- 2014:
*Fractions, tilings, and geometry* - Are there any rectangles whose perimeter and area have the same numerical value? Are there any rectangular boxes whose surface area and volume have the same numerical value? Can the plane be tiled with kites and chevrons? In how many ways can 1/2 be written as a sum of unit fractions? How are all of these questions related?
- 2013:
*Probability, Randomization, and Polynomials* - Focused on probability, the meaning and definition of standard deviation and variance, the effects of repeating an experiment many times, and ways to generate or test random data.
- 2012:
*Moving Things Around: Card Shuffles, Repeating Decimals and Geometric Transformations* - Focused on showing how the geometry of polygons is connected to the algebra of the transformations that preserve that geometry.
- 2011:
*Some Applications of Geometric Thinking* - Focused on geometry as a useful tool for studying and understanding all kinds of phenomena inside and outside mathematics.
- 2010:
*Over and Over* - Focused on learning mathematics by working problems together, this course will explore how iterative processes can be used to investigate Fibonacci numbers, image processing, the calculation of square roots, and more.
*in press for publication in 2015, American Mathematical Society*- 2009:
*Some Questions and Problems in Arithmetic* - Focused on learning mathematics by working problems together, this course explores the algebra of sequences and series as a general-purpose tool for a variety of investigations.
*in press for publication in 2015, American Mathematical Society*- 2008:
*Applications of Algebra and Geometry to the Craft of Teaching* - Focused on learning mathematics by working problems together, this course will use this theme as a springboard into investigations of the structure of different algebraic systems and geometric curves. This applied mathematics - choosing and designing tasks - is mathematics applied to the work teachers do.
*in press for publication in 2015, American Mathematical Society*- 2007:
*Developing Mathematics: Probability Through Algebra* - Focused on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that has its roots in secondary level, and is related to the mathematical theme of the Institute.
*in press for publication in 2015, American Mathematical Society*- 2006:
*Some Applications of Geometric Thinking* - Teachers in this course will look at some basic geometric habits of mind like studying continuous change and looking for things that don't change, and they'll apply these habits to a wide variety of situations.
- 2005:
*Doing It with Differences* - Focused on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that has its roots in the secondary level, and is related to the mathematical theme of the Institute.
- 2004:
*Stories that Count* - This course looks at how combinatorics itself can fit into the 5-12 program, but it also looks at how combinatorics and combinatorial thinking can be used to illuminate ideas from more mainstream courses like algebra, arithmetic, and geometry.
- 2003:
*Sums and Differences* - This course looks at the calculus of finite differences as a unifying theme for these questions and others that connect to the middle and high school curriculum.
- 2002:
*Gaussian Integers* - Focused exclusively on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that is rooted at the secondary level but related to the mathematical theme of the Institute.
- 2001:
*The Euclidean Algorithm* - Focused exclusively on learning mathematics by working problems together, this course explores the fundamental algorithm on which much of arithmetic and algebra is based.
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With program support provided by Math for America This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. |