urban conference walsh presentation

Differentiating Instruction in the

Mathematics Classroom.

ASCD1

Presented byTr. Terry Walsh

MondayIntroduction

2

Cleveland Urban ConferenceCleveland Urban Conference 33

Real World Connections

Who is

this guy?

P. 190P. 190


This is who I am . . .

Who is this guy?

by the numbers.

Terry Walsh:

35, 3, 54, 50, 4

Cleveland Urban Conference 5

By the numbers . . . (one # is used twice)

Tr. Terry Walsh

My draft number was only _ _, but I did not serve in the military.I have been married for ____ years, and have____children.

I retired ___ years ago, after 32 years in two suburban Chicago high schools.

I was born on December 22, 19 __.

50

54353 44

I enjoyed adapting my teaching strategies to include all ___ learning styles.

6

• Don’t Work Harder Than Your Students.”

-- title of a book published in 2009

• “American High Schools are a place where 1500 students go to watch 150 adults work really hard.” --- a Japanese teacher in the late 1970’s, after visiting a several Ohio high schools.

• “Teachers never ask “Why?” if your answer is correct.” -- a student in a math class at Niles West H.S. (Illinois); May, 1972

Three comments about school:

TERRYandSUE

7

• Select 5 numbers that are meaningful to you that will help someone understand who you are.

• Then write a sentence or question for each number, leaving a blank line where the number should go.

• Share you numbers and sentences with your neighbor. See if he or she can match the correct number to the line. For every correct answer you get a point. See who gets more points.

Meet your neighbor by the numbers…

8

• Write each of your numbers on a post it. One number per post it.

• Place all of your numbers from your table in the middle and eliminate any duplicates.

• Then group your numbers and label them according to some common characteristics. Then turn you labels over.

• Visit another table and try to figure out their groupings. (1 pt. each correct ans.)

• Discuss how you can use this activity in your own classroom.

Group and Label

Group and Label

Cleveland Urban Conference9

Page 149

IsoscelesCylinderSquare

Right triangleHexagonRhombus

Oval Octagon

Circle

SphereScalene

TrapezoidRectangleDecagonPentagon

ConeCube

pyramid

Group and label


Page 149

Group and Label

11

Page 152

Group and Label

12

Page 153

Group and Label

13

Page 154

Group and Label

14

Page 155


By the fractions . . .

Terry Walsh

I live in the same state as ____ of my children.

_______ of my children are married.

____ of my children have their own children.

_______ of my children are male.

I have been married for nearly ____of my life.

3/51/3

2/3 3/30/3


Thoughtful Questions: Why do some students succeed in Why do some students succeed in

mathematics and others do not? Is it a mathematics and others do not? Is it a matter of skill or will?matter of skill or will?

How can we use research-based teaching How can we use research-based teaching tools and strategies to address the style of tools and strategies to address the style of all learners so they succeed in all learners so they succeed in mathematics?mathematics?

How do we design units of instruction that How do we design units of instruction that are meaningful, manageable, and make are meaningful, manageable, and make students as important as standards?students as important as standards?


Workshop Assumptions:

• What teachers do and the instructional decisions that they make have a significant impact on what students learn and how they learn to think.

• Different students approach mathematics using

different learning styles and need different things to achieve in mathematics.

• Style-based mathematics instruction is more than a way to invite a greater number of students into the teaching and learning process; it is, plain and simple, good math—balanced, rigorous, and diverse.


Learning Goals:Participants will learn:Participants will learn:• The characteristics of the four basic mathematical learning

styles (Mastery, Understanding, Self-Expressive, and Interpersonal), a start on how to assess your own mathematical teaching style, and students’ mathematical learning styles.

• How to use a variety of mathematical teaching tools to differentiate instruction and increase student engagement.

• How to select mathematical teaching tools to address NCTM process standards, integrate educational “best practices,” and plan Thoughtful lessons or units to meet instructional objectives and the diverse needs of students.

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Now…..What are YOUR personal Learning Goals for What are YOUR personal Learning Goals for

this workshop?this workshop?

Review the Thoughtful Questions, Basic Review the Thoughtful Questions, Basic Assumptions and Goals for the workshop.Assumptions and Goals for the workshop.

Reflect upon your own practice.Reflect upon your own practice.

Record three things you want to take with Record three things you want to take with you as a result of your participation in this you as a result of your participation in this workshop.workshop.

Cleveland Urban Conference

Cleveland Urban Conference


Critical Vocabulary:

• Look at Page 10 in your handout.

• Fill in one number in each row, and find your total score for critical vocabulary for the workshops.

• We will revisit this page, so you will have a chance to improve you score.

What’s Your Favorite?...

21

Page 193

Read the four teaching activities on page 11 of your handout,

select the one you like teaching the most. Write out reasons why

you chose the one you did.

If you have time, which one would be your least favorite

activity to teach?

g1g1

Read the four teaching activities on page 11 of your handout,

select the one you like teaching the most. Write out reasons why

you chose the one you did.

If you have time, which one would be your least favorite

activity to teach?

g1g1

22

4 P’s: Previewing Before Reading

Preview: Scan the entire text. Find out as much as you can about what you are going to read without actually reading it.

Predict: Based on what you learned during your preview, what do you think the text is about?

Prior Knowledge: What do you already know about the subject of the text?

Purpose: What can you expect to accomplish from reading the text?

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Previewing WorksheetPreviewing Worksheet

PREVIEW the workshop materials. List four things you learned from your preview.

Make two PREDICATIONS about what you will learn from the workshop.

What PRIOR KNOWLEDGE will you use to enhance your learning in this workshop?

What is your PURPOSE for participating in this workshop? What can you expect to accomplish.

Mastery Math Students Want to

Like math problems that

Approach problem solving

Experience difficulty when

Want a math teacher who

Learn practical information and set procedures

Are like problems they have solved before and that use algorithms to produce 1 solution

In a step-by-step manner

Math becomes too abstract or when faced with non-routine problems

Models new skills, allows practice time and builds in feedback and coaching sessions


Understanding Math StudentsUnderstanding Math Students Want toWant to

Like math problems thatLike math problems that

Approach problem solvingApproach problem solving

Experience difficulty whenExperience difficulty when

Want a math teacher whoWant a math teacher who

Understand why the math they learn works

Ask them to explain, prove, or take a position

Looking for patterns and identifying hidden questions

There is a focus on the social environment of the classroom

Challenges them to think and who lets them explain their thinking

1/23-24/06 ASCD 26

Self-Expressive Math Students Want to





Use their imagination to explore mathematical ideas

Are non-routine, project-like in nature, and that allow them to think “outside the box”

By visualizing the problem, generating possible solutions, and exploring among the alternatives.

Math instruction is focused on drill and practice and rote problem solving

Invites imagination and creative problem solving into the math classroom

1/23-24/06 ASCD 27

Interpersonal Math Students Want to





Learn math through dialogue, collaboration, and cooperative learning

Focus on real-world applications and on how math helps people

As an open discussion among a community of problem solvers

Instruction focuses on independent seatwork or when what they are learning seems to lack real-world applications

Pays attention to their success and struggles in math


A “Paradox”….A little about two doctors (PhD’s) you should A little about two doctors (PhD’s) you should

know about…..know about…..

Carl Jung Carl Jung

Dr. Harvey SilverDr. Harvey Silver

Five different ways for teaching mathematics

A memory-based approach emphasizing identification and recall of facts and concepts;

An analytical approach emphasizing critical thinking, evaluation, and comparative analysis;

A creative approach emphasizing imagination and invention;

A practical approach emphasizing the application of concepts to real-world contexts and situations; and

A diverse approach that incorporated all the approachesCleveland Urban Conference

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Page 7

Robert Sternberg, IBM Prof. of Psychology and Education, Yale University. Learning Style Research Study

Sternberg and his colleagues drew 2 conclusions

First, whenever students were taught in a way that matched their own style preferences those students outperformed students who were mismatched.

Second, students who were taught using a diversity of approaches outperformed all other students on both performance assessments and on multiple-choice memory tests.


Page 8

ASCD 31

Page 8


A Mathematical Task Rotation…1. Write down a “significant year” in your life. Describe it to

your neighbor using as many numbers as you can.2. Write down the year of your birth.

A Mathematical Task Rotation…1. Write down a “significant year” in your life. Describe it to

your neighbor using as many numbers as you can.2. Write down the year of your birth.

3. Write down your age as of 12/31/20094. Write down the number of years since your

“significant year”.5. Find the sum of your four numbers.6. Compare answers with three other people.7. Explain what you discover three ways (algebraically,

with words, and graphically).

3. Write down your age as of 12/31/20094. Write down the number of years since your

“significant year”.5. Find the sum of your four numbers.6. Compare answers with three other people.7. Explain what you discover three ways (algebraically,

with words, and graphically).

33

ST Mastery Learner:

Thinking Goal:

Environment:

Motivation:

Process:

Outcome:

REMEMBERING

CLARITY & CONSISTENCY

SUCCESS

STEP-BY-STEP EXERCISE & PRACTICE

WHAT? CORRECT ANSWERS

34

NT NT Understanding Learner:Understanding Learner:

TThinking Goal:hinking Goal:

EEnvironment:nvironment:

MMotivation:otivation:

PProcess:rocess:

OOutcome:utcome:

REASONINGREASONING

CRITICAL THINKINGCRITICAL THINKING

AND CHALLENGEAND CHALLENGE

CURIOSITYCURIOSITY

DOUBT-BY-DOUBT EXPLAIN & PROVEDOUBT-BY-DOUBT EXPLAIN & PROVE

WHY? WHY? ARGUMENTSARGUMENTS

35

NF Self-Expressive Learner:

Thinking Goal:

Environment:

Motivation: Process : Outcome:

REORGANIZING

COLORFUL AND CHOICE

ORIGINALITY

DREAM-BY-DREAMEXPLORE POSSIBILITIES

WHAT IF?CREATIVE ALTERNATIVES

36

SF Interpersonal Learner:

Thinking Goal:

Environment:

Motivation:

Process:

Outcome:

RELATE PERSONALLY

COOPERATIVE AND CONVERSATION

RELATIONSHIPS

FRIEND-BY-FRIENDEXPERIENCE & PERSONALIZE

SO WHAT? CURRENT & CONNECTED


What’s Wrong? vs Who’s Right?

Both ask students to find and correct errors. Who’s Right (SF) uses a personal story to set the

stage for the work, whereas What’s Wrong (ST) does not.

P 38 P.196P 38 P.196

38

What’s wrong with the following problem?

32 + 3(2x – 12) > 5 – (4 + 9x)32 + 6x – 36 > 5 – 4 – 9x

- 4 + 6x > 1 – 9x - 5 > - 15x

x > 1/3

TERRYandSUE

Justify/Explain

»Write one or more valid reasons why the man with the full cart is not wrong in being in the lane he is in.

»You may work in pairs, groups, or by yourself.


Real World Connections...

Write ways that numbers are

used to determine the

location of something.

This was in an NCTM journalThis was in an NCTM journal

P. 190P. 190


What if? ...

What if the population of the United States kept increasing at the same percentage that it did

between the first census in 1790 (3.9 mil.) and the second census in 1800 (5.3 mil.)?

What would the population have become in the 2000 census?

P.158P.158


Teaching with Style to Sensing/Thinking Mastery Learners

Guidelines Examples

Start with clear expectations.

Tell students what they need to know and how to do it step-by-step.

Establish opportunities for concrete experiences and for exercise and practice.

Provide speedy feedback on student performance.

Separate practice from performance.

State objectives and outcomes; provide clear criteria for evaluation.

Provide a clear model of what students need to know and should be able to do.Provide hands-on materials; use active games, especially with competition; change tasks often.

Check for understanding regularly; mass and distribute practice over time.Test for mastery; apply specific content and skills to concrete projects and activities.


Teaching with Style to Intuitive/Thinking Understanding Learners

Guidelines Examples

Provide questions that puzzle and data that teases.

Respond to student queries and provide reasons why.

Open opportunities for critical thinking, problem-solving, research projects, and debate.

Build in opportunities for explanation and proof using objective data and evidence.

Evaluate content and process.

Generate questions for understanding; problem-based learning.

“Know, need to know, and want to know”; establish purpose/reason for activity.

Pattern-finding activities; critical thinking strategies: compare/ contrast, decision making, research.

Thesis essays, debates, Socratic seminars, editorials; seek alternative explanations/points of view.

Self-directed learning; projects and performances that demonstrate understanding.


Teaching with Style to Sensing/Feeling Interpersonal Learners

Guidelines Examples

Try to personalize the content.

Reinforce learning through support and positive feedback.

Use the world outside the classroom for current and personally relevant content.

Select activities that build upon personal experiences and cooperative structures.

Take time to establish personal goals, encourage reflection, and praise performance.

Use personal hooks; give examples from your own life, encourage students to do as well.Build trust in the classroom; provide a pleasant physical setting; encourage expression of personal feelings.

Find/use real-world applications; use emotional contexts; apply to current student concerns.

Empathy work; decision-making; cooperative learning; class discussions; peer practice.

Personal reflections; journal writing.

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Teaching with Style to Intuitive/Feeling Self-Expressive Learners

Guidelines Examples

Inspire use of imagination, explore use of alternatives.

Model creative work so students examine/establish criteria for guidance and assessment.

Allow student choice of activities and methods for demonstrating understanding and knowledge.

Give feedback, coach, and provide audiences for sharing work.

Evaluate and assess performance according to established criteria.

“What if?”questions; metaphorical expression; visualizing ideas; invent or imagine; creative problem-solving.

Extrapolate structure; generate performance criteria; model creative process.

Alternative activities and methods; present ideas in a variety of ways; culminating assessment projects.

Opportunities for students to share work/receive feedback from an audience; quality circles.

Holistic and analytic rubrics; student assessment; self-assessment.


Students work with Questions in all four Styles:

Mastery questions ask what students remember.

What?

Interpersonal questions invite students to reflect and share their feelings.

So What?

Understanding questions require explaining and

proving.Why?

Self-Expressive questions require the use of

imagination.What If?

Back in My Classroom After learning about our learners, what does

this mean for us as math teachers? What questions do you have? What solutions do you see that will allow all

students to become more effective mathematics learners?

What actions are you ready to take to meet the needs of all your students?

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50

How much of students’ success in your math classes is How much of students’ success in your math classes is due to their understanding what they read or write?due to their understanding what they read or write?

1/23-24/06 ASCD 51

The Four Functions of Style

SENSING

INTUITION

TH

INK

ING

FE

EL

ING

Physical

Facts

Details

Here & Now

Perspiration

Patterns

Possibilities

Ideas

Past & Future

Inspiration

Objective

Analyze

Logic

Truth

Procedures

Subjective

Harmonize

Likes/Dislikes

Tact

People

TuesdaySession 1

Writing & Reading in Math

52

M&M’s (Math Metaphor, p.129)My favorite math teacher always used to

say that fractions are like politicians. At first I thought she was crazy, but then I started to think about the idea, and found that I agreed with her!

Write three ways politicians and fractions are alike, and three ways they are different from each other.

g1g1 + 2

53

Give One, Get OneDIRECTIONS

Stand up, partner with one other person, GIVE one of yours, GET one of theirs.

If you both have the same, then create a new idea together to add to your lists.

Quickly move to a new partner. Give One, Get One. Repeat 4 times for a total of 6 ideas.

Remember: work in dyads. NO HUDDLING, NO COPYING OF EACH OTHER’S TOTAL LISTS.

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Write to Learn• The more students write and think in

mathematics classes, the more they learn. Doug Reeves reports that the correlation between writing in mathematics classes and scores on mathematics tests is a positive correlation of 0.93.

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When SHOULD students write in mathematics?

1. At the beginning of the lesson.• Access prior knowledge• Generate ideas• Review previous lesson

2. During the lesson• Check for understanding• Practice• Respond to a thoughtful question

3. At the end of the lesson• To review what they have learned• To apply what they have learned• To extend what they have learned to other areas

56

How much writing do your students do in your mathematics class?

None Very Little Some Considerable Amount

A Great Deal

57

What kinds of writing do you want your students to do in your math classes?

Make a list....

58

My Writing List (should we add any to your lists?) Answers in “proper form” (whatever that is!!) Showing their work Good notes ( making, not merely taking notes! – not in the book) Definitions (NOT merely copying the text definition) Complete explanations of their answers when asked for them Summaries of concepts and procedures What graphs or charts tell them Research projects Pre-lab explanations of how to do conduct an experiment or predict the results Creative writing (stories, poems, cinquains, haikus, etc.) Examples of how math really exists in the world, not traditional word problems Error analysis Creating patterns Using complete sentences How they think or feel about a concept Compare and contrast Defend a position

WRITE TO LEARN Provisional: Generate ideas, fluency &

flexibility. Audience: Oneself

Readable: Has Purpose & Audience; coherent & clear, concern with content & organization, write on every other line, knee-to-knee conference.

Polished: Use writing process steps, attention

to mechanics and technique, edited. Reflection of one’s best work. Looks Good, Sounds Smart

Publishable: Edited and revised several times. Audience is the wider public community.


•Voice

•Organization

•Interesting verbs/adjectives

•Correct spelling & mechanics

•Establish Big Ideas & Support w/Details

M ake a comparison or justify a decision

A ccess prior knowledge

Think About Learning or Feelings

H ypothesize

E xplain or define a mathematical concept

M ake real world connections

A nalyze errors in thinking

Take a position

I nterpret data and justify a conclusion

C reative writing

S ummarize(see P. 141 of your book.)

61

Before you use mathematical vocabulary, it might help to use non-math terms. Prepare your students by asking them to write 3 sentences using the term “milky way” and have the term mean something different in each of the 3 sentences!

Before you use mathematical vocabulary, it might help to use non-math terms. Prepare your students by asking them to write 3 sentences using the term “milky way” and have the term mean something different in each of the 3 sentences!

Creative writing can take many forms.

Creative writing can take many forms.

Opposite Adjacent Side

Hypotenuse Acute Obtuse

Right Angle Sine

Cosine Tangent Triangle

Here is an example of what I mean by “creative” writing:

The people who live in Ponent, Illinois call people who move out of town “exPonents”. Use at least 5 terms from the following list of terms to write 5 sentences (using more than one word in a sentence is even more creative).

Here is an example of what I mean by “creative” writing:

The people who live in Ponent, Illinois call people who move out of town “exPonents”. Use at least 5 terms from the following list of terms to write 5 sentences (using more than one word in a sentence is even more creative).

Next we will be some creative writing using these terms.Next we will be some creative writing using these terms.

Here is my one very run on sentence using all 12 words: The three people formed a right triangle with the tan gent adjacent to his very acute angel of a girlfriend as he cosined the loan application she had just sined, he noticed that the obtuse pasta chef in the restaurant on the opposite side of the street was putting the high pot in use to boil spaghetti noodles.

Of the 12 terms I used which 5 are the most “creative” (cheating) uses?

I would also ask the students to compare their use of the term to the actual mathematical definition of the term.

Here is my one very run on sentence using all 12 words: The three people formed a right triangle with the tan gent adjacent to his very acute angel of a girlfriend as he cosined the loan application she had just sined, he noticed that the obtuse pasta chef in the restaurant on the opposite side of the street was putting the high pot in use to boil spaghetti noodles.

Of the 12 terms I used which 5 are the most “creative” (cheating) uses?

I would also ask the students to compare their use of the term to the actual mathematical definition of the term.

How many words did you use?How many words did you use?

Would you rather have a best friend whose views are congruent to yours, or similar to yours? Explain your choice using vocabulary terms from the unit.

Would you rather have a best friend whose views are congruent to yours, or similar to yours? Explain your choice using vocabulary terms from the unit.

Thinking about Learning or Feelings....

Thinking about Learning or Feelings....

Support or Refute (P. 69) Word Problem

You will have a short time to skim over the word problem in the next slide. You will not have time to read the problem carefully. Next, you will be asked to answer several True or False questions about the word problem.

An Atypical Word Problem

A truck is on its way to three different motorcycle dealerships. The truck contains both mopeds and motorcycles. Maggie Sutton, who owns all three dealerships, receives an invoice which tells her that a total of 150 vehicles are on the truck for her three dealerships. However, the invoice doesn’t tell her how many of her vehicles are motorcycles and how many are mopeds. The invoice does show that the total mass of her vehicles is 34,800 lbs.. It also shows the mopeds weigh 100 lbs. each while motorcycles weigh 320 lbs.. How many mopeds and how many motorcycles are on the truck for Ms.Sutton’s dealerships?

Support or Refute: Directions & QuestionsDirections: Write down whether you think each question is true or false. Reread the problem and look for words that either support

your original answer, or refute it. Solve the problem if you want to or if you need to do so in

order to support or refute one of your original answers.Questions:1. The problem tells us the total number of vehicles on the

truck. True or False?2. The fact that there are three dealerships is critical to solving

the problem. True or False?3. The best way to solve this problem is to set up an equation

with two variables. T/F ?4. Motorcycles have a greater mass than mopeds. T/F?5. The solution requires two separate answers. T/F?

Why would students need experience with Support or Refute before using this exact problem?

An Atypical Word Problem

A truck is on its way to three different motorcycle dealerships. The truck contains both mopeds and motorcycles. Maggie Sutton, who owns all three dealerships, receives an invoice which tells her that a total of 150 vehicles are on the truck for her three dealerships. However, the invoice doesn’t tell her how many of her vehicles are motorcycles and how many are mopeds. The invoice does show that the total mass of her vehicles is 34,800 lbs.. It also shows the mopeds weigh 100 lbs. each while motorcycles weigh 320 lbs.. How many mopeds and how many motorcycles are on the truck for Ms.Sutton’s dealerships?

Support or Refute (P. 69 in the Math Tools book)

A Geometry Support or RefuteAgree or Disagree with each of these. Then READ Section 5.4 and

find statements or ideas in the reading that support or refute your original response to each statement.

Write down some reference to the location (page and position) of something in the section that agrees or disagrees with your original response to each statement.

1. All the points of a polygon must lie in the same plane. 2. A diagonal connects any two vertices of a polygon. . 3. A pentagon has five sides but it has ten diagonals. 4. A rhomboid is a type of quadrilateral. 5. A kite is a geometry term as well as a thing you can go fly. __ __6. In rectangle PQRS, RS and PQ are the diagonals. __ __7. In parallelogram ABCD, the diagonals are AC and BD.

.

An Alg2/Trig Support or Refute.

Alg2/Trig Read section 4.4. First write whether you AGREE or DISAGREE with each of these statements. Then, as you read, cite the text to support or refute your original decision.

1. Descartes rule of signs lets us say something about only the positive roots, not the negative roots of a polynomial.

2 If there is only one variation in signs, then there must be exactly one positive or negative real zero.

3 Y = -X3 + X + 1 has either two or no positive real zeros and exactly one negative real zero.

4. For Y = X4 + X2 – 3X – 6, all possible rational zeros are 1, 2, 3, or 6

5. For Y = 5X4 + X2 – 3X – 6, all possible rational zeros are 1, 2, 3, 6, 1/5, 2/5, 3/5, and 6/5 6.The UPPER Bound occurs when the synthetic division work shows all positive values.

7. The LOWER Bound occurs when the synthetic division work shows all negative values

Reading Questions in Styles

Mastery Questions: Read the actual lines finding facts, details, or literal meanings

Understanding Questions: Read between the lines explaining, inferring, or comparing

Self-Expressive Questions: Read beyond the linesconnecting things in new ways or looking

for new methods or ideas

Interpersonal Questions: Reacting to the linesmaking personal connections, or finding

relevanceExample: The term “Detour Proofs” make me uncomfortable.

Note taking vs. Note making

not in your handout

Students who are taking notes are usually copying what the teacher has written or said. They also copy work done by peers at the board or in groups.

Students who are making notes are reading text or example problems and writing out their own explanation of the work as well as questions they have about the problem or concept.s and differences

Note makingExample

32+3(2x – 12) > 5–(4+9x)What did I do? Explain why or ask a ?

32 + 6x – 36 > 5 – 4 – 9x - 4 + 6x > 1 – 9x - 4 > 1 - 15x - 5 > - 15x 1/3 < x x > 1/3

To use this idea, turn off auto format for spelling!!

I cdnuolt blveiee that I cluod aulactly uesdnatnrd what I was rdanieg aoubt the phaonmneal pweor of the mnid. Aoccdrnig to rscheearch at Cmabrigde Uieinrvtsy, it deons’t mttaer in waht oredr the ltteers in a wrod are, the olny ipomoatnt tinhg is taht the fsirt and lsat ltteer be in the rhgit pclae. The rset can be a taotl mses and you can sitll raed it! This is bcuseae the huamn mnid deos not raed ervey lteter by istlef,

but the word as a wlohe. Amzanig ins’t it?

Prbabltiioy can hlep us mkae dcsioines. Wtrei the fowlilong pgaaaprrh ccorrectly, tehn awnesr the fuor qiosteuns: Wehn trehe is a 2%7 cnache of pcrepititioan, yuor paenrt wlil prboalby dedcie to crray his ulmrebla to wrok. If one of yuor sohcos’l blal pyealrs has a .741 bitntag arvreae, you wluod ecpext taht she is mroe lkiely not to bat in a tmmeatae form scneod bsae. Mnay pborabiitly stiauitnos ivlovne a pfaoyf, scuh as pinots secrod; leivs seavd; or pfiorts eeanrd. The “epxcteed vuale” of a stiiaoutn is waht the pofayf oevr a lrgae nebmur of oeeccruncs wloud be. In tihs uint. We wlil eolrpxe qitsneous ivvoilnng pbbrltiiaoy and eepcxtd vulae.

1. Which parent went to work?2. How large is the ball? (or what specific sport is involved?3. One part of one of the paragraphs has two correct possible “translations”, what are they?4. How would you use the above to define “epxcteed vuale”?

The % and decimal below do not obey the “rules”.


Mathematical Summaries...

Write out how we add two

fractionsP. 27P. 27


Math Recipe vs Anchor Walls (not in

book) ...Create a “recipe card” or a fill in

the blank template.P. 132P. 132


In order to add two fractions, the first thing we do is make sure the ________________. If they are not, you have to get ________________. If they are, then you simply ____________. After adding them, remember to__________________.

Anchor WallsAnchor Walls


Making Up Is Fun to Do ...My dad’s sister,

Sally, used to ask me why math

teachers picked on her, so let’s write a new sentence to replace, “My dear

Aunt...”.

P.160P.160

TuesdaySession 2

Vocabulary & Assessment Strategies

83


Fist Lists & SpidersLook at P. 32 of your

handout….Use the spider in your

handout. Write a concept in the center, and write an important characteristic about it

on each leg of the spider.

P. 29P. 29


3 Way TieWrite “fractions”, “percents”, and “decimals” at the three vertices of the triangle in your handout (P. 33). Write a sentence connecting each pair, and a generalization connecting all three in the center.

P.108P.108


Asessment MenusLook at the ConicsAssessment Menu... (p. 34 of the handout). Students need to complete 4 tasks, one from each each Style and each level of difficulty.

P. 239P. 239


Tic-Tac-Toe (Vocab. Games)

(P. 35 in handout)

The example was written by a HS teacher in Bowling Green KY.. Students need to complete a winning line of tasks.

P.213P.213


Task Rotations are a way to use all four styles in a single strategy. Task Rotations

are found in pages 222 to 238 in the book.(The “significant year” activity was a Task Rotation.)

Task Rotations are a way to use all four styles in a single strategy. Task Rotations

are found in pages 222 to 238 in the book.(The “significant year” activity was a Task Rotation.)


Task RotationsThe Calculus Task Rotation (p.36 in handout) shows Styles can be used in all classes, at all levels to improve student learning.

P. 222P. 222


Range FinderThe “Graduated Difficulty” example (P.37 in handout), should be Range Finder. It can be used as a formative assessment, to see where students are.

P. 208P. 208


Convergence Mastery For when they

absolutely, positively need to know a concept in order to succeed.... (not in your handout).

P. 40P. 40


Unit TestsTest Worth Taking is a test that poses questions in all four Styles. Look at the Geometry Test in your handout. (P.38-42)

P. 244P. 244

What are What are words words and and how how are they defined?are they defined?

What What words words are are important to learn?important to learn?


Key Word Strategy = Dictionary Definition

Bicycle

A mode of transportation

With two wheels, a pedal and chain system, with energy supplied by the rider

Types of bicycles: mountain bikes, dirt bikes, 10 speeds

Distinguished from: motor cycles, unicycles, and scooters

(the key word)

(the bigger idea)

(essential characteristics)

(examples)

(non-examples)

95

Take the word ___________

General Category

Key Word

Non-Examples Examples

Essential Characteristics

trapezoid

quadrilateralrectangle

square

trapezoid

Plane figure, four sides, exactly one pair of sides parallel,

parallelogram


Take the word mathematics

General Category

Key Word



mathematics

97

Take the word___________

1

51

91Prime number

2

7

41

General Category

Key Word



Numbers

A number that has only two multiples one of which is itself


These are polygons:

These are NOT polygons:

What makes a polygon a polygon? List critical attributes.

425

10011 0010 1010 1101 0001 0100 1011

What is Mathematical Literacy?


425

1

0011 0010 1010 1101 0001 0100 1011


Literacy in reading means not only being able to pronounce and decode words, but also being able to read and comprehend what one reads.

Mathematical literacy means the same thing--having procedural and computational skills as well as conceptual understanding.


425

1

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Mathematical Literacy

The importance of mathematical literacy and the need to understand and be able to use mathematics in everyday life and in the workplace have never been greater and will continue to increase.

(National Commission on Mathematics and Science for the 21st Century)


425

1

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Jobs requiring mathematical and technical skills are growing the fastest among the eight professional and related occupations.

60% of all new jobs beginning in the 21st century require skills that are possessed by only 20% of the current work force.


425

1

0011 0010 1010 1101 0001 0100 1011


Mastery of procedural and conceptual

knowledge

A language to communicate and solve

real-world problems

Understanding of logical reasoning to explain and

prove a solution

Application of strategies to formulate and solve

problems


Four Reasons to Teach Vocabulary:

• Verbal Intelligence

• Ability to comprehend new information: Academic Achievement

• One’s level of income

• Self-confidence and self-image


TuesdaySession 3

Your ideas & closure (for now?)

105

How Do I Select the Right Tool For the Right

Learning Situation?

106

Page

8

Cleveland Urban ConferenceCleveland Urban Conference

Five Ways to Use Math Tools

107

Page 13

See pages 13 through 15 in the Math Tools book:

• Try one out.• Use tools to help you meet a particular

standard or objective.• Individualize instruction.• Differentiate instruction for the entire

class.• Design more powerful lessons,

assessments, and units.

Cleveland Urban ConferenceCleveland Urban Conference

How Do I Select the Right Tool For the Right Learning Situation?

Use the matrices on pp. 18/19; 64/65; 122/123; & 168/169

See pages 9 through 13 in the Tools book:

• Title and Flash Summary• NCTM Process Standards• Educational Research Base• Instructional Objectives.

108

1/23-24/06 ASCD 110

How many of us would like our students to…

• Think more deeply?• Take more intellectual risks?• Recognize that there are many ways to learn?• Develop greater confidence in their ability to learn and

improve self-esteem?• Develop better relationships with your and their peers?• Have greater respect for others and their differences?• Take more responsibility for their learning?• Develop a deeper understanding of the connection

between what they learn and how they learn?

Clevelaerencend Urban Conf111

Research clearly indicates the impact of each of these on student learning:

Category %ile Gain

Identifying Similarities & Differences 45

Summarizing & Note-taking 34

Reinforcing Effort & Providing Recognition

29

Homework & Practice 28

Non-Linguistic Representation 27

Cooperative Learning 27

Setting Objectives & Providing Feedback 23

Generating & Testing Hypotheses 23

Questions, Cues, and Advance Organizers 22

112

ASCD 113

Mathematics Workshop:

Four Thought

urban conference walsh presentation

Technology