Facilitating Effective Professional
Learning Communities
Welcome!
Region 11 Math and Science
Partnership  K2 Number Sense
Anne Bartel & Nancy Nutting
Today’s Agenda
AM
• Get acquainted
• Set norms
• Focus on # Sense
• Focus on PLCs
PM
• Overview of
training &
responsibilities
• PLC dress rehearsal
• Focus on adult
learners
• Tools: Power and
rapport
Parking Lot & Logistics
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•
•
•
•
•
Timeframe
Lunch
Restrooms
Next 2 meetings: Oct. 24th & Feb. 19th
Parking Lot concerns/questions
“Misery is optional”
Step In – Step Out
• Form a large circle around all the tables and
face each other. Step to the inside of the circle
if the statement is true for you.
Step In – Step Out
• I went to the MN State Fair this year.
• I drove more than 10 miles this morning to get
here.
• I exercised before I came this morning.
• I speak a second language.
• I know what CGI in math education stands for.
• I was in a PLC last year.
• I have previously facilitated a PLC group.
Share at Your Table
What is the most positive experience
you have had in learning or teaching
mathematics?
Debrief: Grounding conversation
Strategy Recording Sheet
Strategy
Name
Grounding
conversation
Description
Ask a low-stress question
and whip around for
responses
This is how I might
use it
Plan a Q to start each meeting;
‘whip’ to keep it fun but short.
Establishing Norms for PLCs
• Think: What do you need in a group or from a
group to make it a valuable learning
experience for you?
• Record: Write one idea to a small post-it.
• Compare and sort: Place similar needs in a
group; label that group with a large post-it.
Establishing Norms for PLCs
• Summarize: Write 1-3 positively stated norms
for each label
• Discuss & reach consensus: What’s missing?
What needs editing? What norms can
everyone commit to?
• Debrief
What do you see ?
Assume . . .
a=
b=
d=
c=
e=
What letters belong in the following boxes?
c+e=
d + e=
d+f=
b + g=
Try these
e=
e+g=
g–b=
d+b=
h–e=
Try these
e=
How many more is i than c?
Which is more: c + f or b + h?
If you have g people at a party, will s cookies be
enough, too many, or just about right? How many will
each person get?
About how many grapes could you hold in one hand:
h or m?
Why these activities?
Our Goals
• To help teachers get better at observing and
listening to students’ mathematical ideas and
understandings
• To help teachers determine instruction based
on what they see and hear from students
Research/Professional Literature
Spotlight
[Number Sense] is an awareness and
understanding about what numbers are, their
relationships, their magnitude, the relative
effect of operating on numbers, including the
use of mental mathematics and estimation.
Fennell and Landis (1994) Windows of Opportunity in Sherry
(2010) Number Talks, www.mathsolutions.com
Research/Professional Literature
Spotlight
Number sense is not a finite entity that a
student either has or does not have but rather a
process that develops and matures with
experience and knowledge.
McIntosh, Reys and Reys. (1992). “A proposed framework for
examining basic number sense.” For the Learning of
Mathematics. 12(3), p. 2-8, 44.
Research/Professional Literature
Spotlight
The Cockcroft Report (Cockcroft, 1982)
uses the phrase
“at-homeness with numbers”
to describe one aspect of number sense.
SciMathMN. (1993). Minnesota K-12 Mathematics Framework. St. Paul, MN.
Research/Professional Literature
Spotlight
Communication in the classroom also can help
make implicit ideas explicit. Often students come
to school with intuitive ideas about how things
work, and intuitive strategies for solving problems..
. . When students’ intuitive strategies are made
public, they can be analyzed more deeply and
everyone can learn from them.
James Heibert, et. al. ( 1997). Making Sense: Teaching and Learning Mathematics for
Understanding. Portsmouth, NH: Heinemann, p 45.
Research/Professional Literature
Spotlight
There is no meaning inherent in symbols.
Symbols always stand for something else . . .
Symbols become meaningful when they are
used to describe numbers and relationships
that children know and understand . . . The key
is that the symbols represent a real
experience that can be written down . . .
Kathy Richardson. How Children Learn Number Concepts: A
Guide to Critical Learning Phases. Bellingham, WA: Math
Perspectives Teacher Development Center. 2012 pp. 68-70.
Research/Professional Literature
Spotlight
. . . in the eyes of children, not all addition and
subtraction problems are alike. There are
important distinctions between different types of
. . . problems, which are reflected in the way that
children think about and solve them . . . The actions
and relationships in a problem tend to influence
the strategies that children use for an extended
period of time . . .
Thomas P. Carpenter, et. Al. Children’s Mathematics: Cognitively Guided Instruction.
Portsmouth, NH: Heinemann. 1999. pp. 2-3
Research/Professional Literature
Spotlight
Messages to give to students:
• Everyone can learn math to the highest levels
• Mistakes are valuable
• Questions are really important
• Math is about creativity and making sense
• Math is about connections and communicating
• Math class is about learning not performing
• Depth is more important than speed
Jo Boaler, Setting up Positive Norms in Math Class
http://youcubed.org/teachers/2014/back-to-school-messages/#more-221, retreived
9/7/14
Take a Break
Evolution of a PLC
• Read the article
• In small groups, share your reactions to the
article using Talking Chips.
• Create a graphic organizer to record the
differences and share with the whole group.
Read the Article
!
.
?
Statements that cause an “ah-ha” or ideas that excite
you in the reading.
Places where you paused because you agree with
the statement, it interests you, or it stands out.
Something that is circling in your mind – it causes
some questions.
Use “talking chips” to provide equal
opportunities to participate.
Evolution of a PLC
NEW
OLD
8:05-8:15 complain
about staff
8:15-8:25 complain
about Admin.
8:25-8:35 complain
about parents
8:35-8:45 complain
about students
8:45-8:55 complain
about NCLB
8:55-9:00 complain
about lack of
collaboration time
8:05-8:10 review group
norms
Textbooks
Curriculum
Supplies
Field Trips
Speakers
Assemblies
Rubrics
Parent Comm.
Student Issues
Staff Issues
8:10-8:30 examine &
discuss student work/data,
common assessments,
instructional strategies
8:30-9:00 reflect, problem
solve, and set goals
6 Characteristics of a PLC
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•
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Shared mission, vision, values and goals
Collaborative teams focused on learning
Collective inquiry into best practice
Action orientation and experimentation
Commitment to continuous improvement
Results orientation
DuFour, R., DuFour, R., & Eaker, R. (2008).
Evolution of a PLC
Something we are
not…
something we do.
Muhammad, A. (2009).
Evolution of a PLC
Learning is …
• Incremental
• Job-embedded
• Ongoing
4 Questions for a PLC
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•
•
•
What is it we expect the students to learn?
How will we know when they have learned it?
How will we respond when they don’t learn?
How will we respond when they already know
it?
DuFour, R., DuFour, R., & Eaker, R. (2008).
Group Process Facilitation
A way of providing leadership without
taking the reins. A facilitator’s job is to get
others to assume responsibility, to take the
lead, and engage in meaningful
collaboration.
- Bens, 2002
30
Group Process Facilitator
One who contributes structure and process
to interactions so groups are able to
function effectively. A helper and enabler
whose goal is to support others as they
achieve exceptional performance.
- Bens, 2002
31
Lunch – OK to bring it back
Roving Number Posters for Sept. 11th
Work with people at your table.
Write in as many expressions for 11 as you can
on your poster paper.
11
2014
Day 1
NUMBER
SENSE
(Sept)
PLC
PLC
Day 2
ADDITION
(Nov)
PLC
PLC
PLC
PLC
2015
Day 3
PLC
SUBTRACTION PLC
(Jan)
PLC
Day 4
PLC
MULT
PLC
DIVISION
(Feb/Mar) PLC
Day 5
PLACE
VALUE
(May)
Professional Reading – articles & books
Developing Mental Math Number Talks
Developing Word Problems
How to fit with curriculum & District Initiatives
3 PLCs
Classroom Conversation #1
– Use Region 11 word problem sets
– Use dot cards, strings of related
equations, own word problems
Interview
– Work with 2 students, individually or
as a pair
– Possibly follow same 2 students all
year
Classroom Conversation #2
– Use Region 11 word problem sets
– Use dot cards, strings of related
equations, own word problems
Classroom Conversations
Short, frequent number talks, 5 – 15 minutes
•
•
•
Students work mentally with mathematics
Dot cards, number strings, types of word problems
Focus on developing number sense
Orchestrating classroom discussions, time varies
•
•
•
Anticipate, monitor, select and sequence student work for
sharing; focus on a particular mathematical goal
Compare and contrast student work/ideas/strategies
Look for relationships and connections among problems
•
Check out problem sets for classroom conversations
Artifacts – Bringing Experiences to a
PLC Group for Reflection
• Teacher notes, photos, or videos from a verbal
discussion, students acting out problems, or
using manipulatives
• Chart paper, photo or video showing a record
of student thinking & strategies
• Written student work
PLC Record Keeping
After each PLC submit the recording sheet for that
session. Region 11 Website:
http://www.region11mathandscience.org/
PLC Online Reporting Forms
 Training Day 1: Classroom Conversations I
 Training Day 1: Student Interview
 Training Day 1: Classroom Conversations II
Watch a Number Talk in Kindergarten
with Dot Cards and Ten Frames
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Clip K1 5:31
Whole group classroom conversation
“Me too” strategy
Artifact to bring would be teacher notes or video
Take a few notes in your power point handout:
• Characteristics of students who have emerging number
sense
• Characteristics of students with strong number sense
• What dot cards or ten frames would you use next and why?
Watch Grade 2 – Use of Ten Frames
and Recording Thinking about 8 + 6
• Clip 2.1, 4:40
• Artifact to bring to PLC would be the class
recording chart
• How does the ten-frame support student
thinking?
• How can number talks help build basic fact
knowledge?
Check out: Number Talks, K-5
• Facilitator’s Guide for Number Talks, p. 301ff +
pages in earlier chapters about the clips, e.g.
Kgn. see p. 36; grade 2 see p. 43ff
• Designing Purposeful Number Talks, chapter 4,
p. 67ff – be aware of design vs. reality
7+7=?
Your
7+8=?
resource
7+9=?
What do you hear from your students?
When assessing mathematical
understanding . . . a teacher is trying
to get a picture of the student’s own
thinking rather than whether the
student can provide the “correct”
answer that the adult has in mind.
Assessment Alternatives in Mathematics, California Mathematics
Council and Project Equals, 1989
Different Types of Word Problems
Investigate strategies students use
• What characterizes students with the least
sophisticated strategies?
• What characterizes students with
sophisticated strategies?
Processing a Classroom Conversation
with Artifacts
Continuum of Strategies
(least to most sophisticated)
1
Characteristics
Students
2
3
PLC Record Keeping
After each PLC submit the recording sheet for
that session. Region 11 Website:
http://www.region11mathandscience.org/
PLC Online Reporting Forms
 Training Day 1: Classroom Conversations I
 Training Day 1: Student Interview
 Training Day 1: Classroom Conversations II
Continuum of Strategies
(least to most sophisticated)
1  DM
Direct
Modeling
2C
Counting
3  DF or FR
Derived Facts or
Fact Recall
See, touch,
count all
Count on or
count by
chunks
Working with
equations,
decomposing &
composing
numbers
Professional Reading – articles & books
Developing Mental Math Number Talks
Developing Word Problems
How to fit with curriculum & District Initiatives
3 PLCs
Classroom Conversation #1
– Use Region 11 word problem sets
– Use dot cards, strings of related
equations, own word problems
Interview
– Work with 2 students, individually or
as a pair
– Possibly follow same 2 students all
year
Classroom Conversation #2
– Use Region 11 word problem sets
– Use dot cards, strings of related
equations, own word problems
Take a Break
Situational Leadership
by Hersey & Blanchard
• You are in a new situation
• With a new group
• And being asked to lead
• Here’s what you need to understand.
Power & Rapport
Power 101
• Compliant Powers
– Coercive: based on the threat of punishment
– Connection: based on the connections to influential others
– Reward: based on your ability to provide reinforcements or
rewards
• Influence Powers
– Referent: based on your personal traits
– Information: based on your possession of valuable
information
– Expert: based on your possession of expertise, skill &
knowledge, which gain the respect of others
Working with Students v. Adults
Students
• You can use your
compliant power
• You have time to
build relationships
• Often, with students,
relationships break
down over time
Adults
• You have only
influence power
• You have much less
time to build
relationships
• It only takes a minute
to break trust &
damage relationships
Behaviors that Influence
Teacher Thinking
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•
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•
•
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Applying Rapport Skills – matching body, tone, language
Structuring – time, space, purposes
Reflective Questioning - positive presuppositions
Using Silence – wait-time, listening
Paraphrasing – restate, summarize
Accepting – both nonverbally & verbally
Clarifying – probing for details, values, meaning
Providing – data, resources
Behaviors that Influence
Teacher Thinking
•
•
•
•
•
•
•
•
Applying Rapport Skills – matching body, tone, language
Structuring – time, space, purposes
Reflective Questioning - positive presuppositions
Using Silence – wait-time, listening
Paraphrasing – restate, summarize
Accepting – both nonverbally & verbally
Clarifying – probing for details, values, meaning
Providing – data, resources
Behaviors that Influence
Teacher Thinking
•
•
•
•
•
•
•
•
Applying Rapport Skills – matching body, tone, language
Structuring – time, space, purposes
Reflective Questioning - positive presuppositions
Using Silence – wait-time, listening
Paraphrasing – restate, summarize
Accepting – both nonverbally & verbally
Clarifying – probing for details, values, meaning
Providing – data, resources
Importance of Rapport
Elements of Rapport
• Elements
– Posture
– Gesture
– Tonality
– Language
– Breathing
Practicing Rapport
• Form groups of 3
• Person 1: Talk about an issue related to the start
of school
• Person 2: Get into rapport and actively listen
(posture, gesture, tone, language, breathing)
• Person 3: Observe
• Debrief as a group – What did you see? hear?
What did it feel like?
• Switch roles and repeat
Rapport
When to Consciously Apply Rapport Tools:
When I anticipate tension or anxiety in another.
When tension or anxiety emerges during a
conversation.
When I can’t understand another person or when
I’m having difficulty paying attention to another.
Adults learn best not merely by listening,
reading or doing but by reflecting on what
they hear, read or do.
York-Barr, Sommers, Ghere, Montie. Reflective Practice to Improve Schools:
An Action Guide for Educators. Thousand Oaks, CA: Corwin Press. 2001.
Strategy Recording Sheet
Strategy
Name
Description
This is how I might
use it
CAPS & Exit Slip
Something that CONFIRMS my thinking . .
A question that was ANSWERED . . .
I am still PONDERING . . .
Something that SURPRISED me . . .
Exit Slip – 3 key points from today’s work
Our Next Two Meetings
Friday, Oct. 24th
Thursday, Feb. 19th
8:30-3:30 at District 287, Plymouth
Remember to SUBMIT the recording form for
each of your 3 PLC sessions.
“Orchestrating” Classroom
Conversations
•
•
•
•
•
Anticipate
Monitor
Select
Sequence
Connect
Five Practices for Orchestrating Productive Mathematical
Discussions, Margaret S. Smith & Mary Kay Stein, NCTM&
Corwin Press, 2011 www.nctm.org