# Uncovering Misconceptions One Array At A Time

Today with my 4th grade intervention group, I noticed a lot of giggling when we were working on Piles. This is a known fact about students who struggle. The more giggling and fooling around, the more lost they are.

I’ve been working on the concept of “rows” with these students because there is almost no understanding of what a multiplication sentence could stand for.  There was a lot of quick matching going on, just putting things together that had similar numbers, hoping they were correct.

So I had to bust that right up.

I asked them to build the card with my square counters, and to make it equal to what they thought the array would look like if it actually had squares. So essentially I’m looking for them to build an array with 6 rows that has 5 squares in each row. We talk a lot about what the counters could represent, like seats in a movie theater.

Look what started to happen…an empty array!

After a brief discussion she and I came to the conclusion that she better fill that one in.  Though I found out later that she didn’t understand why, and only filled it in because I told her to. She very proudly tells me this in the clip below. (Note: No matter how hard I try, I still occasionally slip and tell students what to do. STOP doing that Ms. Smith…)

Here’s another misconception 17 seconds into the video clip. “If you take out this, it’s still the same thing.” (Note: The pitch in my voice becomes noticeably higher, also need to work on my poker voice.):

This is very common when moving from concrete tools to representational models. They have been moving from tools to grids to the empty array models for several weeks now…all along I was assuming they knew what the empty squares and rectangles stood for.  What an awesome thing to see the exact misconception right in front of my eyes because I chose in that moment to question the card.

Teaching point for tomorrow, check!