It's been an incredible experience... |

...and I fully intend to blog about it. But not today. |

I spend 4 days a week supporting instruction in Alex's regularly scheduled math class, and see him once and sometimes twice a week for an additional, individual intervention period. Today was one of those days.

It was my intention to work with Alex on our identified objective, which is counting forward and back on a number line. But I thought I'd warm up with a quick counting activity. I took a bag of small plastic dogs and dumped them out in front of him.

Nothing too crazy. Just 30 little dogs. |

I asked him first to estimate how many dogs were in the pile. I could see him squint, and almost hear him counting to himself. He seemed reluctant to commit, but after a bit of prompting he agreed there were more than 10 and less than 100. He settled on 22 as an estimate, which I had him record on the whiteboard.

Off to what I believed was a good start, I asked him to describe some of his classroom counting experiences. After some more prompting (Alex has trouble expressing himself) he was able to relate that he had counted wooden blocks. He was also able to tell me that he and his partner were successful counting the blocks by 10s. I asked him how he would like to count the dogs, and he said he'd count them by 5s.

Taking one dog at a time, he counted (miscounted, actually) by 5s and here's how 14 dogs turned into 100 dogs:

"5, 10, 15, 20, 25, 30, 35, 40, 50, 60, 70, 80, 90, 100." |

He stopped when he got to 100, leaving the other 16 dogs in the pile. I decided to set aside his miscounting and focus on the set of dogs now in front of us:

**Me:**How many dogs are there?

**Alex:**100.

**Me:**

*(Pause. What now?)*Can you count them again for me? This time one at a time?

**Alex:**

*(Counting with one to one correspondence as he touches each dog)*1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.

**Me:**So how many dogs are there? 100? Or 14?

**Alex:**Both. 100 and 14.

I decided it was time to step in with some direct instruction, and I turned our focus back to the original set of 30 dogs. I tried to explain as best I could that he was counting 1 dog as 5 dogs, and that if he wanted to count the dogs by 5s, he was going to have to first put them in sets of 5. Which he did.

"5, 10, 15, 20, 25, 30." |

**Me:**How many dogs are there?

**Alex:**30.

**Me:**Count them by 1s now.

**Alex:**OK.

*(Touching each one as he counted)*1, 2, 3, 4, 5, 6, ... 30.

**Me:**So how many dogs are here?

**Alex:**30.

I had him write that on the board, and when he came back to the table I took his neatly arranged sets of dogs, smushed them all back into a pile, and asked him again: How many dogs are there? He studied the pile intently, and then, with a little crooked finger, began trying to "air count" them all one by one:

He had no way of knowing which dogs he had already counted, and which were left uncounted. He stopped at 50. |

**Me:**So how many dogs are in the pile?

**Alex:**50.

I took a breath. I had an idea.

**Me:**You told me that when you counted the wooden blocks in class, you counted by 10s. Try counting the dogs by 10s.

**Alex:**

*(Taking one dog at a time and setting it aside)*10, 20, 30, 40,...

**Me:**

*(Bad idea. What now?)*OK, you can stop. Let's go back to class.

We got up from the table, me thinking about how 14 dogs became 100 dogs, how 30 dogs became 50 dogs, and how 4 dogs became 10 dogs. We walked out the door and started down the hallway, me thinking: What just happened? and How did things ever come to this? and, What am I going to do now? And through all the noise in my head I heard his little voice call out: "One".

I looked down, momentarily confused. He was staring straight ahead with a little smile on his face.

Again, "One."

On our walks back to his room, we always play a little game. We alternate counting by ones, sometimes forward and sometimes backward, and stop when we reach his classroom door. He wanted to play.

"One," he insisted.

"Two," I responded.

"Three," he said. We were off, until we got to 88, and he was delivered back into the hands of his teacher.

So now I'm trying to untangle this mess. I know that a lot was revealed, and it needs sorting out before I can map the way forward. I have some ideas, but I'll take all the help I can get.