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.

See below for a shorter middle-school-only version of this workshop.

The Common Core State Standards call for a complete rethinking of geometry in grades 8-11. Instead of basing everything on congruence and similarity postulates, as is traditional, the idea is to build on a foundation of geometric transformations: translation, rotation, reflection, and dilation.

In order to teach this effectively, it is important to have a solid understanding of the underlying math, as well as ideas for rich activities for students. I have been teaching transformational geometry for twenty years, and have a lot to share. This three-day workshop will cover:

• Composition of transformations -- the four isometries and their fundamental properties.
• Symmetry in depth -- around a point, along a strip, in the plane. Connections to art and design. Tiling.
• Computing geometric transformations with the help of complex numbers at first, then matrices -- this is the mathematics that underlies all computer graphics/.
• Intelligent use of technology to support all this, including a highly motivating unit on geometric construction.

We will also discuss the impact of these changes on the teaching of proof, and more generally on secondary school geometry.

This workshop does not overlap with Hands-On Geometry.

In this three-day workshop, I will present a wealth of visual approaches to the teaching of algebra in grades 6-8, 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.

See above for a longer, grades 7-11 version of this workshop.

In this two-day workshop, I will present kinesthetic and manipulative activities. This hands-on curriculum is intended to complement related work in paper-pencil environments: it serves to preview, review or extend key concepts in geometry. The content is aligned with the Common Core Standards for grades 6-8, and lays the groundwork for high school geometry.

• Topics include angles, triangles, quadrilaterals, area, the Pythagorean theorem, congruence, similarity, construction, and tiling.
• Tools include manipulatives (such as pattern blocks and geoboards) and puzzles (such as tangrams and pentominoes.)
• Technology will be used to illustrate concepts.

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.

This workshop does not overlap with Transformational Geometry.