Summer Workshops for Math Teachers

In this four-day workshop, I will present a wealth of visual approaches to the teaching of algebra in grades 7-11, including:

• Lab Gear manipulatives for basic symbol manipulation
• geoboard lattices for slope and radicals
• a powerful parallel axes representation for functions
• intelligent use of technology
• three distinct visual paths to the quadratic formula

Participants will learn techniques that will allow them to serve the whole range of students better by offering:

• greater access, because of addressing multiple intelligences
• greater challenge, because of expecting multi-dimensional understanding
• greater variety, because of using manipulative and electronic tools

The workshop will be aligned with the Common Core State Standards, both in content and in mathematical practices.

For a shorter, grades 6-9 version of this workshop, see below.

In this one-day workshop, I will present lessons that inject meaning into Algebra 2, including:

• Dynamical systems leading to sequences and series
• A kinesthetic and visual introduction to complex numbers
• Labs for exponential, log, trig, and inverse variation functions

The problem in Algebra 2: too many topics, too many formulas that mean too little to most students. A partial solution: teach fewer topics, in more depth, provide access to all students through carefully selected activities, and still try to challenge the strongest students. I will share the best lessons from a course developed over many years for somewhat heterogeneous classes, with an emphasis on assorted learning tools.

This is a subset of No Limits!, a two-day workshop on Algebra 2 and Precalculus. See below.

In this three-day workshop, I will present a wealth of visual approaches to the teaching of algebra in grades 6-9, including:

• Lab Gear manipulatives for basic symbol manipulation
• geoboard lattices for slope
• a powerful parallel axes representation for functions
• intelligent use of technology

Participants will learn techniques that will allow them to serve the whole range of students better by offering:

• greater access, because of addressing multiple intelligences
• greater challenge, because of expecting multi-dimensional understanding
• greater variety, because of using manipulative and electronic tools

The workshop will be aligned with the Common Core State Standards, both in content and in mathematical practices.

For a longer, grades 7-11 version of this workshop, see above.

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 activities 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 kinesthetic and visual introduction to complex numbers
• 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 (particularly GeoGebra,) hands-on activities with concrete materials, and/or creative alternate representations.

For a one-day Algebra-2-only version of this workshop, see above.