Outlines a lesson on the Fibonacci and Lucas sequences that captures student interest by presenting the opportunity for computation practice, mental mathematics, and proof for algebra students. Discusses an extension for solving simultaneous equations. (YDS)

Describes how student thinking about geometric patterns can be used to develop algebraic reasoning and to make sense of mathematical notation and symbols. (Contains 11 references.) (YDS)

Describes students' generalization strategies and justifications as they engage in patterning activities. (YDS)

Demonstrates how to extend student awareness of a common computational pattern into the realm of algebraic thinking through carefully selected, sequenced activities and guided discussion. (YDS)

Describes how students can be guided to find an explicit rule for a pattern from a recursive rule. (YDS)

Helps students develop new insights into mathematical relationships through alternative representations. Examines patterns, symbolic, and functions approaches. (Contains 11 references.) (YDS)

Describes a card trick that provides opportunities for students to discover patterns, work with variables, create tables, and ponder mathematics. Students at various levels of ability are able to enjoy the trick, and mathematical discourse is promoted within the classroom. (AIM)

Middle-school students were asked to determine the dimensions of a hotel atrium so that guests could enjoy the maximum area of scenic view, given that 650 feet of brass railing could be used around each floor. Several solution approaches are described. (MKR)

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…