differentiated instruction and critical thinking wormeli/nelms2010

Differentiated Instruction and Critical

ThinkingWormeli/NELMS2010

q

c d

p

Which letter does not

belong, and why?

For further conversation about any of these topics:

Rick [email protected]

703-620-2447Herndon, Virginia, USA(Eastern Standard Time Zone)

mailto:[email protected]

A. Steps to take before designing the learning experiences:

1. Identify your essential understandings, questions, benchmarks, objectives, skills, standards, and/or learner outcomes.

2. Identify your students with unique needs, and get an early look at what they will need in order to learn and achieve.

3. Design your formative and summative assessments. 4. Design and deliver your pre-assessments based on the

summative assessments and identified objectives. 5. Adjust assessments or objectives based on your further

thinking discovered while designing the assessments.

Quick Reference: Differentiated Lesson Planning Sequence

B. Steps to take while designing the learning experiences:

1. Design the learning experiences for students based on pre-assessments, your knowledge of your students, and your expertise with the curriculum, cognitive theory, and students at this stage of human development.

2. Run a mental tape of each step in the lesson sequence to make sure things make sense for your diverse group of students and that the lesson will run smoothly.

3. Review your plans with a colleague. 4. Obtain/Create materials needed for the lesson.5. Conduct the lesson.6. Adjust formative and summative assessments and objectives

as necessary based on observations and data collected while teaching.


When Designing your Actual Lessons….

1. Brainstorm multiple strategies2. Cluster into introductory, advanced, and

strategies that fit between these two3. Sequence activities in plan book4. Correlate Class Profile descriptors,

Differentiation Strategies, and cognitive science principles to lessons – What do you need to change in order to maximize instruction for all students?

C. Steps to take after providing the learning experiences:

1. Evaluate the lesson’s success with students. What evidence do you have that the lesson was successful? What worked and what didn’t, and why?

2. Record advice on lesson changes for yourself for when you do this lesson in future years.


To provide meaningful context, let’s design a differentiated lesson from

scratch….

[Artist Unknown

1. Are we willing to teach in whatever way is necessary for students to learn best, even if that approach doesn’t match our own preferences?

2. Do we have the courage to do what works, not just what’s easiest?

3. Do we actively seek to understand our students’ knowledge, skills, and talents so we can provide an appropriate match for their learning needs? And once we discover their strengths and weaknesses, do we actually adapt our instruction to respond to their needs?

4. Do we continually build a large and diverse repertoire of instructional strategies so we have more than one way to teach?

5. Do we organize our classrooms for students’ learning or for our teaching?

Are we successfully differentiating teachers?

6. Do we keep up to date on the latest research about learning, students’ developmental growth, and our content specialty areas?

7. Do we ceaselessly self-analyze and reflect on our lessons — including our assessments — searching for ways to improve?

8. Are we open to critique?9. Do we push students to become their own

education advocates and give them the tools to do so?

10. Do we regularly close the gap between knowing what to do and really doing it?

Are we successfully differentiating teachers?

What is fair… …isn’t always equal.

Differentiating instruction is doing what’s fair for students. It’s a collection of best practices strategically employed to maximize students’ learning at every turn, including giving them the tools to handle anything that is undifferentiated. It requires us to do different things for different students some, or a lot, of the time. It’s whatever works to advance the student if the regular classroom approach doesn’t meet students’ needs. It’s highly effective teaching.

Definition

Carol Dweck (2007) distinguishes between students with a fixed intelligence mindset who believe that intelligence is innate and unchangeable and those with a growth mindset who believe that their achievement can improve through effort and learning…Teaching students a growth mindset results in increased motivation, better grades, and higher achievement test results.”

(p.6, Principal’s Research Review, January 2009, NASSP)

To meet diverse student needs,

we need expertise in four

areas .

What is Mastery?

“Tim was so learned, that he could name a horse in nine languages; so ignorant, that he bought a cow to ride on.”

Ben Franklin, 1750, Poor Richard’s Almanac

Working Definition of Mastery(Wormeli)

Students have mastered content when theydemonstrate a thorough understanding asevidenced by doing something substantivewith the content beyond merely echoing it.Anyone can repeat information; it’s themasterful student who can break content intoits component pieces, explain it and alternativeperspectives regarding it cogently to others,and use it purposefully in new situations.

Non-mastery…

• The student uses primarily the bounce pass in the basketball game regardless of its potential effectiveness because that’s all he knows how to do.

…and Mastery

• The student uses a variety of basketball passes during a game, depending on the most advantageous strategy at that moment in the game.

What is the standard of excellence when it comes to tying a shoe?

Now describe the evaluative criteria for someone who excels beyond the standard of excellence for tying a shoe. What can they do?

Consider Gradations of Understanding and Performance from Introductory to Sophisticated

Introductory Level Understanding:

Student walks through the classroom door while wearing a heavy coat. Snow is piled on his shoulders, and he exclaims, “Brrrr!” From depiction, we can infer that it is cold outside.

Sophisticated level of understanding:

Ask students to analyze more abstract inferences about government propaganda made by Remarque in his wonderful book, All Quiet on the Western Front.

• Determine the surface area of a cube. • Determine the surface area of a rectangular prism (a

rectangular box)• Determine the amount of wrapping paper needed for another

rectangular box, keeping in mind the need to have regular places of overlapping paper so you can tape down the corners neatly

• Determine the amount of paint needed to paint an entire Chicago skyscraper, if one can of paint covers 46 square feet, and without painting the windows, doorways, or external air vents.

_______________________________________________

• Define vocabulary terms.• Compare vocabulary terms.• Use the vocabulary terms correctly.• Use the vocabulary terms strategically to obtain a particular

result.

There’s a big difference: What are we really trying to assess?

• “Explain the second law of thermodynamics” vs. “Which of the following situations shows the second law of thermodynamics in action?”

• “What is the function of a kidney?” vs. “Suppose we gave a frog a diet that no impurities – fresh organic flies, no pesticides, nothing impure. Would the frog still need a kidney?”

• “Explain Keynes’s economic theory” vs. “ Explain today’s downturn in the stock market in light of Keynes’s economic theory.”

From, Teaching the Large College Class, Frank Heppner, 2007, Wiley and Sons

Feedback vs AssessmentFeedback: Holding up a mirror to the student,

showing him what they did and comparing it to the criteria for success, there’s no evaluative component or judgement

Assessment: Gathering data so we can make a decision

Greatest Impact on Student Success:

Formative feedback

Be clear: We grade against standards, not routes students take or techniques teachers use to achieve those standards.

What does this mean we should do with class participation or discussion grades?

Assessment OF Learning

• Still very important• Summative, final declaration of proficiency,

literacy, mastery• Grades used• Little impact on learning from feedback

Assessment AS/FOR Learning

• Grades rarely used, if ever • Marks and feedback are used • Share learning goals with students from the

beginning• Make adjustments in teaching a result of

formative assessment data• Provide descriptive feedback to students• Provide opportunities for student for self-and

peer assessment-- O’Connor, p. 98, Wormeli

Teacher Action

Result on Student Achievement

Just telling students # correct and incorrect

Negative influence on achievement

Clarifying the scoring criteria Increase of 16 percentile points

Providing explanations as to why their responses are correct or incorrect

Increase of 20 percentile points

Asking students to continue responding to an assessment until they correctly answer the items


Graphically portraying student achievement


-- Marzano, CAGTW, pgs 5-6

ItemTopic or

Proficiency Right WrongSimple

Mistake?Really Don’t Understand

1 Dividing fractions

2 Dividing Fractions

3 Multiplying Fractions

4 Multiplying fractions

5 Reducing to Smplst trms

6 Reducing to Smplst trms

7Reciprocals

8Reciprocals

9Reciprocals

Benefits of Students Self Assessing• Students better understand the standards and

outcomes• Students are less dependent on teachers for feedback;

they independently monitor their own progress• Students develop metacognitive skills and adjust what

they are doing to improve their work• Students broaden learning when they see how peers

approach tasks• Students develop communication and social skills when

required to provide feedback to others.-- from Manitoba’s Communicating Student Learning, 2008

Student Self-Assessment Ideas

• Make the first and last task/prompt/assessment of a unit the same, and ask students to analyze their responses to each one, noting where they have grown.

• Likert-scale surveys (“Place an X on the continuum: Strongly Disagree, Disagree, ‘Not Sure, Agree, Strongly Agree) and other surveys. Use “smiley” faces, symbols, cartoons, text, depending on readiness levels.

• Self-checking Rubrics• Self-checking Checklists• Analyzing work against standards• Videotaping performances and analyzing them• Fill in the blank or responding to self-reflection prompts (see

examples that follow)• Reading notations

Student Self-Assessment Ideas

• “How Do I Know I Don’t Understand?” Criteria: Can I draw a picture of this? Can I explain it to someone else? Can I define the important words and concepts in the piece? Can I recall anything about the topic? Can I connect it to something else we’re studying or I know?

[Inspired by Cris Tovani’s book, I Read It, But I Don’t Get It, Stenhouse, 2001]

• Asking students to review and critique previous work

• Performing in front of a mirror

Student Self-Assessment Ideas: Journal Prompts

I learned that….I wonder why...An insight I’ve gained is…I’ve done the following to make sure I understand what is being taught…I began to think of...I liked…I didn’t like…The part that frustrated me most was…The most important aspect/element/thing in this subject is….A noticed a pattern in….I know I learned something when I…I can't understand...I noticed that...I was surprised...Before I did this experience, I thought that….What if...I was confused by...It reminds me of...This is similar to….I predict…I changed my thinking about this topic when…A better way for me to learn this would be…A problem I had and how I overcame it was…I’d like to learn more about…

This quarter, you’ve taught:

• 4-quadrant graphing• Slope and Y-intercept• Multiplying binomials• Ratios/Proportions• 3-dimensional solids• Area and Circumference of a circle.

The student’s grade: B

What does this mark tell us about the student’s proficiency with each of the topics you’ve taught?

Unidimensionality – A single score on a test represents a single dimension or trait that has been assessed

Student

Dimension A

Dimension B Total Score

1 2 10 12

2 10 2 12

3 6 6 12

Problem: Most tests use a single score to assess multiple dimensions and traits. The resulting score is often invalid and

useless. -- Marzano, CAGTW, page 13

• Some students [get] more work to do, and others less. For example, a teacher might assign two book reports to advanced readers and only one to struggling readers. Or a struggling math student might have to do only the computation problems while advanced math students do the word problems as well.” (Tomlinson, p. 7)

• Teachers have more control in the classroom.

• Teacher uses many different group structures over time.

Defining D.I. Concept-Attainment Style

A science and math teacher, Mr. Blackstone, teaches a large concept (Inertia) to the whole class. Based on “exit cards” in which students summarize what they learned after the whole class instruction, and observation of students over time, he assigns students to one of two labs: one more open-ended and one more structured. Those that demonstrate mastery of content in a post-lab assessment, move to an independent project (rocketry), while those that do not demonstrate mastery, move to an alternative rocketry project, guided by the teacher, that re-visits the important content. (Tomlinson, p. 24)

Teachers can differentiate:

Content

Process

Product

Affect

Learning Environment

-- Tomlinson, Eidson, 2003

According to:

Readiness

Interest

Learning Profile

Flexible Grouping: Questions to Consider

• Is this the only way to organize students for learning?• Where in the lesson could I create opportunities for students

to work in small groups?• Would this part of the lesson be more effective as an

independent activity?• Why do I have the whole class involved in the same activity at

this point in the lesson?• Will I be able to meet the needs of all students with this

grouping?• I’ve been using a lot of [insert type of grouping here – whole

class, small group, or independent work] lately. Which type of grouping should I add to the mix?

There’s a range of flexible groupings:

• Whole class or half class• Teams• Small groups led by students• Partners and triads• Individual study• One-on-one mentoring with an adult• Wiki’s, Nings, PBWiki’s, and on-line communities• Temporary pull-out groups to teach specific mini-lessons• Anchor activities to which students return after working in

small groups• Learning centers or learning stations through which students

rotate in small groups or individually.

Ebb and Flow of Experiences[Tomlinson]

Individual Individual

Small Group Small Group

Whole Group

Back and forth over time or course of unit

Basic Principles:

• Assessment informs instruction – Diagnosis and action taken as a result of diagnosis are paramount.

• Assessment and instruction are inseparable.

• Change complexity, not difficulty. Change the quality/nature, not the quantity. Structured or open-ended?

Basic Principles:(Continued)

• Use respectful tasks.• Use tiered lessons• Compact the curriculum.• Scaffold instruction.• Organization and planning enable

flexibility.

Basic Principles:(Continued)

• Teachers have more control in the classroom, not less.

• Frequently uses flexible grouping.• Teachers and students collaborate to deliver

instruction.

Models of Instruction That Work

Dimension of Learning:[Robert Marzano]

• Positive Attitudes and Perceptions about Learning• Acquiring and Integrating Knowledge• Extending and Refining Knowledge• Using Knowledge Meaningfully• Productive Habits of Mind

1/3 Model: [Canaday and Rettig]

• 1/3 Presentation of content• 1/3 Application of knowledge and skills

learned• 1/3 Synthesis of the information

Concept Attainment Model: [Summarized from Canaday and Rettig]

• Teacher presents examples, students work with them, noting attributes

• Teacher has students define the concept to be learned• More examples are critiqued in light of newly discovered

concept• Students are given practice activities in which they apply

their understanding of the lesson concept• Students are evaluated through additional applications

CONSTRUCTIVISM

Traditional Learning Constructivist Learning

• Part to whole, emphasize skills

• Strict adherence to curriculum

• Rely on textbooks, workbooks

• Students are “blank slates”

• Teachers disseminate info

• Teachers seek correct answer to validate learning

• Assessment/Teaching separate

• Whole to part, emph. concepts

• Pursue student questions

• Rely on prim. sources, manip.

• Students are thinkers

• Teachers mediate, interact

• Teachers seek students’ knowledge to make decisions

• Assessment/Teaching are interwoven

Direct Instruction Model [Summarized from Canaday and Rettig]

• Review previously learned material/homework• State objectives for today• Present material• Provide guided practice with feedback• Re-teach (as needed)• Assign independent practice with feedback• Review both during and at the end of the lesson• Closure (Summarization)

Learning Profile Models:

Myers - Briggs Personality Styles, Bernice McCarthy’s 4MAT System, Gregorc Scale and Teaching Model, Bramson’s Styles of

Thinking, Left Brain vs. Right Brain, Multiple Intelligences

Additional Differentiated Instruction Strategies

• Use Anticipation Guides• Create personal agendas for some students• Use centers/learning stations• Adjust journal prompts and level of

questioning to meet challenge levels• Incorporate satellite studies (“Orbitals”)

Personal Agenda for Michael R., December 5th, 2008

Daily Tasks:

• ___ Place last night’s homework at the top right corner of desk.• ___ Record warm-up activity from chalkboard into learning log.• ___ Complete warm-up activity.• ___ Listen to teacher’s explanation of the lesson’s agenda.• ___ Record assignments from Homework Board into notebook.

Specific to Today’s Lesson:

• ___ Get graphic organizer from teacher and put name/date at top.• ___ Fill in examples in g.o. while teacher explains it to the class.• ___ Read both sides of the g.o. so you know what you are looking for.• ___ Watch the video and fill in the g.o. during the breaks. • ___ Complete closing activity for the video. • ___ Ask Ms. Green to sign your assignment notebook. • ___ Go to math class, but first pick up math book in locker.

Vividness

• “a lot” – Running to each wall to shout, “a” and “lot,” noting space between

• Comparing Constitutions – Former Soviet Union and the U.S. – names removed

• Real skeletons, not diagrams• Simulations • Writing Process described while sculpting

with clay

CELL BODY

AXON

Myelin sheath

Schwann cellNode of Ranvier

Synaptic terminals

Dendrites NucleusSynapses

Neuron

Oxygen/Nutrient-Filled Bloodflow When the Body is in Survival Mode

Vital Organs

Areas associated with growth

Areas associated with social activity

Cognition

The Brain’s Dilemma:What Input to Keep, and What Input to Discard?

• Survival• Familiarity/Context

• Priming• Intensity• Emotional Content• Movement• Novelty

-- Summarized from Pat Wolfe’s Brain Matters, 2001

Priming means we show students:

1) What they will get out of the experience (the objectives)

2) What they will encounter as they go through the experience (itinerary, structure)

Prime the brain prior to asking students to do any learning experience.

Worthy they were, Rafael, Leonardo, Michelangelo, and Donatello.Theirs’ a chromatic and plumed rebirth,‘A daring reflection upon man. Beyond Hastings and a Wive’s tale in Canterbury, Galileo thrust at more than Windmills, He, Copernicus Gravitas. And for the spectre of debate, religion blinked then jailed, errant no more, thereby errant forever.Cousin to Pericles, Son of Alexander, The cosmology of Adam fanned for all, feudal plains trampled by trumpeters, man and woman lay awake --calves on wobbly legs,staring at new freedomand Gutenberg’s promise.

Creating Background Where There is None

• Tell the story of the Code of Hammurabi before discussing the Magna Charta.

• Before studying the detailed rules of baseball, play baseball.

• Before reading about how microscopes work, play with micros copes.

• Before reading the Gettysburg Address, inform students that Lincoln was dedicating a cemetery.

Creating Background Where There is None

• Before reading a book about a military campaign or a murder mystery with references to chess, play Chess with a student in front of the class, or teach them the basic rules, get enough boards, and ask the class to play.

• In math, we might remind students of previous patterns as they learn new ones. Before teaching students factorization, we ask them to review what they know about prime numbers.

• In English class, ask students, “How is this story’s protagonist moving in a different direction than the last story’s protagonist?”

• In science, ask students, “We’ve seen how photosynthesis reduces carbon dioxide to sugars and oxidizes water into oxygen, so what do you think the reverse of this process called, ‘respiration,’ does?”

Moving Content into Long-term Memory

Students have to do both,

Access Sense-Making

Process Meaning-Making

Beginning Middle

End Lesson Sequence

The Primacy-Recency Effect

The way the brain learns

How many teachers sequence their lessons for learning

Avoid ConfabulationThe brain seeks wholeness. It will fill in the holes in

partial learning with made-up learning and experiences, and it will convince itself that this

was the original learning all along. To prevent this:

Deal with Misconceptions!

Students should summarize material they already understand, not material they are coming

to know.

Perception

• What do you see?• What number do you see?• What letter do you see?

Perception is when we bring meaning to the information we receive, and it depends on prior knowledge and what we expect to see. (Wolfe, 2001)

Are we teaching so that students perceive, or just to present curriculum and leave it up to the student to perceive it?

Recall Success with Individual, Unrelated Items

Age of Student

# of Unconnected, Individual Items

Successfully Recalled (plus or minus 2, Wolfe, 2001)

5 2

7 3

11 5

15+ 7

We file by similarities, and we retrieve by differences.

What does this mean for instruction?

Taking Positive Risks

“The fellow who never makes a mistake takes his orders from one who does.”

-- Herbert Prochnow

“If I had been a kid in my class today, would I want to come back tomorrow?”

-- Elsbeth Murphy

“Nothing ventured, something lost.” -- Roland Barth

Negating Students’ Incorrect Responses While Keeping Them in the Conversation

• Act interested, “Tell me more about that…”• Empathy and Sympathy: “I used to think that, too,” or “I

understand how you could conclude that…”• Alter the reality:

-- Change the question so that the answer is correct-- That’s the answer for the question I’m about to ask

-- When student claims he doesn’t know, ask, “If you DID know, what would you say?”

Negating Students’ Incorrect Responses and While Them in the Conversation

• Affirm risk-taking• Allow the student more time or to ask for

assistance• Focus on the portions that are correct

Remember Who’s Doing the Learning: • Whoever responds to students/classmates is doing

the learning. Make sure the majority of the time it’s the students responding, not the teacher.

• Teachers ask 80 questions each hour on average, while students ask only two during that same hour. (Hollas) Students learn more when they ask the questions. Find ways to make question-asking so compelling and habitual they can’t escape it.

Inquiry Method 1. Something arouses students’ curiosity. 2. Students identify questions regarding topic. There is usually

one main question with several sub-questions that help answer the main question. These questions are submitted to classmates for review.

3. Students determine the process of investigation into topic. Their proposal for how to conduct the investigation is submitted to classmates for review and revision as necessary.

4. Students conduct the investigation. 5. Students share their findings.

Socratic Seminar

Pre-Seminar:A. Shared experiences, chosen for richness of ideas,

issues, ambiguity, “discussability”B. Students reflect on material Group dynamics, ground rules, and courtesy are

understood and accepted. Seminar: A. Teacher asks a provocative question. Opening, Core, and

Closure QuestionsB. Students respond to the provocative question and each

other. C. Teacher offers core questions that help students interpret

and to re-direct, also evalutes and tries to keep mouth shut.

C. Closing – connect to the real world of the student

Post-SeminarWritings, Summations, Artwork, Reflection, Critique, Analysis

Debate Format

1. Statement of the General Debate Topic and Why it’s Important – 1 min.2. Affirmative Position Opening Remarks – 3 min. 3. Negative Position Opening Remarks – 3 min.4. Affirmative Position Arguments – 5 min.5. Negative Position Arguments – 5 min.6. Caucus – Students on both teams consider their

arguments and rebuttals in light of what has been presented. – 3 min.

7. Affirmative Rebuttal and Questioning of the Negative’s Case – 3 min.

8. Negative Rebuttal and Questioning of the Affirmative’s Case – 3 min.

9. Closing Arguments Affirmative Position – 2 min.10. Closing Arguments Negative Position – 2 min.

Meeting of Mindsat Rachel Carson Middle School

Portrayals of Dr. Sally Ride, Albert Einstein, Josef Stalin, Bob Dylan, Boss

Tweed, Dr. Robert Oppenheimer, Senator Joseph McCarthy, the

Unsinkable Molly Brown, Rosa Parks. In the background: Advisors for each

historical figure

Meeting of Minds

Potential Topics for Discussion:• Should Earth have one language or many?

What are the roles of men and women in society?

• Should students be required to wear uniforms in school?

• What are the qualities of a good leader?• Should rap music lyrics be censored?• Should our country have gone to war?

Logical Fallacies

• Ad Hominem (Argument To The Man) -- Attacking the person instead of attacking his argument: “Dr. Jones’ conclusions on ocean currents are incorrect because he once plagiarized an research article.”

• Straw Man (Fallacy of Extension) -- Attacking an exaggerated version of your opponent's position. "Senator Jones says that we should not fund the attack submarine program. I disagree entirely. I can't understand why he wants to leave us defenseless like that." *

• The Excluded Middle (False Dichotomy) -- Assuming there are only two alternatives when in fact there are more. For example, assuming Atheism is the only alternative to Fundamentalism, or being a traitor is the only alternative to being a loud patriot. *

From Jim Morton’s’ “Practical Skeptic” website http://members.aol.com/jimn469897/skeptic.htm)

http://members.aol.com/jimn469897/skeptic.htm

Sleep

• Melatonin production in young adolescents shifts by 3 to 5 hours, but runs for the same length of time.

• Sleep deprivation often invokes the starvation response in the body.

• Sleep helps us encode memories for long-term memory; lack of sleep lowers the brain’s capacity to learn new things

(Dye, 2000, as cited in Sprenger)

Memorization Techniques

Practice reciting facts while looking at your eyes in a mirror, while standing in front of your family or friends, while waiting.

Memorize the lines from the end to the front.Memorize in phrases, and use “bridges” (last word of one

phrase, first word of the next phrase) Use different voices to recite the facts/lines. Have someone call the cues for you.Use memory devices (mnemonics). Have a crazy conversation with someone, in which each time

one of you speaks, you use one of the words or concepts. Let time pass between memorizing sessions. Draw and color a picture of the concepts/lines. Use props.Practice in the same place you’ll be asked to remember

them. Make an outline of the lines or concepts, and memorize that.

“All thinking begins with wonder.”-- Socrates

Our job is not to make up anybody’s mind, but to open minds and to make the agony of decision-making so intense you can escape only by thinking.”

-- Fred Friendly, broadcaster

Motivating Students When Nothing Else Works

• Teacher Assistance Teams• Specialists• Coaches or Pastors/Rabbis• Alternative Instruction• Strong relationship with trusted adult • Diet• Sleep• Doctor’s Physical Exam• Looping• Deal with poverty issues

Motivating Students When Nothing Else Works (cont.)

• Middle school concept

• Teacher training in young adolescence • Videotaping• Behavior checklist• Use inertia• Deal with loneliness and/or powerlessness• Multiple intelligences• Ask the student

Classroom Samples

• Students watch an instructional video. Every 10 to 15 minutes, the teacher stops the video and asks student to summarize what they’ve learned.

• The teacher does several math problems on the front board, then assigns students five practice problems to see if they understand the algorithm.

• Students are working in small groups on an assigned task. One student isn’t cooperating with the rest of his group, however, and as a result, the group is falling farther behind the other groups.

• There are only enough microscopes for every three students. One student uses the microscope to bring items into focus, another draws what the group sees through the eyepiece, then the three students answer questions.

• Students are silently reading content in their textbooks and completing a graphic organizer about the material.

• Eleven students do not do the assignment from last night. Consequently, they are not prepared to move on with the class in today’s task.

• Four ELL students have been placed in your class, but they are far from comfortable with English, especially with the vocabulary associated with your subject area.

TieringCommon Definition -- Adjusting the following to maximize learning:

– Readiness– Interest– Learning Profile

Rick’s Preferred Definition:

-- Changing the level of complexity or required readiness of a task or unit of study in order to meet the developmental needs of the students involved (Similar to Tomlinson’s “Ratcheting”).

Tier in gradations

Tiering Assignments and Assessments

Example -- Graph the solution set of each of the following:

1. y > 2 2. 6x + 3y < 2 3. –y < 3x – 7

2. 6x + 3y < 2 3y < -6x + 2 y < -2x + 2/3

x y 0 2/3 3 -5 1/3

Given these two ordered pairs, students would

then graph the line and shade above or below it,

as warranted.


For early readiness students:• Limit the number of variables for which student

must account to one in all problems. ( y > 2 )• Limit the inequality symbols to, “greater than” or,

“less than,” not, “greater then or equal to” or, “less than or equal to”

• Provide an already set-up 4-quadrant graph on which to graph the inequality

• Suggest some values for x such that when solving for y, its value is not a fraction.


For advanced readiness students:• Require students to generate the 4-quadrant graph

themselves• Increase the parameters for graphing with

equations such as: --1 < y < 6• Ask students what happens on the graph when a

variable is given in absolute value, such as: /y/ > 1• Ask students to graph two inequalities and shade or

color only the solution set (where the shaded areas overlap)

Anchor activities refer to two types of learner management experiences:

• “Sponge” activities that soak up down time, such as when students finish early, the class is waiting for the next activity, or the class is cleaning up or distributing papers/supplies

• A main activity everyone is doing from which the teacher pulls students for mini-lessons

Anchor Lesson Design

Anchor Activity(10-45 min.)

Activity/Group:

Activity/Group:

Activity/Group:

Activity/Group:

• Use activities with multiple steps to engage students• Require a product – ‘increases urgency and

accountability• Train students what to do when the teacher is not

available• Start small: Half the class and half the class, work

toward more groups, smaller in size• Use a double t-chart to provide feedback• Occasionally, videotape and provided feedback

Anchor Activities Advice

[eye] [ear] [heart]

Char.’s of Char.’s of Char.’s of

success we’d success we’d success we’d

see we’d hear feel

Double-T Charts

What to DoWhen the Teacher is Not Available

Suggestions include:• Move on to the next portion; something may trigger an idea• Draw a picture of what you think it says or asks• Re-read the directions or previous sections• Find a successful example and study how it was done• Ask a classmate (“Ask Me,” “Graduate Assistant,”

“Technoids”)• Define difficulty vocabulary• Try to explain it to someone else

General lesson on the topic -- everyone does the same thing

Students practice, process, apply, and study the topic in small groups according to their needs, styles, intelligences, pacing, or whatever other factors that are warranted

Students come back together and summarize what they’ve learned

To Increase (or Decrease) a Task’s Complexity,

Add (or Remove) these Attributes:• Manipulate information, not just echo it • Extend the concept to other areas • Integrate more than one subject or skill• Increase the number of variables that must be considered; incorporate

more facets• Demonstrate higher level thinking, i.e. Bloom’s Taxonomy, William’s

Taxonomy• Use or apply content/skills in situations not yet experienced• Make choices among several substantive ones• Work with advanced resources• Add an unexpected element to the process or product• Work independently• Reframe a topic under a new theme• Share the backstory to a concept – how it was developed• Identify misconceptions within something

To Increase (or Decrease) a Task’s Complexity,

Add (or Remove) these Attributes:• Identify the bias or prejudice in something• Negotiate the evaluative criteria• Deal with ambiguity and multiple meanings or steps• Use more authentic applications to the real world• Analyze the action or object• Argue against something taken for granted or commonly accepted• Synthesize (bring together) two or more unrelated concepts or objects

to create something new• Critique something against a set of standards• Work with the ethical side of the subject• Work in with more abstract concepts and models• Respond to more open-ended situations• Increase their automacity with the topic• Identify big picture patterns or connections• Defend their work

• Manipulate information, not just echo it: – “Once you’ve understood the motivations and viewpoints of the two

historical figures, identify how each one would respond to the three ethical issues provided.”

• Extend the concept to other areas: – “How does this idea apply to the expansion of the railroads in

1800’s?” or, “How is this portrayed in the Kingdom Protista?”

• Work with advanced resources: – “Using the latest schematics of the Space Shuttle flight deck and real

interviews with professionals at Jet Propulsion Laboratories in California, prepare a report that…”

• Add an unexpected element to the process or product: – “What could prevent meiosis from creating four haploid nuclei

(gametes) from a single haploid cell?”

• Reframe a topic under a new theme: – “Re-write the scene from the point of view of the

antagonist,” “Re-envision the country’s involvement in war in terms of insect behavior,” or, “Re-tell Goldilocks and the Three Bears so that it becomes a cautionary tale about McCarthyism.”

• Synthesize (bring together) two or more unrelated concepts or objects to create something new: – “How are grammar conventions like music?”

• Work with the ethical side of the subject: – “At what point is the Federal government justified in

subordinating an individual’s rights in the pursuit of safe-guarding its citizens?”

The Equalizer (Carol Ann Tomlinson)

Foundational ------------------ TransformationalConcrete ------------------------ AbstractSimple --------------------------- ComplexSingle Facet/fact -------------- Multi-Faceted/factsSmaller Leap ------------------- Greater LeapMore Structured --------------- More OpenClearly Defined ---------------- Fuzzy ProblemsLess Independence -------- Greater IndependenceSlower --------------------------- Quicker

William’s Taxonomy

FluencyFlexibility

OriginalityElaboration

Risk TakingComplexity

Curiosity

Imagination

Frank Williams’ Taxonomy of Creative Thinking

Fluency – We generate as many ideas and responses as we can

Example Task: Choose one of the simple machines we’ve studied (wheel and axle, screw, wedge, lever, pulley, and inclined plane), and list everything in your home that uses it to operate, then list as many items in your home as you can that use more than one simple machine in order to operate.

---------------------------------------------------------------------------------------------------------

Flexibility – We categorize ideas, objects, and learning by thinking divergently about them

Example Task: Design a classification system for the items on your list.


Originality – We create clever and often unique responses to a prompt

Example Task: Define life and non-life. -------------------------------------------------------------------Elaboration – We expand upon or stretch an

idea or thing, building on previous thinking

Example: What inferences about future algae growth can you make, given the three graphs of data from our experiment?


Risk Taking – We take chances in our thinking, attempting tasks for which the outcome is unknown

Example: Write a position statement on whether or not genetic engineering of humans should be funded by the United States government.

-------------------------------------------------------------------------------Complexity – We create order from chaos, we explore the

logic of a situation, we integrate additional variables or aspects of a situation, contemplate

connections

Example: Analyze how two different students changed their lab methodology to prevent data contamination.


Curiosity – We pursue guesses, we wonder about varied elements, we question.

Example: What would you like to ask someone who has lived aboard the International Space Station for three months about living in zero-gravity?

-------------------------------------------------------------------------------Imagination – We visualize ideas and objects, we go

beyond just what we have in front of us

Example: Imagine building an undersea colony for 500 citizens, most of whom are scientists, a kilometer below the ocean’s surface. What factors would you have to consider when building and maintaining the colony and the happiness of its citizens?

R.A.F.T.S.

R = Role, A = Audience, F = Form, T = Time or Topic, S = Strong adverb or adjective

Students take on a role, work for a specific audience, use a particular form to express the content, and do it within a time reference, such as pre-Civil War, 2025, or ancient Greece.

Sample assignment chosen by a student:

A candidate for the Green Party (role), trying to convince election board members (audience) to let him be in a national debate with Democrats and the Republicans. The student writes a speech (form) to give to the Board during the Presidential election in 2004 (time). Within this assignment, students use arguments and information from this past election with third party concerns, as well as their knowledge of the election and debate process. Another student could be given a RAFT assignment in the same manner, but this time the student is a member of the election board who has just listened to the first student’s speech.

R.A.F.T.S.

Raise the complexity: Choose items for each category that are farther away from a natural fit for the topic . Example: When writing about Civil War Reconstruction, choices include a rap artist, a scientist from the future, and Captain Nemo.

Lower the complexity: Choose items for each category that are closer to a natural fit for the topic. Example: When writing about Civil War Reconstruction, choices include a member of the Freedmen’s Bureau, a southern colonel returning home to his burned plantation, and a northern business owner

Learning Menus

Similar to learning contracts, students are given choices of tasks to complete in a unit or for an assessment. “Entrée” tasks are required, they can select two from the list of “side dish” tasks, and they can choose to do one of the “desert” tasks for enrichment. (Tomlinson, Fulfilling the Promise of the Differentiated Classroom, 2003)

Tic-Tac-Toe Board

Geometry

Summarize (Describe)

Compare (Analogy) Critique

A Theorem

An math tool

Future Developments

Change the Verb

Instead of asking students to describe how FDR handled the economy during the Depression, ask them to rank four given economic principles in order of importance as they imagine FDR would rank them, then ask them how President Hoover who preceded FDR would have ranked those same principles differently.

Analyze… Construct…Revise… Rank…Decide between…Argue against…Why did… Argue for…Defend… Contrast…Devise… Develop…Identify… Plan…Classify… Critique…Define… Rank…Compose… Organize…Interpret… Interview…Expand… Predict…Develop… Categorize…

Suppose… Invent…Imagine… Recommend…

Thinking Critically with Gifted Students

• No matter what readiness level, we teach essential and enduring knowledge first.

• Gifted experiences illuminate more material during the course of the year, whether by moving more rapidly, by exploring concepts in greater depth, or by offering more breadth in the field of study.

• Gifted students encounter higher order thinking skills (analysis, synthesis, evaluation, application, justification) as standard operating procedure.

• In gifted experiences, tangential thinking is invited. • Subjects are integrated to a larger extent.• Assessment is more authentic and alternative assessment is

more likely to occur in gifted experiences.• Instruction can be differentiated in terms of changing focus

on concept’s depth, frequency, assessment, and/or multi-dimensional understanding.

• Gifted students often think academic struggle is a weakness, something to avoid. We teach otherwise. To seek challenge and to struggle with learning strengthens us. It is an academic virtue.

• Enrichment does not equal fluff. All activities are academically substantive.

• Gifted experiences will have some unique opportunties: Socratic Seminars, Meeting of the Minds, and determining authenticity of historical fiction books are examples.

• Gifted experiences often have more shared leadership in the classroom (‘a bit more democracy).

• Our textbook and novels are resources, not the curriculum.• Primary sources in research are more heavily valued and used

in gifted experiences.

• In general, gifted students do not like whole novels to be read to them. Excerpts are fine.

• Gifted experiences expose children to a larger variety of language and literature.

• Non-traditional grammar, sentence structures, vocabulary words and writer’s voice are encouraged in gifted experiences.

• There can often be a wider range of readiness levels in a classroom of gifted students than there is in a classroom of regular students – be ready for them!

• Gifted students tend to appreciate the teacher’s use of humor more than regular students do.

• Gifted experiences move students toward greater autonomy than would be found in regular education experiences.

As often as possible, compact the curriculum. It actually hurts an advanced student’s education to teach him content and skills he already knows.

Don’t forget to make the implicit explicit. We would never assign students to portray historical figures in a mock trial, for example, and never teach them how to do it.

Two Important Planning Points:

1.Practice turning regular education experiences into gifted/advanced education experiences. Give it a shot right now with anything in your lesson.

2.Anticipate the need for gifted/advanced experiences in every lesson and actively plan for those opportunities.

“Little Geniuses” (Article by Thomas Armstrong about alternative giftedness). http://www.thomasarmstrong.com/articles/geniuses.htm

• Acting Ability• Adventuresomeness• Aesthetic perceptiveness• Artistic Talent• Athletic prowess• Common sense• Compassion• Courage• Creativity• Emotional maturity• Excellent memory• Imagination• Inquiring mind• Intuition• Inventiveness• Knowledge of a given subject• Leadership abilities• Literary aptitude• Logical-reasoning ability

Manual dexterity Mathematical ability Mechanical know-how Moral character Musicality Passionate interest in a specific topic Patience Persistence Physical coordination Political astuteness Problem-solving capacity Reflectiveness Resourcefulness Self-discipline Sense of humor Social savvy Spatial awareness Spiritual sensibility Strong will Verbal ability

http://www.thomasarmstrong.com/articles/geniuses.htm

Great Resources!

• www.nagc.org – National Association for Gifted Children • www.cec.sped.org – Council for Exceptional Children• Tomlinson, Carol Ann, Doubet, Kristina. (2006) Smart in the

Middle Grades: Classrooms that Work for Bright Middle Schoolers. Westerville, OH: NMSA

• Tomlinson, C.A., Kaplan, S.N., Renzulli, J.s., Purcell, J., Leppien, J., & Burns, D. (2002) The Parallel Curriculum: A design to Develop High Potential and Challenging High Ability Learners. Thousand Oaks, CA: Corwin Press

http://www.nagc.org/

http://www.cec.sped.org/

Great Resources!• Winebrenner, Susan. Teaching Gifted Kids in the Regular

Classroom: Strategies and Techniques Every Teacher Can Use to Meet the Academic Needs of the Gifted and Talented, Free Spirit Publishing, 2001

• Wormeli, Rick. (2005) Summarization in any Subject. Alexandria, VA: ASCD; (2006) Fair Isn’t Always Equal: Assessment and Grading in the Differentiated Classroom. Portsmouth, ME: Stenhouse; (2007) Differentiation: From Planning to Practice, Grades 6-12. Portsmouth, ME: Stenhouse; (2009) Metaphors& Analogies: Power Tools for Teaching any Subject, Portsmouth, ME: Stenhouse

• Anything on gifted by Richard Cash or Diane Heacox

Reality Check

•We can offend ELL students.•Some ELL students don’t receive appropriate instruction

for their intellectual level. • There’s a lot of anxiety when we don’t know the

language or culture of the country in which we are living, so much so that many of us would find it hopeless to keep trying. It takes a tremendous amount of energy and patience every day to remain attentive and engaged when you’re first learning a language.

Remember:

Unfortunately, we tend to equate low language proficiency with low mental function as well. As a result, we don’t ask ELL students to make comparisons, analyze data, connect ideas, synthesize concepts, or evaluate performances. By not pushing ELL students this way, these students get further behind. What can we do to move our mindset past this conventional way of thinking?

Language Thinking Proficiency Proficiency

Students in some cultural groups are reluctant to publicly ask questions, particularly of adults, and also may be hesitant to make conjectures. For students from cultures in which students are expected to wait to be asked before speaking, and where students are not expected to ask questions of elders, it is very important for the teacher to explicitly set the expectation for students to ask questions and express their opinions in the…classroom. Otherwise, classroom discourse becomes an exercise in trying to participate in a game where only others know the unwritten rules.

Debra Coggins, Drew,Kravin, Grace Coates, Carroll Davila, Maria Dreux, English Language Learners in the Mathematics Classroom, Corwin Press, 2007, p. 82

1.Speak slowly and clearly.2.Repeat important words/information several

times.3.Extend time periods for responding to prompts. 4.Avoid using idioms and colloquialisms until

students are more advanced with our culture, or if we use them, take the time to explain them to ELL students.

5.Gesture and point to what we are referring.

25 Practical Tips for Assisting ELL Students in the Regular Classroom

6. Ask students to read text more than once.7. Label objects and concepts in the classroom frequently.8. Provide a lot of specific models, including a lot of hands-

on experiences.9. Use a lot of visuals: pictures, illustrations, graphs,

pictographs as well as real objects during instruction.10. Frequently demonstrate what we mean, not just

describe it. From Classroom Instruction that Works with English Language Learners (ASCD, 2006, p. 41), Hill and Flynn offer, “ELLs will have a greater chance of learning and recalling terms if they use their arms to represent the radius, diameter, and circumference of circles or the right, acute, and obtuse angles of polygons.”

11. Make ELL students feel like they belong and have a role to play in classroom learning.

12. Use a lot of thinking aloud or self-talk to model the sequence of doing the task or the language to use when thinking about the concept.

13. Use cooperative learning groups; let ELL students work with English proficient partners.

14. Sometimes let students draw responses instead of writing them; use more than one format for assessing students if the general approach won’t allow ELL students to accurately portray what they know.

15. Find ways to enable ELL students to demonstrate their intellectual skills and maintain dignity.

16. Give students very quick feedback on their word use. 17. Spend time before lessons building personal background in English

language learners so they have an equal chance to attach new learning to what’s already in their minds.

18. Stay focused on how ELL students are doing toward their learning goals, not how they’re doing in relation to other students. We remove ll hope when we ceaselessly cajole ELL students into proficiency by comparing them to language proficient students. It’s a mistake to think they need more motivation or that parading others’ success in front of them motivates them; they desperately want to be proficient.

19. Recognize the difference between conversational language and academic language and that students need help with both; learning one does not mean you’ve learned the other. This means we go out of our way to explain terms like, “similar,” “math exercise,” “vocabulary,” “compare,” “supporting detail,” “analyze,” “instead of,” “not only,” “while,” “unlike,” “common,” “distinct,” “feature,” “trait,” “characteristic,” and, “equal.”

20. Take the time to learn about English language learners home countries.

21. Invite ELL students to learn and explore ideas in their own languages first, then translate them to English

22. Provide ELL students with response stems, such as, “One thing that I learned was….”

23. Ask students to re-state classmates’ comments as they begin their own comments

24. Relate concepts in story format before specific instruction

Additional Ideas from, English Language Learners in the Mathematics Classroom (2007)

25. Incorporate all those vocabulary acquisition strategies you learned years ago as well as the ones that see today. You can’t have too many vocabulary building ideas! Seriously, we all should be vocabulary guru’s no matter what subject we teach.

ELL’s need Authentic Talk -- Is this authentic?

•What is Ben doing?•Ben is holding a picture of a whale in the ocean. •Why is Ben holding a picture of a whale in the ocean?•Ben is holding a picture of a whale in the ocean because

he is interested in protecting whales in the ocean.•Why is Ben interested in protecting whales in the

ocean?•Ben is interested in protecting whales in the ocean

because he is afraid they will become extinct.•What does the word, “extinct” mean?•“Extinct” means there are no more animals of that kind

on our planet.

Is this Conversation Authentic?

•Where can I buy soccer cleats? Mine are too old. I can’t turn fast in them. I’m the “sweep” this weekend.

•Wow, I hate playing sweep. I’m a mid-fielder.•I can’t play mid-field very well. It’s too tiring. You have

to be everywhere. •Yeah, but you can get the other team off sides. •Sometimes, but I don’t think about that a lot. So, ‘the

cleats?•Oh yeah. Over at Fair Oaks Mall, there’s a sports store

near the soft pretzel shop. Who are you playing? My twin sister plays goalie for a team. They might be playing you.

Avoid Painting All ELL Students with Same, Broad Brush Stroke!

Just like regular education students, all ELL students are not at the same point of development in language.

Some ELL students can respond to*:“Show me…,” “Label the….,” “Circle the…,” “Where is…,” “Who

has….,” and yes-no questions.

After a year or three, most ELL students can respond to:“Why…,” “How…,” “Explain…,” “What would happen if…,” “Why do

you think…” and “Decide if….”

Successful teachers respond strategically to this variance in ELL students, including those ELL students whose performance is outside these ranges.

*Hill and Flynn citing a Krashen and Terrell study

Metaphorical and Critical Thinking is Universal!

At every stage of language acquisition, all of humanity thinks metaphorically. Hispanic, Greek, French, Phillippino, Chinese, Japanese, Korean, American, Egyptian, Iraqi, Italian, and Norwegian people think metaphorically. To not include metaphors, analogies, pattern recognition, and critical thinking in ELL students’ learning experiences due to language struggles is like assuming they don’t know how to feed themselves because they don’t eat the same food as we do. It’s pompous, and it denies ELL students their basic instruction. We can’t save advanced thinking only for advance language proficiency students.

Bilinguals tend to outperform monolinguals on some tests of language and nonverbal intelligence, including the ability to think abstractly about language, or meta-linguistic awareness, and one kind of creativity known as divergent thinking. Other studies have shown that bilinguals are better at executive control, or the ability to solve problems that require us to ignore irrelevant information and to focus on what is important. They also have superior working memories, that is, a better ability to keep information in mind while solving a problem.

-- James Crawford and Stephen Krashen, English Learners in American Classrooms: 101 Questions, 101 Answers (Scholastic,

2007, p. 31)

We only remember concepts that we can understand. So, teach subject content to ELL students in their native language whenever possible (Crawford and Krashen, 2007). As students become proficient in the specific content, place them in “sheltered instruction” experiences in which we focus predominantly on that content, but we weave in English as much as possible without diluting full content mastery.

Sheltered Instruction

“The goal in the minds of both students and the teacher is mastering the subject matter, not particular rules of grammar or vocabulary. In this way, students absorb academic English naturally and incidentally, while they are learning useful knowledge. If students are tested, they are tested on subject matter, not language.” (p. 24)

Sheltered Instruction

For Translations if your District Doesn’t have Translation Staff: Translation Web sites. Look also for associations of language translators.

Use the student’s family members.

Contact the Embassy or Consulate in Washington, D.C. or local to you

Contact a bank or investment firm in your area that does a lot of international financing.

Use local associations of individuals from the specific culture in question. They often have liaisons with the larger community and can contact their membership to find someone who can help with translations. Use translation scanners -- often pocket-sized, that can translate almost any language into English and back again.

References, Research, and More Ideas

1.Cary, Stephen. Working with English Language Learners: Answers to Teachers’ Top Ten Questions, 2nd edition, Heinemann, 2007

2.Coggins, Debra; Kravin, Drew; Coates, Grace Davila; Carroll, Maria Dreux. English Language Learners in the Mathematics Classroom, Corwin Press, 2007

3.Crawford, James; Krashen, Stephen. English Learners in American Classrooms: 101 Questions, 101 Answers,

Scholastic, 20074.Feldmand, Jerome A. From Molecule to Metaphor, MIT

Press, 20085.Flynn, Kathleen M., Hill, Jane D. Classroom Instruction

that Works with English Language Learners, ASCD, 2006

6.Wormeli, Rick. Metaphors & Analogies: Power Tools for Teaching any Subject, Stenhouse Publishers, 2009

“The assignment: Build a paper-based data visualization, as directed by the infosthetics.com website…The inspiration: Strips of paper discarded next to the school’s paper trimmer. My yearning for sunlight.

“Description: I currently live in Umeå, a city at latitude 63° 50 N in ′northern Sweden. Our winter days are short and summer days are long. Using the actual and predicted lengths of daylight for the first of each month in 2009, I created a visualization with 12 “petals”. The outer loop of each petal represents the 24 hours in the day; the inner loop is the length of daylight, ranging from 4h 33m on January 1 to 20h 34m on July 1. The white thread where the loops are joined is the start/end point. Each outer loop is 24 cm from start to end point, representing 24 hours. The inner loop for January is a little over 4.5 cm, representing the 4h 33m. When assembled, like a clock, the top loop is 12 (December 1); the bottom one opposite it is 6 (June 1).

“I like how the simple lines suggest the passing of time and the cycle of the months as well as the promise of spring to come. There are multiple flower forms suggested, from the symmetrical outer petals to the drooping flower formed by the inner loops, to the spikier poinsettia-like flower formed by the negative space in the middle.”

From: http://infosthetics.com/archives/2009/02/paper-based_visualization_competition_the_winner_and_more.html, and from, www.charlenelam.com

http://infosthetics.com/archives/2009/02/infosthetics_competition_build_a_paper-based_visualization.html

http://infosthetics.com/archives/2009/02/paper-based_visualization_competition_the_winner_and_more.html

http://infosthetics.com/archives/2009/02/paper-based_visualization_competition_the_winner_and_more.html

http://www.charlenelam.com/

MetaphorFrom the Greek, metapherein, which means “to transfer” and “to bear” (Merriam-Webster’s Collegiate Dictionary, 11th Edition, 2004).

We “transfer” or “bear” one concept/object/attribute to another, comparing something in one domain with an element in another domain. By domain, we refer to the larger categories or themes into which items fit. A metaphor re-imagines or re-expresses something in one category (domain) in terms of another category (domain) to clarify or further thinking: “She is my rock.” “That test was a monster.” “Reading those books created my ladder of success.”

Good metaphors give us new information (Glucksberg, 2001), not the same information. They don’t restate the obvious: cars are like automobiles. To be useful, they must provide fresh perspective or insight: My son’s car is a sports locker on wheels.

Consider this, too: In order to be a good metaphor, they must factually be false!

“Mathematics is not a way of hanging numbers on things so that quantitative answers to ordinary questions can be obtained. It is a language that allows one to think about extraordinary questions...getting the picture does not mean writing out the formula or crunching the numbers, it means grasping the mathematical metaphor.”

- James Bullock

We think primarily in physical terms. Over time we become adept at translating symbolic and abstract concepts into meaningful structures or experiences.

“Physicalizing” the abstract and symbolic:

• Gets oxygen and nutrients to cognitive centers of the brain via the bloodstream

• Relieves bone growth plate stress• Relaxes students and improves their

perspective/attitude – creates mild euphoria • Supports cognitive theory regarding how students

best learn• Makes abstract content vivid and thereby

illuminates it • It’s fun and intrinsically motivating

Physicalizing Process:

• Identify essential components, pieces, or definition of whatever we’re teaching

• Physicalize those pieces and present them to the class.

• Class critiques the physicalization in terms of accuracy, comprehensiveness, appropriateness, and clarity. ‘Makes suggestions for improvement.

All three steps are learning experiences that help students internalize the knowledge.

Have Some Fun – Anything Can Be A Metaphor!

An apple

• a star (the birth place of energy on our planet) in the middle (the seed pattern makes a star if we cut it the right way)

• we must break the surface to get to the juicy good parts• the outside doesn’t reveal what lies inside• the apple becomes soft and mushy over time• the apple can be tart or sweet depending on its family background• its parts are used to create multiple products

A cell phone

• lifeline to the larger world• an unapologetic taskmaster• an unfortunate choice of gods• a rude child that interrupts just when he shouldn’t• a rite of passage• a declaration of independence• a secret language encoder (text messaging abbreviations unknown to adults)• delineation of generations •

A pencil sharpener • Whittler of pulp• Tool diminisher• Mouth of a sawdust monster• Eater of brain translators • Cranking something to precision• Writing re-energizer• Scantron test enabler

Curtains

• Wall between fantasy and reality• Denied secrets• Anticipation• Arbiter of suspense• Making a house a home• Vacuum cleaner antagonist• Cat’s “Jungle Gym”

Railroad

• Circulatory system of the country• Enforcer of Manifest Destiny• Iron monster• Unforgiving mistress to a hobo• Lifeline• Economic renewal• Relentless beast • Mechanical blight• Movie set• A foreshadow of things to come• A hearkening to the past

Look Around your Classroom and Give it a Shot…

• Is that coffee cup a soothing friend or a catalyst for creativity?

• Is the open classroom door an invitation for the rest of the world to join in your discussion, or is it a momentary lapse in security?

• Is the computer sitting in the corner gathering dust an albatross around your neck, or does it represent emancipation from tedium and conventional practice?

Process for GeneratingMetaphors and Analogies

1. Break the topic into its component pieces. 2. Identify comparisons with the topic that are relevant to

students’ lives, making abstract ideas as concrete and personally affecting as possible. Create a common frame of reference in students if necessary.

3. “Test drive” the metaphor or analogy with others whose opinions you trust. Make sure the person can identify the metaphor and message on his own.

4. Double-check that the metaphor or analogy furthers your cause, won’t confuse students, and actually adds to instruction instead of weakens it.

5. After using a metaphor or analogy, ask students to evaluate its helpfulness.

Metaphors – Analysis Chart

• Symbol to Represent• Explanation of Symbol• How this Symbol Connects to Character/Event• Passages Cited to Support this Connection

-- Based on an idea from Kelly Gallagher’s Deeper

Reading

______________________ is (are) a _________________ because _______________________________________.

Ask students to include something intangible, such as suspicion or an odyssey, in the first blank. The tangible comparison---a combination lock or an elliptical trainer---would fit in the second section.

Ask students to justify their choices:

“Suspicion is a combination lock because it secures a possession’s well-being that cannot be assured through trust alone. Odyssey is an elliptical trainer because it has a beginning, middle, and end, and along the way, we encounter moments of endurance, doubt, despair, and elation, leaving comfort and returning again.”

Questioning the MetaphorFind a way to improve the metaphor or

analogy:

“Man has been here 32,000 years. That it took a hundred million years to prepare the world for him is proof that that is what it was done for. I suppose it is. I dunno. If the Eiffel tower were now representing the world's age, the skin of paint on the pinnacle-knob at its summit would represent man's share of that age; & anybody would perceive that that skin was what the tower was built for. I reckon they would. I dunno. - "Was the World Made for Man?“ (from, www.twainquotes.com)

http://www.twainquotes.com/

Metaphors Break Down“You can’t think of feudalism as a ladder because you

can climb up a ladder. The feudal structure is more like sedimentary rock: what’s on the bottom will always be on the bottom unless some cataclysmic event occurs.” -- Amy Benjamin, Writing in the Content Areas, p. 80

“A classroom is like a beehive.” Where does the simile sink? • Students are not bees. • Students have a variety of readiness levels and skill sets for completing

tasks. Bees are more uniform. • Students don’t respond blindly or purely to the pheromones of the

queen bee.• Students are busier throughout the day and night than bees.• Students don’t swarm when angered.

How Do these Metaphors Fall Apart?

1. Life is like an apple tree. 2. The structure of an essay is like a hamburger. 3. The lawyer harvested the information from three

witnesses. 4. She broke the glass ceiling. 5. Cancer is an unwelcome house guest.6. Eyes are windows to the soul.7. Urban renewal was the engine that powered the

committee.8. Their conversation was as risky as Russian roulette.9. That remark was the tipping point in the debate. 10. The purpose of a neuron’s myelin sheath is the same as

the Police Department’s motto: To serve and protect.

Test the Verb StrengthDid we invade the country, or did we liberate it? The choice of verbs frames our thinking. Ask students to change only the verb and explain how the reader or listener’s interpretation of the topic would change as a result.

The senator corralled her constituents. The senator coddled her constituents.The senator ignited her constituents.

The senator stonewalled her constituents.The senator suckered her constituents. The senator mollified her constituents.

The senator lifted her constituents.

Manipulate the Metaphor to See How It Changes Meaning

College# of Students Graduating

Seniors% Graduating

Apple University

10,500 2,009 19

Orange College

20,223 3,189 16

Banana Academy

5,600 1405 25

Grape Institute

15,171 2,335 15

Presenting like this, which one looks better for graduating?

0

500

1,000

1,500

2,000

2,500

3,000

3,500

Apple University Orange College Banana Academy Grape Institute

# of Graduates

# of Graduates

Presented like this, which one looks better for graduating?

0

5

10

15

20

25

30

Apple University Orange College Banana Academy Grape Institute

% Graduating

% Graduating

Conceptual MetaphorConcept: Ideas are food.

• All this paper has in it are raw facts, half-baked ideas, and warmed-over theories.

• There are too many facts here for me to digest them all. • I just can’t swallow that claim.• Let me stew over that for a while.• That’s food for thought.• She devoured the book. (p. 36)• Let’s let that idea simmer on the back burner for a while.

Concept: The mind is a computer • He is hard-wired for action. • My mental software no longer works.• I can’t quite retrieve that memory.• I haven’t yet processed what he said. (p. 113) • Did you store away what I told you?

What Do Conceptual Metaphors Mean for the Classroom?

• Explain conceptual metaphors frequently. “Learning is a journey” -- Do your students know what you mean by this? How about, “Inventors are forward-thinking?” -- Why do we think of invention as progress? Do inventors ever retard development?

• What was the conceptual metaphor that assisted the Nazi Party’s rise to power prior to World War II? What was the conceptual metaphor used by Henry Ford to develop his revolutionary ideas about assembly-line manufacturing, mass production of affordable automobiles, and paying workers high wages? What are the competing conceptual metaphors for dark matter, anti-matter, and what happened during the birth of the universe?

As you guide students’ metaphorical thinking, take the time to identify conceptual comparisons:

• What is the protagonist’s conceptual metaphor for life, and how is that different from he antagonist’s position?

• What are the conceptual metaphors used by both sides of the debate on global warming?

• By what conceptual metaphor do the leaders in Northern Sudan govern Darfur, and is there any hope of changing that metaphor so we can end the death and destruction resulting from this modern-day genocide?

• How did Nelson Mandela change the operative metaphors of South Africa?

• What is the new, post-Hurricane Katrina conceptual metaphor for New Orleans?

Ask Students to Practice Explaining Metaphors

Metaphor: “Google it.” Definition: Google is a common Internet search

engine. Instead of the longer statement, “Go to the Internet, find a search engine, and look for the topic using that search engine,” people shorten it to something that represents that whole process---the name of a common search engine, Google.

Make the Implicit, Explicit• What does it mean to triangulate something?• If our thinking is parallel to someone else’s

thinking, what do we mean?• The character said that life was like a carnival

Tilt-a-Whirl. What did she mean by that?• Kira just said she going to be toast tonight

with these grades. Is this good or bad for her?

Descriptions With and Without Metaphors

Friendship FamilyInfinity ImperialismSolving for a variable TrustEuphoria MercyWorry TroubleObstructionist Judiciary HonorImmigration HomeostasisBalance Temporal RiftsEconomic Principles Religious fervorPoetic License SemanticsHeuristics TautologyEmbarrassment Knowledge

Connotations

Ask students to identify multiple connotations of words. Consider using these terms: cook, light, fire, wall, bleed, read, cold, plant, shade, blanket, sound, wave, mask, book, race, curve, and table. Notice that changing the tense and/or parts of speech shifts the meaning in many cases: “He ran a good campaign.” “Let’s give it a dry run.” “Are you running out of steam?” “Let’s table this conversation until later.” “She sat at the table for dinner.” “The table displays the empirical data for our conclusions.”

Same Concept, Multiple Domains

The Italian Renaissance: Symbolize curiosity, technological advancement, and cultural shifts through mindmaps, collages, graphic organizers, paintings, sculptures, comic strips, political cartoons, music videos, websites, computer screensavers, CD covers, or advertisements displayed in the city subway system.The economic principle of supply and demand: What would it look like as a floral arrangement, in the music world, in fashion, or dance? Add some complexity: How would each of these expressions change if were focusing on a bull market or during a recession?

Geometric progression, the structure of a sentence, palindromes, phases of the moon, irony, rotation versus revolution, chromatic scale, Boolean logic, sine/cosine, meritocracy, tyranny, feudalism, ratios,the relationship between depth and pressure, musical dynamics, six components of wellness, and the policies of Winston Churchill can all be expressed in terms of: food, fashion, music, dance, flora, fauna, architecture, minerals, weather, vehicles, television shows, math, art, and literature.

Learning is to Analogy as Teaching is to _____________

• Identify the relationship between two elements: “Light sprinkle is to torrential downpour” -- the second item is a more intense version of the first one

• Determine what would constitute that same relationship in a completely different domain – In what other pair of items in a different domain is the second item a more intense version of the first one? How about: phrase/essay? smile/laughter? penlight/lighthouse? Battery power/nuclear power? bench/recliner? Seed/tree?

Common Analogous Relationships

• Antonyms • Synonyms • Age• Time • Part : Whole • Whole : Part • Tool : Its Action • Tool user : Tool • Tool : Object It’s Used With • Worker: product he creates• Category : Example • Effect : Cause • Cause : Effect• Increasing Intensity• Decreasing Intensity • Person : closely related

adjective

• Person : least related adjective• Math relationship• Effect : cause• Action : Thing Acted Upon • Action : Subject Performing the Action • Object or Place : Its User • Object : specific attribute of the object• Male : Female• Symbol : what it means• Classification/category : example• Noun : Closely Related Adjective • Elements Used : Product created• Attribute : person or object• Object : Where it’s located• Lack (such as drought/water – one thing lacks

the other)

Meaningful Arrangement and Patterns are Everything

d-a-o-o-u-i-d-y-v-l-e

Visuals and Graphics are Powerful!

Examples: When students are learning

vocabulary terms, significantly more are learned when students portray the words graphically (ex: Shape spellings) instead of defining terms and using them in a sentence.

Students can portray Aristotle’s Rhetorical Triangle (ethos, pathos, logos) by juggling.

• A life-size photo of skeletal children feverishly sewing goods in a garment factory as you discuss the rise of labor unions during the industrial revolution.

• A book or a wizard’s hat would be appropriate symbols for Hermione Granger in J.K. Rowling’s Harry Potter series.

• A magnifying glass could trigger images of detective fiction’s Sherlock Holmes.

• What’s a good visual symbol of the preterite in Spanish class? What icon might remind students to focus on their target heart rates in physical education class? Can you think of a suitable symbol for an economic recession? What graphic would reinforce the proper response of bystanders who see a classmate getting bullied? And how would Democrats and Republicans symbolize their own and each party’s main themes? Why is a particular person in history or character in a novel best portrayed by a brake pedal (because he slows forward progress of something) or a gas pedal (because he speeds things up)? (The gas/brake pedal metaphor is found in Kelly Gallagher’s Deeper Reading, Stenhouse

Publishers, 2005)

Creating and interpreting patterns of content, not just content itself, creates a marketable skill in today’s students. A look at data as indicating “peaks and valleys” of growth over time, noticing a trend runs parallel to another, or that a new advertising campaign for dietary supplements merges four distinct worlds -- Greco-Roman, retro-80’s, romance literature, and suburbia – is currency for tomorrow’s employees.

To see this in a math curriculum, for example, look at algebraic patterns. Frances Van Dyke’s A Visual Approach to Algebra (Dale Seymour Publications, 1998)

A submarine submerges, rises up to the surface, and submerges again. Its depth d is a function of time t. (p.44)

d

t

d

t

A submarine submerges, rises up to the surface, and submerges again. Its depth d is a function of time t. (continued)

d

t

d

t

Consider the following graphs. Describe a situation that could be appropriately represented by each graph. Give the quantity measured along the horizontal axis as well as the quantity measured along the vertical axis.

Statues (Body Sculpture)

Students work in small groups using every groupmember’s body to symbolically portray concepts

in frozen tableau.

Where does the learning occur?

Metaphors (Gallagher)

• Iceberg• Square Peg, Round Hole• Brake Pedal, Gas Pedal• Pencil/Eraser• Billiards Table• Snow Globe• _______ is like a _______ because ________.

Synectics(William J. Gordon)

“The joining together of different and apparently irrelevant elements,” or put more simply, “Making

the familiar strange.”

1. Teach a topic to students. 2. Ask students to describe the topic, focusing on descriptive

words and critical attributes.3. Teacher identifies an unrelated category to compare to the

descriptions in #2. (Think of a sport that reminds you of these words. Explain why you chose that sport.) Students can choose the category, too.

4. Students write or express the analogy between the two: The endocrine system is like playing zones in basketball. Each player or gland is responsible for his area of the game.

4-Square Synectics1. Brainstorm four objects from a particular category

(examples: kitchen appliances, household items, the circus, forests, shopping malls).

2. In small groups, brainstorm what part of today’s learning is similar in some way to the objects listed.

3. Create four analogies, one for each object. Example: How is the human digestive system like each

household item: sink, old carpet, microwave, broom

Example: How is the Pythagorean Theorem like each musical instrument: piano, drum set, electric guitar, trumpet?

Will ____ become the new ____?Samples: Micro-fiber is the new suede.

Red is the new black.

Applied to k-12 curriculum: • What is meant by the statement: “Decimals are the

new fractions?” • Are PDA’s the new paper and pencil? • Is a Constitutional republic the new representative

democracy? • Is M-Theory the new String Theory?• Is this character the Atticus Finch of the story?

Petals Around the Rose

The name of the game is, “Petals Around the Rose.” The name is

very important. For each roll of the game, there is one answer, and I

will tell you that answer.

Petals Around the RoseAnswer:

6

10

0

Petals Around the Rose

Clues to give students if they struggle:

1. All the math you need to solve this problem you learn in kindergarten or before.

2. The sequence of the dice patterns has no bearing on the answer.

Successful Thinkers…• Concede ignorance when they are ignorant. • Find out what’s going on.• Respect intellectuals and don’t deride them. • Speak out after doing their homework. • Examine superstitions. • Play thinking games and amuse themselves by

trying to answer puzzle questions. • Become more informed about history than they

are.

Successful Thinkers…

• Aren’t afraid to change their minds. • Are aware that their opinions, assumptions, and

beliefs are often affected by peer-group pressure.• Are realistically skeptical – even of leaders. • Recognize that they have personal prejudices. • Do not to fall in love with their first answers.

[from Steve Allen’s book, Dumbth: The Lost Art of Thinking: with 101 Ways to Reason Better and Improve your Mind (Prometheus Books)]

The Gettysburg Address

Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But in a larger sense, we can not dedicate -- we can not consecrate -- we can not hallow -- this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract…

Proficient Readers

Aoccdrnig to rseerach at an Elingsh uinervtisy, it deosn’t mttaer in what order the ltteers in a word are, the olny iprmoetnt tihnh is that the frist and lsat ltteer is in the rghit pclae. The rset can be a total mses and you can still raed it outhit a porbelm. This is bcuseae we do not raed ervey letetr by itslef, but the word as a wlohe. -- Sousa, p. 62

Reading Comprehension:16 All-Time Best Practices

Create personal background where there is none. Set or facilitate reading purpose. Prime students’ minds. Teach students how to monitor their own comprehension. Use frequent and varied summarization techniques. Use think-alouds. Teach students “fix up” strategies to use when confused. Make reading a transformative experience.

Reading Comprehension:16 All-Time Best Practices

Facilitate substantive and personal interaction with text. Teach vocabulary for its own sake. Ask students to write a lot, particularly as they come to

know content Teach text structures to students. Teach students metaphors and to think metaphorically. Teach students how to visualize text. Teach reading in context of content studies. Teach students how to adjust reading for different purposes

and texts.

Proficient Readers

• Use “fix up” strategies when something is confusing• Monitor their own comprehension• Set purpose for reading • Use existing knowledge to make sense of new knowledge• Synthesize information• Ask questions throughout the reading process• Draw inferences• Determine what is important

-- Researcher/Educator F. David Pearson

Aren’t these the skills we want students to have in all subject areas, not just reading?

Chronological OrderDefinition and Key words: This involves putting facts, events, a

concepts into sequence using time references to order them. Signal words include on (date), now, before, since, when, not long after, and gradually.

“Astronomy came a long way in the 1500s and 1600s. In 1531, Halley’s Comet appeared and caused great panic. Just twelve years later, however, Copernicus realized that the sun was the center of the solar system, not the Earth, and astronomy became a way to understand the natural world, not something to fear. In the early part of the next century, Galileo made the first observations with a new instrument – the telescope. A generation later, Sir Issac Newton invented the reflecting telescope, a close cousin to what we use today. Halley’s Comet returned in 1682 and it was treated as a scientific wonder, studied by Edmund Halley.”

Compare and ContrastDefintion and Key words: Explains similarities and differences.

Signal words include however, as well as, not only, but, while, unless, yet, on the other hand, either/or, although, similarly, and unlike.

“Middle school gives students more autonomy than elementary school. While students are asked to be responsible for their learning in both levels, middle school students have more pressure to follow through on assignments on their own, rather than rely on adults. In addition, narrative forms are used to teach most literacy skills in elementary school. On the other hand, expository writing is the way most information is given in middle school.”

Cause and EffectDefinition and Key words: Shows how something happens

through the impact of something else. Signal words include because, therefore, as a result, so that, accordingly, thus, consequently, this led to, and nevertheless.

“Drug abusers often start in upper elementary school. They experiment with a parent’s beer and hard liquor and they enjoy the buzz they receive. They keep doing this and it starts taking more and more of the alcohol to get the same level of buzz. As a result, the child turns to other forms of stimulation including marijuana. Since these are the initial steps that usually lead to more hardcore drugs such as Angel Dust (PCP), heroin, and crack cocaine, marijuana and alcohol are known as “gateway drugs.” Because of their addictive nature, these gateway drugs lead many youngsters who use them to the world of hardcore drugs.”

Problem and SolutionDefinition and Key words: Explains how a difficult situation, puzzle, or

conflict develops, then what was done to solve it. Signal words are the same as Cause and Effect above.

“The carrying capacity of a habitat refers to the amount of plant and animal life its resources can hold. For example, if there are only 80 pounds of food available and there are animals that together need more than 80 pounds of food to survive, one or more animals will die – the habitat can’t “carry” them. Humans have reduced many habitats’ carrying capacity by imposing limiting factors that reduce its carrying capacity such as housing developments, road construction, dams, pollution, fires, and acid rain. So that they can maintain full carrying capacity in forest habitats, Congress has enacted legislation that protects endangered habitats from human development or impact. As a result, these areas have high carrying capacities and an abundance of plant and animal life.”

Proposition and SupportDefintion and Key words: The author makes a general statement followed

by two or more supporting details. Key words include: In addition, also, as well as, first, second, finally, in sum, in support of, therefore, in conclusion.

“There are several reasons that teachers should create prior knowledge in students before teaching important concepts. First, very little goes into long-term memory unless it’s attached to something already in storage. Second, new learning doesn’t have the meaning necessary for long-term retention unless the student can see the context in which it fits. Finally, the brain likes familiarity. It finds concepts with which it is familiar compelling. In sum, students learn better when the teacher helps students to create personal backgrounds with new topics prior to learning about them.

EnumerationDefinition and Key words: Focuses on listing facts,

characteristics, or features. Signal words include to begin with, secondly, then, most important, in fact, for example, several, numerous, first, next finally, also, for instance, and in addition.

“The moon is our closest neighbor. It’s 250,000 miles away. It’s gravity is only 1/6 that of Earth. This means a boy weighing 120 pounds in Virginia would weigh only 20 pounds on the moon. In addition, there is no atmosphere on the moon. The footprints left by astronauts back in 1969 are still there, as crisply formed as they were on the day they were made. The lack of atmosphere also means there is no water on the moon, an important problem when traveling there.”

Be a Suspicious Reader

• How does this fit with what I know?• What evidence does he offer for his

claims?• Where is he going next?• Am I safe with where this is going – How is

it affecting me?• What is he not saying?• Why is he presenting it this way?

Logical Fallacies

• Ad Hominem (Argument To The Man) -- Attacking the person instead of attacking his argument: “Dr. Jones’ conclusions on ocean currents are incorrect because he once plagiarized an research article.”

• Straw Man (Fallacy of Extension) -- Attacking an exaggerated version of your opponent's position. "Senator Jones says that we should not fund the attack submarine program. I disagree entirely. I can't understand why he wants to leave us defenseless like that." *

• The Excluded Middle (False Dichotomy) -- Assuming there are only two alternatives when in fact there are more. For example, assuming Atheism is the only alternative to Fundamentalism, or being a traitor is the only alternative to being a loud patriot. *

From Jim Morton’s’ “Practical Skeptic” website http://members.aol.com/jimn469897/skeptic.htm)

http://members.aol.com/jimn469897/skeptic.htm

Reading Notations I agree with this. X I disagree with this. ?? I don’t understand this. !! Wow! (‘Elicits a strong emotion) CL General Claim EV Evidence for the Claim

(These can be numbered to indicate their sequence, too: EV1, EV2,

EV3…)

Reading Math[Adapted from Literacy Strategies for Improving Mathematics Instruction, Joan M.

Kenney, ASCD, 2005]

• Math books have more concepts per sentence and paragraph than any other type of text.

• There is little redundancy in math text. • Words as well as numbers and other symbols are

used throughout text.• Eyes travel in different patterns than traditional

left-to-right.• There are often have distracting sidebars.

Journalistic vs. Encyclopedic Writing

“The breathing of Benbow’s pit is deafening, like up-close jet engines mixed with a cosmicbelch. Each new breath from the volcano heaves the air so violently my ears pop in the changing pressure – then the temperature momentarily soars. Somewhere not too farbelow, red-hot, pumpkin size globs of ejectedlava are flying through the air.”

-- National Geographic, November 2000, p. 54

“A volcano is a vent in the Earth from which molten rock (magma) and gas erupt. The molten rock that erupts from the volcano (lava) forms a hill or mountain around the vent. Lava may flowout as viscous liquid, or it may explode from the vent as solid or liquid particles…”

-- Global Encyclopedia, Vol. 19 T-U-V, p. 627

Sample Anticipation Guide

C

Theme Me My Group Author“AQOTWF is not an accusation nor a confession, and least of all an adventure.” “War changes people.”“War forces people to reject traditional values and civilized behavior.”“Cruel trainers are the best instructors for soldiers about to go to war.”“True friendship endures all.”“Whole generations are destroyed by war.”“Nature is indifferent to mankind’s pain and decisions.”“To no man does the Earth mean so much as to the soldier.”“Every soldier believes in Chance.”

Components of Blood Content Matrix

Red Cells White Cells Plasma Platelets

Purpose

Amount

Size & Shape

Nucleus ?

Where formed

T-List or T-Chart: Wilson’s 14 Points

Reasons President Wilson Designed the Plan for Peace

Three Immediate Effects on U.S. Allies

Three Structures/Protocols created by the Plans

Main Ideas Details/Examples

1.

2.

3.

1.

2.

3.

1.

2.

3

Cornell Note-Taking FormatReduce Record

[Summarize inshort phrasesor essentialquestions next to each blockof notes.]

Review -- Summarize (paragraph-style) your points or responses to the questions. Reflect and comment on what you learned.

[Write your notes on this side.]

Somebody Wanted But So[Fiction]

Somebody (characters)…

wanted (plot-motivation)…,

but (conflict)…,

so (resolution)… .

Something Happened And Then[Non-fiction]

Something (independent variable)…

happened (change in that independent variable)…,

and (effect on the dependent variable)…,

then (conclusion)… .

Narrowing the Topic

The Civil WarPeople

Battles InventionsReasons

Is the topic narrow enough to be focused, but broad enough to have plenty to write about?

Battles of the Civil War

Gettysburg

ManassasAntietam Vicksburg

Battles of Gettysburg

Statistics

GeographyFamous People

Strategies

What was the “Fish hook” strategy used at

the Battle of Gettysburg?

Yeah. That’s it.

Writing Tips• Writers need fivethings to write well:

TIME, CHOICE, STRUCTURE, RESPONSE, COMMUNITY

• Ask students to write a lot – every day is not too much. We don’t learn to swim by staring at the water. From 1998 NAEP Study: There’s a strong correlation between the amount of writing students did and how well they scored on reading assessments. (p. 145, Gallagher)

• If students are anxious about their writing, have

them write under a pseudonym known only to you.

Writing Tips

• Start small. Have the first writings be only a few sentences or lines.

• The best thinking for most writers comes after 15 to 20 minutes of writing.

• “If a student knows that her writing will be

evaluated with heavy emphasis on mechanics and spelling, she will: use only words she’s sure she can spell, keep sentences simple to avoid making mistakes, avoid any unusual punctuation situations, stick to ordinary structures, all of which adds up to no risk, no stretching, little growth, and even less excitement or discovery.”

-- Author and Writing Teacher, Marjorie Frank

·

Writing Tips

• “What you can say, you can write.” -- Marjorie Frank

• Writing is teaching the reader, and teaching is a very effective way to learn.

• We can write our way into a basic

understanding of anything. • Writing is primarily a thinking process,

not putting marks on paper process.

• Immerse students in models. They will outgrow them.

Writing Tips

• Writing makes us vulnerable. Treat students’ writing with elevated sensitivity.

• Tell students to write a paper that begs to be read aloud.

• Every sentence must further the message or it should be tossed.

• Avoid turning students into parrots.

Writing Concisely

Avoid Redundancies and Saying the Same thing in different ways:

more additions, absolutely certain/essential/necessary, advance forward, 2:00 a.m. in the morning, baby puppy/kitten, blended together, brief moment, deliberate lie, foreign imports, necessary requirement, old antique, orbiting satellite, preliminary draft, proceed ahead, raise up, refer back, repeat over, tiny particle, true facts, unexpected surprise, violent explosion, visible to the eye, while at the same time.

Cut to the Chase: “A small number of people” – “three people”“His whole speech bothered me.” – “His speech bothered me.”

-- William Brohaugh’s book, Write Tight, 1993, Writer’s Digest Books

Important:

• Students edit, not the teachers. • Shorten text and edit daily. • Assess students’ editing and revising. • If helpful, edit in waves.

Emphasize the power of editing and revision: “Great books are never written; they are

always re-written.” -- Michael Crichton

Some Great “Silver Bullets” from Janet Allen:

• Vocabulary development is directly proportional to time spent reading.

• Three avenues to effective vocabulary instruction: integration, repetition, and meaningful use. (Nagy et al., 1988)

• Teach no more than 8 to 10 new words outside of reading per week.

• Don’t ask students to write sentences with the vocabulary terms until they’ve studied them in depth.

• Use words over and over in natural flow of conversation – model, model, model – normalize their use. Have students practice saying the words – even choral recitation – just to visualize themselves saying it.

• Definition approach is ineffective by itself. (Baumann and Kameenui, 1991)

• Relying solely on context clues is often ineffective, but knowing the definition with context clues can be very effective. (Baumann and Kameenui, 1991)

Help with Paraphrasing

• Build students’ vocabulary and verbal dexterity. Post word banks. Use vocabulary immersion.

• Provide repeated experiences with varied sentence combinations and word play.

• Use repeated think-alouds of a paraphraser at work from both teacher and students.

• Provide ample opportunities to assess paraphrasings of original text or experience.

• Allow students to copy models -- They’ll outgrow them. • Take a page from the active listening lessons -- “So what

you’re saying is…” • Provide repeated experiences with encapsulation such as

creating newspaper headlines.• Play renaming and clue games such as Password, Taboo, and

$25,000 Pyramid.

Great Vocabulary Acquisition Ideas

Shape spellings

Restaurant Menu

Wanted Dead or Alive Posters

Taboo Cards

Vocabulary Rummy Cards

Competitive Conversation using vocabulary

Word Walls

Onl

y 8-

10 w

ords

per w

eek!

The Frayer Model[Frayer, Frederick, Klausmeier, 1969]

Essential Characteristics

Non- Essential Characteristics

Examples Non-examples

< Topic >

Taboo Cards

Photosynthesis

LightGreenWater

SunChlorophyll

PlantProduce

One-Word Summaries

“The new government regulations for the meat-packing industry in the 1920’s could be seen as an opportunity…,”

“Picasso’s work is actually an argument for….,” “NASA’s battle with Rockwell industries over the

warnings about frozen temperatures and the O-rings on the space shuttle were trench warfare….”

Basic Idea: Argue for or against the word as a good description for the topic.

Exclusion Brainstorming

The student identifies the word/concept that does not belong with the others, then either orally or in writing explains his reasoning:

• Mixtures – plural, separable, dissolves, no formula • Compounds – chemically combined, new properties, has

formula, no composition• Solutions – heterogeneous mixture, dissolved particles,

saturated and unsaturated, heat increases • Suspensions – clear, no dissolving, settles upon standing,

larger than molecules

3-2-13 – Identify three characteristics of Renaissance art that differed from art of the Middle Ages2 – List two important scientific debates that occurred during the Renaissance1 – Provide one good reason why “rebirth” is an appropriate term to describe the Renaissance

3 – List three applications for slope, y-intercept knowledge in the professional world2 – Identify two skills students must have in order to determine slope and y-intercept from a set of points on a plane1 – If (x1, y1) are the coordinates of a point W in a plane, and (x2, y2) are the coordinates of a different point Y, then the slope of line WY is what?

Word Morphology:Teach Prefixes, Roots, and Suffixes!

Mal – badly, poorMeta – beyond, after,

changeMis – incorrect, badMono – oneMulti – manyNeo – newNon – notOb, of, op, oc – toward,

againstOct – eight

Paleo – ancient Para – beside, almost Penta – five Per – throughout, completely Peri – around Poly – many Post – after Pre – before Pseudo – false

Concept Ladder(J.W. Gillet, C. Temple, 1986, as described in Inside Words, Janet Allen)

Concept:

Causes of: Effects of:

Language associated with: Words that mean the same as:

Historical examples: Contemporary examples: Evidence of: Literature connections made:

“Word Link”

1. Each student gets a word.2. In partners, students share the link(s)

between their individual words.3. Partner team joins another partner team,

forming a “word cluster.”4. All four students identify the links among

their words and share those links with the class.

-- Yopp, Ruth Helen. “Word Links: A Strategy for Developing Word Knowledge,” Voices in the Middle, Vol. 15, Number 1, September 2007, National Council Teachers of English

In-Out Game: Students determine the classification a teacher’s statements exemplify, then they confirm their hypothesis by offering elements “in the club” and elements “out of the club.” They don’t identify the club, just the items in and out of it. If the students’ suggestions fit the pattern, the teacher invites them to be a part of the club. The game continues until everyone is a member.

Example: She is in the club but the class is not. They are in the club, but the penguins are not. You are in the club, but the donuts are not. Give me something in and out of the club.” A student guesses correctly that the club is for personal pronouns, so she says, “We are in the club, but moon rocks are not.” To make it a bit more complex, announce the club’s elements and non-elements in unusual ways that must also be exemplified by the students, such as making all the items in and out of the club alliterative or related in some way. This can be as obvious or as complex as you want it to be.

Extreme Vocabulary(Making Words Their Own: Building Foundations for Powerful Vocabulary, 2008)

1. Distribute word pairs of opposites. 2. In partners, students place these words at opposite ends of a continuum

drawn on paper (or hung as tent cards on rope), and in between the extremes, they place words that fall along the continuum of meaning. For example -- extremes of temperature: Freezing --- Cold --- Tepid --- Warm --- Hot --- Boiling

3. Once students ge the idea, try something more complex, such as inconsolable and carefree. Where would despondent fit? How about concerned, content, worried, and satisfied? As students discuss the proper positioning of the words and physically move the tent cards back and forth, students draw on visual cues and cement the definitions in their minds. If finding the specific words to go between the two extremes is difficult at first, provide suggestions that students study then place in the sequence.

4. Ask students to explain their rationale for their choices and positions. Classmates critique their decisions. Does “inconsolable---despondent--–worried--–concerned--–content--–satisfied--–carefree” work sequentially? Why or why not?

Line-up

• Groups of students line up according to criteria. Each student holds an index card identifying what he or she is portraying.

• Students discuss everyone’s position with one another -- posing questions, disagreeing, and explaining rationales.

Line-up

Students can line-up according to:chronology, sequences in math problems, components

of an essay, equations, sentences, verb tense, scientific process/cycle, patterns: alternating,

category/example, increasing/decreasing degree, chromatic scale, sequence of events, cause/effect,

components of a larger topic, opposites, synonyms

Human Continuum

A

D

Human Continuum

Use a human continuum. Place a long strip of masking tape across the middle of the floor, with an "Agree" or “Yes” taped at one end, and "Disagree" or “No” at the other end. Put a notch in the middle for those unwilling to commit to either side. Read statements about the day’s concepts aloud while students literally stand where they believe along the continuum. Be pushy – ask students to defend their positions.

“Haunker Hawser”

Supplies: 100-foot rope, two pairs of gloves, two crates or two, round wood boards:

Ropes Course Games

Ropes Course Games

Electric Fence (Getting over triangle fence without touching)

Spider Web (Pass bodies through “webbing” withot ringing the attached bells)

Group Balance (2’X2’ platform on which everyone stands and sings a short song)

Nitro-glycerin Relocation (previous slide)

Trust Falls (circle style or from a chair)

Resources…• Mindware: www.mindwareonline.com (1-800-999-0398)• Fluegelman, Andrew, Editor. The New Games Book, Headlands Press

Book, Doubeday and Company, New York, 1976• Henton, Mary (1996) Adventure in the Classroom. Dubuque, Iowa:

Kendall Hunt• Lundberg, Elaine M.; Thurston, Cheryl Miller. (1997) If They’re

Laughing… Fort Collins, Colorado: Cottonwood Press, Inc.• Rohnke, K. (1984). Silver Bullets. Dubuque, Iowa: Kendall Hunt.• Rohnke, K. & Butler, S. (1995). QuickSilver. Dubuque, Iowa: Kendall Hunt• Rohnke, K. (1991). The Bottomless Bag Again. Dubuque, Iowa: Kendall

Hunt• Rohnke, K. (1991). Bottomless Baggie. Dubuque, Iowa: Kendall Hunt • Rohnke, K. (1989). Cowstail and Cobras II. Dubuque, Iowa: Kendall Hunt

http://www.mindwareonline.com/

• Begin with NMSA publications on the unique nature of the young adolescent mind! •David Sousa – How the Brain Learns, How the Special Needs Brain Learns, How Brain Learns to Read, How the Gifted Brain Learns, How the Brain Learns Math, How the Brain Influences Behavior, How the Brain Learns in t he Differentiated Classroom (with Carol Ann Tomlinson, 2010)• Pat Wolfe – Brain Matters• Eric Jensen – Different Brains, Different Learners, and others• Marilee Sprenger – How to Teach So Students Remember• Barbara Strauch – The Primal Teen• John Medina – Brain Rules• Robin Fogarty – anything by her

Great Resources on Cognitive Science:

Great Resources to Further your Thinking and Repertoire

• Armstrong, Thomas. Multiple Intelligences in the Classroom. 2nd Edition, ASCD, 1994, 2000

• Beers, Kylene. (2003) When Kids Can’t Read What Teachers Can Do, Heineman

• Beers, Kylene and Samuels, Barabara G. (1998) Into Focus: Understanding and Creating Middle School Readers. Christopher-Gordon Publishers, Inc.

• Benjamin, Amy. Differentiating Instruction: A Guide for Middle and High School Teachers, Eye on Education, 2002

• Burke, Kay. What to Do With the Kid Who…: Developing Cooperation, Self-Discipline, and Responsibility in the Classroom, Skylight Professional Development, 2001

• Forsten, Char; Grant, Jim; Hollas, Betty. Differentiated Instruction: Different Strategies for Different Learners, Crystal Springs Books, 2001

• Forsten, Char: Grant, Jim; Hollas, Betty. Differentiating Textbooks: Strategies to Improve Student Comprehension and Motivation, Crystal Springs Books

• Frender, Gloria. Learning to Learn: Strengthening Study Skills and Brain Power, Incentive Publications, Inc., 1990

Great Resources to Further your Thinking and Repertoire

• Glynn, Carol. Learning on their Feet: A Sourcebook for Kinesthetic Learning Across the Curriculum, Discover Writing Press, 2001

• Heacox, Diane, Ed.D. Making Differentiation a Habit, Free Spirit Publishing, 2009• Heacox, Diane, Ed.D. Differentiated Instruction in the Regular Classroom, Grades

3 – 12, Free Spirit Publishing, 2000• Hyerle, David. A Field Guide to Visual Tools, ASCD, 2000• Jensen, Eric. Different Brains, Different Learners• Lavoie, Richard. How Difficult Can This Be? The F.A.T.

City Workshop, WETA Video, P.O. box 2626, Washington, D.C., 20013-2631 (703) 998-3293. The video costs $49.95. Also available at www.Ldonline.

• Levine, Mel. All Kinds of Minds• Levine, Mel. The Myth of Laziness• Marzano, Robert J. A Different Kind of Classroom: Teaching with Dimensions of

Learning, ASCD, 1992. • Marzano, Robert J.; Pickering, Debra J.; Pollock, Jane E. Classroom Instruction

that Works: Research-based Strategies for Increasing Student Achievement, ASCD, 2001

• Northey, Sheryn. Handbook for Differentiated Instruction, Eye on Education, 2005

• Purkey, William W.; Novak, John M. Inviting School Success: A Self-Concept Approach to Teaching and Learning, Wadsworth Publishing, 1984

• Rogers, Spence; Ludington, Jim; Graham, Shari. Motivation & Learning: Practical Teaching Tips for Block Schedules, Brain-Based Learning, Multiple Intelligences, Improved Student Motivation, Increased Achievement, Peak Learning Systems, Evergreen, CO. 1998, To order, call: 303-679-9780

• Rutherford, Paula. Instruction for All Students, Just ASK Publications, Inc (703) 535-5432, 1998

• Sousa, David. How the Special Needs Brain Learns, Corwin Press, 2001• Sprenger, Marilee. How to Teach So Students Remember, ASCD, 2005• Sternberg, Robert J.; Grigorenko, Elena L. Teaching for Successful Intelligence: To

Increase Student Learning and Achievement, Skylight Training and Publishing, 2001

• Strong, Richard W.; Silver, Harvey F.; Perini, Matthew J.; Tuculescu, Gregory M. Reading for Academic Success: Powerful Strategies for Struggling, Average, and Advanced Readers, Grades 7-12, Corwin Press, 2002

• Tomlinson, Carol Ann -- Fulfilling the Promise of the Differentiated Classroom, ASCD, 2003How to Differentiate Instruction in Mixed-Ability Classrooms, ASCD, 1995 The Differentiated Classroom: Responding to the Needs of All Learners, ASCD, 1999 At Work in the Differentiated Classroom (VIDEO), ASCD, 2001Differentiation in Practice: A Resource Guide for Differentiating Curriculum, Grades 5-9. ASCD, 2003 (There’s one for K-5 and 9-12 as well)Integrating, with Jay McTighe, 2006, ASCD (This combines UBD and DI)

• Tovani, Cris. I Read It, But I Don’t Get It. Stenhouse Publishers, 2001• Wolfe, Patricia. Brain Matters: Translating Research into Classroom Practice,

ASCD, 2001• Wormeli, Rick. Metaphors & Analogies: Power Tools for Teaching any Subject,

Stenhouse Publishers, 2009.• Wormeli, Rick. Differentiation: From Planning to Practice, Grades 6-12,

Stenhouse Publishers, 2007• Wormeli, Rick. Fair Isn’t Always Equal: Assessment and Grading in the

Differeniated Classroom, Stenhouse 2006• Wormeli, Rick. Summarization in Any Subject, ASCD, 2005• Wormeli, Rick. Day One and Beyond, Stenhouse Publishers, 2003• Wormeli, Rick. Meet Me in the Middle, Stenhouse Publishers, 2001

differentiated instruction and critical thinking wormeli/nelms2010

Documents

lesson sequence

lesson changes

students knowledge

summative assessments

learning experiences

pre assessments

learning needs

diverse group of students