Hansel and Gretel Metaphor

The 8th graders are coasting into the last few weeks of their time at our school with a very good wind at their back. They have been working very diligently, and dare I say, happily, on the finances project. Anecdotally I know they have learned so much about what it means to earn a living and try to distribute it out to the various financial demands a “middle income” American family faces.

My 7th graders are soon to be my 8th graders and we are working very carefully but intensely through the first two units of our Algebra text College Preparatory Math. These past weeks have seen us working with the concepts put forth by algebra tiles. Today we struggled with meaning, for example, of a negative tile in a negative region (creating a positive value). I was thinking about algebra and what is challenging and what is plain irritating for a 13 year old to learn. I like to think in metaphors or stories that I can tell my students. Today it occurred to me that one aspect of algebra I emphasize (and my students abhor, for the most part) is the careful notation of the steps taken when working with equations. The metaphor that came to me was of Hansel and Gretel, a story I have read often to my young son these past years. The version I know has Hansel devising a way of finding his way back home by dropping little pebbles that he collected the day before. When his step mother discovers his trick and locks him in, he is forced to use bread crumbs. These bread crumbs are quickly gobbled up by the birds and Hansel and Gretel are lost in the woods.

Using this metaphor, I explained to my students that they needed to leave stone pebbles behind, in the form of clear notation of steps, so that if they get lost, they can return. Anything less than clear notes are like bread crumbs and will leave them lost unless by chance they can remember their way back. I spent the rest of the class indicating whether I saw pebbles or bread crumbs.