By Derek Stoll

Math teacher at Syracuse City School District

As mentioned in the first article of this two-part series, it was clear that things needed to be done differently at Expeditionary Learning Middle School (ELMS) in Syracuse, NY, if we wanted different results from our intervention efforts in mathematics. We’ve shared how we used strength-based approaches to advance conceptual understanding in mathematics, changed the instructional materials to increase opportunities for students to think and reason mathematically, and used focused, flexible, fluid intervention groupings. In part two, we look at the systemic structures that supported our intervention work and the benefits of those structures.

By using tasks or more open-ended items that allow students to share their conceptual knowledge, not just their calculation skills, teachers can find out where students’ assets lie and where their areas of need are. Once those are determined, next steps can be identified for students, not as a whole group, but based on their like strengths and common spaces of unfinished learning. Using progress monitoring while delivering targeted intervention means that students can progress through new learning and teachers can make adjustments to continuously provide the right next learning opportunities for students.

Throughout the year at Expeditionary Learning Middle School (ELMS) in Syracuse, NY, we focus intervention work on different domains that support the tier 1 math instruction going on in the classroom.  As a result, the intervention does not feel “extra” but feels “in conjunction with” the math content they are doing in the classroom.  We adjust this yearly flow based on the needs of the students, but this is one way we have organized our subgroups during the first part of the year.

Give incoming 6th graders three question screeners in the domains:
1. Operations of Algebraic Thinking (OA) – Addition, Subtraction
2. Operations of Algebraic Thinking (OA) – Multiplication, Division
3. Numbers and Operations – Fractions (NF)

Tier 1

Tier 1
Intervention groups

Tier 2
Intervention groups

Tier 3
Intervention groups

6th grade Unit 1 – Area and Surface Area

  • Enrichment group
  • OA –Multiplication/Division strategies
  • Fractions – Comparing, Ordering
  • OA – Addition/Subtraction strategies

6th grade Unit 2 – Introducing Ratios

  • Enrichment group
  • OA – focus on Comparative Multiplication/Division
  • Multiplication, Division strategies
  • Fractions – Addition/
  • Subtraction with Like and Unlike Denominators
  • OA – Addition/Subtraction strategies

6th grade Unit 3 – Unit Rate and Percentages

  • Enrichment – Focus on 7th grade RP
  • Ratio and Proportion – Part:part:whole Ratios
  • Ratio and Proportion – Rates
  • OA – Comparative Multiplication
  • Fractions – Multiplication
  • OA – Multiplication/Division strategies
  • OA – Addition/Subtraction strategies

How does a school make all of this happen? Organizing the teachers and groups of students required considerable buy-in from both faculty and administration to ensure the programming was successful.

Structures that support mathematical intervention – large and small

Create time, space, and support for math interventions to happen and be valued in your classroom and school. I’m sure every teacher and administrator must be thinking, “This makes sense, but how do I get it all in and how do you organize a system that changes so frequently with some many groups?”  I can’t speak for everyone’s schedule, but for ELMS we made a few very small changes to the way we implemented our tutorial/intervention blocks to be able to provide a tier 2 or tier 3 intervention for every student at least twice a week.  We also used the SOAR Intervention materials, published by the Institute for Learning, to provide the screeners and intervention lesson plans that support conceptual understanding of mathematical models and reasoning within specific domains.

Here are some school-wide and classroom-specific structures/guidelines we use at ELMS to support this work.  While they may not all be able to be implemented in every local context, these are some bullets to think about adapting and accommodating when structuring for effective math intervention work.

School Wide Structures

For students:

  • Dedicated math intervention time for all students (might suggest A/B rotation with ELA intervention)
  • Groups of 8 to 10 students with a teacher that provide a targeted intervention cycle

For teachers:

  • Weekly team meetings as a grade level focused on intervention work/data
  • Make a school commitment to every teacher providing a math intervention and an ELA intervention that they can implement successfully. Consider an A/B rotation with ELA intervention. Use additional staff (librarians, TA’s, special educators) to create small, targeted groups based on the data.
  • Unpack progress monitors of student work as a team with a facilitator (could be a math teacher, coach, interventionist) and the intervention group teacher to better understand students’ strengths and areas of unfinished learning
  • Use these team meetings to help build conceptual understanding of the models, strategies and tools of students within the domain of study.
  • Re-screen kids at least three times a year to see the progress of the intervention and assess any adjustments that might be needed by reusing or slightly adapting the pre-existing screeners.
Intervention Classroom Structures

For students:

  • A dedicated folder or binder that organizes the intervention materials as they move between groups.
  • Clear Learning Targets, Objectives, or Focus on the intervention group for students to understanding and reflect on.
  • Use the student work, with your groups of students, to better understand the group’s focus, goal, and criteria for success.

For teachers:

  • Plan to give the progress monitor and review the data from the intervention every 2 to 3 weeks and allow some movement between groups and continue pushing to next steps.
  • Using materials that showcase models, strategies, and methods that push conceptual understanding and procedural fluency within the domain of study
  • Provide Fluency opportunities that push procedural fluency and mathematical reasoning (IE: number talks, discussion boards)
  • Use technology programs (ST Math, Prodigy, Dreambox, etc.) or other resources to allow additional unassisted instruction while you are seeing different small groups.
  • Use a station rotation model (maybe 20 minutes per station) to help manage small groups productivity with the technology programs to be able to see your groups every intervention time.

Implementing these steps above at ELMS has enhanced an amazing math culture focused on students/teachers strengths and needs, as well as, positive growth in mathematical conceptual understanding.  One of the most powerful experiences I have had with my team is laying out the progress monitors of a subgroup with a teacher (that is an ELA teacher) and letting the student work lead.  Seeing what students can do and understand, with a focus on next steps not only helped us tailor the intervention to be focused on students, but also helped build the conceptual understanding of a non-math teacher to implement a strategic, targeted intervention for their group.  As students, it becomes not a conversation of “what level I am in?”, but on “what I know and what I am working on within a domain of study.” 

Benefits from our work for our students and staff:

This work can be used to support our students AND teachers. Using this method at our school has created two tangible and important outcomes for our staff and students.  For students, they are receiving (maybe for the first time in their educational experience) a real tiered intervention model in mathematics two to three times a week for 50 minutes.  Using the staff to create small, targeted groups allows students to get intervention and support in mathematics at their level, not just for the student that has some areas of not-yet-solidified understanding, but also for the student that needs to be pushed and accelerated to continue to grow.  The use of these targeted groups also allows students to better understand their areas of need/next steps and be able to speak to their growth as a mathematician publicly at student-led conferences, and through their work/data.  We use the STAR math assessment to track student growth and through this assessment we have seen tremendous gains across the board. When we look at the progress of our student population, we see a significant increase in the percent of Black and White students meeting or exceeding a year’s worth of growth in one year. It also shows that continued support with some renewed focus is needed to ensure that our Hispanic students are making progress.

Percent of Students Meeting the Student Growth Percentile
(Meeting or exceeding 1 year’s worth of growth in a year.)












Note: Native American and Asian/Pacific Islander numbers are left off due to there being fewer than 10 students in each group.

If we look to state assessment scores reported in the graphs below for three subgroups, we see that ELMS students (shown in blue) are making progress and that proficiency rates are trending up. Additionally, the graphs show proficiency rates at ELMS are closer to and in one case exceeding the average for the state (shown in red).  ELMS’s proficiency rate is increasing faster than the district’s (shown in green), indicating that our programming for intervention is working!

This work has created a vibrant culture of math with focused interventions that pushed all staff members (especially non-math certified/trained teachers) to embrace math as a problem-solving process rather than just a skill building one.  Being able to lay out student work and analyze the “how” students are thinking about the problem, and then address those strengths and areas of need with the SOAR intervention materials allowed teachers to be better facilitators of mathematics learning and drive a culture of support and growth.  After using the guidelines above we created teams of teachers that are “all in” on their roles as math interventionists and contribute to the overall growth of the students.  By letting the student work lead, we have contributed to a better culture of empowerment for our students and staff that allow a rich, student centered, math intervention to help our students flourish as they progress throughout middle school.

Instructional environments can be created that systematically evoke learning goals and their associated behaviors. Learning behaviors are communicated both explicitly and implicitly in schools and in classroom settings that believe in collaboration.

Resnick, L.B., & Nelson-LeGall, S. (1997). Socializing intelligence. In L. Smith, J. Dockrell, & P. Tomlinson (Eds.), Piaget, Vygotsky and beyond (pp. 145-158). London/New York: Routledge.

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Derek Stoll taking a selfie with family

Derek Stoll is a 6th grade math teacher and grade level math interventionist at the Expeditionary Learning Middle School (ELMS) in the Syracuse City School District, in Syracuse, NY. Derek is passionate about crafting experiential learning opportunities for students that are interdisciplinary and help engage students to become leaders of their own learning. He also supports students grades 6-8, as a CREW leader, supporting their SEL, as an academic advocate and character building. An avid golfer, and Buffalo Bills fan, he is supported and encouraged by his wife, Aliza and four children, Duncan (5 years old), Beth (3 years old), Olivia (over a year and a half) and another boy due in January. 

SPECIAL THANKS: This wonderful work would not be possible without the support of our 6th grade ELMS intervention staff, including Jamie Erickson, Amber Talev, Karen Boyle, Carol Coles, Kate Taddeo, and huge administrative support from Jill Znaczko and Kevin Burns and the other supportive staff at ELMS that make such wonderful place for our students!