This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

This article provides computational and rule-based approaches for detecting confusion that is expressed in students' comments in couse forums. To obtain reliable, ground truth data about which posts exhibit student confusion, we designed a decision tree that facilitates the manual labeling of forum posts by experts. However, manual labeling is…

The authors who are mathematics teacher educators, have found that classifying, composing, and transforming shapes (in particular, rotations and reflections) are areas of difficulty for adults as well as for children. However, these are also some of the most important geometric ideas. They are fundamental topics in the K-8 Geometry and Measurement…

This chapter introduces three applications of Bayesian inference to common and novel issues in second language research. After a review of the critiques of conventional hypothesis testing, our focus centers on ways Bayesian inference can be used for dealing with missing data, for testing theory-driven substantive hypotheses without a default null…

There is a large body of literature suggesting that students with emotional and behavioral disorders (EBD) lack appropriate social skills, including deficits in building and maintaining interpersonal relationships, prosocial behaviors (e.g., sharing, helping, cooperation), and self-management strategies. While the literature shows small to modest…

This short report draws attention to an interesting kind of configuration in the lexicon that seems to have escaped theoretical or systematic descriptive attention. These configurations, which we dub SEMPLATES, consist of an abstract structure or template, which is recurrently instantiated in a number of lexical sets, typically of different form…

A wealth of empirical evidence has now accumulated concerning animals' categorizing photographs of real-world objects. Although these complex stimuli have the advantage of fostering rapid category learning, they are difficult to manipulate experimentally and to represent in formal models of behavior. We present a solution to the representation…

A functional class refers to a circumstance in which responding is controlled by features of stimuli that are common to all the class members. We argue that behavior with respect to conceptual stimuli entails more than discrimination among classes and generalization within classes. We suggest that an analysis of substitution of stimulus functions…

The remarkable successes of the physical sciences have been built on highly general quantitative laws, which serve as the basis for understanding an enormous variety of specific physical systems. How far is it possible to construct universal principles in the cognitive sciences, in terms of which specific aspects of perception, memory, or decision…

Recent research in semantics and pragmatics has revived the debate about whether there are two cognitively distinct categories of conversational implicatures: generalised and particularised. Generalised conversational implicatures are so-called because they seem to arise more or less independently of contextual support. Particularised implicatures…

This paper proposes a multidimensional generalization of Coombs' (1964) parallelogram model for "pick any/'n'" data, which result from each of a number of subjects having selected a number of objects (s)he likes most from a prespecified set of "n" objects. In the model, persons and objects are represented in a low dimensional space defined by a…

Classification "rules" in expert and everyday discourse are usually deficient by formal standards, lacking explicit decision procedures and precise terms. The authors argue that a central function of such weak rules is to focus on perceptual learning rather than to provide definitions. In 5 experiments, transfer following learning of family…

This guest editorial describes ways teachers can use guessing games about an unknown item in a "mystery box" to help children improve their abilities to listen to others, recall information, ask purposeful questions, classify items by class, make inferences, synthesize information, and draw conclusions. The author presents information…

A survey of state mental retardation/developmental disabilities agencies found that while most employ a classification system that is compatible with or derived from that of the American Association on Mental Deficiency (AAMD), only 22 are actually using the 1983 edition of the AAMD alone or with another system. (Author/VW)