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Teacher needs to ensure up to date on current trends in education, stay on top of expert research, network with other teachers, anticipate student misconceptions and approach to problem solving. As well, teachers should implement higher order thinking skills through implementing Blooms Taxonomy for example, to enrich student vocabulary and math minds.

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-       network with other teachers to identify common misconceptions made by students.

-       look at the strategies used by their students. Are there strategies that students tend to rely on most?

-       know and communicate the big idea of the task.

-       ensure that the students have the appropriate manipulatives available to solve the task.

-       challenge student thinking (e.g., by using Bloom’s Taxonomy high level thinking verbs)

-       consolidate the learning and restate the big idea(s).

Keshia

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She or he would have to know how to implement problem solving as collaborative amongst peers focusing on big ideas, open task oriented enabling multiple entry points for students of all learning abilities. As well, the teacher in facilitating this form of problem in problem solving would need to ensure he or she has figured out various strategies  and representations of the problem, anticipates misconceptions and responses that may arise, and determines deep questioning in order to enable a high level of reasoning when students work on solving the actual problem. As well, the planning done before hand should allow for rich thinking opportunities for students throughout the minds on, task and consolidation of the problem when being implemented, extending learning where and when necessary. Further, he or she would need to ensure proper manipulatives are out and visible for students to easily access to create representations, along with chart paper, markers, wipe boards and other materials necessary such as construction paper and space for students who wish to "act out " the problem as a strategy.
-Lisa

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-making predictions about strategies chosen by Particular students (Carla)
-provide multiple entry points for students to demonstrate their thinking/problem solving skills (Jen)
-sequence thinking and connect ideas (Katie)
Thanks!
Allana

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-Deep understanding of the Big Idea of proportional reasoning.

-To know, to keep in mind and to be able to use and refer to strategies that work with proportional reasoning.

-To be able to anticipate a variety of possible misconceptions by students and predict which strategies and representations might be used with these misconceptions. Also, understand why students would have a misconception and understand what it tells about the student's understanding of mathematics in a more general sens.

-Being able to associate a variety of representations to specific strategies and be able to go from one to the other.

-Capacity to capitalize on low floor and high sealing of that task by pre-establishing ways to twist the task in order to keep students engaged in their flow by ensuring the task stays just as challenging for each student so each of them struggle with it at the right level. Adjust relationship between challenges and tools/knowlages/skills.

RevisionS:
-Capacity to read and understand a landscape of learning.  (Kelly)
- Capacity to note analysis throughout the process in order to help plan a better "next lesson/task" that will take student from where they truly are and bring them to the very next step. (Carla

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•Students- in order to anticipate how to support them effectively •Big Ideas and Curriculum Expectations- with an understanding of learning on a continuum that is developed over time (ex. moving from additive to multiplicative thinking)•Teaching Network- who to talk to if in need of “math knowledge for teaching,” by co-planning/teaching /assessing or simply being directed towards critical resources•Task- including knowing the solution and multiple ways to get the answer in order to anticipate strategies and key points to facilitate for consolidation of learning big ideas•Misconceptions- with an understanding of how to move thinking forward using effective questioning, and discussion at critical checkpoints•Next Steps- differentiated to ensure that students get what they need for the next lessons

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•Students- in order to anticipate how to support them effectively •Big Ideas and Curriculum Expectations- with an understanding of learning on a continuum that is developed over time (ex. moving from additive to multiplicative thinking)•Teaching Network- who to talk to if in need of “math knowledge for teaching,” by co-planning/teaching /assessing or simply being directed towards critical resources•Task- including knowing the solution and multiple ways to get the answer in order to anticipate strategies and key points to facilitate for consolidation of learning big ideas•Misconceptions- with an understanding of how to move thinking forward using effective questioning, and discussion at critical checkpoints•Next Steps- differentiated to ensure that students get what they need for the next lessons

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By Meg Middleton

REVISIONS:
*Consider learning strengths and needs of all students
*Plan how to support students using manipulatives
*Include reflection and feedback time for students (David)
*Plan tasks that integrate subjects, as well as meaningful and engaging topics that connect to students lives (David and Megan)

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Recognize and be able to solve the problem using various strategies themselves, and understand the concepts behind these strategies and how they make sense.

Predict: Which students would prefer certain strategies

Predict: Misconceptions and errors students may have.

Identify: Which strategies students use initially and why? (Are they missing a certain level of understanding or a concept? Did this differ from the prediction? )

Address: Any and all misconceptions or errors that would allow for a valuable learning experience. Less focus on those that are not valuable to the concept being taught at the time, or are so complex would cause damage to a Growth Mindset

Identify: Which strategies students gravitate to after some discussion.

Plan: Prepare the next lesson based on observations from current lesson.

For instance: Do students need to explore a newer strategy further?

Do students need to clarify a misconception further?
Do students need to discover or explore a concept or big idea further. etc.

- Carla Warner

Revision:
- Provide students with reflections. (David)
- Cross Curricular (David and Megan)
- Authentic and relevant to the student (Jen)
- Make connections to previously taught concepts (Katie)
- Address the gaps (Kelly)

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The teacher needs to understand that each student needs to have an entry point into the question. Along with this the teacher needs to look at the Big Ideas with their topic in mind as well as the students prior knowledge in order to gauge the students outcome. When it comes to the students, as seen in the Caterpillar and Leaves video, they may answer the question in a variety of ways and the teacher needs to have the ability to question the students and make them feel comfortable in speaking about their work and their reasoning. Additionally, I believe that the teacher needs to show their students the relevance in their learning in making the task authentic using real life scenarios so that they see the importance/relevance. 

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The teacher needs to understand that each student needs to have an entry point into the question. Along with this the teacher needs to look at the Big Ideas with their topic in mind as well as the students prior knowledge in order to gauge the students outcome. When it comes to the students, as seen in the Caterpillar and Leaves video, they may answer the question in a variety of ways and the teacher needs to have the ability to question the students and make them feel comfortable in speaking about their work and their reasoning. Additionally, I believe that the teacher needs to show their students the relevance in their learning in making the task authentic using real life scenarios so that they see the importance/relevance. 

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Revision: Thanks to Kelly, The Teacher should look at various continuums/scales (such as the Fosnot) to determine where students are and their next steps to push their learning.)
Jen Ferguson

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When selecting rich, low floor, high ceiling tasks teachers need to look at big ideas. For example, when facilitating a task such as the caterpillar task, teachers need to anticipate responses, monitor student responses, select appropriate strategies, sequence thinking and connect ideas.
Katie Chiappetta

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By: Shayle Graham          The teacher will need to:

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By: Shayle Graham          The teacher will need to:

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-have awareness of the “big” idea and fundamental concepts associated with the low floor, high ceiling task

-have awareness of many strategies students will use to solve the problem

-anticipate students' misconceptions of the math

-provide guided opportunities to work on basic skills associated with the math

-consolidate learning and prepare for next steps to extend student knowledge

-incorporate games and tasks that re-enforce the "big ideas" in the problem

Revisions: Use scales to determine where students are. (Thank you Kelly)

Considering multiple rich tasks and cross-curricular teaching  (Thanks Dave)

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Revision is in brackets.(The teacher chooses a lesson with the big ideas of the mathematics topic in mind.) Teachers need to be aware of the possible strategies and possible pitfalls. Teachers need to be aware of Fosnot’s Landscape of Learning to determine where students are with their learning and where they need to go. The teacher needs to choose the next lesson to best direct the students’ learning. (The teacher needs to choose or create tasks with open entry points for students. Teachers need to be able to follow closely the student’s working enable to choose students to choose at congress.)

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Revision is in brackets.(The teacher chooses a lesson with the big ideas of the mathematics topic in mind.) Teachers need to be aware of the possible strategies and possible pitfalls. Teachers need to be aware of Fosnot’s Landscape of Learning to determine where students are with their learning and where they need to go. The teacher needs to choose the next lesson to best direct the students’ learning. (The teacher needs to choose or create tasks with open entry points for students. Teachers need to be able to follow closely the student’s working enable to choose students to choose at congress.)

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Kelly

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For a teacher to be able to facilitate learning through solving this type of task they would need to ensure the task is accessible to all learners and make it a real-life problem where students can make connections. Having multiple approaches and allowing for multiple representations encourages curiosity, engagement and creativity where students can discuss collaboratively. Finally, the teacher should choose a problem that would allow opportunities for extension of learning.Heidi 

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For a teacher to be able to facilitate learning through solving this type of task they would need to ensure the task is accessible to all learners and make it a real-life problem where students can make connections. Having multiple approaches and allowing for multiple representations encourages curiosity, engagement and creativity where students can discuss collaboratively. Finally, the teacher should choose a problem that would allow opportunities for extension of learning.Heidi 

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I think you are saying that a teacher needs to know how to create or select an open task (low entry, high ceiling task) with a real life context.
Heather

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Thanks!!
Heather

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The teacher needs to understand the ways that their students interpret and understand the math content.  Depending on the grade levels that the students are at, there are strategies that students may not be familiar with in order to grasp the math content being provided.  For example, students may be negatively affected by trying to perform repeated addition with multiplication of double digit numbers instead of utilizing a more appropriate strategy that lends well to the content focus.  By reviewing the big ideas and potential strategies of the math, this may expand the student's interpretation of how to solve the problem effectively through differing and appropriate strategies.  A list may include: (1) Anticipating strategies (2) Big Idea Concepts (3) Making connections (4) Cross-curricular (5) Rich Tasks with multiple reasoning (6) Sharing and reflection           Dave Cho-Chu

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The teacher needs to understand the ways that their students interpret and understand the math content.  Depending on the grade levels that the students are at, there are strategies that students may not be familiar with in order to grasp the math content being provided.  For example, students may be negatively affected by trying to perform repeated addition with multiplication of double digit numbers instead of utilizing a more appropriate strategy that lends well to the content focus.  By reviewing the big ideas and potential strategies of the math, this may expand the student's interpretation of how to solve the problem effectively through differing and appropriate strategies.  A list may include: (1) Anticipating strategies (2) Big Idea Concepts (3) Making connections (4) Cross-curricular (5) Rich Tasks with multiple reasoning (6) Sharing and reflection           Dave Cho-Chu

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The teacher : chooses a lesson that supports one of the big ideas (from the curriculum)- anticipates the strategies that students may use to solve the problem-understands how the different strategies to solve the problem work- anticipates possible questions students may have regarding the lesson- links lessons together so that students can draw on their prior knowledge to make new connections and further their understanding-needs to be open to trying new ideas

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The teacher : chooses a lesson that supports one of the big ideas (from the curriculum)- anticipates the strategies that students may use to solve the problem-understands how the different strategies to solve the problem work- anticipates possible questions students may have regarding the lesson- links lessons together so that students can draw on their prior knowledge to make new connections and further their understanding-needs to be open to trying new ideas

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Revision (thanks to Dave Cho-Chu)
I am adding that the teacher needs to think about incorporating cross-curricular areas (real life situations) into the rich tasks and to take the necessary time for sharing and reflection with students and as a teacher (about the lesson, task, etc)
Megan Major

So the teacher needs to be able to facilitate reflective talk and  needs to know how math connects with other subject areas.

Heather