At the end of the 16/17 school year, our K-8 team was tasked to focus on our mathematical pedagogy and practices during the 17/18 school year. In order to prepare for this work, our faculty was tasked with reading the book Mathematical Mindsets by Jo Boaler last summer. Boaler, a Professor of Mathematics Education at the Stanford Graduate School of Education, is involved in promoting mathematics education reform and equitable mathematics classrooms. Her work seeks to apply to math education the “growth mindset” work pioneered by Carol Dweck. The book blew our teachers’ minds and launched us into a deep self-reflection of our current pedagogy, practices, and programming.

Our ongoing discussions and reflections helped us clearly define areas for future improvement. Two areas stood out to all of us almost immediately: a universal concern that our curricula/programs were not best serving our needs, and that our current approach to grouping learners was antithetical to a healthy, growth mindset approach to learning mathematics. We decided we needed help and so invited a math consultant and teacher for the past 26 years, to visit for several days in the fall and again in the winter to help us examine our road ahead.

Our consultant spent time observing math lessons and then met with teachers individually and in groups. One of her most important initial observations was that our current programs (Singapore and Pearson Common Core) weren’t “aligned with how our teachers teach nor how our students best learn.” Throughout the school day, Mack teachers approach learning through an inquiry-based, constructivist approach, but Singapore (LS) and Pearson Common Core (MS) were leading to a far too teacher-directed approach. She helped remind our team that our pedagogical approach should drive the curriculum, not the other way around.

We also realized that our current practices of grouping by acceleration (mostly in grades 2 onward) are not necessarily the best path/approach for many of our students. As students progressed through Mack, we have been increasing the number of groupings mostly to address the extremes of learners who go need to go slower or faster. In both cases, we have not been serving learners in optimal ways. Those in the slower groups have been developing negative math mindsets (“I must not be good at math”) and those in the faster groups can suffer from rapid acceleration that can lead to a knowledge base that becomes more like “swiss cheese than cheddar.” As a gifted school, however, we know that we are charged with managing this dilemma in the best possible way to address our wide range of learners who need occasional remediation to those who require a faster pace. This balance became part of our decision-making process as we reflected and planned with our consultant’s guidance.

Further discussions that culminated in the winter led us to realize that we needed to make some improvements to our pedagogical approach, and that we needed new math curriculum/programs to help make that happen. Our overarching goal was to find programming that: is aligned with our pedagogical and philosophical approach, is research-based, actively adds updated versions based on feedback, is rich in program materials, and provides a solid base of ongoing PD for our teachers. We all agreed that our current Singapore (LS) and Pearson Common Core (MS) programs have very few of these points at the level we need.

After our consultant spent the days in the classrooms and with teachers, she recommended we pilot two established and respected programs for the K-5 students (Bridges and Investigations). Both of these programs had the criteria we were looking for and were NCTM supported programs with solid track records for success. Many of our teachers taught one of the programs in previous schools and loved them. Over 3-4 months this winter/spring, K-5 teachers piloted both programs in their math classes and then provided feedback. The same process happened in our Middle School, where teachers piloted four major programs that were recommended by our consultant and aligned with our Middle School needs.

In April, a math committee met several times to collect and analyze our findings. Our consultant supported us in the process of aligning our initial goals with feedback on each program. The key areas we focused on during our reflections and subsequent decision-making processes were:

• Overall fit with our curricular and pedagogical needs.
• Level of student engagement/enthusiasm
• Pacing
• Building strong number sense that leads to deep mathematical thinking
• Embedded differentiation support—remediation and extension provided within each lesson
• Regular review and practice
• Resources supplied with the package
• Built-in professional development
• Assessment strategy and materials
• Real-world applications

We were thrilled to find one program that seemed like a perfect fit for our Lower School and two programs aligned with our Middle School. For the Lower School, we selected a long-standing, exemplary program called Investigations in Number, Data and Space (3rd Edition) to best serve our curricular and pedagogical needs. For our Middle School, we selected two programs: Illustrative Math (IM) and Mathematics Vision Project (MVP) to support our needs. After we made these decisions, we done into important work of transitioning and launching the programs in the 18/19 school year.

That process started with a guided approach to year-end assessing (our consultant supported us before/during/after). Our goal with the yearend assessment was to make sure we had enough data to support our work in creating math groupings for the future school year. For Lower School students, our aim was place the vast majority of students in grade-level groupings that will be taught by their homeroom teachers who ensured that students were properly supported and challenged. By creating math groups closer to homerooms, we deliberately moved away from our current math level groupings where some grades (ie: 5th this year) have five separate math classes within the grade.

Our overarching goal was to make groups that moved towards “cheddar” and away from “swiss cheese” development. We were confident that our new programs had the necessary elements for supporting students who need more time to process as well as students who process at a faster pace. We also purchased the entire package for all of the math programs. Our Lower School teachers were thrilled about the many resources that Investigations provides, including manipulatives, assessment materials, fluency support, and games.

We are also hiring our consultant to run two full days of PD in June to launch the new programs and train our teachers. She helped us analyze our assessments to create math groupings. She returned in August during staff week, and then again once a month or so the following next school year as a math coach to ensure everything is happening as planned. Thank you to our auction’s Stand by Mack Live Appealfor providing this funding!

Some additional information on Middle School Improvements: Our Middle School also worked with our consultant since the fall of 2017 to align our pedagogy to be more in line with our inquiry-based, constructivist approaches to learning. After much research into local, national, and IB MYP best practices, we decided to create a more clearly defined pathway for math learning. Our updated plan was not a radical divergence from what we had before, but we did feel it has been more logical, aligned, and manageable. Here is a snapshot of the new levels and how they correspond to various grade-levels and courses:

• MYP Math 1 (utilizes Illustrative Math Grade 7 Curriculum) → This is “on grade level” course for our 6th graders, single subject acceleration (1 year) for our 5th graders
• MYP Math 2 (utilizes Illustrative Math Grade 8 Curriculum) → This is “on grade level” course for our 7th graders, single subject acceleration (1 year) for our 6th graders
• MYP Math 3 (utilizes MVP Honors Algebra 1 curriculum- HS/IM Algebra 1 curriculum) → This is a traditional Algebra 1 course using H.S. CCSS standards and rigor
• Honors Geometry → (utilizes MVP Honors Geometry curriculum + IM Geometry curriculum) → This is a traditional “proof” geometry course traditionally encountered in 9th or 10th grade
• Algebra 1B (18/19 year only): this was a phase-out of our 1A/1B sequence

We continue to support MS acceleration (ie: 2 year) as needed for current and future students. This can be more easily achieved in the MYP program. In addition to aligning our MS program with our LS program, some of our goals and reasoning for making changes to our Middle School program included:

• Goal: to compact Algebra 1 to a single year, as per traditional standards
• Goal: To provide Algebra 1 as an 8th grade course
• Goal: To create a cohesive, rigorous math course sequence that gets more students in the “right” place (on grade level or single subject acceleration – one year)

 

As a school, we committed the following goals to help us improve collectively in the future:

• Move away from “I Do/We Do/You Do” model toward problem-solving classroom practices in which students are expected to be active contributors to creating their understandings.
• Move away from memorization/procedural repetition/”simultaneous operation” (everyone in the classroom doing the same thing at the same time at the same speed).
• Move toward building toolboxes of problem-solving strategies.
• Move toward collaborative problem-solving with development of SEL skills within that structure.
• Emphasize depth of knowledge, constructivist teaching methods, investigation, and curiosity.
• Develop stronger mathematical fluency in basic operations (math facts) and provide solid systems for supporting students and families who need extra support or practice.