5 Practices for Orchestrating Productive Mathematical Discussions: Anticipate, Monitor, Select, Sequence, Connect

Use Anticipate, Monitor, Select, Sequence, and Connect to plan, organize, and facilitate productive mathematical discussions
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About This Strategy

The Five Practices: Anticipate, Monitor, Select, Sequence, and Connect, from the book 5 Practices for Orchestrating Productive Mathematical Discussions by Margaret S. Smith and Mary Kay Stein, is a strategy used to help teachers guide classroom mathematical discussions. This is an instructional routine used in the Open-Up Math curriculum. This strategy can be used in any grade level Math class.

Implementation Steps

30 minutes

This is an instructional routine to develop and support effective, student-driven, academic discourse, created by Margaret Smith of the Institute of Learning and used in the Open Up Resources 6-8 Math Curriculum. It is appropriate for all math classrooms and could be adapted to other content areas. Using the 5 Practices, teachers strategically organize discourse for a math lesson. When determining an appropriate activity to use the 5 Practices, consider how active the student task or lesson is. Active learning is described as “involving students in doing things and thinking about what they are doing” (Bonwell and Eison 1991, p. 5). Does it provide students with more than one way to solve? Is it providing opportunities for students to problem solve, discuss, and explain their thinking?  In the Open-Up Math curriculum, several of the steps (anticipating, sequencing, and connecting) are addressed through the materials provided in the activity narrative, launch, and synthesis sections.

  1. Before the activity or lesson, complete the first step of the five practices: Anticipate.
    • Anticipate: It is important t do the Math as a “learner” to experience what students will experience when they are given the task. While doing the task, determine the approaches students may take and their misconceptions, I think it becomes unclear. If you are utilizing the Open Up Curriculum, use the teacher guide to review anticipated misconceptions. Next, consider the purpose of the task. Not all math tasks are intended to “do math”. They might be a way to surface misconceptions, elicit different strategies, introduce a new concept (Activity Before Concept), or to use and practice math vocabulary.  Within that concept, anticipate student response, making notes of possible student misconceptions, sticking points, possible strategies. Here's where you also make adjustments to scaffold and differentiate. This includes planning open-ended probing, guiding, and assessment questions. 
  2. While students are working on the lesson or activity, complete the Monitoring step.
    • Monitor: Listen and observe students as they work on the problem or activity. Make notes of student responses, questions, sticking points, etc. Here is where your Anticipate step really begins to pay dividends. Your primary role is as a close listener. You are gathering critical information on student understandings, so it is important to note the strategies, the sophistication of those strategies, the questions that are coming up, as well as the mathematical language students are using - all towards the goal of measuring to see if students are headed towards meeting the purpose of the task. While monitoring, because you anticipated student responses to the task, you are also prepared to ask probing, guiding, and assessing questions when/if needed. You can fold in an instructional routine here to support discussion, such as Take Turns or sentence stems.
  3. When students have completed their work, bring them back together for a class discussion or share out using the Selecting and Sequencing steps. You can fold in an instructional routine here to support discussion, such as sentence stems.
    • Select: Identify from the notes during the monitoring step what needs to be highlighted for the whole class. Correct steps and responses as well as common misconceptions, questions, or various approaches should be highlighted. Make sure to select responses that will ultimately help all students master the content and advance the mathematical idea or topic.
    • Sequence: Decide what order the students will share their work from the selection step. This is based on the teacher's preference. Some teachers like to highlight common misconceptions first, while others like to highlight correct approaches or common steps students used.
  4. Once students have shared their work and thinking, use the last step, Connect.
    • Connect: Help students make connections between the work that was shared by themselves and peers.
    • This is the synthesis step where you have orchestrated all of this planning into arriving at the intended learning. You do not have to be the person who "teaches" the synthesis, you might have students doing that. But you are there to make sure the teaching point of this activity is reached. Students could compare and contrast what they notice. They could give each other feedback, and share ideas using an instructional routine. To push student thinking, continue to use the guiding, assessment, probing, and stretching questions that you planned.

Special Education Modification

Nedra Massenburg
Special Education Specialist

Using the Five Practices to effectively create and sustain a productive mathematical discussion during a differentiated lesson is a foundational tool teachers can use to better support all students  with disabilities.    In order to use the Five Practices effectively to support students with disabilities teachers should consider the following modifications: 

Modifications:

  1. Before deciding on a differentiated lesson plan to use the Five Practices in, teachers should consult with special education department administrators or special education that can give extra guidance on both the accommodations and modifications that should be considered on assessments and the best types of lesson plans to use given the disability types in a classroom.  See the "Differentiating Instruction for Success in Special Education" and “Differentiated Instruction for Students with Learning Disabilities” in the resource section below for more information.

  2. If multiple teachers are present in a classroom, careful thought should be put into co-teaching models and how they integrate into a differentiated lesson plan using the Five Practices.    See the "How to Choose a Co-Teaching Model" and “Differentiation Within the Inclusion Classroom Model” in the resource section below for more information.

EL Modification

Shannon Coyle
English Learner Specialist

This strategy provides teachers with strong supports to use while engaging English learners in applying mathematical language and skills. 

English learners may be required to use all four domains of language, reading, writing, speaking and listening while engaging in learning activities related to to the 5 practices. In order to support English learners consider the following modifications:

Modifications: 

  1. Write language objectives. Consider language objectives alongside purpose during the anticipate practice. Like content objectives, language objectives frame for learners where they are going in a lesson. Language objectives describe for learners how they will express their learning and establish the importance of using the target language in their academic discussions. Post language objectives, target language and vocabulary during lessons. See the “Linguistic Scaffolds for Writing Effective Language Objectives” and “Academic Discussion Objectives, Templates and Scaffolds” resources in the resource section below for more information. 
  2. Differentiate lesson materials and ways of expressing learning. English learners at all levels of proficiency require scaffolds to support their acquisition of English language concurrent with content learning. Alongside considering misconceptions, consider supports and/or alternative means of express learning English learners may require during the lesson. Consult data about learners’ language level when determining appropriate supports and learning products. See the “Descriptions of What English Learners “Can Do” at Various Language Levels” resource in the resource section below for more information. 

Questions to Consider

  1. Which problems will most likely be the most useful in addressing the mathematics?

  2. What do you want to highlight during the select and sequencing steps?

  3. How will students share their work with the class?