After one month as a missionary in Argentina I was ready to raise the dead. Or at least that is what the woman at the door must have thought. Let me explain.
As we were proselyting door to door, it was my turn to talk to whoever answered the door. A woman happened to answer the door and, as was the custom in Argentina, I asked to speak to the man of the house. I thought she responded el salió, meaning he stepped out. I asked when he would return so we could speak with him.
At this moment, my more experienced partner stepped in and thanked the woman for her time and shuttled me away. Amidst his laughter, he informed me the woman had actually said that her husband was desfaleció, he passed away. It was a small difference to my novice ear, but a big difference in meaning.
As we have been working with students on trying to identify what they understand about number, sometimes a small difference in what a child has done made a big difference in what it means to them. For example, one student, Gabriella, showed us she could figure out how many dots were hidden on a strip of dots where some of the dots had been covered, as long as we told her how many dots were on the strip all together. She would count the dots that were still visible and then continue counting and use her fingers to keep track of the numbers she said until she got to the total. Then she would look at her fingers to see how many were hidden.
We then devised a task for her small group that we thought she could do with just a little work. We told her there were a certain number of items in a pile, but in one part of the pile there were only some. Then we asked her how many would be in the other pile. She looked at us and said “I don’t get it.” She honestly had no idea what we were even asking.
We thought that the prior tasks she had completed with the missing dots and the missing addend were close enough to for her to take what she knew and use that knowledge for another task, but it wasn’t. We had to go back to the task she could do and gradually make changes to the task until it was like the task she could not even understand.
We started by not letting her look at the dots that were still visible on the strip. Instead, we told her how many were not covered. Then, we didn’t have her count the dots on the strip to figure out how many were on the strip in all, we just told her. Once she could do that, we then tried the problem that she could not understand and she was able to do it.
We hadn’t noticed the small differences in the task she did and the one we gave her, and the result was a big misunderstanding on her part and ours. We continue to see how important communication is to our work with students.