Systems Thinking Institute

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:

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

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 ( 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 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

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.


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

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.

If you’d like to participate in a Math cohort like this, please let us know:

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

Contributing Factors


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


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



  • 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


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