So Easy?!

I find that the math teacher candidates and special education teacher candidates struggle with breaking down math topics, especially “easy” ones like the one below, into simple steps. To help students who struggle with math breaking down the math topic is imperative. The analogy I use is to break the topic down into bite-sized pieces like we cut up a hot dog for a baby in a high chair. Adding ones digits in 2 digit numbers with carrying

First, I target the step of identifying the ONES and TENS place in the 2 digit sum in the ONES column (below it is 12). In a scaffolded handout I create a box to for the sum with the ONES and TENS separated. At first I give the sum and simply have the student carry the one. Then I have the student find the sum and write it in the box (14 below). Once mastered I have the student write the sum and carry the 1. Finally, the student attempts to add without the scaffolding. I continue with color but then fade it.  Teaching students to add appears to be a very linear, skill driven endeavor. Hidden in this is the concept of what it means to add and how to assess this conceptual understanding. Here is an approach to address and assess the concept of adding.

In the photo above a student is prompted to pull both groups into 1 pile (see photo below). The word, add, is not addressed. The symbol is absolutely not introduced yet. Once the student has demonstrated a consistent performance of pulling the groups into 1 pile (addition) two other tasks are introduced, taking away and sorting. The student is presented each of these individually (field of 1).  After showing consistent performance in demonstration of these skills, the skills are then presented using a generalized mat (see below). Then two skills as pairs. First  “pulling together” and “taking away” are randomly prompted individually, e.g. “pull into a pile” using the generalized mat above. Then combine “pull together” and “sort” then “sort” and “take away.” Finally all 3 are randomly chosen (field of 3).

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