Situations Interests

Chat With Your 12:00 Partner

� What are some of your personal interests and how might you connect the content to those? What about situational interests…what worked for you when you were in school?

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Watch ItSituational Interest

http://players.brightcove.net/268012963001/default_default/index.html?videoId=5309714523001 (1:29)

Interest ProblemText

TraditionalAsampleoftenmiddleschoolstudentswasaskedtocountthenumberofwritingutensilsthattheyown.Theirresponsesarerepresentedinthefollowingsetofnumbers:

5,4,2,10,6,14,8,5,1,8• Whatisaverageofthesetnumbers?• Whatisthemedianofthesetofnumbers?• Createa“five-numbersummary”ofthedataanddisplayitinboxplotformat• Whatpatternsdoyouseeinthedata?

VideoGames

Asampleoftenmiddleschoolstudentsthatplayvideogameswasaskedhowmanyhourstheyspendplayingeachweek.Theirresponsesarerepresentedinthefollowingsetofnumbers:

5,4,2,10,6,14,8,5,1,8[samequestionsastraditionalproblem]

SocialMedia

AsampleoftenmiddleschoolstudentsthatuseFacebookwasaskedhowmanystatusupdatestheyposteachweek.Theirresponsesarerepresentedinthefollowingsetofnumbers:


Sports Thegirl’sbasketballcoachwasfrustratedwiththeamountofplayersfoulingout.Forthenextfivegames,thecoachkeptarecordofeverytimeaplayercommittedafoul.Thenumbersbelow

representeachplayer’stotalamountoffoulsoverafive-gameperiod.


Adjusting Algebra Problems to Appeal to Student Interest

From Carbaugh, E.M. & Doubet, K.J. (2015). The differentiated flipped classroom. Thousand Oaks, CA: Corwin Press.

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A RAFT is…� … an engaging, high level strategy that encourages writing

across the curriculum� … a way to encourage students to…

¡ …assume a role¡ …consider their audience, while ¡ …writing in a particular format¡ …examine a topic from their chosen perspective, and

� All of the above can serve as motivators by giving students choice, appealing to their interests and learning profiles, and adapting to student readiness levels.

Algebra RAFT

Role Audience Format Topic

Coefficient Variable Email We belong together

Scale / Balance

Students Advice column

Keep me in mind when solving an

equation

Variable Humans Monologue All that I can be

Variable Algebra students

Instruction manual

How and why to isolate me

Algebra Public Passionate plea

Why you really do need me!

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Angle Relationship RAFT

Role Audience Format Topic

One vertical angle

Opposite vertical angle

Poem It’s like looking in a mirror

Interior (exterior)

angle

Alternate interior

(exterior) angle

Invitation to a family reunon

My separated twin

Acute angle Missing angle Wanted poster

Wanted: My complement

An angle less than 180

Supplemen-tary angle

Persuasive speech

Together, we’re a straight angle

**Angles Humans Video See, we’re everywhere!

°

ROLE AUDIENCE FORMAT TOPIC

Equivalent Fractions Farmers Poster Ad for Fertilizer How do I get bigger

Event Mutually exclusive event

Love letter We’ll never be together… sob, sob, sob

3 line segments Polygons Application Do we belong?

Pythagoras Home Buyers Floor plan It’s hip to be Square!

Basic Facts Students working on a multi-step problem

Persuasive Speech You need me!

Denominator Numerator Song You’re a part of me

Equivalent Fractions TV viewers Reality TV Show Biggest Reducer

Divisor Dividend Rap Song Let me Count the ways

3-D shapes Humans Photo Journal Where do you find me?

Area of Circle Humans Sales Ad Get the most pi for your dollar

Scientific Notation Large numbers Health Ad The benefits of being small

Radius Diameter Letter How do I fit into your life?

Scale Map Poem Why do we need to be together

2 line segments All segments Wanted Poster for a complete triangle

Are you our missing link?

Multiples Factors Storyboard To Infinity and

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KINDS of MENUS

� MENU: Main Dishes, Side Dishes, and Desserts (for younger learners).

� AGENDA: Imperatives, Negotiables, and Options(for older learners).

� THINK TAC TOE: Complete a row, column or diagonal line of activities.

� WINDOW PANES: Selection of different product options in rows, columns allow for readiness differentiation.All four options can be differentiated according to

interest, learning profile, or readiness (see enclosed examples).

Proportional ReasoningThink-Tac-Toe

Create a word problem that requires proportional reasoning. Solve the problem and explain why it requires proportional reasoning.

Find a word problem from the text that requires proportional reasoning. Solve the problem and explain why it was proportional.

Think of a way that you use proportional reasoning in your life. Describe the situation, explain why it is proportional and how you use it.

Create a story about a proportion in the world. You can write it, act it, video tape it, or another story form.

How do you recognize a proportional situation? Find a way to think about and explain proportionality.

Make a list of all the proportional situations in the world today.

Create a pict-o-gram, poem or anagram of how to solve proportional problems

Write a list of steps for solving any proportional problem.

Write a list of questions to ask yourself, from encountering a problem that may be proportional through solving it.

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Similar Figures Menu

Imperatives (Do all 3):1. Write a mathematical definition of “Similar Figures.”

It must include all pertinent vocabulary, address all concepts and be written so that a fifth grade student would be able to understand it. Diagrams can be used to illustrate your definition.

2. Generate a list of applications for similar figures, and similarity in general. Be sure to think beyond “find a missing side…”

3. Develop a lesson to teach third grade students who are just beginning to think about similarity.


Negotiables (Choose 1):1. Create a book of similar figure applications and

problems. This must include at least 10 problems. They can be problems you have made up or found in books, but at least 3 must be application problems. Solve each of the problems and include an explanation as to why your solution is correct.

2. Show at least five different applications of similar figures in the real world, and make them into math problems. Solve each of the problems and explain the role of similarity. Justify why the solutions are correct.

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Optionals:1. Create an art project based on similarity. Write a cover

sheet describing the use of similarity and how it affects the quality of the art.

2. Make a photo album showing the use of similar figures in the world around us. Use captions to explain the similarity in each picture.

3. Write a story about similar figures in a world without similarity.

4. Write a song about the beauty and mathematics of similar figures.

5. Create a “how-to” list or book about finding and creating similar figures.

Learner Profile Card

Auditory, Visual, Kinesthetic

Modality

Multiple Intelligence Preference

Gardner

Analytical, Creative, Practical

Sternberg

Student’s Interests

Array Inventory

Gender Stripe

Nanci Smith, 2002

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Our Agenda:



Activities can be designed to access different ways for making sense. Some structures will be more natural for learning than others for students, and this can change based on topic and circumstances.

Learning Profile


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Learning Profile

Learning Style

How we take in and process information.

Refers to prefs. re: environmental

elements, interactions, and personal needs.

Cultural Background/Gender

Assumption: People learn in different ways. Teaching & learning would be more successful if learners could

explore and express content in ways that work best for them.

Visual-Auditory-Kinesthetic/

Dunn & Dunn/McCarthy

(4MAT)/Gregoric, etc.

Intelligence Preference

“Ways of thinking”—rooted in theories

about human intelligence. Ceiling-

less.

Robert Sternberg (Analytical, Creative,

Practical)Howard Gardner

(Spatial, Linguistic, Bodily-Kinesthetic, Musical, Logical-

Mathematical, Interpersonal,

Intrapersonal, Naturalist …and Existential?)

e.g., patterns of communication,

views of authority, perception of time,

preference for competition vs. collaboration

Hockett, J.; Based on Tomlinson, Feb 2009

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Visual• Take numerous detailed notes • Tend to sit in the front • Are usually neat and clean • Often close their eyes to visualize or remember

something • Find something to watch if they are bored • Like to see what they are learning • Benefit from illustrations and presentations that

use color • Are attracted to written or spoken language rich in

imagery • Prefer stimuli to be isolated from auditory and

kinesthetic distraction http://www.usd.edu/trio/tut/ts/styleres.html

Auditory• Sit where they can hear but needn't pay attention to

what is happening in front • May not coordinate colors or clothes, but can

explain why they are wearing what they are wearing

• Hum or talk to themselves or others when bored • Acquire knowledge by reading aloud • Remember by verbalizing lessons to themselves (if

they don't they have difficulty reading maps or diagrams or handling conceptual assignments like mathematics).

http://www.usd.edu/trio/tut/ts/styleres.html

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Kinesthetic• Need to be active and take frequent breaks • Speak with their hands and with gestures • Remember what was done, but have difficulty recalling what was said or seen • Find reasons to tinker or move when bored • Rely on what they can directly experience or perform • Activities such as cooking, construction, engineering and art help them perceive and learn • Enjoy field trips and tasks that involve manipulating materials • Sit near the door or someplace else where they can easily get up and move around • Are uncomfortable in classrooms where they lack opportunities for hands-on experience • Communicate by touching and appreciate physically expressed encouragement, such as a pat on the back

http://www.usd.edu/trio/tut/ts/styleres.html

Modality Task PromptsVisual Auditory Kinesthetic

Pictures Speeches Matching games

Graphic Organizers Discussions Modeling

Color coding Infomercials or PSAs “Becoming” the task

Posters Creating Question Lists Hands-on tasks / touching

Charts / Graphs Read Alouds “Peg Board” yarn game

Videos Books / Instructions on tape

Gestures and Motions

Detailed Notes Self Talk (Whispies) Motion

Visualizing Tape Recording Answers

Drama / Skits

Making Books Interviews Charades

To Do Lists Lectures / Tone & Inflection

Manipulatives

Written Directions Spoken Directions Modeled Directions

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Sandra Page [email protected] 2008

Possible Formats to use to Differentiate by Learning ModalityWritten Visual Auditory Kinesthetic•diary entry•bulleted list•obituary•invitation•product guide•game rules•recipe•movie critic•FreqAskQues•editorial•character monologue•job application•gossip column•mag. article

•cartoon/comic•crossword puzzle•map•scale plan or drawing•graphic org.•concept web•illustration•print ad•photograph•powerpoint•‘how to’diagram•fashion design

•song•set of discussion ?s•conversation•monologue•sermon•radiocast•museum guide•commercial•reader’s theater•interview•tasting•political speech•puppet show•storytell

•model•cheer•mime•reenactment•wax museum•demonstration•sales pitch with demo elements•physical analogies•taste tests•‘how to’ video•game•sew, cook, build•design a ....

Partial List of Learning Modality Tasks/Skills

Kinesthetic•model •demonstrate •build

•act out •use tools to.. •dance

•produce •simulate •craft

•transform •show in lab •make

Visual•diagram •overlay •map

•chart •timeline •web

•illustrate •cartoon •model

•graph •video •pop-up

Oral•recite •broadcast •speech

•discuss •question •interview

•debate •cook/taste •sing

•argue •converse •perform

Auditory•radiocast •soundscape •music

•preach •commercial •chant

•persuade •ad/jingle •rhythm

•compose •speech •phone

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� Visual: Make posters showing all the angle relations formed by a pair of parallel lines cut by a transversal. Be sure to color code definitions and angles, and state the relationships between all possible angles.

12 3

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8

Smith & Smarr, 2005

Parallel lines cut by a transversal

� Auditory: Play “Shout Out!!” Given the diagram below and commands on strips of paper (with correct answers provided), players take turns being the leader to read a command. The first player to shout out a correct answer to the command, receives a point. The next player becomes the next leader. Possible commands:¡ Name an angle supplementary

to angle 1.¡ Name an angle congruent

to angle 2.

Smith & Smarr, 2005

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6

7

8


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� Kinesthetic: Walk It Tape the diagram below on the floor with masking tape. Two players stand in assigned angles. As a team, they have to tell what they are called (ie: vertical angles) and their relationships (ie: congruent). Use all angle combinations, even if there is not a name or relationship. (ie: 2 and 7)

Smith & Smarr, 2005

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Multiple Intelligences

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EIGHT STYLES OF LEARNINGTYPE CHARACTERISTICS LIKES TO IS GOOD AT LEARNS BEST BY

LINGUISTICLEARNER“The Word Player”

Learns through the manipulation of words. Loves to read and write in order to explain themselves. They also tend to enjoy talking

ReadWriteTell stories

Memorizing names, places, dates and trivia

Saying, hearing and seeing words

LOGICAL/MathematicalLearner“The Questioner”

Looks for patterns when solving problems. Creates a set of standards and follows them when researching in a sequential manner.

Do experimentsFigure things outWork with numbersAsk questionsExplore patterns and relationships

MathReasoningLogicProblem solving

CategorizingClassifyingWorking with abstract patterns/relationships

SPATIAL LEARNER“The Visualizer”

Learns through pictures, charts, graphs, diagrams, and art.

Draw, build, design and create thingsDaydreamLook at pictures/slidesWatch moviesPlay with machines

Imagining thingsSensing changesMazes/puzzlesReading maps, charts

VisualizingDreamingUsing the mind’s eyeWorking with colors/pictures

MUSICAL LEARNER“The Music Lover”

Learning is often easier for these students when set to music or rhythm

Sing, hum tunesListen to musicPlay an instrumentRespond to music

Picking up soundsRemembering melodiesNoticing pitches/ rhythmsKeeping time

RhythmMelodyMusic

EIGHT STYLES OF LEARNING, Cont’d

TYPE CHARACTERISTICS LIKES TO IS GOOD AT LEARNS BEST BYBODILY/KinestheticLearner“The Mover”

Eager to solve problems physically. Often doesn’t read directions but just starts on a project

Move aroundTouch and talkUse body language

Physical activities(Sports/dance/acting)crafts

TouchingMovingInteracting with spaceProcessing knowledge through bodily sensations

INTERpersonalLearner“The Socializer”

Likes group work and working cooperatively to solve problems. Has an interest in their community.

Have lots of friendsTalk to peopleJoin groups

Understanding peopleLeading othersOrganizingCommunicatingManipulatingMediating conflicts

SharingComparingRelatingCooperatinginterviewing

INTRApersonalLearner“The Individual”

Enjoys the opportunity to reflect and work independently. Often quiet and would rather work on his/her own than in a group.

Work alonePursue own

interests

Understanding selfFocusing inward on feelings/dreamsPursuing interests/

goalsBeing original

Working alongIndividualized projectsSelf-paced instructionHaving own space

NATURALIST“The Nature Lover”

Enjoys relating things to their environment. Have a strong connection to nature.

Physically experience natureDo observationsResponds to patterning nature

Exploring natural phenomenonSeeing connectionsSeeing patternsReflective Thinking

Doing observationsRecording events in NatureWorking in pairsDoing long term projects

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Multiple Intelligence Ideas for Proofs!

� Logical Mathematical: Generate proofs for given theorems. Be ready to explain!

� Verbal Linguistic: Write in paragraph form why the theorems are true. Explain what we need to think about before using the theorem.

� Visual Spatial: Use pictures to explain the theorem.

Multiple Intelligence Ideas for Proofs!

� Musical: Create a jingle or rap to sing the theorems!

� Kinesthetic: Use Geometer Sketchpad or other computer software to discover the theorems.

� Intrapersonal: Write a journal entry for yourself explaining why the theorem is true, how they make sense, and a tip for remembering them.

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Beyond IQ

� Robert Sternberguse of intellect rather than quantity of itintelligence as problem-solving

analyticalpracticalcreative

Triarchic Theory

Linear – Schoolhouse Smart - SequentialANALYTICALThinking About the Sternberg Intelligences

Show the parts of _________ and how they work.Explain why _______ works the way it does.Diagram how __________ affects __________________.Identify the key parts of _____________________.Present a step-by-step approach to _________________.

Streetsmart – Contextual – Focus on UsePRACTICAL

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.

CREATIVE Innovator – Outside the Box – What If - Improver

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” perspectives to help us think about ____________.

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Watch It!

� http://players.brightcove.net/268012963001/default_default/index.html?videoId=5309815420001 (HS)

Analytical Thinkers

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Analytical Thinkers

Likes to break things into its parts, likes to know how things work, enjoys facts as well as ideas, likes to argue, attracted to logical thinking and logical ideas, likes to “think” as opposed to “doing,” typically does well at school tasks, enjoys solving problems, can focus for long periods of time on a single task, may balk at “creative” assignments, likes to find one, right “answer,” may see things as black and white

Needs: assignments that require thought as opposed to rote memorization, extended assignments that allow for focused, long-term study, “problems” to figure out, time to discuss ideas with others, support with how to present ideas in a non-argumentative way, support with listening to and accepting others’ ideas, opportunities to struggle with open-ended questions that have no right/wrong answer

Analytical

• Bullets• Lists• Steps• Worksheets• Tables• Venn Diagrams• Timelines• Sequential Items• Flow Charts• Compare and Contrast

• Find the error• Evaluating• Sorting and Classifying• Appealing to logic• Critique and Criticize• Explaining Difficult

Problems to others• Making Inferences and

Deriving Conclusions• Puns and Subtleties

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Analytical, cont.

• Chart• Graphic organizer• Timeline• Venn diagram• T-chart• Patterns• Sequencing

• Classifying• Definitions• Cause and effect• Code• Graph• Database• Blueprints• Newspaper• Fact file

Smith, 2008

Practical Thinkers

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Practical Thinkers

Likes to see the real-world application of things, excellent at implementing plans, a “doer,” highly effective in making things “happen,” organized, less interested in ideas than in action, likes to move and do when learning, can be an excellent leader, may struggle with creativity-for-creativity’s-sake assignments, may resist completing assignments for which they see no real-world purpose, can work very well in group situations, may not be traditionally “book smart”

Needs: Hands-on activities, assignments that are connected to the real world, opportunities to share ideas with practitioners and experts, experiences with more creative, open-ended activities, support with being patient with activities for which they see no immediate application, opportunities to lead (even when they are not the highest achievers, these students can be highly effective at leading groups and delegating responsibilities)

Practical

• Working your way out of a problem• Notes to Self (what questions to ask myself, how to make sense of

for myself)• Here is a problem, explain what happened• Analogies• Draw real world examples• Advising and convincing others (Advice columns)• Hands-on Activities• Taking things apart and fixing them• Understanding and Respecting others / Friendships / Resolving

Conflicts• Putting things into Practice• Adapting to New Situations

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Practical, cont.

• Explaining how things can be used

• Developing a plan to address a problem

• Help classmates understand• Scenarios• Role plays• WebQuest• Job shadowing• Dialogs• Newscasts

Smith, 2008

• Letters to the editor• Flyers• Demonstrations• Experiments• Surveys• Field trips• Petitions• “Cheat sheets”• Lesson plans

Creative Thinker

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Creative Thinker

Attracted to novelty, likes to produce knowledge or ideas instead of consuming them, sees the world from a unique perspective, often prefers working alone, does not like to be rushed toward completion of tasks, often works in “bursts,” with long periods of incubation (which can look like unproductiveness) followed by quick, highly productive working periods, often has unique sense of humor.

Needs: support with setting deadlines and timelines, open-ended assignments with structure, assignments that allow for creative thinking and novel products, support working with other students, frequent outlets for creative thought, support with turning “ideas” into “reality.”

Creative

� Figure out a way to explain� Idiot’s Guide To… (Book for Dummies)� How to represent� Make your own interpretation� Pictures or news bulletins to describe� Designing new things� Alternative solutions and methods� Thinking in pictures and images� Noticing things other people tend to ignore� Suppose something was changed… What would happen

if?� Acting and Role playing� Inventing

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Creative, cont.

� Become a … and use your new perspectives to help us think about…

� Use humor to show…� Explain or show a new and better way to…� Figure out a way to explain…� Pictures, picture books, doodles and icons� Songs� Riddles� Mime or charades (think vocabulary!)� Play� Bumper stickers

Smith, 2008

Some Verbs That Might HelpsAnalytical Practical Creative

AnalyzeJudgeCritiqueCompareContrastEvaluateDiagramIdentifyExplainAssessPresentastep-by-stepapproach

ImplementApplyUseDemonstrateTeachPutintopracticeConvinceShowhowEmployRelatetoexperienceorworldMakepractical

InventDiscoverImagineSupposeDesignPredictPromoteEncourageDevelopWhatifyou(were)…FindanewwayUseunusualmaterials

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AnalyticalCompare the various forms of equations of lines. You may make a flow chart, table or any other idea to present your findings to the class. Be sure to consider advantages and disadvantages of each. Show how to move from one form to another.

Practical:Decide how and when each form of the equation of a line is best used. What are the strengths and weaknesses of each form? What specifically should you look for in order to decide which form to use? Find a way to present your conclusions to the class.

Creative:Put each form of an equation of a line on trial. Prosecutors should try to convince the jury that the form is not needed, while the defense should defend its usefulness. Group members are the various equation forms and the prosecuting and defense attorneys. The rest of the class will be the jury, and the teacher will be the judge.

Equations of lines

Circle Vocabulary

All Students:Students find definitions for a list of vocabulary (center, radius, chord, secant, diameter, tangent point of tangency, congruent circles, concentric circles, inscribed and circumscribed circles). They can use textbooks, internet, dictionaries or any other source to find their definitions.

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Circle Vocabulary

AnalyticalStudents make a poster to explain the definitions in their own words. Posters should include diagrams, and be easily understood by a student in the fifth grade.

PracticalStudents find examples of each definition in the room, looking out the window, or thinking about where in the world you would see each term. They can make a mural, picture book, travel brochure, or any other idea to show where in the world these terms can be seen.

Circle Vocabulary

CreativeFind a way to help us remember all this vocabulary! You can create a skit by becoming each term, and talking about who you are and how you relate to each other, draw pictures, make a collage, or any other way of which you can think.

ORRole Audience Format Topic Diameter Radius email Twice as niceCircle Tangent poem You touch me!Secant Chord voicemail I extend you.

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Array Interaction InventoryDirections:

• Rank order the responses in rows below on a scale from 1 to 4 with 1 being “least like me” to 4 being “most like me”.

• After you have ranked each row, add down each column.

• The column(s) with the highest score(s) shows your primary Personal Objective(s) in your personality.

In your normal day-to-day life, you tend to be:

NurturingSensitive

Caring

LogicalSystematicOrganized

SpontaneouscreativePlayful

QuietInsightfulreflective

In your normal day-to-day life, you tend to value:

HarmonyRelationships are

important

WorkTime schedules are

important

StimulationHaving fun is

important

ReflectionHaving some time alone is important

In most settings, you are usually:

AuthenticCompassionate

Harmonious

TraditionalResponsible

Parental

ActiveOpportunisticSpontaneous

InventiveCompetent

Seeking

In most situations, you could be described as:

EmpatheticCommunicative

Devoted

PracticalCompetitive

Loyal

ImpetuousImpactful

Daring

ConceptualKnowledgeable

Composed

You approach most tasks in a(n) _________ manner:

AffectionateInspirational

Vivacious

ConventionalOrderly

Concerned

CourageousAdventurous

Impulsive

RationalPhilosophical

Complex

When things start to “not go your way” and you are tired and worn down, what might your responses be?

Say “I’m sorry”Make mistakes

Feel badly

Over-controlBecome critical

Take charge

“It’s not my fault”Manipulate

Act out

WithdrawDon’t talk

Become indecisive

When you’ve “had a bad day” and you become frustrated, how might you respond?Over-please

CryFeel depressed

Be perfectionisticVerbally attack

Overwork

Become physicalBe irresponsible

Demand attention

DisengageDelay

Daydream

Add score:

Harmony Production Connection Status Quo

Array Interaction Inventory, cont’d

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PERSONALITY ARRAYYour personality is a critical element in the classroom dynamic. The Array Model (Knaupp, 1995) identifies four personality types through the use of several personality descriptors. Take a look at the personality types, below, and see which character you match up with.

Cooperation(positive behavior)

Reluctance(negative behavior)

Needs

Ways to Meet Needs

HundredAcreWoodPersonalityArray

CaringSensitiveNurturingHarmonizingFeeling Oriented

LogicalStructuredOrganizedSystematicThinking Oriented

SpontaneousCreativePlayfulEnthusiasticAction Oriented

QuietImaginativeInsightfulReflectiveInaction Oriented

Over adaptedOver pleasingMakes mistakesCries or gigglesSelf Defeating

Over criticalOver worksPerfectionistVerbally AttacksDemanding

DisruptiveBlamesIrresponsibleDemands AttentionDefiant

DisengagingWithdrawnDelaysDespondentDaydreams

FriendshipsSensory Experience

Task CompletionTime Schedule

Contact with peopleFun activities

Alone timeStability

Value their feelingsComfortable andpleasing learning environmentWork with a friendSharing time

Value their ideasIncentivesRewardsLeadership PositionSchedulesTo-do lists

Value their activityHands-on activitiesGroup InteractionGamesChange in routine

Value their privacyAlone timeIndependent ActivitySpecific directionsComputer ActivityRoutine tasks

Character

Students taught in their preferred learning styles demonstrated higher levels of achievement, showed more interest in the subject matter, approved of instructional methods, and wanted other subjects to be taught similarly.

Bell, L. (1986). Learning styles in the middle school classroom: Why and how. Middle School Journal, 18(1), 18 – 19.

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Take Away Points…

� Individuals learn differently in different contexts� We need to offer varied ways for students to take in and explore

information, including teaching in a variety of ways� We need to make sure students are aware of the fact that their brains are

malleable (growth mindset).� Don’t use and trust inventories to make high-stakes decisions about

student learning� Don’t categorize learners, assign students without good cause, generalize

learners.� Focus on options for processing and demonstrating essential content;

helping students know themselves as learners.� Learning profiles are also essential for classroom community (joy in

learning, student voice and creativity, increased variety in classroom, sense of personal relevance).

Doubt, of whatever kind, can be ended by action

alone.

- Thomas Carlyle

teaching math for each and every student! - e2c2.come2c2.com/files/hs di math...

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