Monday-Tuesday, June 27-28, 2011 (SF)
9:00 a.m. to 3:30 p.m.
(1 continuing education unit from the University of Southern California's School of Education.)
This two-day workshop is designed for high school mathematics teachers who want to make Algebra 2, Trigonometry and Precalculus more accessible, richer and more fun. I will present a number of units to enrich and deepen the corresponding lessons in any textbook, whether traditional or reform.
- Concrete introductions to exponential, logarithmic, inverse variation, and trig functions
- Functions from patterns; functions from geometry
- Function diagrams: upper level applications
- Iterating functions as a gateway to sequences, series, mathematical induction and chaos
- A visual approach to complex numbers and matrices
- Geometry of the parabola (2D, 3D)
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, several of the units presented in the workshop involve the intelligent use of electronic tools, hands-on activities with concrete materials, and/or creative alternate representations.
Monday-Wednesday, August 15-17 2011 (DC)
9:00 a.m. to 3:30 p.m.
(1.5 continuing education unit from the University of Southern California's School of Education.)
In this three-day workshop, I will present many hands-on and electronic tools and activities to preview, review or extend key concepts in geometry, as well as some enrichment lessons. This work is intended to complement - not replace - related work in paper-pencil and compass-straightedge environments.
- The tools include manipulatives (such as pattern blocks and geoboards) and puzzles (such as tangrams, pentominoes, and supertangrams)
- The activities include "walking geometry," "soccer angles," "tile design," and "slicing a cube"
- We will use interactive geometry software to extend these activities, and to work through a challenging and highly motivational construction unit
- I will also present an authentic approach to proof, which tries to navigate a middle course between the too-abstract traditional curriculum and the insufficiently rigorous nature of some reform programs.
These lessons were developed in somewhat heterogeneous classes, and reach a wide range of students. They provide support for the less visual by complementing the drawing and studying of figures, and enrichment for the more talented by offering deep and challenging problems.