Demonstrates how students' power to recognize and express patterns and generality can be exploited in a variety of different ways that are connected to both arithmetic and algebra. Uses the Tunja sequence approach to teach multiplication of negative numbers and simplification of factors. (KHR)

Presents activities to find Pythagorean triples using the TI-83, a graphing calculator. (KHR)

Presents a project that addresses several components of the Algebra and Communication Standards for Grades 9-12 presented in Principles and Standards for School Mathematics (NCTM, 2000). Describes doing mathematical modeling and using the language of mathematics to express a recursive relationship in the perimeter and area of the Koch snowflake.…

Describes a problem-solving lesson involving 24 attribute blocks in which students discuss relationships between patterns, colors, shapes, and quantity. (ASK)

The ability to use algebra in describing and analyzing real-world situations is becoming a basic skill for all students. The main focus of this book is on patterns, functions, and relationships. Information and ideas on how algebraic thinking can be developed in the years leading to a formal algebra course are included. K-8 teachers are offered a…

This paper is based on research work carried out in the Foundation Course in Mathematics at Goldsmiths College, University of London. The theme of the investigation was to investigate the hidden faces of cubes placed on a table. In order to do this, the following investigational teaching styles and learning strategies were adopted: investigate…

Presents a quilting problem that engages students at many levels, has multiple possible solution paths, lends itself to a variety of representations, and connects many mathematical ideas. (KHR)

Presents the problem of points and the development of the binomial triangle, or Pascal's triangle. Examines various attempts to solve this problem to give students insight into the nature of mathematical discovery. (KHR)

Describes an investigation-based, lecture-free first-year algebra course in which students are responsible for compiling their own textbooks. Discusses the purpose and procedures of the activity. Includes student worksheets. (KHR)

Examines existing research literature which suggests that introducing computing tools can help students focus on the relevant aspects of a problem, function at higher levels of geometric understanding, distinguish between drawings and constructions, and develop and reason about conjectures on the basis of generalization of patterns. (KHR)

Outlines several recommendations for teaching probability in the secondary school. Offers an activity that employs simulation by hand and using a programmable calculator in which geometry, analytical geometry, and discrete mathematics are explored. (KHR)

Presents a project used to help students make connections between linear and exponential models and between arithmetic and geometric sequences. (KHR)

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…