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AIM - TRU �PLT Orientation

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Building a Teacher Knowledge Base �for the Implementation of High-quality

Instructional Resources Through the �Collaborative Investigation of Video Cases

An NSF Collaborative Research project partnering

SUNY Buffalo State, MƒA, Montclair State University, and DePaul University

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Thank you for your interest in participating!

You are participating in a professional learning community that includes �Chicago, Buffalo and New York City Public School teachers.

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Agenda

Part 1: Community Introductions

Community Builder
Community Agreements

Part 2: Developing a Big Mathematical Picture

Text rendering protocol
Applying ideas to a Lesson

Part 3: Framework for Effective Mathematics Teaching

What really matters in classrooms?
Tools for supporting powerful classroom instruction

Part 4: Introduction to AIM-TRU Model

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Part 1:

Community Introductions

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Community Builder

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Here are recommendations for ice breaker activities aligned with teaching and learning.

(ex. Find 2 things you have in common and create a group of__; What inspired you to become a teacher?)

Getting to Know you Grid

In this activity, teachers are given a grid three squares across by four squares down. In each of the 12 squares is a descriptive statement like "a person who has traveled out of the state within the last 12 months," "a person who worked in another field before becoming a teacher," and "a person who is a professional development junkie." Have fun with the choices. Once the grid has been created, make enough copies for those attending the professional development session. Give each teacher a paper and tell them that they must go around to the others in attendance and find someone who fits the description of each box in the grid; put each person's name in the appropriate grid square. The only rule is no one's name will fill in more than one box on the grid. This is a great way for everyone to learn about one another before starting the professional development session.

Group Story

The facilitator will break the attendees up into groups of four or six. Each group is then given a table topic relating to either education or whatever the professional development is covering. The table topic is given as a preliminary statement like "I came to school early in the morning last week and you will not believe what I saw in the parking lot." Each person adds a sentence to the story until the group has a complete story. Give teachers anywhere between 5 to 10 minutes to complete their stories. Allow them sharing time. This activity will get everyone laughing and help to focus everyone back on the day's activities.

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Community Agreements

Stay open-minded and assume we are all learning - (teaching, technology, kids, theory, race, culture, life).
Step up and step back in order to build a strong community where all voices are valued.
Be present, invest this time together. Resist multitasking.
Aim for understanding. We aim to create a safe place to share experiences and ask questions.

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Goals for AIM-TRU PLT

In order to better understand this high quality resource and how we can use them to best effect in our classrooms, our PLT will:

Become aware of components of formative assessment lessons, their benefits, and how they can be implemented during instruction.
Learn how the TRU framework can be used to describe classroom learning environments in order to impact instructional decisions.
Diagnose challenges from actual classrooms and make proposals to meet them with justifications/rationales based on the TRU framework.
Reflect on these proposals in relation to personal experiences within a collegial environment.

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Part 2:

Big Mathematical Picture

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Goals Text Rendering

Goal 1

Develop common definitions for ideas to be used throughout PLT

Goal 2

Answer the question: Why are big mathematical ideas and understandings important?

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Text Rendering Protocol

Split into groups of 3 or 4

Select a timekeeper to keep pace

Presenter 1

Read a quote or passage and then reads it aloud without explanation

Other members

Each take 1 minute to respond to the passage

Presenter 1

3 minutes share building on responses after all other members share

Repeat until all group members have been presenter
Whole Group Discussion

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Participants will have completed the reading and accompanying homework of Big Ideas and Understandings as the Foundation for Elementary and Middle School Mathematics by Randall I. Charles, prior. Ask that they take out their notes -

Protocol:

1. Split into groups of 3 or 4, In each group, select a timekeeper to keep pace.

2. Each participant should select a quote or brief passage from the article.

3. One member volunteers to go first. This presenter identifies the quote or passage and then reads it aloud without explanation.

4. Each of the other three members gets 1 minute to respond to the passage, which could be used to say what the passage makes them think about, what questions or comments it raises, and so on.

5. The first participant takes 3 minutes to state why she or he chose that passage and then responds or builds on what her or his colleagues have stated.

6. Repeat the pattern until all participants have been a presenter.

7. Come back to the whole group. Have each small group share a key idea or thinking that emerged from the discussions.

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Facilitating Whole Group Discussion

Goal 1: Develop common definitions for ideas to be used throughout PLT

What’s the difference between a big mathematical idea and an understanding?
What is an understanding? How is different from knowledge, skills, comprehension…?

Goal 2: Answer the question: Why are big mathematical ideas and understandings important?

Help students access prior knowledge for current situation
Help teachers plan for instruction in ways that support student learning and align with TRU
Help teachers use formative assessment to meet students where they are and help them gain new understanding

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Applying Ideas to Practice

Think about the math task you completed for homework.

What big mathematical relationships, patterns, or principles do we want students to understand in this lesson?
What is one (or more) key mathematical understanding that this lesson builds upon? What is one (or more) key mathematical understanding that this lesson builds towards? What connects those understandings?
How might different representations or solution strategies within the lesson connect to each other in order to deepen our students’ mathematical understandings?

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Facilitator notes: Spend no more than (3-5 min on this slide)

Say: We have read the Charles article, completed the text rendering protocol, and talked about mathematical ideas and understandings, here is how we are going to apply these ideas in our sessions.

· In a PLT session after completing the mathematics, each member will think about one of these three questions

· These questions are from your perspective.

· We will then continue to talk about the math and think about things, bringing in the student's perspective as well.

Take a moment a read through the questions just so you get a sense of what they will look like.

Would anyone like to share any initial reactions,

Share for about three to five minutes and then move onto the next slide

say: While we just focused on mathematical content, we also need to consider other important aspects of teaching mathematics.

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Part 3:

Framework and Tools for

Effective Mathematics Teaching

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Teaching for Robust Understanding

What makes a mathematically powerful classroom?

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May be reproduced for non-commercial purposes under the Creative Commons BY-NC-SA license detailed at https://creativecommons.org/licenses/by-nc-sa/4.0/ - All other rights reserves

Facilitator notes:

There is a leader guide and handouts for this section, which can be found at: https://www.mathnic.org/tools/01_tru.html (Do not distribute Handout 3, 4, or 5 until this part of orientation is complete).
Adapt as necessary – though we recommend sticking with this activity sequence the first time or two. To save time, we use only the first and third videos from the TRU leader guide to develop the dimensions.
Introduce the session by saying (in your own words) that the purpose of the session is to provide participants with a deep sense of the Teaching for Robust Understanding (TRU) framework.

Copying

Except where noted/credited otherwise, these materials are Copyright © 2015-2017 Mathematics Assessment Resource Service, UC Berkeley. They are published under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license, so they may be copied and adapted for non-commercial use under certain conditions and with appropriate attribution. Please see the license for details, or contact us via http://mathnic.mathshell.org/contact.html if in doubt.

All MathNIC materials can be freely downloaded from our website http://mathnic.mathshell.org/

March 2017 Release

Title Slide

You may like to customize this slide and/or the last one with your own institutional and contact details. Please leave the copyright attribution, however. Possible comments below are in plain text. Suggestions for what to say are in italics.

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Part 1:

What really matters in classrooms?

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Establishing a Focus

If you had 5 things to focus on in order to improve mathematics teaching, what would they be?

How would you know they’re the right things?

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1. A Lesson on Finding Angles

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NORMS for Watching Video

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Speak from the “I” perspective.

“If I could rewind the tape and ask students a question, I would ask…”

Be inquisitive, not judgmental.

“I wonder what might happen if,” instead of “the teachers should have…”

Justify your ideas and conjectures based on the video clip, and not other parts of the lesson that you didn’t see.

“I think that the student understands...because in the video she…”

Focus on how what you learned from the video might help you implement this (or similar lessons) with your own students.

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A Lesson on Finding Angles

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Think, Pair, Share

What did you notice?�
What was the experience like from the point of view of the students?

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Facilitator notes:

After 1 minute of individual think time, have teachers share their observations (~2 minutes) with a partner or in a small breakout room if online.
Bring everyone back and start collecting comments. You need to mark out 5 columns on a whiteboard, 5 flip charts, or in case of online we recommend using and interactive sharing space such as Padlet or Jamboard.
Have the 5 TRU dimensions in your head, but do not write them on the whiteboard, flipchart or online sharing space yet. Leave room at the top for putting the headings after you’ve looked at all three videos.
When a comment about mathematics is made, write it in the first column. Comments about cognitive demand go in column 2, equity column 3, agency and identity column 4, and formative assessment column 5.
Don’t say anything about why; just move to the second video after a few minutes.

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Fractions, Decimals, Percents

Take turns to:

Fill in the missing decimals and percents.
Place the cards in order of size.
Check that you agree.

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Fractions, Decimals, Percents

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The gray cards are the ones that students had to create for themselves.

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Fractions, Decimals, Percents

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3. Fractions, decimals percents

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Think, Pair, Share

What did you notice?�
What was the experience like from the point of view of the students?

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Comment Headings

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The Mathematics

What’s the big idea in this lesson?
How does it connect to what I already know?

Cognitive Demand

How long am I given to think, and to make sense of things?
What happens when I get stuck?
Am I invited to explain things, or just give answers?

Access and Equity

Agency, Ownership

What opportunities do I have to explain my ideas? In what ways are they built on?
How am I recognized as being capable and able to contribute?

Formative Assessment

Do I get to participate in meaningful math leaning?
Can I hide or be ignored? In what ways am I kept engaged?

How is my thinking included in classroom discussions?
Does instruction respond to my ideas and help me think more deeply?

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TRU:

There’s one problem with what you’ve seen thus far. Text is linear, but the ideas aren’t. So here’s a re-framing.

The math is at the heart of everything; and everything is connected, either by adjacency or across. For example, access to the math is a key ingredient on the way to developing agency, but you get it by working at the right level of cognitive demand (“productive struggle”), which is best set if you have a chance to hear what students think and adjust instruction accordingly (formative assessment).

It’s all connected, BUT, you can take it apart to work on any dimension you want to focus on.

Going back to the videos we just watched, now let’s try to consider how we can talk about the strengths and places where there might be room for improvement using these TRU dimensions. (include a note about revisiting the charting artifacts as a focus for discussion - maybe even focus on the two dimensions that the On Target discuss will be about)

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Our Claim

Research suggests that:

Classrooms at all grade levels that do well along these five dimensions will produce students who are powerful mathematical thinkers.
Instructional materials, professional development, and classroom observations will be most powerful if they are aligned with these five dimensions.

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Tools for supporting powerful classroom instruction

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On Target Reflection Tools

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Exploring On Targets

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I notice...	I wonder...

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Part 4:

Introduction to the AIM-TRU Model

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Model Overview

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Reflect on students' experiences in the classroom to understand how to implement FALs more closely aligned to the TRU dimensions

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University of Michigan

Teaching and Learning Exploratory

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Preview of Our Next Sessions

Session 1 - Building Norms

Session 2 - Understanding the components of a FAL

Session 3 - Collegiality in or PLT

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Homework

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Next session:

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PLT Session 1

Building Norms

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Hopes and Fears

If this is the worst PD you’ve experienced, what will or will not have happened?

If this is the best PD you’ve experienced, what will or will not have happened?

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Write an answer to each of these questions on one side of a post it note.

We will use these to create our group’s norms!

We are investigating FALs with respect to TRU in our classrooms, what are the hopes and fears to engage in this work?

This icebreaker can be found on page ? of the facilitator’s guide, and is also outlined here.

Hand out index cards and ask participants to write down their greatest fear about the AIM-TRU meetings. Ask: “If this is the worst professional development you’ve ever experienced, what will or will not have happened.” Don’t worry about starting on a negative note – this activity paves the way for positive outcomes!
Ask participants to share what they wrote. Write what participants say exactly as they say it in a public place such as a white board or if online Padlet or Jamboard is recommended. If multiple participants have the same fear, acknowledge this but do not write the same fear multiple times.
After all fears are listed, as participants to write down their greatest hope for the AIM-TRU meetings. Ask: “If this is the best professional development you’ve ever experienced, what will have happened?”
Record hopes in a public place using the same procedure as in step 2.
Say: “now we will make a list of group norms that should help us realize our hopes and assuage (or at least work through) our fears.” When participants suggest a norm, such as “make sure no one person dominates the conversation,” or “assume good intent when critiquing others ideas,” take a moment to make sure the whole group agrees with the norm. The norms can be debated and adjusted until you have a decent list that the group is mostly satisfied with. Write the final norms on a chart paper.

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Our Group’s Norms

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NORMS

WE WILL work together
WE WILL be fully present
WE WILL invite and welcome the contributions of every member
WE WILL actively listen to each other
WE WILL be involved by participating in the discussion and asking questions
WE WILL create a collegial atmosphere
WE WILL use humor as appropriate to help us work better together

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Norms for Virtual Sessions

We want to engage in a professional learning experience built on mutual respect, trust and support

Norms for Leading / Learning

Be vulnerable - share your challenges as well as strengths.
Speak up and ask questions when things aren’t clear.
Honor all voices in small groups.
Give positive and constructive feedback that will help us advance our work!

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Norms for Focusing

Expect to share with other in the session via chat and discussion.
Turn on video camera.
Keep microphone muted except when speaking.
Minimize distractions

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Intro to PLT Session 2

Formative Assessment Lessons

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Components of a

Formative Assessment Lesson

Diagnostic Task
Common Issues and Implications for instruction
Lesson Launch
Card Sort or Partnered Activity
(Card Sort/Activity Extension)
Lesson Conclusion

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Diagnostic Task Before the Lesson

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Every morning Jane walks along a straight road to a bus stop 160 meters from her home, where she catches a bus to college. The graph shows her journey on one particular day.

Describe what may have happened. Is the graph realistic? Why?

Distance from home in meters

Time in seconds

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Common Issue	Possible questions and prompts
Student interprets the graph as a picture E.g. as the graph goes up and down, Tom’s path goes up and down.	If a person walked at a steady speed up and down a hill, directly away from home, what would the graph look like?
Student interprets graph as speed–time E.g. The student has interpreted a positive slope as speeding up and a negative slope as slowing down.	How can you tell if Tom is traveling away from or towards home?
Student fails to mention distance or time E.g. The student has not worked out the speed of some/all sections of the journey.	Can you provide more information about how far Tom has traveled during different sections of his journey?
Student fails to calculate and represent speed	Can you provide information about Tom’s speed for all sections of his journey?
Student adds little explanation as to why the graph is or is not realistic	Is Tom’s fastest speed realistic? Is Tom’s slowest speed realistic? Why?/Why not?

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Lesson Beginning: Which Story Best Fits?

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A. Tom took his dog for a walk to the park. He set off slowly and then increased his pace. At the park Tom turned around and walked slowly back home.

C. Tom went for a jog. At the end of his road he bumped into a friend and his pace slowed. When Tom left his friend he walked quickly back home.

B. Tom rode his bike east from his home up a steep hill. After a while the slope eased off. At the top he raced down the other side.

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Students Annotate and Explain

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Matching Graphs and Stories

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Students Convert Graphs to Tables

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Tables are Added to the Card Sort

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...And the class compares solutions together

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End of Lesson Task

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Sylvia bikes along a straight road from her friend’s house home, a distance of 7 miles. The graph shows her journey.

Describe what may have happened. Include details like how fast she bikes.

Distance from home in miles

Time in minutes

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The Mathematics
How rich – connected, conceptual – is the mathematical content?
The lesson focuses on developing deep understandings of concepts like slope, and its use to describe real world phenomena; it provides opportunities to make connections across different representations (graphs, tables, stories).

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Cognitive Demand
To what extent are students supported in grappling with and making sense of mathematical concepts?
The card sort and poster activities provide plenty of room for sense making – if the students are gently supported when they need it. �(Remember the list of support questions.)

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Access to Mathematical Content
To what extent does the teacher support access to the content of the lesson for all students?
The classroom structures – which include whole group conversations, small group work, and student poster presentations – provide opportunities for teachers to support every student in engaging meaningfully with the mathematics. But . . . this takes hard work, even with the opportunities.

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Agency, Ownership, and Identity
To what extent are students the source of ideas and discussion of them? How are student contributions framed?
The classroom structures – which include whole group conversations, small group work, and student poster presentations – provide opportunities for teachers to support every student in building powerful mathematical identities. But . . . this takes hard work, even with the opportunities.

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Formative Assessment
To what extent is students’ mathematical thinking surfaced; to what extent does instruction build on student ideas when potentially valuable or address misunderstandings when they arise?
They’re known as Formative Assessment Lessons for a reason… ☺

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Intro to PLT Session 3

Collegiality

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Three Levels of Text Protocol

Split into groups of 3 or 4

Select a timekeeper to keep pace

Each group member has up to 3 minutes to:
Read aloud the passage they have selected. If another participant has previously read one of your passages, select another to read.
Say what they think about the passage (interpretation, connection to past experiences, etc.)
Say what they see as the implications for their work within this PLT
The group then has up to 2 minutes to respond to what has been said.
Whole Group Discussion

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Participants will have completed the reading of Harness the Energy of Collaboration by Ann Lieberman and Lynne Miller and identified passages that they feel may have important implications for their work.

The full protocol can be found at The School Reform Initiative http://schoolreforminitiative.org/doc/3_levels_text.pdf

Split into groups of 2 or 3

Select a timekeeper to keep pace

Each group member has up to 3 minutes to:
Read aloud the passage they have selected. If another participant has previously read one of your passages, select another to read.
Say what they think about the passage (interpretation, connection to past experiences, etc.)
Say what they see as the implications for their work within this PLT

The group then has up to 2 minutes to respond to what has been said.
Once each group is finished bring everyone back together a facilitate a discussion on what collegiality is and how it will appear in this PLT