#### Incorporating modeling into your classroom works best if you scaffold the delivery throughout the entire year.

#### As we teach, we should think about our students’ understanding of content and our expectations of them. As students gain competency with content standards and practice standards, our expectations of them can move to higher levels on the Bloom’s Taxonomy.

#### The same teaching and reflecting process applies to modeling. Students need to first be able to use and understand models before being able to apply existing models to problems and analyze the results of the model. Gaining competency in understanding the results of a model will allow students to then evaluate the model’s accuracy. Only once these five areas are mastered will a student have the ability to improve a model, expand a model, or create their own model.

#### The Modeling process is cyclical. During the modeling process students will use all 6 levels of Bloom’s Taxonomy. As shown below, they will need to define a problem which requires them to remember and understand information about the topic area. They will need to apply the knowledge of the topic area and analyze the results of both the physical and computational processes. Finally, they will evaluate the model’s strengths and weaknesses in order to work on improving the model. This begins the process anew. Each iteration of this cycle brings the model closer to representing reality.

#### The Bifocal Modeling Process is illustrated above. Stanford University also offers training on incorporating Bifocal Modeling in the classroom. Their program can be found here.

#### More importantly, the modeling process reinforces learning. Students must look critically at both their model and the knowledge they have. They will often re-evaluate their understanding of concepts like scale, unit conversion, mathematical formulas, small scale behavior, and large scale behavior. The modeling process very often leads to a more complete understanding of a system by revealing gaps in understanding.

#### While the model may never be perfect, through refining the model students will not only learn – they will learn about the limits of the model as well as the limits of their own understanding. This process can transform unknown unknowns into known unknowns. This process can inspire students to pursue areas of study they were never aware of – areas like high level mathematics, theoretical physics, micro biology, or even computer science. Their desire to solve problems – to create accurate models – can drive their pursuit of knowledge and broaden their horizons to new fields.