What to Count?

In this video clip, Declan, Luther and Quinton are building towers by spanning toilet paper tubes with cardboard rectangles. During the construction, Luther and Declan try to compare the number of levels between their two towers. They make quantity judgments in the same way.  There are other interesting moments in this video clip.  Rather than giving you our analysis of the clip, we have provided you with a set of questions that you can use to discover the significance of this clip:

·  The teacher comments that Luther starts with a "bottom level"(cardboard rectangle) on the table, which is different than his previous construction.  Why do you think the teacher uses this strategy?

·   Declan hears the teacher's question about the bottom level and volunteers that he chose not to start with a cardboard rectangle on the table.  The teacher asks him, "How come?"  What might a child his age likely answer (Assuming Quinton had not interrupted him with the comment about the “taco”)?

·   Do you notice that Quinton is intrigued with the tube he is holding?  It is not round like the others.  Can you think of other examples when a child feels compelled to name something because it has a funny (non-conventional) shape?

·   Declan feels compelled to tell Quinton that the "taco" is really a "toilet paper thing." Would you say that the comments about the identity of the tube that follow Declan's correction are useful or constructive?

·   How would you characterize the teamwork between Quinton and Luther when Quinton tries to add more columns and levels to Luther's structure?

·   Luther counts and determines that his tower has “four levels.” Declan quickly responds by saying, “I have more levels” (time code01:05). Why do you think Declan believes he has more levels than Luther?

·   Does Declan rethink his claim later in the video?  

·   Why do you think Luther believes Declan does not have more levels?  Does Luther change his mind?

·   Offer some summary comments about why learning to compare quantities requires more than learning the correct number of items.