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.     

A study of the relationship between the Stroop effect and reading age in dyslexic subjects

40 dyslexic subjects were given a version of the Stroop test and the magnitude of interference was plotted as a function of reading age as measured by the British Ability Scale. A negative linear relationship emerged, such that greater reading proficiency was associated with less interference. This result is discussed in the context of LaBerge and Samuel's theory of automatic information processing in reading.     

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.     

Learning opportunities from group discussions: warrants become the objects of debate

In the mathematics education literature, there is currently a debate about the mechanisms by which group discussion can contribute to mathematical learning and under what conditions this learning is likely to occur. In this paper, we contribute to this debate by illustrating three learning opportunities that group discussions can create. In analyzing a videotaped episode of eight middle school students discussing a statistical problem, we observed that these students frequently challenged the arguments that their colleagues presented. These challenges invited students to be explicit about what mathematical principles, or warrants, they were implicitly using as a basis for their mathematical claims, in some cases recognize the modes of reasoning they were using were invalid and reject these modes of reasoning, and in other cases, attempt to provide deductive support to justify why their modes of reasoning were appropriate. We then describe what social and environmental conditions allowed the discussion analyzed in this paper to occur.

Genetic Change and Continuity from Fourteen to Twenty Months: The MacArthur Longitudinal Twin Study

Genetic change as well as continuity was investigated within the domains of temperament, emotion, and cognition/language for 200 pairs of twins assessed at 14 and 20 months of age in the laboratory and home. The second year of life is marked by change rather than continuity: correlations from 14 to 20 months averaged about .30 for observational measures of temperament and emotion, about .40 for language measures, and about .50 for mental development. 2 types of genetic change were examined: changes in the magnitude of genetic influence (heritability) and genetic contributions to change from 14 to 20 months. In general, heritability estimates were similar at 14 and 20 months. Evidence for genetic influence on change from 14 to 20 months emerged for several measures, implying that heritability cannot be equated with stability. Analyses of continuity indicated that genetic factors are largely responsible for continuity from 14 to 20 months.     

Causal modeling of secondary science students' intentions to enroll in physics

The purpose of this study was to explore the utility of the theory of planned behavior model developed by social psychologists for understanding and predicting the behavioral intentions of secondary science students regarding enrolling in physics. In particular, the study used a three-stage causal model to investigate the links from external variables to behavioral, normative, and control beliefs; from beliefs to attitudes, subjective norm, and perceived behavioral control; and from attitudes, subjective norm, and perceived behavioral control to behavioral intentions. The causal modeling method was employed to verify the underlying causes of secondary science students' interest in enrolling physics as predicted in the theory of planned behavior. Data were collected from secondary science students (N = 264) residing in a central Texas city who were enrolled in earth science (8th grade), biology (9th grade), physical science (10th grade), or chemistry (11th grade) courses. Cause-and-effect relationships were analyzed using path analysis to test the direct effects of model variables specified in the theory of planned behavior. Results of this study indicated that students' intention to enroll in a high school physics course was determined by their attitude toward enrollment and their degree of perceived behavioral control. Attitude, subjective norm, and perceived behavioral control were, in turn, formed as a result of specific beliefs that students held about enrolling in physics. Grade level and career goals were found to be instrumental in shaping students' attitude. Immediate family members were identified as major referents in the social support system for enrolling in physics. Course and extracurricular conflicts and the fear of failure were shown to be the primary beliefs obstructing students' perception of control over physics enrollment. Specific recommendations are offered to researchers and practitioners for strengthening secondary school students' intentions to study physics.