Pathways to mathematics: longitudinal predictors of performance.

A model of the relations among cognitive precursors, early numeracy skill, and mathematical outcomes was tested for 182 children from 4.5 to 7.5 years of age. The model integrates research from neuroimaging, clinical populations, and normal development in children and adults. It includes 3 precursor pathways: quantitative, linguistic, and spatial attention. These pathways (a) contributed independently to early numeracy skills during preschool and kindergarten and (b) related differentially to performance on a variety of mathematical outcomes 2 years later. The success of the model in accounting for performance highlights the need to understand the fundamental underlying skills that contribute to diverse forms of mathematical competence.

Gender differences in the correlates of self-referent word use: authority, entitlement, and depressive symptoms.

Past research shows that self-focused attention is robustly positively related to depression, and women are more likely than men to self-focus in response to depressed mood (e.g., R. Ingram, 1990; S. Nolen-Hoeksema, 1987). The goal of the current study was to further delineate gender differences in the correlates of self-focus as measured through the frequency of spontaneous use of self-referencing words. The frequency of such word use during a life history interview was correlated with self-reports, observations by clinically trained interviewers, and personality judgments by acquaintances. Results indicated that the relationship between self-reference and observations of depressive symptoms was stronger for women than men, and the relationship between self-reference and narcissistic authority and entitlement was stronger for men than for women. Acquaintance ratings supported these correlates. These findings illuminate the importance of using multiple measures and paying attention to gender differences in research on self-focus.

Knowledge of counting principles: how relevant is order irrelevance?

Most children who are older than 6 years of age apply essential counting principles when they enumerate a set of objects. Essential principles include (a) one-to-one correspondence between items and count words, (b) stable order of the count words, and (c) cardinality-that the last number refers to numerosity. We found that the acquisition of a fourth principle, that the order in which items are counted is irrelevant, follows a different trajectory. The majority of 5- to 11-year-olds indicated that the order in which objects were counted was relevant, favoring a left-to-right, top-to-bottom order of counting. Only some 10- and 11-year-olds applied the principle of order irrelevance, and this knowledge was unrelated to their numeration skill. We conclude that the order irrelevance principle might not play an important role in the development of children's conceptual knowledge of counting.

Personality as manifest in word use: correlations with self-report, acquaintance report, and behavior.

The use of words is one of the most direct means of expressing thoughts and feelings. However, past studies have had limited success in correlating word use with personality. The purpose of the present study was to identify categories of word use relevant to personality using a broad range of personality data. Using data from 181 participants, the present study correlated word use within a 1-hr life history interview with self-judgments of personality, judgments of personality provided by close acquaintances (who were not exposed to the language sample), and behavioral ratings based on direct observation from a context entirely separate from that from which the language sample was derived. Several categories of word use yielded a large number of correlates with self- and acquaintance personality ratings and behavior. It is suggested that word use is related to personality to a larger degree than previously observed and deserves increased attention as a source of data in personality assessment.

What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through Grade 2.

The development of conceptual and procedural knowledge about counting was explored for children in kindergarten, Grade 1, and Grade 2 (N = 255). Conceptual knowledge was assessed by asking children to make judgments about three types of counts modeled by an animated frog: standard (correct) left-to-right counts, incorrect counts, and unusual counts. On incorrect counts, the frog violated the word-object correspondence principle. On unusual counts, the frog violated a conventional but inessential feature of counting, for example, starting in the middle of the array of objects. Procedural knowledge was assessed using speed and accuracy in counting objects. The patterns of change for procedural knowledge and conceptual knowledge were different. Counting speed and accuracy (procedural knowledge) improved with grade. In contrast, there was a curvilinear relation between conceptual knowledge and grade that was further moderated by children's numeration skills (as measured by a standardized test); the most skilled children gradually increased their acceptance of unusual counts over grade, whereas the least skilled children decreased their acceptance of these counts. These results have implications for studying conceptual and procedural knowledge about mathematics.