In the study of music from a mathematical perspective, several types of counting problems naturally arise. For example, how many different rhythms of a specified length (in beats) can be written if we restrict ourselves to only quarter notes (one beat) and half notes (two beats)? What if we allow whole notes, dotted half notes, etc.? Or, what if…

Categorization is one of the fundamental building blocks of cognition, and the study of categorization is notable for the extent to which formal modeling has been a central and influential component of research. However, the field has seen a proliferation of noncomplementary models with little consensus on the relative adequacy of these accounts.…

We study the properties of two specification tests that have been applied to a variety of estimators in the context of value-added measures (VAMs) of teacher and school quality: the Hausman test for choosing between random and fixed effects and a test for feedback (sometimes called a "falsification test"). We discuss theoretical…

Learning Curves has its roots in economics and behavioral psychology. Learning Curves theory has several business applications and is widely used in the industry. As faculty of Operations Management courses, we cover this topic in some depth in the classroom. In this paper, we present some of our teaching methods and material that have helped us…

The method for geometric transforms (probability generating functions) is used to study the expected number of observations until the pattern 123123 . . . 123 is obtained. These results provide a first generalization of similar problems considered by other authors. (Contains 1 figure.)

Arithmetic programming for students with mild mental disabilities requires a comprehensive perspective that includes attention to curriculum, instruction, and appraisal. Arithmetic computation should not dominate educational programming, but should be included in ways that are functionally relevant and meaningfully presented within a framework of…