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Middle School Math

Spreading Number Talks

Pete Reynolds Blog, Embedding Discourse ,

Goals for 2018-19 School Year

Our workgroup met Tuesday evening to walk through our goals for the 2018-19 school year which are focused on getting Number Talks to take root within schools.

  • Validate assumptions about what needs to be in place for Number Talks to take root and spread within a school
  • Pilot effort with Brown Street Academy and Prince of Peace
  • Recruit and prepare additional educators in round 2 schools
  • Develop community of practitioners that can support pilot and round 2 schools

Assumptions

Our assumptions about what needs to be in place for Number Talks to take root and spread within a school come out of our workshop at the Systems Thinking Institute in March, and our ongoing work with educators involved with the project.

Support

  • Overt support of building leadership
  • Community Partners (Learn Deep, Milwaukee Succeeds, UWM)

Resources

  • In-building expertise/support for Number Talks in a role that can serve classroom teachers
  • Willing cohort of teachers
  • Time for in-building collaboration
  • Cross-school network of practitioners willing to share problems and ideas
  • Peer-based professional development

Tools

  • A shared set of tools teachers can use in their practice:
    • Common Terms
    • Sentence Starters
    • Anchor Charts
    • etc.

Collaborative Feedback Processes

  • In-building
  • Cross-school/district

 

Pilot School Criteria

Our assumptions about what is required for Number Talks to take root and spread, guide our criteria for where it makes sense to pilot the effort:

  • Supportive Building Leadership
  • In-school resource in a role that can support colleagues working to establish Number Talks as a regular practice.
  • 3+ teachers willing to establish Number Talks as a regular practice within their classrooms from the start of the school year.
  • Participants willing to collaborate across school/district boundaries

We’re excited to be able to pilot the effort with Brown Street Academy (MPS) and Prince of Peace Elementary School (Seton Schools), and will be working with both schools over the summer to prepare for a fall start.

 

Tools

A number of the tools teachers planning to implement Number Talks are looking for were produced and archived as part of the GE Foundation project within MPS.  These include:

  • Sentence Stems
  • Discussion Prompts
  • Math Strategies
  • Planning Guide
  • Teacher Moves

These tools, and others are available on the project’s legacy site:

https://sites.google.com/milwaukee.k12.wi.us/gefvideos/math-resources

In our work this year, we also saw the need for a couple of additional tools– first, what we’ve been calling a Strategy Map– a quick guide for teachers that, for a given Number Talk, gives them a sense of the types of strategies they might see, common errors, and for those common errors, strategies a teacher can use to allow students to recognize and correct the error.  We’ll explore what these might look like over the summer.

We’ve also heard a need for a tool that can allow a teacher easily note where a student is in their thinking or level of comfort with a strategy that does not disrupt the flow of the discussion.  A simple checklist may suffice and we’ll look to test out some options within our pilot schools.

 

Collaborative Feedback Process

In-Building

For teachers to quickly develop competence and comfort in a new practice, effective, timely feedback is key.  We envision a process that borrows from Scrum, an agile methodology used in software development.  The idea here is a quick daily meeting that allows team members working on a common project (in this case Number Talks) to communicate where they are, where they are headed, and what they need help with. Our suggestion is to do these on the same frequency as Number Talks, 3-5 days a week.

Cross-school/District

For the 2018-19 school year, our workgroup meetings will shift towards peer-based professional development.  We look to continue the schedule of meeting every 4 to 6 weeks, but the focus will be on what teachers see, learn, and need help with as they use number talks in their lessons.  We’ll expand the group to include not only the teachers at our pilot schools working with number talks, but teachers at other schools that are using the practice on their own, or from schools that are looking for more widespread use.

Role of Community Resources

Throughout the year, we’ve had help from Kevin McLeod and Gabriella Pinter from UWM’s Mathematics program. UWM has a couple of professional development opportunities this summer, that Brown Street teachers will take advantage of in preparation for the work they will be doing next fall.

Strong Start Math Project — June 18-29
Early Math Seminar — July 30 – August 3

We touched briefly on the potential to connect after school programming at the Boys & Girls Clubs to the work schools are doing around Number Talks, as well as leveraging the Milwaukee Area Math Council to reach additional teachers interested in bringing the practice into their schools.

 

Metrics & Evaluation

As we look to scale the use of Number Talks within schools, we see the need for two sets of metrics.  The first, is focused on the spread of the practice:

  • Number of teachers using Number Talks as a regular practice
  • Number of schools with teachers using Number Talks as a regular practice
  • Number of students participating in Number Talks on a regular basis
  • Frequency of Number Talks for teaches, schools and students

The second set of metrics is aimed at evaluating the effectiveness of the program.  There we can look not just at test scores, but

  • Movement along learning trajectories/where students are in their thinking
  • Level of participation in discussions
  • Improvements in classroom culture

UWM’s Master of Sustainable Peacebuilding Program put together a workbook of tools that MPS might use to assess them impact of Systems Thinking in Schools.  They see that Systems Thinking training ought to have impacts beyond simple mastery of of the ideas.  As those ideas are put to use by students and staff the impact should be felt in the culture of the school, how students deal with conflict, etc. Given that number talks establish a pattern of respectful discourse where the students’ ideas are valued, we expect the practice to show impacts beyond understanding in math, and that a similar approach could be useful in assessing the effectiveness of Number Talks.

 

Next Steps

As we look forward to our fall pilots with Brown Street Academy and Prince of Peace, we’re moving on to what we need to get done over the summer:

  • Get the resources/tools in place for pilot teachers
  • Identify schools/teacher leads for who are interested in following the pilot efforts/participating in next year’s work group series
  • Confirm roles for community resources
  • Solidify the evaluation process
  • Secure funding to support the effort

If you’d like to join or support the effort, please let us know.

Scaling Meaningful Discourse – Recap

Pete Reynolds Collab Labs, Embedding Discourse, Workshops , ,

Our workshop at this year’s System Thinking Institute focused on how to increase the adoption of meaningful discourse within math lessons. As we noted in our last post, recognizing that a practice is effective is not enough. If we want to see widespread and sustainable adoption, the practice must be part of a larger solution that solves a real problem for teachers.

To understand how we might do that, we teamed up with Danielle Robinson, the Math Interventionist from Brown Street Academy.  Danielle lead the group through an exploration of their hopes and fears around introducing meaningful discourse into the classroom.  In the afternoon, we used that to guide a discussion of the factors that drive the decisions teachers make as they plan their lessons.

After the first day’s session ended, we sifted through everything we heard to construct a profile, written from a teacher’s perspective, that summarizes how they think about meaningful discourse, and what that means for their planning.  Day 2 began with a discussion of this profile. You can view the complete profile here.

Moving Towards a Solution

With our profile in hand, Danielle led us through a look at factors that drive or hinder quality math discourse in the classroom.  That set the stage for us to identify four key problems teachers face as they seek to introduce discourse or Number Talks in their classrooms:

  • Number talks are new to me and I’m not comfortable trying them out on my students
  • I don’t know how I will assess how my students are doing when I use a number talk as part of a lesson
  • I worry about being to reach all students in my class
  • I don’t have the resources (tools, time, support) to do number talks well/get good at doing so quickly

Using a version of the Lean Startup Canvas we’ve adapted for looking at programs within schools, we had the group sketch out what a solution might look like.  You can see the canvas we put together here.

The approach we arrived at equips classroom teachers with tools, resources, and support to drive quality discourse in a way that allows it to take root, and commit to seeing that it does.  Here’s what that looks like:

Tools

  • Set of common terms/behaviours to be used by teachers working on meaningful discourse
  • List of sentence starters teachers can use to guide students
  • Quick Checklist for Number Talk lessons, that identifies strategies students might use in the exercise as well common misunderstandings. The checklist should provide an easy way for the teacher to make note of the strategies and/or misunderstandings of individual students. It should also indicate how the lesson relates to standards (MTAP?)
  • Best practice anchor charts for Number Talks
  • Use Reflection Journals to have students reflect on their own learning/approaches
  • List of ideas for math challenges teachers can use to check understanding

Resources

  • In-building math specialist who is available for in-classroom modeling of meaningful discourse and ongoing support/mentoring as teachers develop their skills in leading math discourse.
  • In-building cohort of teachers working to integrate meaningful discourse into their lessons, and support each other in doing so.
  • Cross school network of teachers working to expand the use meaningful discourse in their schools.
  • Peer-based professional development that respects the voice of teachers.
  • Schedule changes that would allow teachers to observe/provide feedback to each other.

Support

  • Overt support from building leadership for teachers who elect to integrate meaningful discourse into their math lessons.
  • Permission from district administration for teachers to deviate from the pacing guide based on their students’ needs.

Next Steps

We treat everything on the canvas as a hypothesis to be tested.  The key assumption to validate first is that the problems we identified are issues for teachers beyond those in our session. There is no point investing time and money in a solution if we aren’t focused on the right problem.

We had a number of Danielle’s colleagues from Brown Street in our session, but as a first step, we’ll look to review the list of problems we came up with to confirm that these are important to a wider group of teachers at her school.  Assuming these teachers see the same set of issues, the group identified a series of actions we could take both before the end of this school year as well as over the summer to lay the groundwork for a strong start in the fall.

  • Converting a CAB to a number talk
  • (continue to) Provide intervention to students that need extra instruction
  • Practice Number Talk procedures
  • Establish a common language for Number Talks (“turn and talk” vs “shoulder partners”)
  • Create prototypes for tools– sentence stems, anchor charts, checklist

We’ll review were we landed at the next meeting of our Middle School Math workgroup. We don’t want to lose momentum coming out of the workshop, so we’ll continue to work with Milwaukee Succeeds and Danielle and her colleagues from Brown Street Academy to move this forward.

Middle School Math Workgroup – February 26th Recap & Notes

Pete Reynolds Blog, Embedding Discourse

The focus for our workgroup is now shifting to explore how we can speed the adoption of meaningful discourse/Number Talks within schools.  If we want to scale an effective practice, we need to get beyond simply asking (or telling) teachers to use the practice because it is effective. As teachers plan their lessons, they need to balance a number of competing forces. For Number Talks to be part of their solution, we need to understand those forces, and set up the conditions where the regular inclusion of Number Talks becomes the easy choice for them to make.  This will be the focus of our two day workshop at the Systems Thinking Institute next week.

Our February workgroup meeting was a chance to start down this path.

We began our session with a clip from Clayton Christensen, the Harvard professor who coined the term “disruptive innovation”. In this clip, he describes work he and his colleagues did to get a handle on why so many milkshakes are sold to commuters in the morning.  The key insight was not to look at the demographics of the buyer, but asking what problem they were buying the milkshake to solve — the “Job to be Done”.  In the case of this group of commuters, the Job to be Done was to give them something to do on a long commute, not leave them hungry by 10:00 in the morning, and not make a mess on the way.  As Christensen puts it, by understanding the requirements of the Job to be Done, we can craft solutions that allow customers to pull the solution into their lives.

To start down the path to understand the forces that guide the decisions teachers make when planning a lesson, Danielle Robinson, the Math Interventionist for Brown Street Academy led our group through an exploration of the hopes and fears they hold around Number Talks.

Our big question: How can we facilitate meaningful math discourse in our classroom?

What do you hope will happen when you implement math discourse in your classroom?

  • Kids help teach each other, and are excited about learning
  • Increased conceptual understanding
  • Increased student to student relationships
  • Build confidence in their math identity
  • Teachers would have better understanding of math learning process
  • Evidence-based conversations
  • Students make their own connections
  • Increased student engagement
  • Students learning multiple strategies from each other
  • Disagreement and testing new ideas
  • Teachers utilize feedback/take in student reactions
  • School-level, better attention paid to increased comprehension of math principles
  • Collect evidence
  • Inter-grade coherence
  • Raises the visibility of ah-ha moments for students
  • Coherence between subjects
  • Equity
  • Build community (students feel safe enough to share their thinking)
  • Students build relationships with each other
  • Learn to disagree respectfully

What do you fear will happen when you implement discourse in your classroom?

  • Non-stop discourse
  • Students get off-topic
  • If a teacher can’t properly define meaningful/productive discourse
  • Teacher will not value discourse/only values certain students discourse
  • Loss of Equity of voice
  • Teacher compliance vs. fidelity
  • If a principal wants discourse in a building, but how do they support
  • Fear of lacking support in the school
  • Students not becoming fluent in skills
  • Discourse time inconsistent with test time, basically how do you test learning
  • Difficult to measure the results of math discourse
  • Grading can be difficult, in terms of what a teacher values

Danielle asked the group to pick key hopes and fears for meaningful discourse and graph how they expected what they hoped for/feared would change over time.  Across the group, the top fears centered on classroom management issues. The top hope was that students would share their thinking rather than just their answers.

Testing this process with the workgroup has given us a sense of what we might expect in our Institute Workshop. In that longer session we’ll be working with Danielle to further explore the factors that drive teachers’ decisions around the practices they incorporate.  We’ll look for common themes and identify measures one might that can make meaningful discourse a solution teachers want to pull into their lesson plans.

 

 

Systems Thinking Institute: Scaling Meaningful Discourse (aka Collab Lab 18)

The Waters Foundation has been working with teachers and administration at MPS to leverage systems thinking tools.  The Systems Thinking Institute returns to Milwaukee in March, and we are delighted to again be partner in that effort.

As part of the Institute we’ll lead a two-day workshop on crafting and scaling a solution once the factors that influence current practice are understood. Our focus for this effort comes out of our Middle School Math project with Milwaukee Succeeds– we’ll review and refine our system model of factors that drive performance, use systems thinking tools to understand what blocks wider adoption of these practices, and chart a path forward.  We’ll have an excellent partner in the room for this workshop, Danielle Robinson, from Brown Street Academy, a math interventionist who is well versed in both effective practices and systems thinking.

Details and registration info are here:  http://watersfoundation.org/systems-thinking-institute-2

Middle School Math Workgroup: November 13th Session – Recap & Notes

Pete Reynolds Blog, Embedding Discourse ,

Gabriella Pinter from UWM’s mathematics department joined us for our November 13th session. Gabriella runs a Math Circles program at UWM for middle and high school students (http://uwm.edu/news/math-circle-taps-kids-creativity-in-problem-solving/) as well as a second program for area K12 teachers. She gave our group a minds-on experience of the process.

The Math Circles approach is to explore a problem (which may or may not have a known answer) to see where the ideas lead, test whether a solution can be proven, and see what new questions those discoveries raise.  As with meaningful discourse, it allows students to collaboratively build their understanding of the problem at hand, drives students to think carefully about what they do and do not know, and, as the problem is discussed, makes that thinking visible not only to the teacher but the other students in the room.

For our exercise, Gabriella asked us to play a game within a 4 x 4 grid. The rules of the game are pretty simple: You may put a single diagonal line running from corner to corner in any cell of the grid, so long as neither end point of that diagonal touches an end point of a diagonal in any adjoining cell. Go.

It doesn’t take long for the question to surface– how many diagonals can one place in the grid? The group’s consensus, 10.

How about a 3 x 3 grid? 6.

2 x 2 Grid? 3.

1 x 1 grid? Well yeah, 1.

5 x 5? 15…. Are you sure?

 

Well it looks like we have a pattern of triangular numbers…

Grid Size 0 1 2 3 4 5
Diagonals 0 1 3 6 10 15

Take the last number of diagonals, add to it the next grid size, get the next number of diagonals:

0 + 1 = 1

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

So we have a pattern and that looks like a pretty good rule.  Is it a proof? er…. maybe?

What else have we seen?  Well, each diagonal we place uses up two potential end points on the grid.  On a 4 x 4 grid, if we mark these potential end points as alternating rows of blue and red dots, starting with blue, we will have 3 rows of 5 blue dots and 2 rows of 5 red dots.  With that pattern, every diagonal must touch a red dot.  There are only 10 red dots, seems like a pretty good proof that 10 is the limit for a 4 x 4 grid.

Ok, what about a 5 x 5 grid?  Now, for both blue and red dots, we have 3 rows of 6, and therefore an upper limit of 18 diagonals.  So what is possible 15, which we found, 18 which is clearly the upper limit, or something in between?  Please tell us how you found 16.

……………………..

The wonderful thing to see in this process was how Gabriella slowly released a little bit more of the problem to explore just as the group thought it had arrived at an answer.  It was a very effective way of keeping engagement and interest high by continually adjusting the bounds of the problem to a point just beyond what we knew.

Gabriella pointed us to www.mathpickle.com which has a wonderful collection of problems to explore for any grade level.

Up next for the group, math journals.

The Middle School Math Workgroup is a collaborative effort with Milwaukee Succeeds to explore practices which drive student performance and share ideas and experiences about bringing those practices into the classroom.

 

 

 

 

 

Middle School Math Work Group: October 9th Session– Recap & Notes

Pete Reynolds Blog, Embedding Discourse ,
Causal Loop Diagram for middle school math performan
Our revised diagram highlighting key factors and adding a couple of new ones.

This was the first working session for a group of educators focused on middle school math that is part of a collaborative effort with Milwaukee Succeeds. We began our October 9th session with a silent discussion: using post-it notes to determine what is missing on the causal map, and dots to determine what three factors have the most impact on student learning.  Our goal in doing so is build a model that can help us chart a course to improved student performance.

Reflections

At the end of our first session we challenged the group with a reading assignment (Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding) and to experiment with meaningful discourse in their math classes.  The group took a bit of time to reflect on what worked, what was challenging, and ways to we get past that.

What stuck with you

  • Process is important (engaging in routines and creating common language)
  • Temptations to resist (not putting words into students mouths)
  • Mindset check, reminder on what really does help a student
  • Actually prod student confusion, and allow students that space

If you had a chance to experiment, were you able to? What worked and what didn’t work?

  • Peer-peer convos, non-verbal responses, but students have a hard time explaining what they really mean beyond the algorithm
  • Number talks: intentionally planning these talks
  • Multiple ways of talking about the numbers
  • Thought patterns, find out where the kids are at
  • Kids ping-pong off each other to see each other ideas and ways of thinking about things
  • Kids being so ingrained in rote-memorization, have a hard time getting out of that, and that there isn’t only one way of finding the answer to the math problem

Exercise in meaningful discourse

For the bulk of the evening, Kevin McLeod from UWM’s Department of Mathematical Sciences led the group through a discourse session on a single math problem appropriate for middle school students. This helped provide context for the higher level conversation which ran in parallel around the reasoning behind the process. The problem and his notes are available to download here.

 

Collab Lab 12 Recap & Notes

Pete Reynolds Blog, Collab Labs, Embedding Discourse ,

Middle School Math – What should we be trying?

Yesterday’s Collab Lab was a joint effort with Milwaukee Succeeds.  We pulled together a small group focused on middle school math– what factors lead to student success and what gets in the way.  We’ll reconvene the group in October as they work as a cohort to implement the strategies we discussed. Notes from our session are below.

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    A visual recap of the discussion from Collab Lab 12 on middle school math.

    Contributing Factors

    Strategies
    High quality instruction*

    • Procedural vs. conceptual knowledge
    • Real world application
    • Productive struggle
    • Engaging/interactive content
    • Project based learning
    • Teacher approach
    • Facilitating math discourse/connections
    • Culturally responsive practices
    • Clear objectives
    • Small group instruction
    • Student-centered
    • Differentiation
    • Student goal setting

    Committed leadership*

    Teacher support (coaching/mentoring)

    Culture of taking risks and experimentation

    Parent engagement/advocacy/attitude

    Curricula

    Common Core State Standards

    Cross-sector collaboration and best practice sharing

    Math enrichment programs

    • Coding

    Growth Mindset of principals, teachers, parents, and students

    Role models mirror students

    		 Increase discourse in math class

    • Begin math discourse in early grades
    • Track student responses to ensure equity
    • Provide wait time
    • Try “Bounce back”
    • Use “Turn and talk”
    • “I notice, I wonder” stems
    • Pose open ended questions
    • Setting up the physical space to promote discussion

    Build committed leadership

    • Brookhill (One day PD to show quality instruction)
    • Schools That Can Milwaukee

    Predict where students may struggle and set them up for success

    Continued Learning for teachers:

     Hindering Factors
    Student and/or teacher fixed mindset*

    Teacher content knowledge

    Math licensure

    Communication/language barrier

    ACEs

    Curricula

    • Low quality
    • Lacks rigor
    • Frequent changes
    • Lacks cultural responsiveness

    No K-12 math scope and sequence within schools, districts, and/or the city

    Metrics can be misleading

    • Emphasis on certain metrics (standardized tests or STAR)
    • Alignment between curricula and assessments
    • Data not triangulated

    Teacher evaluations

    Prior school experiences of students

    Student motivation

    Challenges at home

    Students living in poverty

    Reliance on computer instruction

    Prior school experiences of adults

    Lack of resources in the classroom

    • Technology
    • Materials

    Absence of early interventions

    “Tracking” students

    Key:

    Items discussed by the group
    Items that were noted but not discussed
    * designates strong support around the factor

    2023-24 Collab Labs

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