Joyful Mathematical Noise

Screen Shot 2019-06-26 at 9.18.50 PMTwo decades ago, I began my teaching career as an elementary school teacher.  Pairing students up to collaboratively read these poems was always a highlight.  Diverse talents, coming together to blend their voices into a unifying theme.

Thanks to a very generous Strategic Impact Grant by the Berkeley School Fund and additional funds from Susanne Reed, BUSD Professional Development Coordinator, Berkeley Unified math teachers spanning grades 4-9 had the opportunity to spend a week together creating some incredibly joyful mathematical noise.

All three middle schools have elective classes for students who need additional support in math.  This summer work was the culmination of a year-long, teacher-led focus on creating more collaboration and coherence between the content of these courses at all 3 sites.

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Monday through Wednesday was an intense focus on how we support struggling students in middle school.  Geeta Makhija, King 7th Grade Math and Intervention teacher co-led these days with me.  As we have built relationships with our struggling students we have learned that many previous teachers have not believed that they could succeed in grade level math because of lower grade skills they lacked.  Teachers continue teaching without carving out targeted instruction to support these necessary foundational skills because we often don’t know how these elementary math skills were taught in the first place.  This 3-day institute allowed us the opportunity to learn from elementary experts so that we can better support students who still need time to learn this foundational math.

Our mornings were led by Ana Delgado, former K-5 BUSD Math coach and current Math TSA at two of our elementary schools.  We wanted to more deeply understand how multiplication and fraction concepts are taught in 4th and 5th grade as they are the biggest gate-keepers to success in higher level mathematics.  

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Ana used this graphic to discuss the importance of using three types of representations when teaching math.  She said the word “cat” and asked us to share what came to mind.  Teachers verbally shared the mental images which came to mind, “Grey; puffy, striped, cuddly…etc.”  No one shared the letters c-a-t.  Ana contrasted this with the teaching of mathematics where we often ONLY discuss the abstract, symbolic representation of an idea, without also discussing the concrete and visual representations.  I loved this notion and am excited to think more deeply about how to build students’ mental models of math concepts for everything that I teach.

Ana then gave us the opportunity to compare and contrast how we solve elementary math problems with how students are taught to do them.  We practiced partial quotients for division and explored both an area model and number line for fraction multiplication.

In addition to Ana, we had presentations by several teachers on classroom routines and pedagogical strategies which have been successful in their Math Support classes.

  • Wendy Lai (King) presented on how she uses math stations.
  • Robert MacCarthy (Willard) presented on what he has learned from Jo Boaler’s work on Mathematical Mindsets and how he incorporates mindset work into his classes for Mindset Mondays.
  • Geeta Makhija (King) led us in a 3-act task focused on multiplication and fractions (The Big Pad by Graham Fletchy) and discussed the power of using rich tasks in our Math Support classes
  • Joshua Paz (Longfellow) presented on how he has students doing error analysis and how he sets up his grade-book for students to understand which concepts they are strong in and which they need to continue working on.
  • Kinjal Shah (Willard) taught us how she spirals the math in her course, with explicit times each week to review material from earlier grades and other times to preview the math coming up in the grade level course.  One resources she uses for students to independently practice & keep track of their progress in foundational skills is a web site called That Quiz.
  • I presented on how Desmos’ Snapshot’s Tool can be used to bring multiple perspectives on problem strategies into class discussions and allow more students’ voices to guide class conversation.

Our end-goal was for our courses to be more aligned, so our afternoons were spent collaborating, putting shared resources into folders and co-planning our courses.   In addition to Ana, we were joined by elementary RTI teacher Vanessa Sinai.  This was truly a collaborative effort. Tons of ideas and links were shared which are all found at the bottom of our agenda here. 

We used some of our grant funds for a daily raffle where we had tons of incredible math resources as prizes including, of course, a #mathgals t-shirt.

As our team planned for this summer work, we realized that a broader outcome for this grant was to bring math teachers, together, from upper elementary through middle to 9th grade to more deeply understand students’ needs.  Thursday and Friday were led by our 6-8th grade Math Coach, Ryan Keeley.  One day was a collaboration between 7th grade math teachers and the following day was 4th-7th grade teachers.  The goals of both days were similar: develop deeper professional relationships between sites and grade levels in order to increase our common pedagogy and mathematical approaches to the teaching of big ideas.  We talked about how an idea introduced in one grade level (integer addition in 6th and 7th grade, for example) leads into ideas in later grades (vector problems involving distance and time) and the importance of using models in the lower grade which will inform those bigger ideas.  IMG_6520

For me, this week demonstrated the power of teacher-leadership and the need for sustained partnership between elementary, middle and high school teachers.  Every day we were reminded that we teach the SAME students and that improving student learning depends on us continuing to learn from one another’s expertise.  I have such gratitude to the Berkeley School Fund and Susanne Reed, Professional Development Coordinator for valuing and funding this summer work.

Evidence of this learning was evident throughout our evaluations:

“All of my learnings will go directly toward informing instruction for my students that is more relevant, engaging, thought-provoking, and personalized, and that will promote deeper conceptual understanding. I have spent the past few days excitedly building my toolbox, reflecting, and recharging to begin a deep dive into reshaping what support class can look like this year. I believe that with these new additions students will grow even more in enjoyment of the class and growth in mindset and as problem solvers, and increase retention and understanding of topics covered. I’m confident that my students will benefit because even as a participant in this work I’ve grown in these ways – I can’t wait to see where my students will go with these additions.”

“I had a blast participating and am taking away so much that I’m eager to put into play for this upcoming school year. To have this kind of energy and momentum going into summer is awesome. I can’t wait to roll up my sleeves and start weaving together all that I’ve learned, all of these best practices, to make a more effective and impactful support program for our students. Truly a wonderful professional development time.”

I am so looking forward to returning to teaching next year with these amazing colleagues and so many more not captured in this lunchtime photo.  I’m honored to be a part of this powerful group of reflective teacher-leaders.

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1 thought on “Joyful Mathematical Noise

  1. Ali – your posts energize me! Thank you for writing about the great work the teachers in your district are doing. I’m tutoring a 5th grader who gets plenty of concrete work, but hasn’t been able to leap to abstract work, and she is getting left in the dust now. I think she has never been explicitly taught the third piece, the representational/visual. While I’ve been able to identify that, your description of Ana’s presentation helped me put better words to it.

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