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Annotated Site Map
for Henri Picciotto's Math Education Page
- I have designed some algebra manipulatives (the Lab Gear) and co-authored, with Anita Wah, an algebra textbook (Algebra: Themes, Tools, Concepts -- ATTC). Start on these pages:
- The Lab Gear
- ATTC
- A New Algebra: Tools, Themes, Concepts
- This article (published in the Journal of Mathematical Behavior, v 12, #1, March 1993) summarizes much of the pedagogical and curricular thinking behind ATTC.
- Algebra for All?
- A short presentation of how the Lab Gear and ATTC help make the algebra course both more accessible and more mathematically rich.
- ATTC turned out to be somewhat controversial. Read the debates!
- My response to a critic.
- A discussion about geoboards.
- Seeking Depth in Algebra 2
- An outline of some units, and links to some lessons.
- Comparing Cell Phone Plans
- A "real world" application of linear functions and equations, in a fully spelled-out lesson.
- Constant Sums, Constant Products
- An untraditional approach to several traditional topics, including the quadratic formula.
- Equations vs. Identities
- Three downloadable lessons from ATTC.
- Function Diagrams
- A parallel axes representation, which provides a way to look at many familiar ideas from a fresh perspective. Includes many Cabri animations and PDF worksheets.
- Iterating Functions
- A rich topic, which can serve as an introduction to sequences and series, and is prerequisite to the study of dynamical systems and chaos.
- Letters and Postcards
- An introduction to linear programming.
- Parabolas and Quadratics
- A series of worksheets I developed, the core of an Algebra 2 unit at the Urban School, plus some interesting follow-up lessons for teachers. Includes two non-standard proofs of the quadratic formula.
- Sequences and Series
- A dozen preview / introductory lessons on arithmetic and geometric sequences and series, from ATTC.
- Using the Graphing Calculator
- Sample lessons on linear functions, equations and inequalities, quadratics, polynomials, exponential functions, logarithms, square roots, absolute value.
- Introduction to Abstract Algebra
- A playful approach to group theory for a pre-college audience.
Alternate electives after Algebra 2:
See also the site map by grade level.
- My book Geometry Labs.
- Three sample lessons:
- Angles
- An extension:
- Soccer Angles
- Background, links, activities, and articles on:
- Geometric Puzzles in the Classroom
- A book of related activities: Polyomino Lessons
- Four books of geometric puzzles, using plastic superTangrams:
- SuperTangram Activities, Books 1 and 2
SuperTangrams for Beginners, Books 1 and 2
- Information about a book I co-authored with George W. Hart, about polyhedra and many other topics in two, three and four dimensions:
- Zome Geometry (off site)
- Teaching Proof
- Proofs "without words":
- Sum of angles in a triangle
- Pythagorean theorem
- Completing the square
- Parallelogram area
- The geometry of graphs:
- y = mx + b. (Similar triangles and the graphs of linear functions)
- Geometry of the Parabola: 2D (Geometric definition of the parabola, the reflection property, evidence that all parabolas are similar)
- Geometry of the Parabola: 3D (Proof that it is indeed a conic section)
- The Geometry of Conic Sections: 2D | 3D
- Unexpectedly related problems: minimizing certain sums of distances, and the locus of points from where a triangle...
- looks isosceles!
- Before working in a high school, I taught elementary school for many years. This article summarizes my ideas on K-8 math education.
- Early Mathematics: A Proposal for New Directions
- A visual approach to this topic, using an area model:
- Fractions Arithmetic on Grid Paper
Manipulatives
/ Kinesthetics
- Physical, in-the-body lessons, spanning many topics in secondary school math:
- Kinesthetic Activities
- Brief video introduction, and links:
- Manipulatives
- Introduction to Base 10 blocks and the Lab Gear, followed by a general discussion of the uses and limitations of manipulatives:
- Manipulatives (in "Early Mathematics")
- Sample activities using the geoboard and the Lab Gear:
- Area (in "A New Algebra".)
- Links and curricular materials about algebra manipulatives:
- The Lab Gear
- Debate on the appropriateness of using the geoboard to introduce the Pythagorean Theorem:
- An exchange with Don Chakerian.
- Information about a book of activities that use a broad range of manipulatives:
- Geometry Labs
- Sample activities using pattern blocks:
- Angles (from Geometry Labs)
- Perimeter Patterns (in "Early Mathematics".)
- ...extended for teachers in Pattern Block Trains
- Sample activities using the circular geoboard:
- Angles
- The Ten-Centimeter Circle
- Background, links, activities, and articles on:
- Geometric Puzzles in the Classroom
- Four books of geometric puzzles, using plastic superTangrams:
- SuperTangram Activities, Books 1 and 2
SuperTangrams for Beginners, Books 1 and 2
- Information about a book (co-authored with George W. Hart) using the Zome System -- the ultimate 3D manipulative:
- Zome Geometry
- Teachers' Mathematics
- Math Lessons for Math Teachers
- Good problems for math teachers (and their students?)
- Iterating f(x)=2|x|-2
- Mapping Triangles to Points
From 1981 to 2013, I was part of the Math Department at The Urban School of San Francisco.
I have written several articles about teaching.
- I coordinate a sharing and collaboration network for math teachers:
- Escape from the Textbook!
- Using the computer...
- Math: Visual and Interactive!
- Using the Graphing Calculator
- Many activities to deepen students' understanding of fundamental concepts (middle school to precalculus.)
- The Turtle in the Age of the Mouse
- This article on why I still teach programming can also serve as an introduction to Boxer, a programming language and computational medium for education.
- The Ten-Centimeter Circle
- A hands-on introduction to the trig ratios.
