Open Mathematics PLC Protocols

Created Feb. 7, 2024 by Barbara Soots


Circular arrows showing progression of study from content to unit to lessons.
Year_1_PLC.pngCircular arrows showing progression of study from content to unit to lessons.

Circular arrows showing progression of study from content to unit to lessons.


The first year of the PLC is devoted to a deeper understanding of content and purposeful sequencing of concepts within the materials. A careful look at the course overview itself is followed by iterative cycles of unit exploration and deeper dives into the lessons.





Course Overview

Why start with a course overview (the progression of content for the year)?

Knowing the scope and sequence of the year and where the domains and clusters from the standards are addressed will provide teachers a clearer understanding of the content their students will be engaged in over the course of the year and it will set the stage for the deeper dive into the unit work. Building a common understanding of the progression in content standards is an important piece for all teachers.

Note: If you have someone on the PLC who has been part of the review or curriculum adoption process, it may be helpful to have them be part of the facilitation process.

Unpacking the Course

70-90 minutes  - if possible, complete this section before the school year begins

Materials (one copy per teacher)

  • Chart paper or template for teachers to walk away having access to the work from the day


Teacher Task   Facilitator Questions 
 Teachers read through the curriculum overview individually and make comments about the scope on their own overview copy.

     identify the big ideas addressed
     identify the sequence

Teachers share the scope for their grade level with the rest of the PLC to create a big-picture map.

  You will begin to create the large scale map of the work for each grade level.

“How do the ideas progress and connect over the course of the year at each grade level?”
 Facilitator will introduce the focus documents to ground teachers in the major work of the grade. Teachers begin to read the overview for each module or unit  “In which unit(s)/module(s) is the major work of the grade level being addressed?”
 With their grade level standards and overview in hand, teachers will highlight the area where their grade level standards are addressed.

Compare the new design with what they’ve done in the past.

  “Where are the standards being addressed/reinforced?”

“How do they progress?”

“How does each subsequent module or unit build on the previous content?”

“How are the mathematical concepts addressed the same as our last curriculum?”

“What’s different?”
 As a team (grade level or department), decide on a focus to develop content understanding.  “What is your year-long goal or focus in developing content understanding in your PLC?”


Unit Overview

Why continue with the unit overview?

As teachers, we all come to the table with our own experiences in how we learned and experienced mathematics. As we engage in this process of familiarizing ourselves with the materials we are using, it is important to identify our possible biases and understand that we are going to be engaging as learners and need to have an open mind to approaching the teaching (and learning) of mathematics differently.

Where is the unit situated in the storyline - what are the big math ideas and concepts in the unit, 

Materials

  • Unit Assessment
  • Unit Overview
  • Large Notecards
  • Unpacking Unit Assessment Worksheet (download below)
  • Unit Teacher/Student Materials


Download: Open_PLC-Unpack_Assessment


Unpacking Unit Assessment

10 minutes

Teacher Task  Facilitator Questions
 

1. Break the unit assessment into 2 or 3 problems and assign one set to at least two teachers.

2. Teachers individually work through the problems and answer the questions on the "Unpacking the Assessments" worksheet.

3. Teachers with the same problem sets discuss the questions together. Compare and contrast the two columns.

As you work through the assessment, keep the following questions in mind:

“What would you do to prepare students for the problems you were assigned?”

“What are the misconceptions or challenges students might experience”


NOTE:

Watch out for looking at assessment through teacher lens of what they think students might not be able to do – teacher misconceptions

Be sure to focus on content itself rather than teacher experience.


Big Ideas of the Unit

25 minutes

Teacher Task Facilitator Questions
 

1. Read the unit overview and/or table of contents.

2. In pairs, determine the lessons aligned with the assessment problems for your set.

3. For these lessons, identify the big ideas. Look at the lesson summary, exit tickets, cool downs, learning goals/learning targets.

4. Identify how the math ideas are developed in the lessons.

5.  On the note cards, write down the big math ideas and how they are developed in the lesson(s).

“As you read the overview and how the lessons progress, keep the following questions in mind:

     a) What are the “big ideas” for the unit and how are they developed?

     b) How do the instructional materials prepare students for the assessment?

“How will your approach to using these  materials compare to ways you have taught these concepts in the past.”



Progression of Mathematical Ideas

10 minutes

Teacher Task Facilitator Questions
 

1. As a group, share the big ideas and how the math ideas are developed from each set of lessons.

2. Take the cards identifying the big ideas and progression of math ideas and build a “map” on the wall to see how math ideas build from lesson to lesson and throughout the unit or module.


“What do you notice and what do you wonder about the progression of math ideas for this unit/module?”


Identify Focus for Lesson Overview

15 minutes

Teacher Task Facilitator Questions

1. Considering the exploration and discussion, identify what aspects of the unit where the instructional materials prepare students in a different way than you had thought about preparing students and/or where students might have some misconceptions of the math ideas.

2. As a team, identify a math task, lesson, or activity from the unit to engage the PLC in the Lesson Overview Protocol.


“Is there a new idea or approach the unit uses to build understanding of math ideas?”


“Are there some math ideas that you anticipate student misconceptions?”


“What tasks, lessons, or models are used in the unit that differ from how you would approach preparing students?”


“What math task, lesson, or activity do we want to engage in as a learners for the Lesson Overview protocol?”


Lesson Overview

Why continue with the lesson overview?

Now that teachers have identified a lesson or a task from the unit overview, they are ready to continue to study math materials at an increasingly smaller grain size as we learn from individual lessons within the units. By focusing on the math within the lessons, teachers will continue to broaden and deepen their own understanding of the mathematics content for teaching. They also grow their knowledge of the progression of student learning in order to support equitable access to the mathematics. As teachers engage in this work, they will compare and contrast this learning to how they have taught concepts or ideas in the past. It is important they know that they may have uncomfortable experiences as they engage as math learners in this work. If they aren’t uncomfortable, they aren’t learning. They become more aware of the shifts in the standards that are embedded in the curriculum.  

Resources/Materials


Pre-Work

Reflecting from the Unit Overview protocol, select a lesson situated in the middle of a key learning objective that is an anticipated struggle for students or a new way of thinking about the content. (Done from either the unit overview protocol or by PLC leader)

Necessary Reading

Subheader 1


Teacher Task Facilitator Questions
 

Looking at only the lesson objective (facilitator should have it posted) and share how you have presented this idea to students in the past. (5 minutes)

Presented with a printed math task from the lesson, work individually to solve the problem(s) (10 minutes)


As you finish with the task, read a copy of the math standards and try to identify which one(s) are being addressed Share/Compare solution strategies/approaches and math standards being addressed in partner/table groups (10 minutes)


Identify the aspect of rigor called for in the standard(s)--conceptual understanding, application, and/or procedural skill/fluency, Key words in the standard(s) can be highlighted to determine the aspect(s) of Rigor, however, read carefully as the word ‘apply’ in the standards does not usually signify application. (in partner table groups) (5 minutes)


Achievement Network - Aspects of Rigor


“How have you taught this concept in the past?”









“Which standard(s) matches the work of this lesson?




“What solution methods/strategies/approaches did you use when solving the problems? How do they compare with the ones your colleagues used?”


“What aspect(s) of Rigor are called for in the standard(s) you identified? (There may be more than one) What language in the standard(s) lead you to determine this?



Subheader 2



Teacher Task Facilitator Questions
 

Select 2-3 of the following questions for your group to discuss as you begin to think about what’s next (10 minutes)

What is the big mathematical idea--the mathematical take-away from the task?


What does success look like? How could it be shown? Anticipate/Brainstorm some possible models, strategies, or representations students may use to present their thinking/approach


What will be challenging for students?


What are the foundational skills/prerequisites for students to access the skills needed for this lesson/task?




Subheader 3


Teacher Task Facilitator Questions
 

Examine the lesson (teacher guide) the Math Task/Activity came from. (5 minutes)


“What is the goal/objective of the lesson in your own words?”

“What are the standards the publisher has identified and how does this compare to your identification?”

“How does the goal/objective of the lesson align to the intended aspect of Rigor?”


Subheader 4


Teacher Task Facilitator Questions
 


What are the connections between past and future lessons?

“Where does this fit within the progression of learning?”

Is there a progression from concrete to abstract or conceptual to procedural that is developed? (5 minutes)  Concrete to Abstract

Are there standards that are being addressed, extended or building towards?


Subheader 5


Teacher Task Facilitator Questions
 

How are the mathematical ideas presented in the materials the same and different from how you have presented it in the past? (5 minutes)

What ideas will be important to remember as you the plan for your lesson.(5 minutes)

“Why might the materials have students engage in the mathematical thinking the way that they do? (Is it developing conceptual understanding before procedural skills or fluency?)”

Here teachers need to generalize their learning into their own practice.

“What are they going to commit to doing with the learning from the day?”

(This may be a good opportunity to have teachers rehearse a particular part of the lesson that is new learning for them if there’s time. This could be done in partnerships.)



Repeat this protocol, beginning at the Unit/Module Overview Protocol, for each unit or module.

Note: Lesson protocol may be repeated, as needed, prior to moving to a new module.


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