I noticed two strategies to take back to my classroom. First, I like how Kristin Gray asked, "Where did the 6 go in Alaira's work?" This modeled how a second adult in one the of co-teaching model might look. Second, I will try to get my group to do a front-to-back turn and talk versus a chat with an elbow partner just to mix up my math conversations a bit.

Hi Joseph - I suppose this is the drawback of only having a short video and a few PDFs as they can only capture so much because assumptions are often made. What I wish people were able to see and hear is the planning that took place in each of our individual journals, the articles, papers, and books (often CGI) we read during our short planning time around how students build mathematical understandings, discussion of what students are building on, the ideas they are building towards, and how the standard is elicited through the Standards of Math Practices. When you watch the video, what I tried to capture in the opening segment is what you are discussing - the goal in terms of how students may solve the problem. I also think Jenn did an amazing job facilitating the discussion to illuminate the Standards of Mathematical Practice in students' mathematical thinking. I love that this series has sparked so much thinking for you sine the intention was not to show a perfect model, but more to help us as a community to learn, grow and improve our practice. I would love to see templates you have created that do what you are describing because I think that would be helpful for others watching this video.

Thanks you for your quick response Kristin. Both the use of routines and learning cycles (which can be embedded in learning labs) came out of the research from the LTP project which led to TEDD.org at UW and Teaching Works at the University of Michigan amongst other new applications of the research. You and I and others are building on this powerful research meant to highlight Ambitious Math Teaching. This is a very exciting time for math teaching and learning! These math instructional routines as you know were chosen because they are containers of core practices, principles, and important knowledge for math teaching. These routines are responsive routines. Responsive to student thinking and broad participation specifically. Math learning goals (can be social as well) for a routine or activity is what drives everything from the facilitation of discourse, to the questions we pose, to the strategies selected for sharing, to how we as teachers engage students with each other's math ideas, and to the connections between strategies. The creation of a math learning goal comes not just from core math ideas (highlighted by parts of content standards and cluster headings) but in response to the current mathematical thinking of our students (regardless of whether students' strategies are correct, incorrect, or incomplete) and knowledge of children's math development with a focus on positioning all children as competent. Behind their thinking are important math ideas that we want to make public and linger on. Chapter 10 of the 2nd edition of Children's Mathematics: Cognitively Guided Instruction pages 159-160 talk more about this. In brief I think math learning goals are informed by important math ideas and understandings in the standards, our knowledge of the development of student mathematical thinking, and our knowledge and responsiveness to our students' current mathematical thinking and participation goals for all students, especially those who don't participate much. I'm wondering how the math goals for these routines might be crafted in your lesson plan template so that the focus is not just on performance (the standard or what student are to do) but what important mathematical understanding and the Common Core Math Practices they will have the opportunity to demonstrate during the routine through their strategies (thinking) and participation. These routines are designed to specifically elicit certain understandings and Common Core Math Practices and we, as a classroom community, have an opportunity to respond to and connect these math understandings which undergird the strategies used by students during these routines. Chapter 2 of the book Taking Action K-5: Implementing Math Teaching Practices pages 17-21 articulate and delve deeper into this idea around math learning goals.

Thank you so much Joseph for your comments and link to Tedd.org on both. They are definitely an inspiration for this work and linked in many of my blogs and resource page. Good question about the learning goal. The work in our PLCs focused around better understanding the Standards, so while the wording is from the standards on the planning sheet, we unpacked it in the PLCs to discuss the goal in the design of the problems and structure of the routine. If you would like to see how that looked, you can search for my video on Teaching Channel called Creating a Culture of Learning.

With this activity and other math instructional routines I've found that the planning templates that include anticipated strategies and the teacher board or poster are really helpful. Additional resources related to implementing Number Talks (Mental Math) are provided at TEDD.org at this link and they have a really great planning template: https://tedd.org/activities/mental-math/. One concern I have with the lesson plans for all of the math routines in this video series is that what is listed as the mathematical goal is a verbatim Common Core Math Standard. Principles to Actions and the new grade span Taking Action books define a math learning goal as a description of what students should understand about a mathematics topic as an outcome of instruction. Math learning goals connect to big math ideas and are not merely performance goals which the Common Core Math Standards are. This is also different from a learning target which is for students, but even a learning target would not be a Common Core Standard verbatim.