The formula [image omitted] is closely related to combinatorics through an elementary geometric exercise. This approach can be expanded to the formulas [image omitted], [image omitted] and [image omitted]. These formulas are also nice examples of showing two approaches, one algebraic and one combinatoric, to a problem of counting. (Contains 6…

This article focuses on the nature of the "transitional minutes" in "any" music class. When transitional minutes before, during, and after rehearsals and classes are unplanned and left to chance, much viable and valuable teaching time is lost. When transitional minutes are well structured, learning can proceed efficiently. One…

The Name Game activity that raises challenging mathematical questions is used to explore random permutations. A permutation of a set is an arrangement of the elements in some order.

The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

Well-known questioning strategies, built on question classification systems, are examined. Types of question classification systems are identified as: "hierarchical," which are sequential and cumulative; "non-hierarchical," which are based on elements which should not be rank ordered; systems which are "context-bound" to specifics; and…