Meaningful math coaching with the Collaborative Lesson Design Cycle

I have been teaching mathematics since 1989 and during this time I have experienced no less than 3 or 4 math coaching initiatives either as the recipient of the math coaching or the deliverer of said math coaching. These sudden moments of interest in math coaching are ALWAYS connected to some external event: the state providing districts with a short-tern bucket of money for coaching; or transitioning to Algebra for All reorganization of standards; or implementation of the new Common Core standards.

Each and every wave of math coaching eventually fizzled out after a few years. Either the coaching position was shut down completely sending the coaches back into the classroom or the coaching position was watered down to such a degree that the focus was no longer on MATH coaching.

As districts look toward adopting a much needed new math curriculum, I see that we are entering yet another two or three years of district suddenly being interested in plucking teachers out of the classroom to be coaches…ostensibly to improve math instruction…with no fundamental difference from the previous math coaching initiatives that have fizzled out.

Despite lots of evidence that math-specific curriculum-based professional learning (CBPL) increases teacher effectiveness and improves student achievement,[1] it is remarkably challenging for districts to provide the necessary CBPL necessary for teachers.

Rather than providing sustained and ongoing math-specific instructional coaching, it is common for districts to mistakenly believe TOSAs, acting as general instructional coaches (coaching a wide variety of subjects), is good enough. Plucking teachers out of the classroom and asking them to be general instructional coaches is NOT sufficient. Too often, these newly minted coaches never receive proper training in andragogy (the science of adult learning), nor do they receive the requisite math content training to develop their mathematical knowledge for teaching (MKT) that would enable them to provide the curriculum-based professional learning.

Nine Essential Math Coaching Actions

The National Council of Supervisors of Mathematics (now branded simply as NCSM) has nine essential actions[2] for mathematics coaching for empowering teachers to improve student learning. Unpacking each of these actions should be a series of blog posts themselves, but for now I’ll just list them here…

  1. Demonstrate a commitment to coaching
    • Develop foundational elements (vision, beliefs)
    • Create coaching programs
    • Clarify the purpose of a math coach
    • Develop commitments to coaching through roles and responsibilities
  1. Apply the equitable learning principles to adult learners and model them during all coaching interactions
    • Understand and employ the principles of adult learning
    • Model equity and move toward vision through coaching
  1. Understand and use a variety of coaching interactions to improve teaching and learning
    • Understand the continuum of coaching functions
    • Clarify coaching individuals versus coaching teams
    • Understand coaching cycles and strategies for each part of the cycle
  1. Provide and engage in relevant and ongoing professional learning
    • Plan for effective mathematics professional learning
    • Develop a culture of ongoing professional learning
  1. Support the gathering and use of data to inform continuous improvement
    • Clarify data needed for ensuring continuous improvement
    • Gather data about mathematics coaching
    • Use data for goal setting, coaching, and analysis of instruction and student learning
  1. Know, understand, and do mathematics
    • Build mathematics content knowledge
    • Grow strategies for incorporating mathematics process standards in lessons
  1. Know, understand, and implement effective mathematics teaching and learning
    • Develop a quality lesson planning process
    • Build capacity for effective instructional strategies and task implementation
    • Grow pedagological content knowledge
  1. Develop and foster curriculum coherence
    • Develop coherence in mathematics curriculum
    • Utilize learning progressions
    • Close the gap between the intended, implemented and attained curriculum
  1. Develop and use evidence of student learning to inform instructional decisions
    • Respond to mistakes and misconceptions during instruction
    • Implement formative strategies
    • Plan for differentiated instruction
    • Develop strong classroom management

To ensure teachers receive the benefits of all nine essential math coaching actions, school districts must do three things SIMULTANEOUSLY:

  1. Utilize existing math-specific coaching providers (the Merced COE Math Team is but one example) to provide coaching for ALL teachers and additional coaching support for lead teachers the district has identified.
  2. Provide ongoing and sustained support for lead teachers who have been identified as district math coaches.
  3. Preserve the integrity of the math coach role, while not allowing the job to disappear or be repurposed.

Let’s keep it real: It is remarkably difficult for school districts to have the internal capacity to fully equip the coaches, freshly plucked from the classroom, to deliver on the nine essential actions. This is why districts should contract with their LOCAL service providers (like their county office of education) rather than fancy third-party outsiders for coaching support. The local COE math coaches know the community, know the students, and are often personal invested in the success of the school. After all, the school may have been where they grew up…or their own children go to that school…or they see the teachers at church or the soccer field or at the grocery store.

How does the Merced COE Math Team do the nine essential actions? It begins with what we call the Collaborative Lesson Design cycle.

 

Collaborative Lesson Design Cycle

Keeping andragogy in mind as we work with teachers, we acknowledge this statement from the California Math Framework:

The central goal of mathematics coaching is to support mathematics teacher learning and do so embedded in the contexts in which mathematics teachers do their work. Coaches can engage individual teachers and groups of teachers in a variety of potentially productive activities (Gibbons and Cobb, 2017), such as co-planning, examining student work, modeling instruction, and side-by-side coaching. In each, the teacher and coach co-participate in some way in the work of teaching—e.g., preparing, enacting, or reflecting—and work together to make sense of mathematics content, student thinking, and pedagogy. (2023)

In adhering to the recommendations of the framework, the professional development we provide is content-focused and closely connected with the curriculum the teachers are already using. We support teachers in developing their own mathematical knowledge for teaching through collaborative lesson design, followed by delivering the lesson to actual students, and then reflecting on how students responded to the lesson.

Collaborative Lesson Design (CLD) is similar to Lesson Study (LS) in that both are structured processes in which teachers plan, observe, analyze, and refine an actual classroom lesson. The difference is a CLD cycle is completed in about 3 hours over the course of a single day while a lesson study might take as long as 10 hours over the course of three weeks.[3]

In a typical work plan, math coordinators will find themselves working with teachers in one of three loosely-defined stages of the CLD cycle.

Stage 1: Collaborative Lesson Design PD

Teachers benefit most from professional development that engages them in the process of actively designing and trying teaching strategies and that provides them with opportunities to engage in the same style of learning they are designing for their students.

CA Math Framework (2023)

In this initial stage, cohorts of teachers are pulled out of their classroom for 2 to 3 hours to receive professional development. The purpose of this stage is for us to develop rapport with the teachers, guide them in deepening their mathematical knowledge for teaching (MKT) for the concepts they are currently doing with their students, and then involve teachers in actively designing, delivering, and debriefing a math lesson.

A sample agenda for this might be…

  • Pebbles in your shoe
    • NOTE: It is essential to plan in advance for how to navigate toxic conversations.
  • MKT development
    • Do some math with the teachers. The specific math topic might be a request from the teachers themselves. It also might connect to the lesson we will be designing later in the PD session.
    • Use CRA to model the math concept
  • Lesson Design
    • Address student learning gaps through the lens of Remediate vs Accelerate
    • We emphasize “just in time” support more than “just in case”
    • Design lesson using Teaching Through Problem-Solving
    • All teachers do all the math problems in the lesson being designed. This is an additional opportunity for teachers to develop their MKT.
    • Use lesson template linked below (inserting pics) for anticipating responses
  • Deliver the demo lesson in a classroom.
    • Determine where on the demo vs co-teach spectrum this will be.
    • Consider giving teachers small roles to play in delivering the lesson even if the MCOE Math coordinator will be the one primarily doing the instruction.
    • Teachers observe using a reflection form
  • Debrief
    • Share noticings and wonderings(reflection tool), next steps
    • Make sure ALL teachers fill out the MCOE Reflection form
    • Work with teachers to create your schedule for Stage 2

Resources for Stage 1: PD

Stage 2: Continue delivering the CLD lesson

In Stage 1 we used the Collaborative Lesson Design to create a lesson and demo it in one teacher’s classroom for all to observe and debrief. The purpose of Stage 2 is to deliver the lesson in the remaining classrooms…or at least as many additional classrooms as time permits. Coaches will likely create timeslots of 30 to 60 minutes to deliver this lesson. It is also possible the coach and/or the teacher might not teach the entire lesson, but highlight specific pieces of the lesson instead.

The coach and the teacher will collectively decide where on the Coaching Continuum you will be. Will the coach be doing nearly all the instruction (demonstration) or will the teacher be doing all the instruction (you will be providing mentoring services). Or perhaps somewhere in between in a co-teaching posture.

The CMF tells us that teachers benefit when they engage “in the same style of learning they are designing for their students”. During a demonstration you are delivering, therefore, it is not unreasonable for you to ask the teacher to participate as a student during the entire lesson. In doing so, teachers might improve their understanding the math content.

A sample agenda for this stage might be…

  • Arrive in classroom
  • Confirm or negotiate with the teacher how they want you to serve them.
  • Determine how might the lesson be different from yesterday’s lesson with this new set of students.
  • Do the lesson
  • Consider occupying the students with some sort of computer activity (iReady, ST Math, etc.) while you and the teacher quickly debrief and reflect on the experience.
  • Make sure the teacher fills out the MCOE Reflection form

Stage 3: Follow-up coaching in classroom with individual teachers

It has long been recognized that mathematics-specific instructional coaching leads directly to improved math instruction in the classroom and to increased student achievement. The purpose of this stage is to support teachers in the classroom as they learn to implement the new instructional strategies with integrity. The teacher’s comfort level with mathematics and with the new instructional strategy will inform whether you will be providing yet another demonstration or providing co-teaching/mentoring services.

Stage 3 is what makes the MCOE Math Team so special. We are keenly aware that teachers are very unlikely to implement the new instructional skills they learned during the PD of Stage 1 and the demonstrations of Stage 2. It is long term, consistent in-class coaching that will support teachers on their journey to authentically implement the new instructional strategies in their classroom.

It is during the in-class coaching that we build upon the trust and meaningful relationships we built during Stage 1 and Stage 2. Also, the andragogy we have been employing all along will further increase the likelihood that teachers will invite us into their classrooms for coaching.

It seems every school has their own preference for how it is determined which teachers will receive the in-class coaching when you are on their campus. Some principals want the coaching to be entirely voluntary on the part of the teachers. Sign up sheets are used for teachers to self-select the time and purpose of the in-class coaching.

At other schools, teachers are assigned time slots for the in-class coaching.

Regardless of how the coaching schedule is created, our goal is to maximize the number of teachers receiving Stage 3 services. We try to avoid “down time” while on campus. Some down time is unavoidable for example during recess, lunch, and transitions between blocks (PE, music, library, etc.).

What might this coaching look like?

  • Arrive in classroom at the mutually agreed upon time
  • Negotiate with the teacher how they want me to serve them.
    • This might already be established in your sign-up sheet, but you’ll still need to make sure you know what the teacher wants from you.
  • Do whatever coaching (or demonstration) the teacher wants
  • Debrief/reflection
    • Consider occupying the students with some sort of computer activity (iReady, ST Math, etc.) while you and the teacher quickly debrief and reflect on the experience.
    • Make sure the teacher fills out the MCOE Reflection form

Wrapping things up

Folks, math-specific instructional coaching is an essential ingredient if school districts want to see the transformational change that is needed. We know the nine essential actions math coaches need to provide teachers. Providing this type of  math coaching is far more sophisticated than merely plucking some teachers out of the classroom. While districts are building the internal capacity to provide and maintain meaningful math coaching to their teachers, districts should contract with their local county office of education to deliver math coaching services that is customized to meet the localized needs of the community and their teachers.

Please contact Duane Habecker if you have any questions: dhabecker@mcoe.org

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