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Anticipating helps to inform how we launch the task - specifically, how we ensure kids have an entry point and how we maximize our chances of seeing the representations/approaches that will move the class forward. Anticipating also helps to inform how we intervene or give feedback during work time.

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Carefully selecting and sequencing work is necessary (but not sufficient) for kids to see and hear the things that will move them forward in their understanding. Without careful selection, kids may or may not see a strategy or approach that helps them. Without careful sequencing, kids who struggled with the task are unlikely to make sense of the approaches being shared.

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Anticipating student responses may increase the amount of time spent lesson planning but the payoff is that teachers will be better prepared to support student problem solving, address misconceptions, and prepare questioning strategies that can help students make connections or self-correct.
- Mirella Sales

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Carefully selecting and sequencing students' responses is a precursor to facilitating a quality discussion. Selecting and sequencing allow students to see a variety of problem-solving methods and make connections from concrete to abstract and strategic. Providing space for students to process their thinking out loud creates cognitive connections and those who are listening have the opportunity to learn from their classmates.
- Mirella Sales

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Anticipating student responses is crucial in the planning process, as the student work sets the stage for the entire discussion and key understandings. It will help teachers both prepare for discourse and help them more deeply understand the standard. Anticipating will help teachers feel confident and more prepared in the work they will see, but more importantly it will help them be able to better chart their plan for discourse so students leave with deep conceptual understanding. It is definitely worth the time investment.

-Christina

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Students will only be able to have a rich discussion, if the student work provides a strong foundation to start from. Carefully selecting and sequencing allows the teacher to control the flow of the discussion and ensure that scholars are moving towards the deep understandings of the unit. This practice helps you know what the students will be sharing to start, so then you can assess and advance the conversation. Also, scholars being able to see what an idea looks like on paper, will help engage all learners.

-Christina

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Anticipating student strategies has a very high payoff even though it is an investment in time. The first payoff is that a teacher has insight into what students may use as solutions during the lesson. This offers another payoff which is that when a teacher can anticipate student responses they can plan scaffolds or guiding questions to help students who need help accessing the problem.
-Griselda

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Selecting student strategies can make or break the course of a discussion. Carefully selecting AND sequencing strategies is important because it determines where the flow of a discussion will go. Starting with a concrete/visual model will help students access the problem in a more friendly manner and moving on to concrete models will help students see the complexity behind a problem.
-Griselda

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Anticipating is a key component of planning. It's not just about anticipating correct and incorrect answers, it's about anticipating the thought process that students will have when solving this problem. By taking the time to do this, teachers are able to think from the perspective of a student, and only then can they think about how to use effective questioning to lead strong discourse.
-Melanie

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Sequencing work strategically really sets the foundation for strong discussion. The entire discussion should be grounded in student thinking and student work. It's important to have the end learning goals in mind, and then using the work that you see students producing to lay the roadmap for the discourse. It wouldn't be high impact to start with a really interesting, abstract strategy that only one student used. But rather, you want to think about how to provide an entry point for the highest amount of students, and then guide them to deeper understanding.
-Melanie

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Engaging in anticipatory planning helps teachers to get a gauge on what they will likely see during this lesson, furthermore preparing them to strategically plan around the predicted trends and generate goals and takeaways that will move the majority of their class. Once the takeaway is named, teachers can begin to think of the strategies that they'll want to highlight to guide students towards understanding of that particular goal as well as think through how to address misconceptions they're expecting to witness as well. -Corey

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Selecting & Sequencing allows teachers to give students the opportunity to showcase work that compliments the goals for that particular lesson. Therefore the discussion will naturally be more targeted to the goal or skills the teacher was looking to implant, and there is less likelihood that the conversation amongst students will get off track (or honed in on details unrelated to the goal). Like the article mentioned student work selection and sequencing depends on what the teacher is looking to drive towards but the goal is always to provide work that students can access or connect with while also highlighting work that provokes students and inspires conversation or attempts at approaching problems in a different way. The article mentioned having conversation with students beforehand which is imperative to making sure that the conversation is student driven but aligns with the teacher's purpose for discourse. -Corey

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Anticipating the many ways a student might approach/solve a problem creates a clear pathway for the teacher. Anticipating gives the opportunity for the teacher to plan targeted questions to probe further at a student's understanding. This allows the teachers to see more clearly where the student is in their conceptual understanding and plan for next steps.  Anticipation of the solution paths students may take can provide a much clearer insight on understanding rather than a correct or incorrect answer.

-Mary Elizabeth

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In order to build strong, meaningful discourse, the selection and sequence of student work is key. Beginning with the most abstract and sophisticated strategy can be tempting. As teachers, we can get excited and proud of a student's impressive work. However, this can deflate some students' confidence and shut down the conversation. Presenting incorrect work can lead to confusion and misunderstanding. Selecting and sequencing work around the goal of day allows teachers to create discourse to further the students' understanding. Students seeing clear connections between strategies, beginning with a concrete example, allows them to create a bridge for themselves.

-Mary Elizabeth

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Anticipating is a key step in the intellectual preparation for math discourse.  By completing problems as many ways as they can think of, the teacher does the intellectual lift of the students and is cognizant of the strategies, thinking, and barriers within a task.  Anticipating is a key planning step because it sets teachers up to effectively monitor and look for trends in student work that address the skill and conceptual focus of the task.
-John

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By intentionally selecting and sequencing student work teachers are equipped to meet the goal of discourse.  A thoughtful sequence could serve numerous discourse goals: strengthen student work by addressing a trending misconception, deepen conceptual understanding by establishing connections between student work, or developing more efficient mathematical procedures.
-John

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Anticipating is a critical component of facilitating meaningful mathematical discourse with students.  Anticipating student strategies allows the teacher to understand multiple strategies that students might use, uncover potential misconceptions, and plan thoughtful questions to making students' thinking visible and/or help unscramble confusion.  By having these items planned in advance, the teacher is better able to analyze student work in the moment and truly listen to students, because the teacher knows what they are looking for and they know how they will respond.  For any unexpected strategies that do come up, the teacher can respond flexibly, using what they have already planned and anticipated.

--Carrie

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Carefully selecting and sequencing students' responses improves the quality of discussion and gives the teacher more control over the direction and outcome of the discussion.  By selecting which strategies will be shared, the teacher can ensure that specific mathematical ideas linked to the goal of the lesson will most likely be brought up in students' discussion of the strategies.  By sequencing the strategies thoughtfully, key mathematical ideas are highlighted, and it is more likely that students will notice and make explicit the mathematical goal of the lesson.  Carefully selecting and sequencing students' responses in a way that aligns with the goals of the lessons sets the stage for students to develop powerful mathematical ideas over the course of the discussion and maximizes the chances of reaching that goal within the lesson in a student-centered way.

--Carrie

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The payoff for the investment of time spent on anticipating lesson activities will show up as the following: confident and knowledgable teachers as facilitators of learning, greater student access and achievement on problem solving tasks, purposeful prompting and intentional questioning techniques, rich discourse structured to help students make connections and correct misconceptions.
-Patricia T.

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Anticipating is critical to effective discourse because it enables us to be better prepare for discussions and guide them in the most impactful way. As all teachers know, we cannot fully predict what children will do or say, but we can make educated guesses about likely strategies and methods of solving problems. When we take the time to do this in advance and think through all the ways a child may approach a math problem, we are better prepared to highlight a problem solving path that pushes students to higher level thinking. By taking the time to anticipate, we know exactly what to look for during class and can be more effective in guiding student understanding.
-Kendrick

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Carefully selecting and sequencing responses is the best way to ensure all students have access to the problem and to push student thinking. When we carefully craft discussions based on a leveled approach to showing student work, we are able to guide students to see more sophisticated or efficient strategies. By planning for this and anticipating the work students might do, we can also better enable students to see connections across strategies. When students are able to see these connections, they are then able to connect their own work to more efficient strategies and increase their problem solving abilities.

-Kendrick

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When selecting and sequencing the display of student work, it's important to know that, you, as the facilitator of learning, is directing and driving your whole classes discourse based on the way you make math work visibly accessible to all learners. This practice can ultimately help students make deeper connections, understand various methods, representations and pathways, from the concrete to abstract solutions in math. This gives the teacher even more control when needing to make "in the moment" decisions about how to highlight student thinking. You are able to coach their thinking and provide scaffolds in the most effective way and with minimal misconceptions/misunderstandings.
-Patricia

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Carefully selecting and sequencing students' responses allows us to differentiate the learning that happens during the discussion - providing different examples that address different needs we saw in our students as they worked. We can often increase the sophistication of students' understanding, including moving from concrete to pictorial to abstract (or within those that are relevant to this specific class's present level of understanding). - Nina

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Carefully selecting and sequencing students' responses allows us to differentiate the learning that happens during the discussion - providing different examples that address different needs we saw in our students as they worked. We can often increase the sophistication of students' understanding, including moving from concrete to pictorial to abstract (or within those that are relevant to this specific class's present level of understanding). - Nina

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In some ways, I expect the pay off from the investment of anticipating student responses to be similar to all high-quality planning and preparation: an ability to be light on one's feet, responding to expected and unexpected moments in thoughtful, meaningful, and timely ways. To this last point, being able to provide immediate and purposeful feedback to students while they're engaged in the work may strengthen their understanding and model some of the mindsets we're hoping to cultivate, which is especially important in math classes that utilize the 5 practices, as this is a pretty large departure from how math has "traditionally" been taught. -Nina

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In some ways, I expect the pay off from the investment of anticipating student responses to be similar to all high-quality planning and preparation: an ability to be light on one's feet, responding to expected and unexpected moments in thoughtful, meaningful, and timely ways. To this last point, being able to provide immediate and purposeful feedback to students while they're engaged in the work may strengthen their understanding and model some of the mindsets we're hoping to cultivate, which is especially important in math classes that utilize the 5 practices, as this is a pretty large departure from how math has "traditionally" been taught. -Nina

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Anticipating take more time when prepping lessons and it’s totally worth it. It helps you think as the student and as you are preparing as a student you are also thinking as a student. Thinking as such helps you consider ways to make landing a key point more effective.

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Carefully selecting work helps improve the discussion assuming that you are using work that speaks to a trend in student understanding. Without it you could potentially be confusing students more or closing the loop for only a portion of students.

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Anticipating positions the teacher with substantially greater awareness of the conceptual understandings and possible misconceptions that students are likely to encounter in their work. Thus teachers are better positioned to monitor, ask assessing and advancing questions, sequence problems, facilitate dialogue, and make connections in the discussion between students. Doing this pre-work means that the teacher has already internalized the outcome -- and is able to look for and capitalize upon student thinking that will lead to the learning outcome for everyone.

-Jon

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The sequence in which student work is shared may open or close different ways of thinking about the solution. Starting with student work that approaches the problem in a  visual/concrete manner often creates greater points of entry for all students. These solution pathways can also often be powerful for illustrating why more abstract conceptual strategies work. Many conceptual strategies, while more obscure in their function, provide efficiency with with larger quantities or unknown values. By sequencing these strategies intentionally, the teacher can draw attention to connections as well as strengths of each strategy.

-Jon