A Different Take on the Fishbowl

Jeanne Villeneuve, Loomis, CA

Last year I invited four teachers into my room to solve The Locker Problem in front of my  senior math class.  The students chose this problem because they found it especially challenging, and wanted to see how a group of non-math teachers would make sense of this problem.  I think some delighted just a bit in the idea of watching their teachers squirm.  Upon entering the room, the Spanish teacher, Mrs. McKinney, grabbed a box of Kleenex and pronounced to the students, who were seated in a large circle around the teacher group, that math had made her cry all through high school.

After another member of the team read the problem, Mrs. McKinney joked that they should go to the hallway to act out the problem, and then quickly added “Could we use less lockers though?”  The students exchanged surprised and impressed glances…she had figured out something it took them quite a while to do.  Imagine her surprise when I told her she was on to something.  What proceeded was an experience that was quite informative to my students, myself, and the participating teachers.  Students witnessed strategizing, persistence, frustration, aha moments, and some excellent and not so excellent teamwork.  During the debriefing I mentioned my concern that I did not know if Mrs. Smith, an English teacher, was following for a very long time, because she was so quiet.  To this, Mr. Zimmerman, a Science teacher who had been pushed farther out of his comfort zone than he had anticipated, exclaimed “Oh my gosh, I hadn’t even noticed.”  Afterwards, this was the exchange that had made the biggest impact on my students:  The realization that they both needed to speak up when they were confused, and also be much more cognizant of whether the rest of their group members were following along.  During the debriefing I also had each teacher graph their confidence level throughout the process and discuss their graphs.  The biggest takeaway for me was witnessing the dialogue of my colleagues, which sounded much more similar to that of my students, than that which I experience with my math colleagues when we are solving problems at a workshop.

Everyone agreed that this was a worthwhile experience and my students encouraged me to continue to do this with future classes.  This year I invited my colleagues to participate, and was able to get two groups of four faculty for my two senior math periods.  One of those classes includes students from another campus who participate in distance learning via cameras and a television.  These students are part of a group with students who are in my classroom.  It seemed only natural, then to include a teacher from their campus who worked together with teachers from my campus to solve a problem written by Tom Sallee; the problem involved recognizing Fibonacci’s pattern to reach the solution.  English teacher, Joel Agee, quickly discerned that this problem involved the use of permutations.  Students raised their eyebrows and began writing this on their observation sheets, while some called me over to ask me what that was.  On their observation sheets students were required to record strategies, comments and questions.  Prior to the problem, I had given my students control over the process, instructing them that it would be up to them to decide when and how to intervene if the group got stuck, or headed down a wrong path.  The next day Mr. Agee sent me an email saying “As fun as it was, what sticks with me is the feeling I know our students have regularly: getting stuck.  With everybody watching you…They’re the experts in coping with it; it validates their struggle to see teachers share it, and it gives them occasion to use their past success to provide genuine help.”

Colleague Joe Hancock, who solved The Pizza Problem with another group commented “We approached (the problem) from several different angles and while the math we needed to learn was in many ways just out of reach, with very little teaching, we arrived at the answer to the problem.”

My students found this experience both fun and informative. Next week a group of them are looking forward to being a part of their own fishbowl as they demonstrate effective math discourse for my Integrated 2 class.

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Algebra Tiles Blue Icon

Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.