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

• • • • • • Timeframe Lunch Restrooms Next 2 meetings: Oct. 24 th & Feb. 19 th 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 Shee

t

Strategy Name

Grounding conversation

Description This is how I might use it

Ask a low-stress question and whip around for responses 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 = c = d = 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

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

Textbooks Curriculum Supplies Field Trips Speakers Assemblies Rubrics Parent Comm.

Student Issues Staff Issues NEW 8:05-8:10

norms review group

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

• • • • • • 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

• • • • 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. 11 th

Work with people at your table. Write in as many expressions for 11 as you can on your poster paper.

11

Day 1 NUMBER SENSE (Sept) Day 3 SUB TRACTION (Jan)

PLC PLC PLC 2014 PLC PLC

Day 2 ADDITION (Nov)

PLC 2015

Day 4 MULT DIVISION (Feb/Mar)

PLC PLC PLC PLC PLC PLC

Day 5 PLACE VALUE (May)

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 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 = ?

7 + 8 = ?

7 + 9 = ?

Your resource

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 2 3 Characteristics Students

PLC Record Keeping

After each PLC submit the recording sheet for that session. Region 11 Website: http://www.region11mathandscience.org/ PLC Online Reporting Forms  T raining 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

See, touch, count all

2



C

Counting

Count on or count by chunks

3



DF or FR

Derived Facts or Fact Recall

Working with equations, decomposing & composing numbers

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 • • • • • • • • 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 Shee

t

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. 24

th

Thursday, Feb. 19

th

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