Mathematical Discourse, Part 4: Putting it All Together

  • Mathematical Discourse, Part 4: Putting it All Together

    By Zack Hill, posted September 12, 2016 —

    In the previous 3 posts, ( part 1, part 2, part 3) we have discussed how to plan for a purposeful mathematics discussion. What does this look like, though, when all the planning (see the completed monitoring chart here) comes together? Video presents a unique opportunity to virtually visit a colleague’s classroom. Back in February, our district personnel shot a video of me teaching a lesson using a revised version of Smith and Stein’s (2011) caterpillar task: 

    A fifth-grade class needs 4 leaves each day to feed its 2 caterpillars.

    (a) How many leaves would the students need each day for 12 caterpillars?

    (b) Describe how the caterpillar pattern is related to the leaf pattern.

    One of the principles that NCTM has outlined in Principles to Actions is professionalism. This doesn’t just mean arriving at work on time and being polite to colleagues, although those things are good. NCTM states,  

    Within a culture of professionalism, educators embrace the transparency of their work, their accomplishments, and their challenges, and they share ideas, insights, and practices as they collaborate in ways that build on individual strengths and overcome individual challenges to ensure mathematical success for all students. (2014, p. 99)  

    The transparency that NCTM describes is a shift away from the closed doors that have long been the norm in our profession. I hope that the video creates conversation around what worked in this lesson, what challenges were evident, and how to overcome them. As an attempt to focus our discussion around this video, here are some questions that reference specific clips in the video:

    •    What evidence shows that students were making sense of their group’s solution strategy? (9:20-10:55)

    •    How was the student who used the wrong operation to solve the problem supported? (11:40-14:30)

    •    How were students encouraged to make connections to one another’s strategies? (14:30-15:56)

    •    What evidence is there that students were able to identify an apparent relationship between the terms? How were they further challenged? (16:00-18:22)      

    •    How were students encouraged to make sense of the strategy used by a fellow student? (19:04-19:25)

    •    What evidence shows that students connected the two highlighted methods for solving the problem? (23:40-24:24)

    •    How was the big mathematical idea of the lesson made clear during the wrapup? (26:27-29:00) 

    Your turn

    I’m looking forward to connecting with you over the next few weeks! Please respond to the questions above, or share your general thoughts on the video, in the comments section or reach out on Twitter (@zack_hill). 


    National Council of Teachers of Mathematics (NCTM). 2014. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.

    Smith, Margaret S., and Mary Kay Stein. 2011. 5 Practices for Orchestrating Productive Mathematical Discussions. Reston, VA: National Council of Teachers of Mathematics.

    2016-07 Hill Aupic Zack Hill has worked in education for fourteen years and is currently an elementary school mathematics staff developer for Pinellas County Schools in Florida. He is currently serving on the board of the Florida Council of Teachers of Mathematics (FCTM) and is a member of NCTM. He earned his Master’s in Education from the University of Florida and is interested in how mathematical discourse supports understanding of mathematical concepts.

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