Writing about Multiplication - a Good Way to Assess Understanding

I've heard more than one parent confess that they did not REALLY understand some basic math concepts, like multiplication, until "rather embarrassingly" late in life. It is all well and good to be asked to memorize facts and to be able to recite them, but another thing to know what is happening. In math lessons for the very young, it really behooves teachers and parents to know that children need to manipulate objects, to discuss and examine, and to draw or tell stories, in order to deepen understanding.

A big project happening now in our math class is a group book. We are illustrating and writing about all the multiplication facts, from 2 to 12. It will take a long time to complete, but we are having fun doing it - and, more importantly, are learning how to clearly show and articulate what multiplication is.

Today, I took the sheets done by the students for the 2 times table. As we looked at each page done by our classmates, we gave a thumbs up, and thumbs down, or a thumbs sideways. A thumbs up meant the author/illustrator clearly pictured what the problem was, gave the correct answer, and that we were able to check the answer by counting. A sideways thumb (given frequently at this point, as we are new to this), was an indication that the picture was muddled and made it hard to count to get the correct answer. A thumbs down meant the wrong answer was given, or the picture was misleading. We got a lot of powerful (and positive) peer feedback, and are determined now to make the rest of the book clear and concise (with extra credit for humor, color, and creativity).

Here are just two examples (both thumbs up), to give you an idea of what I'm talking about.

Very clear, funny, colorful.

Extra credit for exploding heads.