Update from the Second Grade Landscape

So this year I have been working with second grade again. I am attempting to learn from what we did last year. I think that our understanding about how the students work with base ten ( and especially my host teacher's understanding) has grown. A recurring issue is the representation of base ten blocks with stick and ball drawings that almost immediately replaces the actual blocks after a few limited counting experiences with the blocks. This, apparently, has become common practice and is partly a result of teachers feeling pressured to increase the number sizes too fast, which keeps the students in the direct modeling stages longer since they have not developed a good understanding of the use of facts and related facts to solve the smaller number problems. Teachers also feel that the time spent in getting the blocks out, managing them and putting them back wastes precious time. Of course I am constantly pushing against this practice, but it is not my classroom and I am only there once a week.

Nevertheless the kids and their teacher are making progress, the conversations and discussions are pretty complex and meaningful and the kids love doing real math. No M&Ms needed.  Here is an example of the board work from one of our problem solving discussions. This year, we frequently write problems after reading a book. The photo is the board work from a problem written by a student after reading the book Porkenstein by Kathryn Laskey (the gist of the book is friendship). The problem was:

Porkenstein has 35 friends. Some don't like him anymore. Now he has 19 friends. How many friends don't like him anymore?

The strategies were presented from left to right. The sticks in the upper left were a problem for the girl who drew them, so as a class we talked about what she did instead (insert: the problem was that she did not believe that a stick had ten in it, and she was treating the problem as a separate result unknown: 35-19 = ?). When she explained her second drawing (5 by 7 circles below), she said she covered up 19 and counted how many needed to be taken away (now she was treating the problem as a separate change unknown: 35 - ? = 19). Two more students shared, one who subtracted 19 from 35 using the base ten representation and another who used the number line to count back 19, and then as a class we used the numberline to count from 19 to 35. My goal for this lesson was to help kids see that problem can be solved a number of ways, and I hoped that they would treat the problem like a join change unknown and use the anchor of 19 close to 20 ( e.g. 19 + 1 >>20 + 10 >>30+ 5 >> 35; so 1 + 10 + 5 = 16.) Instead we ended up talking more about base ten approaches and recording number sentences that matched their thinking.