The graphic organizer below is used to show the student the steps for addition. It also addresses the concept of addition (which I have addressed previously) as an act of pulling “together” two parts to form a whole.

The student is prompted to move the first part (set of coins in this case) to the number chart. This can be completed with 1 to 1 correspondence or with subitizing (identifying the number of items without counting). Then, the student is prompted to move the second part while counting on, e.g. 7, 8 etc. (as opposed to starting from the left and counting from the first coin: 1, 2 etc.). The chart scaffolds the counting on and allows the student to see the total as a magnitude.

It is important to first teach the students the “rules of the game”, i.e. how to use the graphic organizer. To do this have the student simply move the first part to the number chart then the second part. The student can also be prompted to state the addition problem (written at the top). When the student is fluent with these steps the counting on can be implemented.

The next step would be to replace the coins with the symbolic representation, numbers.

## So Easy?!

### For new teachers I use a formal task analysis approach to teach candidates how to cut up the math into bite-sized pieces. A task analysis for the problem above was an assignment given to a group of graduate level special ed candidates. As is common, they overlooked many simple little steps hidden in the problem. These steps are hidden because they are so simple or so automatic in our brains that we don’t think about them. See below for how I break this topic into several pieces or steps. For example, before even starting the addition the person doing the problem has to identify that 43 is a 2-digit number with 4 in the TENS place and 3 in the ONES place. Understanding that the problem is addition which entails pulling the numbers together to get a total (sum) is an essential and overlooked step. If a student struggles with a step the step can be addressed in isolation, as I show in another blog post.

In a previous post I presented an approach to teach and assess the concept of addition. ThisÂ document showsÂ all the steps I use including the one shown inÂ the photo above.

## Assessing the Concept of Addition

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 Â “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).