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 (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.






Collab Lab 13: Recap & Notes

Problem Finding

Bring King joined us for Collab Lab 13 to walk us through an exercise to identify problems worth solving at attendees’ schools.  The idea was to give participants the feel for a process they could use with their students to identify challenges students could take on as authentic learning experiences.  Thanks also go out to David Howell (MSOE/Epiphany Consulting) who, with Brian, helped us pull together the process (below).

Our participants look to take the process back to their schools to see what their students might come up with.  We’re scheduling a follow up meeting at the beginning of December to re-group and share feedback from the process, see what problems students are willing to take on and, and share ideas about how to help the students dive into a problem solving exercise.  If you are interested in joining in, let us know:


The Process:

Step 1: Rapid Fire Problem Finding

  • Break into teams of 4 to 8 participants
  • On their own, each participant writes as many “problems at your school” as they can think of on note cards– one note card per problem
  • Collect all the note cards and put them into the bag o’ problems

Step 2: Mix and Redistribute the Cards

  • Shuffle the cards and distribute them equally between the teams
  • Each team categorizes and notes duplicates
  • Each team prepares a categorized list of problems to share with the entire group on a white board or large Post-it sheet.

Mixing the cards ensures that members are exposed to ideas from outside of their own team

Step 3: Large Group Sharing

  • Each team reports on the problems on their list
  • Teams share anything noteworthy about their process
  • The team may refine the categorization and list based on feedback from the group

Step 3a: Optional — Identify More Problems.

If the teams had a hard time coming up with an initial set of problems, prompt for additional ones to consider by asking

  • Are there categories of problems that are missing?
  • Are we missing the problems of any groups at the school (teachers, staff, administration, parents, students, neighbors) or subgroups of those (new students, minorities, impoverished students, etc.)?

Step 4: Drilling Down

In teams, but remaining all together in the room, consider the following questions:

  • Are there any problems on the wall that are actually dilemmas?
  • Are there any problems on the wall that aren’t actually problems?
  • Are there any problems on the wall that would benefit from re-articulation?
  • How might we “triage” these problems?
  • Is it realistic for you/your group to actually solve the problem?
  • Are there new problems to articulate based on your reading of all the problems?

Each team then drafts a revised list:

  • Based on the drill down questions, narrow to 3-4 issues and write them on a white board or large Post-it note.
  • Put a circled D or circled P next to each issue to identify it as a problem or dilemma
  • Record any problems/dilemmas that need further clarification before decision/asking
  • Each group shares their revised list

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:

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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

Collab Lab 11 Recap & Notes

We held our final Collab Lab for the 2016-17 school year on Thursday June 15th, where the topic for the evening was “Creating a culture of innovation in schools”.

We prompted the discussion with three questions:

  • What does a culture of innovation look like?
  • What stands in the way?
  • How can you create one anyway?

Our notes from the evening are below.  Thanks again to all who were able to join us.  It was a great group and a really interesting set of conversations!

Big Ideas

  • Innovation (continuous improvement) works in a system that instills a feeling of safety and encourages risk taking as a dedicated team.
  • Look for cross disciplinary problems that have meaning for students
  • Permission from the top for bottom up innovation
  • Autonomy allows bright spots which can then spread
  • Culture needs to come from school leadership
  • Use the right metrics
  • Start with what inspires the student

What does a culture of innovation look like?

  • Inquisitive
  • Focused risk taking
  • Failure is ok — fail forward
  • Collaboration
  • High engagement
  • interesting/fun
  • Student ownership of learning
  • Authentic
  • Healthy level of trust within the organization
  • Involvement
  • Empathetic
  • Public — welcomes feedback
  • There is a purpose and time for innovation
  • Innovation days — re-energizes staff
  • Hackathons — new products/committed block of time
  • Everyone drinks the Kool Aid
  • Encourage the design process
  • Inquirey
  • Opportunistic
  • Curiosity
  • What education means
  • Innovation is a value & aspiration, it does not equal effeciancy
  • One can innovate around people, process, technology
  • Leverage other resources, get kids involved
  • Cross domains
  • Power to the edge
  • Teams w/autonomy w/in safety construct
  • What is the smallest thing to start w/to start a feedback loop
  • Autonomy “fails” all the time– acknowledge failure, know it, work past it.
  • More difficult/important problems typically get less $$, time, resources
  • Teachers develop understanding about what’s happening in industry


What stands in the way

  • Taxpayer expectations
  • Teacher training
  • Uncertain ROI
  • Implementation Fidelity
  • Not everyone is innovative
  • It’s tough socially to be an innovator
  • Building (e.g. school) climate
  • Schools are structured to resist change
  • Mental models (of what school should look like)
  • Expectations of students, teachers
  • We train to technology rather problem solving/leadership
  • Are we selling it well?
  • Structure — no time to see what else is out there/what is possible
  • Scaling 35 x 5
  • It’s a big ledge to jump off of
  • Lack of courage to go off script
  • Lack “well functioning” partnerships w/industry
  • Those in charge of designing the system impact the level innovation capability
  • [Feeling that] “we’re looking good already”
  • Parents


How can you create one anyway?

  • Play to strengths
  • Give permission
  • Visit other rooms/schools
  • Use different metrics:
    • Engagement
    • 21st century skills
  • Focus on problems that matter to kids
  • Start with problems in school
  • Find a one off opportunity and then do it again
  • Show that it is valued by school/district leadership
  • Ask for something small at first
  • Transparency– get ahead of perception
  • Start as elective then tie into curriculum
  • Look for bright spots
  • Focus on interest in problems and who students need
  • Acknowledge self discovery
  • Leadership action
  • Organize PLCs
  • Align goals w/innovative initiatives
  • Focus on the real problem
  • Assemble the right people
  • Incentivise problem solving
  • Create a “Vision of the graduate”


Collab Lab 10 Recap

Building Resilience

Over the course of our Collab Labs this year, we’ve often heard that well crafted, collaborative, authentic learning experience provide students a safe place to fail and recover and through that, build resilience.  At Collab Lab 10, we focused on resilience directly, asking the following questions:

  • What do you see that worries you?
  • What drives that behavior?
  • What strategies do you use to overcome that?

Our discussions ranged from students dealing with trauma to those who’s main source of stress is continual pressure to perform at a high level.

Sheri Marlin from the Waters Foundation was able to join us again, and provided a couple of causal loop diagrams as part of our reflection at the end of the session:

  • Trust/Resilience : Increased levels of trust lead to increased resilience. Increased resilience leads to an increased ability to trust.
  • Environment/Resilience: A supportive environment leads to increased resilience. Increased resilience helps create a more supportive environment for others

As part of the wrap up, Lori Lange from Beloit Memorial High School shared the story of the laundry program she put together to develop the capacities of special ed students and help address a basic need of those that are economically disadvantaged.  It’s a great story of students working together to build resilience. You can read more here: https://beloitschools.org/loads-to-success/

Thanks to all of our participants for joining us for another great evening of discussion. Notes from our breakout groups are below.

Group 1

What do you see that worries you?

  • Wandering halls — unfocused
  • So focused on discipline that there is no self-discipline
  • Focus on trauma misses developing resilience
  • Adults losing their ability to be resilient in front of kids
  • Absence of consequences
  • Compassion fatigue
  • How to teach it?
  • Reactive — social norm is don’t worry until it is too late
  • Kids have to stay in resilience mode constantly
  • Trauma — complexity of trauma/lack of support systems
  • What do you “bounce back” to?
  • Facade of perfection (self told stories)

What drives (resilient) behavior?

  • Resilience is a muscle
  • Adapting
  • Knowing when to use strategies
  • Survival instinct
  • Past failure and recovery
  • Self talk – resilient people have a unique ability to control thoughts, beliefs and attitudes
  • Good support — relationships — trust
  • Mentoring — modeling — role models
  • Infant bonding
  • Coping vs resilience
    • peer pressure
    • fate?
    • social norms
    • unexpected change
  • Reading history
  • Perspective
  • Family stories (immigration)
  • Exposure — expectation — hope — dreaming
  • Knowing healthy ways to cope
  • Sense of constancy
  • Diet — sleep — routine
  • Purpose
  • Faith

What strategies do you use to overcome that?

  • Develop a common understanding of resilience
    • from ambiguous to concrete
  • Self discovery
  • Providing experiences — not teaching “it”
  • Pedagogy of confidence– building on students’ life stories
    • “Learning to Walk” — “trial and learn”
  • Design thinking
    • providing experience
    • healthy risk taking vs risk adverse
  • Catching kids being resilience — name it
  • Creating safe space — language
  • Trusting relationships — time/space
  • Community
    • multi-age interactions
  • Perspectives
    • avoid over managing
    • discovery
    • sharing experiences
  • Modeling mentoring
  • Re-teach coping strategies
  • Remove barriers to healthy coping strategies
  • Brave space vs safe space
  • Accountability/Voice

Group 2

What do you see that worries you?

  • Lack of understanding of level of stress
  • We don’t use failure as a teaching tool
    • “You didn’t fail, you are just not there yet!”
  • Life events – conflict at home/in community
  • Meet people’s basic needs (kids →families)
    • not happening
    • laundry program (in Beloit HS to meet that need)
  • No emergency room for mental health
  • Increased occurrence of trauma among youth
  • Rigidity of the classroom
  • Lack of connection/dependable suppport
  • Teacher burnout
  • Lack of purpose in life

What drives that (worrisome) behavior?

  • Institutional roadblocks
    • teachers can do it anyway with leadership support
  • Erosion of supports
  • Culture
    • preconceived notions
    • us vs them
    • political climate
  • Structural poverty
  • Violence as a taught behavior
  • Food desert
  • State pressure on school districts to perform
  • State testing!
  • Parent expectations
  • incarceration of minority men

What Strategies do you use to overcome that?

  • Bike program
  • Boundary program
  • Mental health clinic in the school (may cause problems at home)
  • Empowerment
    • resources access
    • break through co-dependency
  • Peer examples/role models
  • Student ownership of changing one’s circumstances
  • Separating by gender
    • break through stereotypes (STEM)
  • Trauma informed care at the school
    • reduce expulsion numbers
  • Teach children to rely on each other
  • Build context to relate to in “why” decisions
  • Accommodate different learning styles

Group 3

What do you see that worries you?

  • Lack of motivation (students, parents, teachers)
  • Unhealthy coping — cutting
  • Kindness is getting lost (cooperation/caring)
  • Inability to connect
  • Lack of history/common experience
  • Disconnect from culture
  • Frustration with how to reach kids
    • How to connect
  • Self validation vs validation from others
  • Inequity
  • Lack of caring for kids
  • Sense that no one cares/I am heard
  • Sadness/anxiety
  • Kids don’t move
  • Integration of social/emotional health
  • Relevance– lack experience/context

What drives that (worrisome) behavior?

  • Lack of skills/understanding
  • Parents are lost
  • Use of social media
  • Sitting all day for classes
  • Liability of going out on a limb
  • Teachers lack skills for trauma informed care
  • Teacher/students from different cultures
  • Empathy fatigue
  • Who can I ask for help
  • Teachers are forced to triage
  • Parents don’t value education
  • Too much stress in personal life
  • Survival — all I see is failure
  • Pressure for material goods
  • Divorce — parents are overworked
    • single moms working 2-3 jobs
  • Kids aren’t safe alone
  • Lack of opportunities to fail well
  • Low expectations
  • Parents in survival mode
  • Mismatch between teacher evaluations and what is important (to do for students)
  • Kids pushed through system
  • Grades
  • Fear of talking about emotions

What strategies do you use to overcome that?

  • Mindfulness
  • PBIS (Positive Behavioral Interventions and Supports)
  • 4 days of instruction, 1 day job embed
  • Bring awareness of trauma
  • Awareness of different situations
  • Support from outside to take the load off of teachers
  • Understand why students struggle
  • Use research — let kids experience failure
  • Alternative evaluations
  • Exercise/physical activity
  • Community service
  • Policies adapt to community
  • Self care/set boundaries
    • start early
  • Care of others/empathy
  • Building community
  • Having system support

Makerspace Challenge: Pitch Night

Makerspace ChallengeTuesday was pitch night at 88.9 for The Commons. The Betty Brinn/Learn Deep team shared their vision of CSA-farm-box meets up-cycling. The solution looks to offer schools a subscription service that delivers a mystery box of materials for use in a makerspace on a monthly basis.  Great idea, go team!

We have an idea on how to make this happen in Milwaukee. If you’re interested, let us know.


Recap: MJDS Innovation Hub tour

Tour Q & A
Questions from participants on the wall of the Big Idea Room.

A big thanks to Brian King for opening up the MJDS Innovation Hub for our visit and willingness to entertain all questions that could fit on the wall.

Thanks also to Quentin Allums from Mad Genie who came out before the tour with his 360° camera.  Quentin showed a group of MJDS students how to capture still and video images for video and VR and with some occasional advise, turned them loose to capture the Innovation Hub.  A first look at what they produced is here:


Collab Lab 9 Recap & Notes

Collab Lab 9 360 Selfie
360 Selfie under the guidance of Quentin Allums at the close of Collab Lab 9

Collab Lab 9 focused on evaluating success of makerspaces and FabLabs.  We used three questions to guide the discussion:

  • What does success look like?
  • What makes it difficult to assess?
  • How can those barriers be addressed?

Our discussion groups came up with these three big ideas to take home:

  • We have to learn to be comfortable with failure (and willing to model it for our students).
  • Makerspaces are a tool for developing a mindset
  • Successful makerspaces are the definition of individualized learning — teachers have the opportunity for one on one interaction with students, students are able to follow their passions.

And as a bonus: If students aren’t having fun, you aren’t there yet.

Links to things people heard about at Collab Lab 9:

April 20th: Tour of Milwaukee Jewish Day School’s Innovation Hub

April 27th: Betty Brinn’s Making in Education Community of Practice

May 11th: Collab Lab 10: Building Resilience

NEXT.cc: NEXT.cc supports making across the curriculum with STEAM based project learning set to NEXT Generation Science, Art & Design, and North American Association for Environmental Education Standards.  Scaffolding cognitive learning with discovery, NEXT.cc’s eLearning DESIGNopiedia introduces skills and integrates K12 classrooms with apps, virtual field trips, TEDed courses, free data sets, mapping, and science interactives bringing our youth into the future of lifelong learning.

21st Century Classrooms
Outdoor Classrooms

Mark Keane’s architecture classes for high school students:

Draw to Build I & II
UWM SARUP now offers two dual enrollment Architecture courses for juniors and seniors in high school.  They can be accessed via Youth Options or PLA. Contact Prof. Keane for more information: keane@uwm.edu.  Here’s a brief piece on the course featuring Collab Lab attendee Cindy McClinn and her students: http://uwm.edu/news/area-students-explore-architecture-100-and-perhaps-a-career/

Notes from breakout groups:

Group 1: We have to learn to be comfortable with failure (and willing to model it for our students)

What does success look like?

Dewy — Congnition — Metacognition
Mistakes & Failure
Outputs:  What does it look like? What does it sound like?
Growth Mindset
Common Process

What makes it difficult to assess?

Teacher/Educator thinking
Tasks — What is authenticity?
Questions are unwelcome
Grade based system
Lack of experience with failure/open tasks
Kids are trained to think about school in “school” ways
Behaviorist vs Constructivist

How can those barriers be addressed?

Common processes
Digital modeling
Community involvement
What is making?

Group 2: Makerspaces are a tool for developing a mindset

What does success look like?

Passion for a career path
Meaningful collaboration
Focused engagement on task
Problem solving
Equality of ideas/contributions
Success is nurtured and progressive
Teachers as facilitators & learners
Learning through experimentation
High level of resilience to change
Authentic experiences
Makerspaces is a process/culture

What makes it difficult to assess?

Traditional buildings
Lack of exposure/access to tech
“Accounting mindset” of leadership
How do I manage the learning process?
How do I track learning that takes place 24 x 7?
Gather the info that leadership needs
Kids don’t know how to self-assess/be accountable for their learning
There is not time to teach anything that doesn’t lead to a 22 on the ACT
Don’t know how to reach outside businesses for real higher level learning
Teacher education is not continuous and focused on designing engaging project opportunities
Tine to do something other than standardized tests


Group 3: Successful makerspaces are the definition of individualized learning — teachers have the opportunity for one on one interaction with students, students are able to follow their passions

What does success look like?

Start with purpose– of the space; of the school
For who?  Student, teacher, school, community
Attendance up
Increased engagement– students and teachers
Curiosity is sparked
Students (and teachers) are not afraid to fail
Becomes part of the culture of the the school/community
It is demonstrated
Ability to transfer and apply the skills learned
Hit high standards
Finding one’s self
Be able to adapt/be responsible
Kids set their own expectations
Compliance does not equal success
Integrated with curriculum
Other teachers are comfortable using the space
Students understand how to be life long learners
Teachers have an individual connection with students

What makes it difficult to assess?

Who is asking– district, school, parent, student
Long time frame required to see the results
Figuring out what is important
Pressure for standardized testing
Students are handed off to someone else (for the makerspace work)
Changing expectations
Getting teachers to adopt a new role– mentor/guide

How can those barriers be addressed?

Agreement on what you want to see happen
Ask how the community can help
Ask students for self evaluations
Classroom teachers should work with students within a makerspace (rather than handing them off)
Show off the results of student efforts