SymmetryA unifying thread across grades and cultures.
with Henri Picciotto
Symmetric designs are found in virtually every culture, and are interesting to students across the grades. We will use that as a foundation for lessons about essential and enrichment math topics for grades 6-8. This approach will allow us to build on student creativity while furthering their visual sense and their mathematical growth.
We will explore line and rotational symmetry with activities using manipulatives and free online platforms. We will discuss rosette symmetry (finite figures), frieze symmetry (infinite designs that extend in one dimension), and wallpaper symmetry (two-dimensional designs and tessellations).
Along the way, we will analyze examples from all over the world and touch on the following concepts: special triangles and quadrilaterals, regular polygons, factors and multiples, rigid motions, and dilation.
Participants will receive the needed manipulatives and handouts in the mail. For some of the work we will be using online manipulatives. Some of the content will be drawn from the Symmetry material on my website.
Participants will also get to join short sessions on assorted topics, and do math together as part of a Math Teachers' Circle.
No Limits!with Henri Picciotto and Rachel Chou
This workshop is designed for high school mathematics teachers who want to make Algebra 2, Trigonometry, and Precalculus more accessible, richer, and more fun. A frequent challenge in teaching upper level high school classes is the limited pedagogical range of most textbooks and curricula. This is particularly harmful to the students who find symbol manipulation difficult, but it is also cheating our stronger students of the multi-faceted understanding that would serve them best.
To address this, we will present a number of activities to complement the corresponding lessons in any textbook, whether traditional or contemporary. Our lessons involve the intelligent use of electronic tools (Desmos and GeoGebra), creative alternate representations, and problem-solving throughout. Our goal is to help students develop meaningful intuitions for the concepts being studied.
- Iterating functions as a gateway to sequences, series, and chaos
- Thoughtful approach to graphing: domain and range analysis, transformations
- Trigonometry: student discovery of all the basics and the elementary identities
- Function diagrams to visualize rate of change, inverse functions, composition
- Binomial expansion and story proofs
- Geometry of the conic sections (2D, 3D)