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Teachers need to know…

Have an understanding of the content being taught

Know the Big Ideas and have a goal for this particular lesson. Use backwards design to plan with an end goal in mind.

Know their students and what accommodations/modifications they may need to put in place before teaching the lesson.

Have an idea of how they are going to approach the concept.

Explore a variety of ways of approaching the problem - be  open to new ideas and strategies.

what resources and supports are available to them within the school/board both for themselves and for student use.

Teachers need to understand…

That students are going to use a variety of strategies to solve the problem. They will attempt the problem at a point of entry that feels comfortable for them and their level of understanding.

That students will have misconceptions, be prepared to address them and or open to addressing them with your support network (colleagues, math coach, etc.)

Students will solve the problem in alternate ways - allow them to share their thinking with the class.

Understand that  there are a variety of learners within the classroom not all students will connect or understand with the problem in the same way.

Students need time to share their thinking with each-other to expand their own knowledge and apply their mathematical skills

Teachers need to be able to …

Understand the content and be able to complete the task themselves

Identify the learning goal and help students understand the importance & learning occurring during the task

Have a solid understanding of their students current level of knowledge and understanding before introducing the task and/or expanding the task.

Make the appropriate accommodations and modifications to meet the needs of their students

Engage in reflective practice to evaluate what went well, what did not go so well, what needs to be reviewed and how to move forward.

Collaborate with colleagues or seek advice from other board members such as a curriculum lead or math coach.

teachers need to know how to support all learners using manipulatives (ELL, LD, low achievers, etc.)

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Teachers need to know: The content being taught. They need to have a deep understanding of what is being taught. Need to promote learning even if it is not traditional. They need to be able to continue a student's solving problem process even if the teacher thinks they are in the wrong direction. They must continue the learning without stopping the growth. They must obviously understand the curriculum so they are able to promote multi strand learning when it arises.

Teachers need to understand: Kind of what I mentioned in the above post but they need to understand that in a class there could be 30 different ways the students get to an answer. Teachers also need to understand that they have to prepare all possible answers they can come up with in order to best support students.

Teachers need to be able to: Anticipate, anticipate. It is preached in all the articles we read. Be ready for anything and all. Ask questions when they need help. We learn from experience so sometimes we need to reach out to those who have done this before. Teachers need to be able to handle failure in order to succeed. We have to learn from ourselves.

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Teachers need to know...

what the learning is

the big ideas

how they want to get there

the curriculum

available resources and supports

Teachers need to understand...

various strategies students will use; what are they using effectively? What do they need further instruction on?

needs and strengths of their learners; academically, emotionally, socially

family backgrounds; different learning experiences, different support systems

the curriculum (where students are coming from, what they need to know now and what they need to know moving forward; start bridging connections in content)

Teachers need to be able...

to anticipate misconceptions in learning and plan to navigate  around them

support students moving forward; a good understanding of the curriculum

to be flexible and adaptable; lessons don't always go as planned; learn, reflect and move forward

ask for help, seek support, engage in conversations with colleagues

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Teachers need to know…

The ‘big ideas’ and how to guide student thinking and choice of strategy to more effective strategies that highlight the ‘big idea’.

The overall expectations of previous grades and future grades. Where have they come from and where are they going.

How to take student thinking and show the students how it connects to other more effective mathematical operations OR introduce math vocabulary that describes what they did.

A variety of ways (strategies) that can be utilized to solve the problem (not just one!)

available resources and supports

Teachers need to understand…

That student thinking is a jump off point to more explicit teaching of strategies.

The repertoire of possible strategies students may know or use.

Teachers need to understand the value of learning from student work.

Students need time to share their thinking with each-other to expand their own knowledge and apply their mathematical skills

Teachers need to be able to …

To know where the students are currently at before moving forward.

Help guide their students to understand and use more effective strategies or more appropriate representations.

Collaborate with other colleagues in professional learning and discussion.

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Teachers need to know…

1.      The actual content itself

2.      Effective problem solving strategies

3.      How to facilitate number talks

4.      The variety of approaches to solving the task

5.      The way in which the content ties to content from previous grades and how it leads into future content in higher grades

6.      The learning profile of their students

7.      How to represent the problem in a variety of ways

Teachers need to understand...

1.      There are many different ways that students will approach and work to solve the problem

2.      Some strategies will be more efficient

3.      Students need time to share their thinking with each-other to expand their own knowledge and apply their mathematical skills

4.      That there are many ways to support student entry into problem solving

5.      These tasks can’t be rushed and important information can be gained from them

Teachers need to be able to ...

1.      Plan for creating these type of tasks

2.      Anticipate students responses and plan to respond

3.      Represent student thinking using a variety of modalities

4.      Facilitate number talks and help students work through communicating their thinking

5.      Articulate why they are doing the task and how it connects to the Big Ideas in mathematics

6.      Support students who are struggling and provide enrichment opportunities for students who move quickly through the task

7.      Take anecdotal notes for evidence of student learning and identify next steps

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Teachers need to know…
Mathematic curriculum 
number flexibility
Different strategies 
Misconcpetions
 
Teachers need to understand…
Mathematics holistically
Current pedagogy 
Teachers need to be able to …
Network
Learning through their teaching
Be open to new ideas and concepts 
Listen for the mathematics when their students are speaking 

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Teachers need to know that the process is more important than the final answer.
Teachers need to be able to ensure all students can access the problem.
Teachers need to know students will work at different paces.
Teachers need to understand what concepts are being highlighted.
Teachers need to be able to do the task themselves to anticipate possible strategies.
Teachers need to know what questions they ask to nudge the students’ thinking.
Teachers need to be able to anticipate possible roadblocks for solving the problem.

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Teachers need to know they’re own strengths and needs in mathematical concepts and continue learning about them in a multi-entry point way.
Teachers need to know that there are many ways to solve a problem and anticipate student responses so that everyone learns from each other.
Teachers need to understand the value of learning from student work.  Teachers need to listen to the different ways students solve problems so that they can engage and drive their own thinking of the mathematical concepts.

-Teachers need to know the problem solving model in order to support students and develop their mathematical thinking in each area.

Teachers need to understand the value of co-teaching and setting up a ‘buddy’ math system with colleagues in order to expand their math content knowledge.
Teachers need to be able to recognize that they were trained in a methodical / procedural but they do not have to approach or design their math program  in the same way.  So that they can ask open / rich questions and students can explore a variety of ways to answer the question based on their understanding.
Teachers need to be able to look to their Admin and Leader Coaches as examples of Professional Learning Collaborative Inquiry and be inspired by it.

I LOVE your point about teachers doing the math work themselves and anticipate their students' responses. This is something I did in my Grade 3 class because I had to defamiliarize myself with some of the concepts. It's something that I need to incorporate more in my Kinder Classroom too! -

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In order to facilitate learning through a low-floor, high ceiling math task:

-teachers need to know their own strengths and needs relating to math concepts

-teachers need to understand the problem-solving model

-teachers need to know the curriculum expectations that students have done/need to learn/will learn next year

-teachers need to know about learning goals and success criteria, and how each task builds on these

-teachers need to know what math tools are available (in their building, or that can be borrowed from the school board)

-teachers need to know how to use math tools and models effectively

-teachers need to understand the progression of math strategies

-teachers need to understand students strengths/needs

-teachers need to understand the CRA model and how to apply it

-teachers need to be able to select the right math tools for each concept

-teachers need to know how to support all learners using manipulatives (ELL, LD, low achievers, etc.)

-teachers need to be able to collaborate with others in a professional way in order to continuously improve their own math understanding and math programming

-Tiffany