Urban Conference Walsh Presentation

Differentiating Instruction in
the Mathematics Classroom.

Presented by
Tr. Terry Walsh

1 ASCD

Real World Connections

Who
is
P. 190 this
guy?

Cleveland Urban Conference 3

Who is this guy?

This is who I am . . .
by the numbers.
Terry Walsh:
35, 3, 54, 50, 4


Tr. Terry Walsh
By the numbers . . . (one # is used twice)
I was born on December 22, 19 __.
My draft number was only _ _, but I did not
serve in the military.
I have been married for ____ years, and
have____children.
I enjoyed adapting my teaching strategies to
include all ___ learning styles.
I retired ___ years ago, after 32 years in two
suburban Chicago high schools.
3 4 35 50 54

Three comments about school:
• 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

6

Meet your neighbor by the numbers…

• 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
7 points.

Group and Label
• 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.
8

Group and Label

Isosceles Sphere
Cylinder Scalene
Square Trapezoid
Page Right triangle Rectangle
149 Hexagon Decagon
Rhombus Pentagon
Oval Cone
Octagon Cube
Circle pyramid

9 Cleveland Urban Conference

Group and label

Page
149


Group and Label

Page
152

11

Group and Label

Page
153

12

Group and Label

Page
154

13

Group and Label

Page
155

14

Terry Walsh

By the fractions . . .
I have been married for nearly ____of my life.
_______ of my children are male.

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

____ of my children have their own children.
0/3 1/3 3/5 2/3 3/3

Thoughtful Questions:
♦ Why do some students succeed in mathematics
and others do not? Is it a matter of skill or will?

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

♦ How do we design units of instruction that are
meaningful, manageable, and make 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:
• 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.


Now…..
What are YOUR personal Learning Goals for this
workshop?

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

 Reflect upon your own practice.

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

Cleveland Urban
Conference 19

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?...

Read the four teaching activities
on page 11 of your handout,
Page select the one you like teaching
193 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
21

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?

22

Previewing 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.
23

Mastery Math Students
 Want to Learn practical information and set
procedures

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

 Approach problem solving In a step-by-step manner

 Experience difficulty when Math becomes too abstract or when faced
with non-routine problems
 Want a math teacher who
Models new skills, allows practice time
and builds in feedback and coaching
sessions

Understanding Math Students
 Want to Understand why the math they learn works

 Like math problems that Ask them to explain, prove, or take a
position

 Approach problem solving Looking for patterns and identifying hidden
questions
 Experience difficulty when
There is a focus on the social environment of
the classroom
 Want a math teacher who
Challenges them to think and who lets them
explain their thinking


Self-Expressive Math Students
 Want to Use their imagination to explore
mathematical ideas

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

 Approach problem solving By visualizing the problem, generating
possible solutions, and exploring among the
alternatives.
 Experience difficulty when
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 26

Interpersonal Math Students
 Want to Learn math through dialogue, collaboration,
and cooperative learning

 Like math problems that Focus on real-world applications and on how
math helps people

 Approach problem solving As an open discussion among a community
of problem solvers
 Experience difficulty when 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

1/23-24/06 ASCD 27

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

Carl Jung

Dr. Harvey Silver


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

Five different ways for teaching mathematics
A memory-based approach emphasizing
identification and recall of facts and concepts;
Page An analytical approach emphasizing critical
7 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
approaches
29
Cleveland Urban Conference

Sternberg and his colleagues drew 2 conclusions

First, whenever students were taught
in a way that matched their own
style preferences those students
Page
8
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.

A Mathematical Task Rotation…
2. Write down a “significant year” in your life. Describe it to
your neighbor using as many numbers as you can.
3. Write down the year of your birth.

• Write down your age as of 12/31/2009
• Write down the number of years since your
“significant year”.
• Find the sum of your four numbers.
• Compare answers with three other people.
• Explain what you discover three ways (algebraically,
with words, and graphically).

ST Mastery Learner:

 Thinking Goal: REMEMBERING

 Environment: CLARITY & CONSISTENCY
 Motivation: SUCCESS
 Process: STEP-BY-STEP EXERCISE & PRACTICE
 Outcome:
WHAT? CORRECT ANSWERS

33

NT Understanding Learner:

 Thinking Goal: REASONING
 Environment: CRITICAL THINKING
AND CHALLENGE
 Motivation: CURIOSITY
 Process: DOUBT-BY-DOUBT EXPLAIN & PROVE
 Outcome: WHY? ARGUMENTS

34

NF Self-Expressive Learner:

 Thinking Goal: REORGANIZING

 Environment: COLORFUL AND CHOICE

 Motivation: ORIGINALITY

 Process : DREAM-BY-DREAM
EXPLORE POSSIBILITIES
 Outcome: WHAT IF?
CREATIVE ALTERNATIVES

35

SF Interpersonal Learner:
 Thinking Goal: RELATE PERSONALLY

 Environment: COOPERATIVE AND CONVERSATION

 Motivation: RELATIONSHIPS

 Process: FRIEND-BY-FRIEND
EXPERIENCE & PERSONALIZE
 Outcome:
SO WHAT?
CURRENT & CONNECTED

36

What’s Wrong? vs
Who’s Right?
Both ask students to find and
correct errors. Who’s Right (SF)
P 38 uses a personal story to set the
P.196 stage for the work, whereas
What’s Wrong (ST) does not.


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

38

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
P. 190
determine the
location of
something.
This was in an NCTM journal


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
P.158 (3.9 mil.) and the second
census in 1800 (5.3 mil.)?

What would the population have
become in the 2000 census?


Teaching with Style to Sensing/Thinking Mastery Learners

Guidelines Examples
State objectives and outcomes; provide
S tart with clear expectations. clear criteria for evaluation.
T ell students what they need to Provide a clear model of what
know and how to do it step-by-step. students need to know and should
be able to do.
E stablish opportunities for concrete Provide hands-on materials; use
experiences and for exercise and active games, especially with
practice. competition; change tasks often.
Check for understanding regularly;
P rovide speedy feedback on mass and distribute practice over
student performance. time.
Test for mastery; apply specific
S eparate practice from content and skills to concrete
performance. projects and activities.


Teaching with Style to Intuitive/Thinking Understanding Learners

Guidelines Examples
Provide questions that puzzle Generate questions for understanding;
problem-based learning.
and data that teases.
“Know, need to know, and want
Respond to student queries and to know”; establish
provide reasons why.
purpose/reason for activity.
Open opportunities for critical Pattern-finding activities; critical
thinking, problem-solving, research thinking strategies: compare/ contrast,
decision making, research.
projects, and debate.
Build in opportunities for Thesis essays, debates, Socratic
seminars, editorials; seek alternative
explanation and proof using explanations/points of view.
objective data and evidence.
Self-directed learning; projects and
Evaluate content and process. performances that demonstrate
understanding.

Teaching with Style to Sensing/Feeling Interpersonal Learners

Guidelines Examples
Use personal hooks; give examples
Try to personalize the content. from your own life, encourage
students to do as well.
Reinforce learning through support Build trust in the classroom; provide a
pleasant physical setting; encourage
and positive feedback.
expression of personal feelings.

Use the world outside the classroom Find/use real-world applications;
for current and personally relevant use emotional contexts; apply to
content. current student concerns.

Select activities that build upon Empathy work; decision-making;
personal experiences and cooperative learning; class
cooperative structures. discussions; peer practice.

Take time to establish personal Personal reflections; journal
goals, encourage reflection, and writing.
praise performance. 46

Teaching with Style to Intuitive/Feeling Self-Expressive Learners

Guidelines Examples
“What if?”questions; metaphorical
Inspire use of imagination, expression; visualizing ideas; invent or
explore use of alternatives. imagine; creative problem-solving.
Model creative work so students Extrapolate structure; generate
performance criteria; model creative
examine/establish criteria for guidance
and assessment. process.

Allow student choice of activities Alternative activities and methods;
present ideas in a variety of ways;
and methods for demonstrating culminating assessment projects.
understanding and knowledge.
Give feedback, coach, and provide Opportunities for students to share
audiences for sharing work. work/receive feedback from an
audience; quality circles.
Evaluate and assess Holistic and analytic rubrics;
performance according to student assessment; self-
established criteria. assessment.
47

Students work with
Questions in all four Styles:
Mastery questions ask Interpersonal questions
what students remember. invite students to reflect
and share their feelings.
What? So What?

Understanding questions Self-Expressive questions
require explaining and require the use of
proving. imagination.
Why? What If?

48

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?

49

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

50

The Four Functions of Style

SENSING
Physical
Facts
Details
Here & Now
Objective Perspiration Subjective
THINKING

Analyze

FEELING
Harmonize
Logic Likes/Dislikes

Truth Tact

Procedures People
Inspiration
Past & Future

Ideas
Possibilities
Patterns
INTUITION
1/23-24/06 ASCD 51

Tuesday
Session 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 One
DIRECTIONS

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.

54

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.

55

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 A Great Deal
Amount

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.

•Voice  Polished: Use writing process steps, attention to
•Organization mechanics and technique, edited. Reflection of
•Interesting verbs/
adjectives
one’s best work. Looks Good, Sounds Smart
•Correct spelling
& mechanics
•Establish Big
Ideas & Support
w/Details
 Publishable: Edited and revised several times.
Audience is the wider public community.


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

Creative writing can take
many forms.

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!

Next we will be some creative writing using these terms.

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).
Opposite Adjacent Side

Hypotenuse Acute Obtuse

Right Angle Sine

Cosine Tangent Triangle

How many words did you use?

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.

Thinking about Learning
or Feelings....

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.

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 & Questions
Directions:
 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?

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

A Geometry Support or Refute
Agree 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 lines
connecting things in new ways or looking
for new methods or ideas

Interpersonal Questions: Reacting to the lines
making personal connections, or finding
relevance
Example: 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?

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

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”?

Mathematical
Summaries...
Write out how
we add two
fractions
P. 27


Math Recipe vs
Anchor Walls ... (not in book)

Create a “recipe
card” or a fill in
the blank
P. 132
template.


Anchor Walls

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__________________.


Making Up Is Fun to Do ...
My dad’s sister,
Sally, used to ask
me why math
P.160
teachers picked on
her, so let’s write a
new sentence to
replace, “My dear
Aunt...”.


Tuesday
Session 2
Vocabulary & Assessment
Strategies

83

Fist Lists & Spiders
Look at P. 32 of your
handout….
Use the spider in your
handout. Write a
P. 29 concept in the center,
and write an important
characteristic about it
on each leg of the
spider.


3 Way Tie
Write “fractions”, “percents”,
and “decimals” at the three
vertices of the triangle in
your handout (P. 33). Write
P.108 a sentence connecting each
pair, and a generalization
connecting all three in the
center.


Asessment Menus
Look at the Conics
Assessment Menu...
(p. 34 of the handout).
P. 239 Students need to
complete 4 tasks, one
from each each Style
and each level of
difficulty.


Tic-Tac-Toe (Vocab. Games)

(P. 35 in handout)
The example was
written by a HS
P.213 teacher in Bowling
Green KY.. Students
need to complete
a winning line of
tasks.


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
The Calculus Task
Rotation (p.36 in
handout) shows
P. 222 Styles can be used
in all classes, at all
levels to improve
student learning.


Range Finder
The “Graduated
Difficulty” example
(P.37 in handout),
P. 208 should be Range
Finder. It can be
used as a formative
assessment, to see
where students are.


Convergence Mastery
For when they
absolutely, positively
need to know a
P. 40 concept in order to
succeed.... (not in
your handout).


Unit Tests
Test Worth Taking is
a test that poses
questions in all four
P. 244 Styles. Look at the
Geometry Test in
your handout.
(P.38-42)


What are words and how are
they defined?

What words are important to learn?

Key Word Strategy =
Dictionary Definition
Bicycle (the key word)

A mode of transportation (the bigger idea)

With two wheels, a pedal and chain (essential characteristics)
system, with energy supplied by the
rider

Types of bicycles: mountain bikes,
dirt bikes, 10 speeds (examples)

Distinguished from: motor cycles,
unicycles, and scooters
(non-examples)

Take the word ___________
trapezoid

Non-Examples General Category
Examples

rectangle quadrilateral

square Key Word

trapezoid
parallelogram

Essential Characteristics

Plane figure, four sides, exactly
one pair of sides parallel, 95

Take the word mathematics

Examples

Key Word

mathematics


96

Take the word___________

Examples

1 Numbers
2

51 Key Word
7
Prime number
91
41

A number that has only two
multiples one of which is itself
97

These are polygons:

These are NOT polygons:

What makes a polygon a polygon?
List critical attributes.


What is Mathematical Literacy?

1
2
4
0011 0010 1010 1101 0001 0100 1011


Literacy in reading means not only
0011 0010 1010 1101 0001 0100 1011
being able to pronounce and decode
words, but also being able to read

2
and comprehend what one reads.
Mathematical literacy means the same
1
4
thing--having procedural and
computational skills as well as
conceptual understanding.


Mathematical Literacy
0011 0010 1010 1101 0001 0100 1011
The importance of mathematical
literacy and the need to understand

2
and be able to use mathematics in
everyday life and in the workplace
1
4
have never been greater and will
continue to increase.

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


Jobs requiring mathematical and technical
skills are growing the fastest among the
0011 0010 eight professional and related
1010 1101 0001 0100 1011
occupations.

2
60% of all new jobs beginning in the 21st

1
century require skills that are possessed

4
by only 20% of the current work force.


0011 0010 1010 1101 0001 0100 1011
Mastery of procedural A language to
and conceptual communicate and solve

2
knowledge real-world problems

1
4
Understanding of logical Application of strategies
reasoning to explain and to formulate and solve
prove a solution problems


Four Reasons to Teach
Vocabular y:

• Verbal Intelligence

• Ability to comprehend new
information: Academic Achievement

• One’s level of income

• Self-confidence and self-image


Tuesday
Session 3
Your ideas & closure
(for now?)

105

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

106

Five Ways to Use Math Tools

See pages 13 through 15 in the
Math Tools book:
• Try one out.
Page
• Use tools to help you meet a
13
particular standard or objective.
• Individualize instruction.
• Differentiate instruction for the
entire class.
• Design more powerful lessons,
assessments, and units.
107

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

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?

111 Clevelaerencend Urban Conf

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

Mathematics
Workshop:
Four Thought

ASCD 113

Urban Conference Walsh Presentation

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