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Two strategies can be connected to each other. The teacher needs to facilitate both proper sequencing and questioning that will allow for these connections to occur. If they are not connected then it can turn into a show-and-tell for student strategies and less of a learning opportunity. pg. 71

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"For example, if a misconception surfaces during work on a task, the teacher may want to begin the discussion by addressing this issue directly." p.45
"Another alternative is for the teacher to have students present strategies that move from concrete to abstract." p.46

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Connecting is the most challenging of all the five practices because is calls on the teacher to craft questions that will make the mathematics visible and understandable. The questions must go beyond merely clarifying and probing what individual students did and how. Focus on meaning and relationships and make links between mathematical ideas and representations. - p.70

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Pg 70-71

Connecting is the most challenging part of the 5 practices. Questions must go beyond merely clarifying and probing what individual students did. Questions must focus on mathematical meaning and make links between ideas and representations. The key to connecting is to make sure the mathematics to be learned is openly addressed.

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Through selecting, sequencing, and connecting teachers make key ideas public so all students have the opportunity to make sense of the learning goal for that lesson.

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This book complements the work I am learning and practicing in my Math Fellows, CGI, and other Math workshops this year. The Anticipation Set, Monitoring, Student work sample selection sequencing of presentations, and making connections is my mathematical dream lesson.

Backwards planning - how I was originally taught to plan a lesson - is coming back, and I'm on board. It's easy to get overwhelmed at the overabundance of text in Bridges; however, I am reminding myself to keep it simple - focus on the target, and think of how to best present concepts, practicing them, and implementing them effectively and efficiently. I talk with other teachers around the district, and they're all going by the book. This is a detriment, I think, to ALL students, and it doesn't allow for reteaching, for enrichment, or for differentiation.  Super excited to have Dr. Henry as our role model and guru to help guide even this most seasoned math teacher - reminding me to use my professional discretion to help lead my thinking.
Anticipating students’ solutions to a mathematics task

Monitoring students’ in-class, “real-time” work on the task

Selecting approaches and students to share them

Sequencing students’ presentations purposefully

Connecting students’ approaches and the underlying mathematics

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Pg. 63 Teachers must select which ideas and students to focus on to advance the mathematical understanding of the group. Pg. 65 If a misconception surfaces during work on a task, the teacher may want to begin the discussion by addressing this issue directly. Pg. 66 Present strategies that move from concrete to abstract. Pg. 81 He clearly identified his goals early in the planning process and never lost sight of them as he moved through the actual implementation of the lesson.

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p. 64 Selecting is critical because it gives the teacher control over what the whole class will discuss, ensuring that the math that is at the heart of the lesson actually gets on the table. We have come to think of the question, "who wants to present next?" as either the bravest or most naive invitation that can be issued in the classroom. By asking for volunteers to present, teachers relinquish control over the conversation and leave themselves--and their students--at the mercy of the students whom they have placed at center stage.

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p. 65 Although having the most commonly used strategy presented first is one approach to sequencing solutions, it may not always be the best way to proceed. For example, if a misconception surfaces during work on a task, the teacher may want to begin the discussion by addressing this issue directly.

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Pg. 71- It is important to note that in order to make connections, you must understand the mathematics well enough to know that two strategies can be connected to each other.
Pg. 81- ... it is through selecting, sequencing, and connecting that teachers guarantee the key ideas are made public so that all students have the opportunity to make sense of mathematics.

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Pg. 81 -It is through selecting, sequencing, and connecting that teachers guarantee that key ideas are made public so that ALL students have the opportunity to make sense of the mathematics. Although there are many ways to select, sequence, and connect responses, these decisions must be guided by what the teacher is trying to accomplish in the lesson.

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Connecting (p.70)
This is one of the most challenging parts of mathematical instruction because it requires a great deal -- of not only understanding the mathematical learning goal, but also the students' current mathematical understanding so that you can bridge the two.  "...questions must go beyond merely clarifying and probing what individual students did and  how.  Instead, they must focus on mathematical meaning and relationships and make links between mathematical ideas and representations."  Even with the best planning and anticipation for productive conversations in the classroom, it can be difficult to draw out what students actually understand and how to take them to a deeper level of understanding.

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This chapter was all about formulating clear, explicit learning goals and how they set the stage for everything else. The idea that all stakeholders ideas should be made public really resonates with me. I think that's why I love using technology in the classroom so much. Technology is one of the tools I can us to give students the opportunity to have their mistakes and questions and strategies made public for peer review. (All participants have the opportunity to "collect more pieces of information about the issue of the discussion and to understand the issue more deeply." p.81

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I viewed a comment made on page 81 as a salient point that underpinned the purpose of this chapter and, in many respects, the purpose of instruction. The key sentence(s) are: "Hence, the goals for the lesson serve as a beacon toward which all activity is directed...Formulating clear, explicit learning goals sets the stage for everything else."
The process of selecting, sequencing and connecting serves to guide student understanding toward the goal(s) of a lesson and they are more successful elements of a procedure if the students are apprised of the goal from the beginning. MH

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Galen
"The key is order the work in such a way as to make the mathematics accessible to all students and to build a mathematically coherent story line." pg64

This resonated with me because I felt that it validated my thinking and instructional strategies in my own classroom. A students are working independently, I look for "levels" of thinking. 

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Galen
"The key is order the work in such a way as to make the mathematics accessible to all students and to build a mathematically coherent story line." pg64

This resonated with me because I felt that it validated my thinking and instructional strategies in my own classroom. A students are working independently, I look for "levels" of thinking. 

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Holman Take Away
P. 81-"...it is through selecting, sequencing and connecting that teachers guarantee that key ideas are made public so that all students have the opportunity to make sense of mathematics."

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Holman Take Away
P. 81-"...it is through selecting, sequencing and connecting that teachers guarantee that key ideas are made public so that all students have the opportunity to make sense of mathematics."

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Matthews Take Away

P. 70 “Connecting may in fact be the most challenging of all of the five practices because it calls on the teacher to craft questions that will make the mathematics visible and understandable.”

This quote stood out to me because it highlights the enormous job we have as teachers to not only understand the content, but also be able to interpret students misconceptions, understandings and assumptions all in split second time frames and be able to ask questions that will help them create meaning and understanding. This task is overwhelming to me especially because math does not, and has not ever, come easy to me. I have never worked harder at being a student of math and a good math teacher than I have this year. In order for me to breath and not be hard on myself I have to get to a place where doing this is second nature.

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P. 70 - Moving between where a child is and where one ultimately wants him or her to end up mathematically "is continuous reconstruction"..."I must consider the mathematics in relation to the children and the children in relation to the mathematics," suggesting the teacher's needs to know both the mathematics to be learned and what students know about mathematics bridge the two worlds. To consider one without considering the other can result in questions that draw blank stares because they make no connection with students' current ways of thinking. To consider one without the other can also result in students' thinking remaining stagnant, instead of moving towards new mathematical understandings. For this reason, framing questions in the context of students' work is critical.