Day 1
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Welcome!
It became a great day when you
joined us!
Please draw a card to
find your team and
take a handout.
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Strategies Used to Promote
Student Discourse and
Engagement in Math
Classrooms
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Introductions
Goal of these two days is to have
participants be actively involved
using strategies to talk about
mathematics and also use brain
research to see how to enhance
your math class.
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Eric Jensen
author of Teaching with the
Brain in Mind
Says “Purposeful Teaching Uses
Energizers That Raise Heart Rate and
Memory Chemicals.”
The faster your heart rate, the more
memory chemicals are formed.
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Think of your favorite relaxing chair…
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Team Roles
Clubs –
Facilitator
DiamondsRecorder/Reporter
Hearts Resource Manager
Spades –
Task Manager
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Jigsaw
Let’s learn
About the
team roles.
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Icebreaker
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Proximity Partner
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Dyad
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Dyad
What do you hope
to get out of these
two days?
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Give One, Get One
Let’s talk about
norms
in a studentcentered
Classroom.
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Red Light, Green Light
We are going to
do this as a
Dragon’s Tail.
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Walk and Talk
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Walk and Talk
Share some
ideas and
thoughts
that you have
about what
we have been
doing.
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Jigsaw
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Laws of
x
e ponents
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Teammates Consult
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40 Holes of Golf
The Hookenslice Corporation is having
its annual charity fundraising event. In
order to encourage donors to attend,
the Hookenslice organizes a fun game
called “40 Holes of Golf” and gives
away prizes. Each team plays 40 holes of
golf. There is a prize for the team that is
consistently closest to the hole.
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40 Holes of Golf
Your teacher has set up a “hole.” Your
team will “swing” 40 pennies toward
the “hole.” You will then represent your
data on a graph and with numerical
statistics, decide which team
was the most consistently
close to the hole.
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40 Holes of Golf
Your Task: Your teacher will give you ten pennies.
Have one team member stand 200 cm from the
“hole.” That team member will toss all ten pennies,
one at a time. No “do-overs” and no practice shots
are allowed. Then record the distance from the
center of each penny to the “hole” (to the nearest
centimeter), even if the penny rolled far away.
Repeat with different team members until 40
pennies have been tossed. Do not take turns each
tossing one a penny at a time—each team member
should toss all ten of their pennies in one turn.
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40 Holes of Golf
Decide how you want to represent your data on your
poster: dot plot, box plot, circle graph (“pie chart”),
scatter plot, histogram, or bar graph. Create a poster.
Leave room for the task below.
Decide the five most important facts you wish to
report about your team’s golf shots and add them to
your poster.
Your teacher will direct you on how to compare your
team’s results with the other teams.
Which team was most consistently close to the hole?
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Traveling Salesman
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Kinesthetic Math works 3X
better: Use Gestures
In the study, 90% of students who had
learned algebraic concepts using gestures
remembered them 3 weeks later vs. 33%
of speech only students. And 90% of
students who had learned by gestures
only with no speech at all recalled what
they had been taught. (Cook, SW, et al,
2007)
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Make sure that you say
Welcome Back to your team
members.
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Make sure that you say
Welcome Back to your team
members.
Changing teams-pack up
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Hot Potato
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Math Chat
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No Screen Shots Allowed!
You are emailing a friend the directions s/he will
need to draw a specific diagram that must exactly
match the shape (and size) of the one you have.
Write a clear set of directions using words only.
Your partner must draw the picture based on
your directions. S/he may not use any tools such
as a compass, ruler, protractor or straight-edge.
Use precise mathematical vocabulary to ensure
her/his diagram will match yours.
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Reflection
Prompt: Write down three things
you learned today.
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From Eric Jensen
Mind-Body Connection
“Activity not only fosters survival of
our species, but it serves as a
strategy for learning, emotional
regulation, affiliation, resource
acquisition and stress
management.”
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Treasure Hunt
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Treasure Hunt
Today your teacher will give you several descriptive
clues about different relations. For each clue, work
with your team (or a partner) to find all the possible
matches among the relations posted around the
classroom.
Remember that more than one relation may match
each clue. Once you have decided which relation(s)
match a given clue, defend your decision to your
teacher and receive the next clue. Be sure to record
your matches on paper.
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Treasure Hunt
Your goal is to find the match (or
more than one match) for each
of eight clues. Once you and
your team (or partner) have
finished, only one relation will
be left unmatched. That relation
is the treasure!
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Silent Debate
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Silent Debate Topic
Proof is an important topic to
teach.
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Silent Debate Topic
Substitution is the best method
for solving a system of equations.
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Reciprocal Teaching
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Closure
Feedback form
One more activity
Before we go….
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Exit Slip
Something you learned
today…
Something you would like
to learn about….
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Proximity Partner
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Day 2
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Welcome!
It’s a great day to learn!
Please draw a card to
find your team.
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Team Roles
Shape A is the Facilitator
Shape B is the Recorder/Reporter
Shape C is the Resource Manager
Shape D is the Task Manager
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Silent Shapes
No Talking
No Taking
No Gestures
Each person must make a square
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The hard work involved in
teambuilding is worth it and pays many
benefits, including:
Social support for learning math
Success for more students
Opportunities to see and discuss multiple approaches
More meaningful learning by discussing and explaining
Better mastery of basic skills
Greater mathematical exploration and creativity
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Research shows that collaborative problem
solving in the math classroom leads to:
 Higher achievement
 Higher self esteem
 Increased retention
 More on-task behavior
 Greater use of higher-level
 Better attitudes toward
reasoning
teachers and school
 Greater intrinsic motivation  Greater social support
 More positive heterogeneous  More positive psychological
relationships
adjustment
 Greater collaborative skills
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Laser lights
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YOU ARE GETTING SLEEPY
Legend has it that if you stare
into a person’s eyes in a special
way, you can hypnotize them into
squawking like a chicken. Here’s
how it works.
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Place a mirror on the floor.
Your victim has to stand exactly
200 cm away from the mirror
and stare into it. The only tricky
part is that you need to figure
out where you have to stand so
that when you stare into the
mirror, you are also staring into
your victim’s eyes.
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If your calculations are correct
and you stand at the exact
distance, your victim will squawk
like a chicken!
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Think-Ink-Pair-Share
Think about the scenario
and then draw
a picture of what you
think it would look like.
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Place a mirror on the floor.
Your victim has to stand exactly
200 cm away from the mirror
and stare into it. The only tricky
part is that you need to figure
out where you have to stand so
that when you stare into the
mirror, you are also staring into
your victim’s eyes.
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YOU ARE GETTING SLEEPY
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Your Task
Are there similar triangles in your
diagram? Justify your conclusion.
(Hint: Remember what you know about
how light reflects off mirrors.) Then
calculate how far you will need to stand
from the mirror to hypnotize your
victim.
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Your Task
Now for the moment of truth! Have
your teammate stand 200 cm away from
the mirror, while you stand at your
calculated distance from the mirror. Do
you make eye contact? If not, check
your measurements and calculations
and try again.
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Algebra Walk
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Please memorize the following 9 symbols. No
writing. You will be allowed 1 minute.
There will be a quiz!
a:
b:
c:
d:
e:
f:
g:
h:
i:
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What is this word?
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Will this help you to remember
the letters/symbols?
a
b
c
d
e
f
g
h
i
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“Mathematics makes more sense and is
easier to remember and to apply when
students connect new knowledge to
existing knowledge in meaningful ways.”
Principles and Standards for
School Mathematics, 2000
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Participation Quiz
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The Big Race
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The Big Race
Today is the final event of “The Big Race”!
Your teacher will give you each a card that
describes how you travel in the race. You and
your study team will compete against the heat
1 and 2 winners, Leslie and Elizabeth, at
today’s rally in the gym. Unfortunately, Mark,
the winner of heat 3, is absent from school and
will not be participating against you.
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The Big Race
o Your study team must work cooperatively to solve the
problems. No team member has enough information to
solve the puzzle alone!
o Each member of the team will select rider A, B, C, or D.
You may not show your card to your team. You may only
communicate the information contained on the card.
o Assume that each racer travels at a constant rate
throughout the race.
o Elizabeth’s and Leslie’s cards will be shared by the entire
team.
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The Big Race
Your Task: As a team, do the following:
Draw a graph (on graph paper) showing all of
the racers’ progress over time. Identify the
independent and dependent variables.
Write an equation for each participant.
Figure out who will win the race!
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Use your results from “The Big Race – Finals ” to
answer the following questions. You may answer the
questions in any order, but be sure to justify each
response.
a. Who won the finals of The Big Race? Who came in
last place? How do you know?
b. How fast was Rider D traveling? How fast was
Elizabeth traveling?
c. At one point in the race, four different participants
were the same distance from the starting line.
What was that distance? Who were they and when
did this happen?
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Proximity Partner
Walk around until the music
stops and then find a partner
near you that you have not
worked with.
Introduce yourself and await
directions.
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Proximity Partner
I Like to Move It!
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Reflection
Summarize what you have learned so
far and what questions you still
have.
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Reciprocal Teaching
Person A:
Tell your partner about similar shapes and
corresponding sides and angles.
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Reciprocal Teaching
Person A:
Tell your partner about similar shapes and
corresponding sides and angles.
Person B:
Tell your partner how you solve for missing
sides of similar shapes.
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Process

promoting Team work

assessing Math Understanding

addressing Status Issues

enhancing/encouraging Communication

highlighting the Mathematical Practices
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Pairs Check
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Teammates Consult
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Listening Post
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Polygonia
The beautiful young princess of
Polygonia is very sad. A mean ogre has
locked her into a tower of a castle. She
could escape through the window, but it
is 50 feet above the ground, a long
distance to jump! A moat full of
alligators surrounds the tower. Naturally,
Prince Charming wants to rescue her.
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Polygonia
The prince has some rope. His plan is to
use an arrow to shoot one end of the
rope up to her window. The princess can
then slide down the rope to the other
side of the moat, and off they will ride
into the sunset.
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The Power of Context and
Exercise
Move students around.
Let them encounter the
same content in
different contexts.
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Music and Movement
My Bonnie
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Icebreaker: Compromise
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Hot Seat
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Growing, Growing, Growing
Patterns are everywhere! You may have noticed them
in pinecones, flowers, stacks of cans in the grocery
store, or many other places. Patterns are interesting
partly because of the different ways that you can see
how the parts of a pattern are changing. In this course,
you will often look for different ways of seeing a
pattern or concept. As you study the pattern in this
lesson, work with your team to find several ways to see
and describe the pattern and how it is growing. The
following questions can help guide your discussion.
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Growing, Growing, Growing
How can we describe the pattern?
Is there another way to see or describe it?
Does anyone see it differently?
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Swapmeet
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Reflection
Describe how an effective team looks
and sounds.
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Win-a-Row
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Elevator Talk
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Human Graphs
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More brain talk…
“Brain research confirms that
physical activity—moving,
stretching, walking—can actually
enhance the learning process,”
Jensen says.
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Cross-lateral movements
It’s also important to build cross-lateral exercises into
your day. Cross-lateral movements are those in which
arms and legs cross over from one side of the body to
the other. The left side of the brain controls the right
side of the body, and the right side of the brain
controls the left side. Both sides are forced to
communicate when arms and legs cross over. This
“unsticks” the brain and energizes learning.
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Cross the Midline
Stand with arms at sides. Touch right hand to left knee. Stand with
arms at sides and touch left hand to right knee. Count or sing as you
do this.
Elbow Tap
Stand with arms at sides. Bend and touch right elbow to left knee as
you raise your leg. Stand and then touch left elbow to right knee.
Windmills
Feet spread apart and arms extended. Bend over at waist and tap
right hand to left foot. Back up and then bend and tap left hand to
right foot.
Backwards
Bend left knee and put foot behind right leg. Reach back around
with right hand and touch left foot. Reverse and put right foot
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behind your left leg as you touch it with your left hand.
Hand Jive - Here is a pattern you can do with your
hands. Slap hands on thighs twice. Clap hands twice.
Shuffle right palm over left twice. Shuffle left palm
over right twice. Make fists with fingers and thump
right fist on top of left fist twice. Then thump left fist
on top of right fist twice. Stick out thumb on right
hand and move over right shoulder as if hitchhiking.
Stick out thumb on left hand and hitchhike behind
left shoulder. Continue repeating this pattern. (There
are many variations, or you can make up your own.)
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The end of this talk, but hopefully not the end of your
interest in brain based learning.
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How our brains really learn
 There is no one single way we process all types of
information.
 Context and the learner‘s own background are huge
variables.
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Let’s try an experiment
 Next slide has a list of simple words
 Leave your pen/pencil down-no note taking,
please.
 Look over the words for 30 secs. Try to store
them in your brain.
 You’ll learn something new about how your
memory works.
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snooze
snore
slumber
siesta
soundly
doze
nightlight
rest
nap
bed
yawn
dream
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Think Ink Pair Share
Without talking, make a list of all the
words that you remember from the list.
Turn to a partner and compare lists.
Share at your table.
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snooze
snore
slumber
siesta
soundly
doze
nightlight
rest
nap
bed
yawn
dream
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Yoga + Physical Education
HOW COME WE DIDN’T
THINK OF THIS BEFORE?!
Easy...it’s different, unknown, has challenges
Why we need to consider & implement this as a part of quality, standardsbased PE:
Positive effect on student concentration & stress (Angus, 1989; Hopkins,
1979)
Improved behavior, self-esteem, academic focus, & fitness (Slovacek, Tucker,
& Pantoja, 2003)
Reductions in aggression, helplessness
Increases in static balance & stress-coping
(Stueck & Gloeckner, 2005)
Yoga is a lifetime physical activity that provides both desired physical &
mental benefits
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The Montillation of Traxoline
It is very important that you learn about traxoline
Traxoline is a new form of zionter. It is montilled
in Ceristanna. The Ceristannians gristeriate large
amounts of fevon and then bracter it to quasel
traxoline. Traxoline may well be one of our most
lukized snezlaus in the future because of our
zionter lescelidge. (from Judy Lanier)
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