Alternating series have the simplest of sign patterns. What about series with more complicated patterns? By inspecting the alternating series test closely, we find a theorem that applies to more complicated sign patterns, and beyond.

If a series of real numbers converges absolutely, then it converges. The usual proof requires completeness in the form of the Cauchy criterion. Failing completeness, the result is false. We provide examples of rational series that illustrate this point. The Cantor set appears in connection with one of the examples.

Linear measurement is more than just learning how to use a ruler. In the early grades, measurement activities develop students' understanding of the properties of objects as well as what it means to measure objects. Hands-on activities can enable students to explore such measurable properties as height and length, and direct comparisons of various…

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…