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Chapter 1 – Option 2:

01/04/2019 8:07 PM | Anonymous

React to the Avenues of Thinking framework presented on page 3 of “lead actors” and “supporting actors” among the Mathematical Practices (MPs).  How does this structure help you make sense of these standards?


The framework is also found here.

Comments

  • 01/05/2019 6:13 PM | Nicole Gilson
    I thought that the authors presented a strong argument regarding the "lead actors" and "supporting actors" and this was evident in the figure/diagram they used to visually represent this idea. The statement "this math practice emphasizes sense making and perseverance and is one of our lead actors because of the necessity of this overarching goal to students’ success in mathematics. All the other math practices sit in service of this goal, because if a student gives up, there is no opportunity for any other mathematical thinking to occur." Perseverance is definitely the key to mathematical success and confidence.
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  • 01/08/2019 1:03 PM | Terry Onofreo
    This chapter helped me organize my own thinking about the math practices. I don’t think I had previously given enough time to consider how the practices related to each other and, as a result, had a hard time keeping them straight in my mind. Considering MP1 as the overarching goal in which “all other math practices sit in service” and MP 2, 7, and 8 as the avenues of thinking one might take in service of a problem helped me to see the remaining practices as the ways one might tackle the journey down each of those avenues.
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    • 01/20/2019 2:53 PM | Sarah Giaquinta
      I also don't think I really thought about how each of the MP's relate to each other. I had in my head that they were all distinct. While creating problems and lessons, I mentally checked which ones were "covered" in what I was doing, but never really thought about nesting them. During a PD that our math department did about Routines for Reasoning, we were introduced to this idea, and I love it! It makes the math practices less overwhelming to tackle in my opinion.
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  • 01/08/2019 4:42 PM | Barbara Rock
    The Avenues of Thinking framework was new to me. I've done professional development around the MPs, but had always treated them as equal. I appreciate how Grace and Amy have organized them. It helps to think about quantities, structure, and repetition being the routes to making sense and persevering in solving problems. I like thinking about the big 3 (MP 2, 7, 8) being supported by the rest and that all are in support of MP 1.
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  • 01/08/2019 10:09 PM | Susan Lukianov
    The Avenues of Thinking framework shine a new light on the SMPs for me. The terms "lead actors" and "supporting actors" was freeing. Initially, when trying to emphasize the importance of the practices, it became too easy to give them equal importance or preferential importance depending on the topic (content standards) of the unit. The figure (p.3) provides a powerful visual organizer that clearly supports perseverance (and engagement) as an overarching goal. I was relieved to read that MPs 7 and 8 are considered as part of the troupe of lead actors. These two practice standards often get pushed aside or "mislabeled" when educators try to make sense of them. This framework supports the idea that perseverance is a must and that understanding reasoning, structure, and regularity are entry points. "These practices focus on ways for students to successfully enter and remain engaged in mathematical reasoning..." (p.4)
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    • 01/10/2019 10:23 PM | Anonymous
      Susan, yes, MP7 Structure and MP8 Regularity in Repeated Reasoning are somewhat intimidating at first glance, and many math teachers avoided addressing them in favor of some that were "easier" to grasp, like MP1 Problem-solving/Perseverance, and the "supporting actors" MP6 Precision, MP3 Construct Arguments, and MP4 Using Tools Strategically.
      With the "lead actors" designation, MP7 and MP8 get credit for how powerful they can be in furthering mathematical thinking.
      Karen
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  • 01/10/2019 8:44 PM | Luke
    I think the presentation of the lead actors and supporting actors is well done. I read as if it was my first time learning about the mathematical practices and how they could be implemented. It makes sense the MP1 is first so kids have a clear understanding of the problem and what it is asking them to do. I have a new understanding "next step" for kids through the avenues of thinking, MP2, MP7, MP8, as they relate to how students access a problem/math. These practices allow for an initial understanding of the math as the students explore their own procedural thinking and develop a more critical stance. I am looking forward to reading more about these avenues and how to implement the process with my kids.
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  • 01/10/2019 10:16 PM | Anonymous
    I also have found the Avenues of Thinking framework helpful to understand the relationships among the MPs. In my workshops and presentations, I've used a graphic from Bill McCallum (one of the CCSS authors) which pairs up the MPs: https://goo.gl/Q16TKi ; however, I’m finding the Lead/Supporting Actors structure from R4R page 3 even more helpful!

    Another source of discussion about understanding the MPs is Robert Kaplinsky’s blog post series in which he presents “readable versions” of each of the paragraph descriptions of the mathematical practices. He aims to preserve the essence of each MP while trying to significantly simplify its presentation to be more accessible for educators, parents & students.
    https://robertkaplinsky.com/tag/make-ccss-math-practices-readable/
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    • 01/13/2019 2:38 PM | Dawn Campbell
      I have always used McCallum's graphic to illustrate the types of MPs. And I do think that it does a nice job highlighting the similar nature of some of the practices. The "Lead & Supporting Actor" model in RfR helps make sense of how we use the practices in relation to one another in an interconnected way. Like characters in a film, the relationships and connections among them help the audience make sense of the story.
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    • 01/14/2019 2:34 PM | David Wees
      I think Math Practice 8 is the least well understood practice and is often confused with Math Practice 7

      Math Practice *: "Look for and express regularity in repeated reasoning.

      Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x2 + x + 1), and (x - 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results."

      What's often missing in some simplifications of this practice is the focus on the repetition in the process rather than repetition in general. For example, someone proficient in math practice 8 might mess around with some calculations for a while when looking at an equation and ask themselves, "What process or calculations am I repeating? Can I generalize this process from these repeated steps?"

      I think seeing this distinction is pretty important in being able to support students with developing Math Practice 8.
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  • 01/11/2019 9:09 AM | Jill D'Amico
    The Avenues of Thinking framework was new learning for me. I have done professional learning with my teachers around the Math Practices but never came across this way of looking at them. I am excited to share this new way of thinking about them with my teachers. I think figure 1.1 is a great visual for teachers to have as a reference particularly with my Grades 3-5 teachers who have been doing work with problem solving this year. I think it will help them to think about quantities, structure, and repetition being the routes to making sense and persevering in solving problems.
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    • 01/20/2019 10:53 AM | David Shimchick
      Hi, Jill.
      I am interested to see how the authors structure the routines so that students learn the different reasoning avenues without getting so hung up on a process that they lose sight of the problem being solved. I am also curious to know how they will suggest students learn to determine when the avenue they are on is a dead end.
      David
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  • 01/11/2019 11:35 AM | Anonymous
    I really liked how this was organized. I never really thought of them supporting each other and that some were about our math thinking and some were about the avenues we take to solve. I think this graphic will really help people to understand how the SMPs work and can easily incorporated into everyday math classrooms.
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  • 01/11/2019 5:54 PM | Leah Frazee
    The Avenues of Thinking framework is helpful for me to think about how to look for evidence of the practices. When I view all 8 of them as unconnected, it is more difficult for me to find evidence of them in student work. I really appreciated the three main examples of MPs 2,7, and 8 and how each of the examples also had evidence of the supporting actors. I will start to look for examples of the MPs in student work and classroom discussions by first identifying 2, 7, and 8 and then looking for the supports.
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  • 01/18/2019 8:19 AM | Kristofer Carlson
    I find the clustering here really helpful in terms of thinking about the math practices in our curriculum - even just the visual of the overarching MP1 helps reframe the whole shebang in my mind and makes pieces click together more easily. Trying to process all of the SMPs simultaneously can easily feel overwhelming on both the individual and departmental level, and chunking them in this fashion makes it more likely to have productive discussions with fewer, but deeper entry points. There are only so many times we can unpack each of the SMPs in district wide department meetings and have discussions on them discretely (and discreetly if we're quiet about it, I suppose).

    I think this also makes it easier for us as a department to focus on hitting 2, 7, and 8 with support from other SMPs instead of arbitrarily adding the same standards to our curriculum documents to check off necessary boxes. It's much more likely that teachers work together productively if there are fewer chunks to tackle, and therefore less of what feels like added work to our plate.
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  • 01/20/2019 4:54 PM | Marianne Springer
    The structure makes sense to me, and I think it will also facilitate our efforts to better integrate the math practices into our curriculum in a coherent fashion. I had previously thought of Modeling with Mathematics as the overarching standard. My perspective is that all of the mathematics that we teach is done because mathematics is a tool for problem solving. Breaking down that process into the three lead actors seems like a good way of breaking down and talking about the process of developing problem solving skills.
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  • 02/18/2019 9:50 PM | Melissa Manning
    The Avenues of Thinking framework was an "A-ha!" moment for me. I have explored math practices and speak of them often in professional development. I feel like I am always stating how students need to make sense of problems and persevere in solving them. The figure 1.1 gives teachers and students a road map on how to be successful with MP1. It is a great visual to show the relationship of the practices to each other. Can't wait to share with my teachers.
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  • 02/24/2019 12:15 PM | Kerin Derosier
    The Avenues for thinking really made sense to me. Each year I try to decide exactly how I will incorporate the MP's into my teaching without realizing how naturally they fit in already. I love the quote regarding MP1 where it says "All other math practices sit in service of this goal, because if a students gives up, there is no opportunity for any other mathematical thinking to occur." I agree that before any of the other practices can occur we have to get the students engaged in the problem, making sense of the quantities, and teach them how to risk take and not give up! I found the visual on page 3 also to be very helpful.
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