The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges

This paper, written within a discursive perspective, explores the co-shaping of public and private discourse, and some of the circumstances under which one occasions the other, in the evolution of mathematical thinking by pairs of 13-year-olds. The discourse of six pairs of students, engaged in interpreting and graphing problem situations involving rational functions, was analyzed by means of recently developed methodological tools. The nature of the mathematics that emerged for each pair was found to be related to several factors that included the characteristics of the interpersonal object-level utterances both before and after the solution path had been generated, the degree of activity of the personal channels of the interlocutors, and the extent to which the thoughts of participants were made explicit in the public discourse. The analysis of the discursive interactions provided evidence that adolescents within novel problem situations can experience some difficulty in making their emergent thinking available to their partners in such a way that the interaction be highly mathematically productive for both of them. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dyslexia in Higher Education: an abuse of the system?

Following on from a previous article which examined concerns regarding the growing demand for public examination concessions on the basis of specific learning difficulties, this article further argues against the much used one‐off psychometric assessment procedure. The appropriateness is queried of a process which does not take into account such other factors as anxiety and emotional disturbance, inappropriate teaching, parental pressure, and socio‐cultural opportunity, all of which can produce a very similar pattern of failure. The nature of specific learning difficulties is also examined, plus a comment on differing assessment techniques. It was concluded that the ‘specific’ needs to be put back into an assessment of ‘specific learning difficulty’. So‐called dyslexia should be identified as the student's major special educational need and not merely as part of a more general learning problem. To do otherwise leaves the system open to abuse, and the long‐term interests of the students concerned will not be best served. The article does not necessarily reflect the views of Carolyn Blyth's employing authority.     

Acquisition of the Novel Name–Nameless Category (N3C) Principle

Toddlers' acquisition of the Novel Name–Nameless Category (N3C) principle was examined to investigate the developmental lexical principles framework and the applicability of the specificity hypothesis to relations involving lexical principles. In Study 1, we assessed the ability of 32 children between the ages of 16 and 20 months to use the N3C principle (operationally defined as the ability to fast map). As predicted, only some of the children could fast map. This finding provided evidence for a crucial tenet of the developmental lexical principles framewor: Some lexical principles are not available at the start of language acquisition. Children who had acquired the N3C principle also had significantly larger vocabularies and were significantly more likely to demonstrate 2-category exhaustive sorting abilities than children who had not acquired the principle. The 2 groups of children did not differ in either age or object permanence abilities. The 16 children who could not fast map were followed longitudinally until they attained a vocabulary spurt; at that time, their ability to fast map was retested (Study 2). Results provided a longitudinal replication of the findings of Study 1. Implications of these findings for both the developmental lexical principles framework and the specificity hypothesis are discussed.     

A Method for Studying Differential Distractor Functioning

A method of analyzing test item responses is advocated to examine differential item functioning through distractor choices of those who answer an item incorrectly. The analysis, called Differential Distractor Functioning, uses log-linear models of a three-way contingency table to examine whether there is an interaction of population subgroup and option choice when ability is held constant. The analysis is explained and is exemplified in an analysis of the Verbal portion of a recent Scholastic Aptitude Test.     

Capturing classroom context: The observation system as lens for assessment

Paper presented at the annual meeting of the American Educational Research Association, 1988, New Orleans.