Sparks in the Desert: A Beginning Conversation on “Counting-On” – Part 1

vanvleet1_11_23 I had the opportunity to attend my first California Mathematics Council, Southern conference, in Palm Springs. The title of this year’s conference was “Sparking Deeper Understanding.” I headed out early the first morning of the conference with my notebook in hand, not really knowing what to expect. I have attended other conferences for different content areas and interests, but nothing prepared me for the scope of the CMC South conference. It is two days and there are four sessions per day, two in the morning and two in the afternoon. There are so many presenters per session that the conference is spread out over four hotels, each hotel containing at least 15 meeting rooms for presentations. Hmm, 15 meeting rooms times four sessions per day times four venues . . . you do the math, it’s a little overwhelming. Everyone attending and presenting has a passion for mathematics and teaching; the energy is incredible!

From the sessions I attended, it is evident that with the shift to the Common Core Standards there is a renewed focus on analyzing student thinking. The Effective Mathematics Teaching Practices that are called out in NCTM’s Principles to action: Ensuring Mathematics Success For All (Reston, VA, 2014) were referred to several times. They are:

  • Establish mathematics goals to focus learning.
  • Implement tasks that promote reasoning and problem solving.
  • Use and connect mathematical representation.
  • Facilitate meaningful mathematical discourse.
  • Pose purposeful questions.
  • Build procedural fluency from conceptual understanding.
  • Support productive struggle in learning mathematics.
  • Elicit and use evidence of student thinking.

The last practice, “elicit and use evidence of student thinking,” resonated with the presentation that AIMS facilitated at the conference. The title of our presentation was, “Don’t Be Quick to Count On: Teaching with Deep Understanding.” (presentation slides shared below).




We had the opportunity to share with participants the work our research team has been doing around the research of Dr. Les Steffe. Dr. Steffe wanted to understand the mathematics of children and how they come to construct their understanding of number. In the presentation, we shared video of kindergarten, first, and second grade students engaged in some of the same “protocols” or tasks Dr. Steffe presented to children in his teaching experiment. Through students’ engagement in these protocols, Dr. Steffe illuminated a developmental progression that students go through when coming to construct their understanding of number.

At the AIMS Center our goal is to help translate the knowledge of this progression to teachers. We hope to help them elicit and use evidence of thinking to have a laser-like focus on their students’ behaviors and then to be able to use that evidence to design the most effective next steps for student instruction in mathematics. Check out our team’s webpage, Counting and Additive Situations: Unit Construction. Our next few blog posts will go more in depth into the CMC South presentation on “Counting-On”. Our hope is that our work sparks a deeper understanding of the mathematics of children. Stay tuned next week when Beverly Ford continues the conversation!

One Response to Sparks in the Desert: A Beginning Conversation on “Counting-On” – Part 1

  1. In order to better serve and help our students, we need to be able to understand how students’ think. If we use evidence of student thinking, we would be able to see where they are in their thinking process and help them get to the next transition or level. Along with this we also need to have students go through productive struggle in order for them to gain a deeper understanding of counting on numerically.

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