A method of organizing studies on sequencing problems in mathematics according to a theoretical model based on characteristics of empirical science is explained. The conceptual framework underlying eight studies that follow this article in JRME (SE 508 022 through SE 508 029) is discussed and a brief overview of each study is given. (DT)

A learning strategies program emphasizing primary (text-oriented) and support (affective) strategies was evaluated. Strategy training significantly improved performance on both text-processing and self-report measures. The primary-support group scored higher on the text-processing measures; the support-primary group reported more positive…

Presents a sequence for mathematics lessons designed to facilitate students' competency in executing mathematical processes and to apply the processes to real-life situations. The sequence involves: conceptualization of the process, knowledge of terminology, knowledge of algorithms, and ability to recognize when the process is applicable to…

A plausible set of concepts useful for theory, research, development, and evaluation concerned with content sequencing is explicated. These concepts provide a framework for discussing sequencing alternatives and their implications. (Author/RC)

Outlines a set of terms which can be used (in sequencing writing assignments from simple to complex) to make distinctions between kinds of sequences and notions of complexity. Shows how these terms allow teachers to understand the logic of various sequences, compare and contrast related sequences, and evaluate the concept of assignment sequence.…

In contrast to exemplar and decision-bound categorization models, the memory and contrast models described here do not assume that long-term representations of stimulus magnitudes are available. Instead, stimuli are assumed to be categorized using only their differences from a few recent stimuli. To test this alternative, the authors examined…

If a curriculum developer's goal is to create a single linear sequence of tasks that lead to the development of some important mathematical concept, then some researchers have suggested that these sequences should follow progressions similar to stages of development that have been identified in Piaget-like research on the relevant concept(s).…

Some band teachers wonder why they often have to repeat themselves several times for their band students. Of course there may be more than one reason, but it is possible that some teachers are accommodating only one learning style with their teaching. After the author of this article did a bit of study, he thought this might have been happening to…

This paper proposes a genetic development of the concept of limit of a sequence leading to a definition, through a succession of proofs rather than through a succession of sequences or a succession of epsilons. The major ideas on which it is based are historical and depend on Euclid, Archimedes, Fermat, Wallis and Newton. Proofs of equality by…

Universal design for assessments is an approach to educational assessment based on principles of accessibility for a wide variety of end users. Elements of universal design include inclusive test population; precisely defined constructs; accessible, non-biased items; tests that are amenable to accommodations; simple, clear and intuitive…