Counting Blocks in a Mirror

Delivery Method: 

This videative is one of three about a five-year-old’s math experiences with Learning Material Workshop Blocks; the other two videatives are titled “A Hole Problem Solved” and “Symmetrical Structures.” Sometimes we arrange materials in such a way that they almost “beg” to be counted. Try placing a strip of polished Mylar on a table covered with blocks. With the added reflection, the number in a stack of blocks is instantly “doubled.”

In this videative we see how Ria grapples with the total number of blocks that she perceives. Watch as the teacher invites Ria to consider both the set of real wooden blocks and the set of blocks reflected in the mirror. By pointing as she counts, Ria guides her own ability to maintain a one to one correspondence between each block and each numeral she says. Ria counts, “One, two, three...” for the blocks that she sees in the mirror, “Four, five, six...” for the wooden blocks that she has physically placed. Notice she also says, “seven,” and points to the space where she plans to add the next block. Perhaps because Ria is busy thinking about adding a block to the top of the stack, she does not include in her count the reflected block (eight) that will be created by the additional placement.

As we study the entire videative we note the skillful questions the teacher asks to help Ria distinguish the blocks counted versus the blocks not counted, and the total number of blocks versus the number in the two subsets of blocks (real blocks and reflected blocks). Ria hangs in there and, much to our pleasure, shares her thinking out loud.

Keywords: Fives, Blocks, Child-Teacher, Counting, Cardinal, Ordinal, Counting-On, videative

Length of videative: 8 pages, 5 video subclips
Length of stand-alone master video clip: 2 minutes

Click here to see Learning Material Workshop Blocks.