**Philosophy of Education**

Mathematics and Discovery** Resume**

M

The most successful learning occurs when students can connect to the concept.

I begin by asking students what they know. Sometimes the background they need comes from formal education. Sometimes they draw on intuition and everyday observations. Usually it is a combination of both.

This ensures students have the proper footing so that they can move on – especially helpful for students with math anxiety.

I act as a guide while they search for, recognize, and formalize patterns. In an algebra class, this has taken the form of working in groups to match equations, graphs, and tables, so that they may discover families of functions. In geometry, they discuss the validity of a statement, search for counterexamples, and build a logical argument in the form of a proof. In this way, having ownership of their discoveries enables them to retain knowledge and skills they might otherwise forget.

I begin by asking students what they know. Sometimes the background they need comes from formal education. Sometimes they draw on intuition and everyday observations. Usually it is a combination of both.

This ensures students have the proper footing so that they can move on – especially helpful for students with math anxiety.

I act as a guide while they search for, recognize, and formalize patterns. In an algebra class, this has taken the form of working in groups to match equations, graphs, and tables, so that they may discover families of functions. In geometry, they discuss the validity of a statement, search for counterexamples, and build a logical argument in the form of a proof. In this way, having ownership of their discoveries enables them to retain knowledge and skills they might otherwise forget.

## Real problems are word problems.

My students have used mathematics to analyze politics, medicine and epidemiology, technology, sports, insurance, and socioeconomic issues such as birth, mortality, and crime rates. Conversely, I employ history, games, philosophy, and popular culture to help students reach and understand mathematical abstraction. The recognition of these cross- and extra-curricular interconnections gives students a deeper understanding of the material and builds the critical-thinking skills they need for the future.

Each slide below represents an example or exercise my students have encountered in the classroom.