Rumination from MPX10 from the week of Aug 31

On the Values and challenge of models

As we explore and set our projects and experiences around the big theme of climate change this year in our 10th grade exploratory classes, I am continually designing into our experiences the important framework of modeling. It is no surprise to me that the latest versions of the Next Generation Science Standards (NGSS) and the Math framework in the common core (here) emphasize heavily the importance of the generation, exploration and elaboration of modeling, and more particularly mathematical modeling. When we ask learners to work with models, we push them to deepen, extend and anchor their understanding of relationships between variables: position and time, force and acceleration, parts per million of carbon and global average temperature, really any defined system of interest.

In our class this week we have been working on the mathematics of linear expressions and the physics of Constant motion (broader target: developing the language and understanding an engineer needs for looking at transportation). As a means to deepen our understanding of the modeling of constant motion (broadly leaning of the work of the modeling pedagogy of ASU) we generated experimental data (position and time) of the motion of 2 battery powered cars that move at different speeds. From that data the students use a modeling tool (in our case the wonderful *free* Graphical Analysis App from vernier software http://www.vernier.com/products/software/ga-app/) to create a mathematical model for each car.

The culminating activity was a predictive model session. The students were given a scenario (the red car starts 7 seconds ahead of the green car) and needed to use their models and data to try and predict when the faster green car would catch the red car. The first pass at this activity generated a LOT of conversation, questions and difficulty for the students as they moved from superficial understanding to deeper meaning making.

This kind of learning in our class provides so many layers of learning. It challenges students to truly show they understand the models they have created. It gets to the heart of experimental science in designing experiments that generate meaningful and reliable data. It requires students to be active – to analyze, explain, predict and defend their work. Importantly it starts to replace naive thinking of the real world with internally constructed models that real scientists use to observe and understand phenomena. Oh – and it is fun!

In the process of planning for our modeling I found a great quote from statistician George E. P. Box “all models are wrong, but some are useful”. In order to appreciate the power of this statement my goal is to nurture a real awareness and appreciation for modeling as well as its limitations.