In this paper, we present data from two iterative teaching experiments involving students' constructions of four basic counting problems. The teaching experiments were designed to leverage the generalizing activities of relating and extending to provide students with opportunities to reflect on initial combinatorial activity when constructing…

Latent partially ordered sets (posets) can be employed in modeling cognitive functioning, such as in the analysis of neuropsychological (NP) and educational test data. Posets are cognitively diagnostic in the sense that classification states in these models are associated with detailed profiles of cognitive functioning. These profiles allow for…

It has been recently argued that some machine learning techniques known as Kernel methods could be relevant for capturing cognitive and neural mechanisms (Jakel, Scholkopf, & Wichmann, 2009). We point out that "String kernels," initially designed for protein function prediction and spam detection, are virtually identical to one contending proposal…

Researchers have proposed that an explicit reasoning system is responsible for learning rule-based category structures and that a separate implicit, procedural-learning system is responsible for learning information-integration category structures. As evidence for this multiple-system hypothesis, researchers report a dissociation based on…

Working memory is crucial for many higher level cognitive functions, ranging from mental arithmetic to reasoning and problem solving. Likewise, the ability to learn and categorize novel concepts forms an indispensable part of human cognition. However, very little is known about the relationship between working memory and categorization. This…

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models…

In this article, I survey the integrated connectionist/symbolic (ICS) cognitive architecture in which higher cognition must be formally characterized on two levels of description. At the microlevel, parallel distributed processing (PDP) characterizes mental processing; this PDP system has special organization in virtue of which it can be…

A biologically detailed computational model is described of how categorization judgments become automatic in tasks that depend on procedural learning. The model assumes 2 neural pathways from sensory association cortex to the premotor area that mediates response selection. A longer and slower path projects to the premotor area via the striatum,…

From Aesop to Sun Tzu, the importance of working together has long been acknowledged. Yet as long as cooperation has existed, so have the difficulties associated with it. Pooling two fields might mean twice the power, but this union also brings twice the jargon, twice the competing theories, and twice the head butting. Nonetheless, in this…

The study involving 60 learning disabled (LD) and 30 normal achieving seventh through ninth graders was designed to identify adolescents homogeneously defined as exhibiting a "specific learning disability in arithmetic" and to determine if the cognitive processes (visual-spatial, visual-reasoning, and visual-memory) are related to the academic…