November 2022 Message from the Board

Written by Peter Zola, Region 3 Representative

Welcome to the November 2022 CCTM Newsletter. CCTM is a non-profit designed to support educators with the teaching and learning of mathematics. This month our board message is by Peter Zola, our CCTM region 3 representative and his  thinking around multi-digit division and the division algorithm. 

Why is it so hard to teach two-digit and three-digit division for meaning? When the Common Core math standards were introduced, many math concepts and practices moved to earlier grades.  But this is not the case with long division!  Those of us who learned math before the Common Core likely were introduced to long division as early as third or fourth grade. These days, students begin working with discrete division strategies in third grade, but the division algorithm is not introduced in the Common Core until sixth grade. Additionally, those of us who learned in the "before times" learned through rote procedure without much conceptual development. Through this lens, the conflict between what we as teachers know and how we know it, versus the concepts we need our students to understand becomes evident. This conflict requires us to examine our own understanding of division, and may help us to understand why we jump to long division before we develop the foundation for the algorithm.

So then, how do we support our students in mastering early division concepts in the intermediate grades without bringing in the long division algorithm? Even in the intermediate grades, giving kids concrete tools like counting cubes, or base-10 manipulatives can be helpful in building conceptual development and problem solving. We can help students pay attention to both "equal sharing" and "grouping" contexts in problems. We can work to help them understand where they can see division operations in familiar multiplication models such as arrays. These ideas can help students extend their existing multiplication strategies to work for division operations.  

It is also important that we as teachers take the time to dive into the work that we will be asking our students to engage in and actually do the math ourselves to anticipate their strategies and misconceptions. Resources such as this blog post and this website are great places to engage with division concepts. This practice of intellectual preparation is helpful in bridging our adult understandings to those of our students. 

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