David F. Lohman

Adaptive reasoning: Componential and eye movement analysis of geometric analogy performance ☆

Abstract The present study explored individual differences in performance of a geometric analogies task. Whereas past studies employed true/false or two-alternative items, the present research included four-alternative items and studied eye movements and confidence judgements for each item performance as well as latency and error. Item difficulty proved to be a function of an interaction between the number of response alternatives and the number of elements in items, especially for subjects lower in fluid-analytic reasoning ability. Results were interpreted using two hypothesized performance strategies: constructive matching and response elimination. The less efficient of these, response elimination, seemed to be used more by lower ability subjects on more difficult items. While two previous theories resemble one or the other of these strategies, neither alone seems to capture the complexity of adaptive problem solving. It appears that a comprehensive theory should incorporate strategy shifting as a function of item difficulty and subject ability. Componential models, based in part on past research, revealed that a justification component was activated and deactivated depending upon the nature of the analogy being solved. In addition, two new components, spatial inference and spatial application, were identified as important on some items, suggesting that different geometric analogy items invoke different cognitive processing components. Thus, a comprehensive theory should also describe component activation and deactivation.

The Role of Nonverbal Ability Tests in Identifying Academically Gifted Students: An Aptitude Perspective

The first goal of this article is to discuss the role of nonverbal ability tests in the identification of academically gifted children. I note that most nonverbal tests measure verbally mediated cognitive processes, that they are neither “culture free” nor “culture fair,” and that we have known these facts for a very long time. I show that selecting students for gifted and talented programs on the basis of such tests would exclude the majority of the most academically accomplished students in all ethnic groups. The second goal is to propose a better method for identifying gifted students. I argue that the critical issue is readiness for a particular type of educational opportunity. The cognitive aspects of readiness are evidenced first in students’ levels of knowledge and skill in particular domains and secondarily in their abilities to reason in the symbol systems used to communicate new knowledge in these domains. This applies to both minority and majority students. Therefore, the most academically talented minority students are those who show the strongest current achievement in particular domains and the best ability to reason in the symbol systems required for the acquisition of new knowledge in those domains. I also argue that, although current accomplishment can be measured on a common scale, judgments about potential must always be made relative to circumstances.

Human Intelligence: An Introduction to Advances in Theory and Research

Recent advances in three research traditions are summarized: trait theories of intelligence, information-processing theories of intelligence, and general theories of thinking. The discussion of trait theories of intelligence focuses on the theory of fluid and crystallized abilities, particularly recent elaborations of this theory proposed by Horn (1985) and by Snow (1981): Their work provides a convenient framework for the discussion of information-processing theories of intelligence. I summarize attempts to build process theories of the major ability factors identified in Horn’s (1985) version of this ability model: mental speed, verbal-crystallized abilities, fluid-reasoning abilities, and spatial-visualization abilities. I discuss Sternberg’s (1985) recent attempts to develop a comprehensive theory of intelligence and ask how a theory of intelligence might be derived from the sort of general theories of thinking currently advanced in cognitive psychology and artificial intelligence (AI). The paper concludes with some speculations about the meaning of the construct intelligence and some suggestions for research on it.

The effect of speed-accuracy tradeoff on sex differences in mental rotation

This experiment examined the effects of sex differences in the form of speed-accuracy curves on sex differences in rate of mental rotation. Eighty-nine subjects attempted 1,200 rotation problems similar to those used by Shepard and Metzler (1971). Stimulus exposure was varied systematically over a wide range, and response accuracy was determined at each exposure. Speed-accuracy curves were then fit using an exponential function similar to one proposed by Wickelgren (1977). Results showed that apparent differences between males and females in rate of rotation are explained by sex differences in the shape of the speed-accuracy curves, with females reaching asymptote sooner on trials requiring more rotation. Similar effects were obtained in a comparison of subjects high and low in spatial ability.

Teaching and Testing to Develop Fluid Abilities

Fluid abilities are important both as aptitudes for success in formal schooling and as outcomes of formal schooling. However, the aptitude function has been overemphasized, and the outcome function ignored altogether, primarily because fluid abilities are often mistakenly thought to be innate. Two methods for developing and assessing these abilities are discussed. In the first method, students are asked to solve increasingly unfamiliar problems in a domain. This usually requires the adaptation of existing problem-solving strategies or the assembly of new strategies to solve increasingly ill-structured problems. In the second method, students are required to organize knowledge in new ways or to view it from different perspectives. In both cases, assessment requires that students’ personal perspectives be elicited. This raises several difficult philosophical and psychometric problems. These problems and the implications for education are discussed.

Training spatial abilities: Effects of practice on rotation and synthesis tasks

Abstract Three studies are reported. In the first study, changes in performance on four spatial tests were examined for eighty-three subjects who attempted 1,200 three-dimensional rotation problems. Gains in accuracy in solving these problems averaged over 1 SD from the first to the last block of trials. Gains on the reference tests were also substantial, ranging from over 1 SD on a speeded rotation test to approximately .5 SD on a more difficult form-board test. In the second study, fifty subjects were administered the same spatial tests, but without practice on rotation problems. The large gains in Study 1 appeared to be attributable to practice on the tests. In the third study, 385 subjects attempted 144 mental synthesis problems. Subjects were randomly assigned to a feedback or to a no-feedback condition. Females in the feedback condition showed the greatest reduction in errors from the first to the second half of the test. However, improvements were noted only for a specific type of foil. Results of all three studies are discussed in terms of Andersons (1983) model of skill learning and fact acquisition.

Identifying Academically Gifted English- Language Learners Using Nonverbal Tests A Comparison of the Raven, NNAT, and CogAT

In this study, the authors compare the validity of three nonverbal tests for the purpose of identifying academically gifted English-language learners (ELLs). Participants were 1,198 elementary children (approximately 40% ELLs). All were administered the Raven Standard Progressive Matrices (Raven), the Naglieri Nonverbal Ability Test (NNAT), and Form 6 of the Cognitive Abilities Test (CogAT). Results show that the U.S. national norms for the Raven substantially overestimate the number of high-scoring children; that because of errors in norming, the NNAT overestimates the number of both high-scoring and low-scoring children; that primary-level ELL children score especially poorly on the NNAT; that the standard error of measurement was twice as large for the NNAT as for the Raven or the CogAT; that ELL children scored .5 to .67 standard deviations lower than non-ELL children on the three nonverbal tests; and that none of the nonverbal tests predict achievement for ELL students very well. Putting Research to Use: Do nonverbal reasoning tests level the field for ELL children? Many practitioners have assumed that they do. However ELL children in this study scored 8 to 10 points lower than non-ELL children on the three nonverbal tests. The study also shows that practitioners cannot assume that national norms on the tests are of comparable quality. When put on the same scale as CogAT, Raven scores averaged 10 points higher than CogAT and NNAT scores. For NNAT, the mean is correct but the variability was up to 40% too large. Thus, when using national norms, both the Raven and NNAT will substantially overestimate the number of high-scoring children.

Dimensions and Components of Individual Differences in Spatial Abilities

The goal of this chapter is to review advances in the study of individual differences in spatial abilities and to consider some of the practical implications of this work. There are many reasons for the study of spatial cognition in general and spatial ability in particular. First, it is of theoretical and practical significance to understand how individuals represent the physical world in which they operate. Evidence exists for a theoretical separation of spatial representations and semantic representations. Second, there is a substantial literature suggesting the existence of several spatial abilities which are differentiable from general ability and from verbal abilities. Third, there appear to be important sex differences in some spatial abilities. Fourth, measures of spatial ability frequently add unique variance to the prediction of performance in certain courses such as engineering design or graphics and occupations such as mechanic, architect, or pilot.

An Aptitude Perspective on Talent: Implications for Identification of Academically Gifted Minority Students.

The identification of academically gifted children from the perspective of aptitude theory is discussed. Aptitude refers to the degree of readiness to learn and to perform well in a particular situation or domain. The primary aptitudes for academic success are (a) prior achievement in a domain, (b) the ability to reason in the symbol systems used to communicate new knowledge in that domain, (c) interest in the domain, and (d) persistence in the type of learning environments offered for the attainment of expertise in the domain. Careful attention to the demands and affordances of different instructional environments enables educators to identify those individuals who are most ready to succeed in them. Although the principles discussed here are useful for all students, they are particularly important for the identification of academically promising minority students.

Consistencies in sex differences on the Cognitive Abilities Test across countries, grades, test forms, and cohorts.

BACKGROUND Strand, Deary, and Smith (2006) reported an analysis of sex differences on the Cognitive Abilities Test (CAT) for over 320,000 UK students 11-12 years old. Although mean differences were small, males were overrepresented at the upper and lower extremes of the score distributions on the quantitative and non-verbal batteries and at the lower extreme of the verbal battery. AIMS We investigate whether these results were unique to the UK or whether they would be seen in other countries, at other grades, cohorts, or forms of the test. SAMPLE The sample consisted of three nationally representative cohorts of US students in grades 3 through 11 (total N=318,599) for the 1984, 1992, and 2000 standardizations of the US version of the CAT. METHODS We replicated and extended the Strand et al. (2006) results by comparing the proportions of males and females at each score level across countries (UK vs. US), grades (3-11), and cohorts/test forms (Forms 4, 5, and 6 standardized in 1984, 1992, and 2000, respectively). RESULTS The results showed an astonishing consistency in sex differences across countries, grades, cohorts, and test forms. CONCLUSIONS Implications for the current debate about sex differences in quantitative reasoning abilities are discussed.