Lindsey E. Richland

The pretesting effect: Do unsuccessful retrieval attempts enhance learning?

Testing previously studied information enhances long-term memory, particularly when the information is successfully retrieved from memory. The authors examined the effect of unsuccessful retrieval attempts on learning. Participants in 5 experiments read an essay about vision. In the test condition, they were asked about embedded concepts before reading the passage; in the extended study condition, they were given a longer time to read the passage. To distinguish the effects of testing from attention direction, the authors emphasized the tested concepts in both conditions, using italics or bolded keywords or, in Experiment 5, by presenting the questions but not asking participants to answer them before reading the passage. Posttest performance was better in the test condition than in the extended study condition in all experiments--a pretesting effect--even though only items that were not successfully retrieved on the pretest were analyzed. The testing effect appears to be attributable, in part, to the role unsuccessful tests play in enhancing future learning.

Teaching the Conceptual Structure of Mathematics

Many students graduate from K–12 mathematics programs without flexible, conceptual mathematics knowledge. This article reviews psychological and educational research to propose that refining K–12 classroom instruction such that students draw connections through relational comparisons may enhance their long-term ability to transfer and engage with mathematics as a meaningful system. We begin by examining the mathematical knowledge of students in one community college, reviewing results that show even after completing a K–12 required mathematics sequence, these students were unlikely to flexibly reason about mathematics. Rather than drawing relationships between presented problems or inferences about the representations, students preferred to attempt previously memorized (often incorrect) procedures (Givvin, Stigler, & Thompson, 2011; Stigler, Givvin, & Thompson, 2010). We next describe the relations between the cognition of flexible, comparative reasoning and experimentally derived strategies for supporting students’ ability to make these connections. A cross-cultural study found that U.S. teachers currently use these strategies much less frequently than their international counterparts (Hiebert et al., 2003; Richland, Zur, & Holyoak, 2007), suggesting that these practices may be correlated with high student performance. Finally, we articulate a research agenda for improving and studying pedagogical practices for fostering students’ relational thinking about mathematics.

Early Executive Function Predicts Reasoning Development

Analogical reasoning is a core cognitive skill that distinguishes humans from all other species and contributes to general fluid intelligence, creativity, and adaptive learning capacities. Yet its origins are not well understood. In the study reported here, we analyzed large-scale longitudinal data from the Study of Early Child Care and Youth Development to test predictors of growth in analogical-reasoning skill from third grade to adolescence. Our results suggest an integrative resolution to the theoretical debate regarding contributory factors arising from smaller-scale, cross-sectional experiments on analogy development. Children with greater executive-function skills (both composite and inhibitory control) and vocabulary knowledge in early elementary school displayed higher scores on a verbal analogies task at age 15 years, even after adjusting for key covariates. We posit that knowledge is a prerequisite to analogy performance, but strong executive-functioning resources during early childhood are related to long-term gains in fundamental reasoning skills.

A computational account of children's analogical reasoning: balancing inhibitory control in working memory and relational representation

Theories accounting for the development of analogical reasoning tend to emphasize either the centrality of relational knowledge accretion or changes in information processing capability. Simulations in LISA (Hummel & Holyoak, 1997, 2003), a neurally inspired computer model of analogical reasoning, allow us to explore how these factors may collaboratively contribute to the development of analogy in young children. Simulations explain systematic variations in United States and Hong Kong childrens performance on analogies between familiar scenes (Richland, Morrison & Holyoak, 2006; Richland, Chang, Morrison & Au, 2010). Specifically, changes in inhibition levels in the models working-memory system explain the developmental progression in US childrens ability to handle increases in relational complexity and distraction from object similarity during analogical reasoning. In contrast, changes in how relations are represented in the model best capture cross-cultural differences in performance between children of the same ages (3-4 years) in the United States and Hong Kong. We use these results and simulations to argue that the development of analogical reasoning in children may best be conceptualized as an equilibrium between knowledge accretion and the maturation of information processing capability.

Young Children's Analogical Reasoning across Cultures: Similarities and Differences.

A cross-cultural comparison between U.S. and Hong Kong preschoolers examined factors responsible for young childrens analogical reasoning errors. On a scene analogy task, both groups had adequate prerequisite knowledge of the key relations, were the same age, and showed similar baseline performance, yet Chinese children outperformed U.S. children on more relationally complex problems. Children from both groups were highly susceptible to choosing a perceptual or semantic distractor during reasoning when one was present. Taken together, these similarities and differences suggest that (a) cultural differences can facilitate better knowledge representations by allowing more efficient processing of relationally complex problems and (b) inhibitory control is an important factor in explaining the development of childrens analogical reasoning.

A Randomized Trial of an Elementary School Mathematics Software Intervention: Spatial-Temporal Math.

Abstract Fifty-two low performing schools were randomly assigned to receive Spatial-Temporal (ST) Math, a supplemental mathematics software and instructional program, in second/third or fourth/fifth grades or to a business-as-usual control. Analyses reveal a negligible effect of ST Math on mathematics scores, which did not differ significantly across subgroups defined by prior math proficiency and English Language Learner status. Two years of program treatment produced a nonsignificant effect. Publication of evaluation results from large-scale real-world supplemental mathematics instructional implementations such as this one can provide a realistic view of the possibilities, costs, and limitations of this and other computer aided instruction supplemental interventions.

The effects of mathematics instruction using spatial temporal cognition on teacher efficacy and instructional practices

This paper examined the effects of an instructional approach known as Spatial Temporal Mathematics (ST Math) on teacher beliefs about mathematics teaching. Participants were 339 elementary teachers teaching grades 2-5 who were randomly assigned to a control or treatment group. Hierarchical linear modeling was used to determine the effects of the intervention on self-efficacy, outcome expectancy, and instructional practices using scientific reasoning. While the treatment did not yield significant effects in teacher outcomes, our secondary analysis indicated that time on ST Math and the integration of ST Math into daily instructions were positively associated with teacher efficacy and instructional practices using scientific reasoning. Implications of the results on teacher beliefs about mathematics teaching are discussed.

Linking Gestures: Cross-Cultural Variation During Instructional Analogies

Deictic linking gestures, hand and arm motions that physically embody links being communicated between two or more objects in the shared communicative environment, are explored in a cross-cultural sample of mathematics instruction. Linking gestures are specifically examined here when they occur in the context of communicative analogies designed to link two distinct yet mutually informative representations. Video coding of eighth-grade mathematics lessons in the United States, Japan, and Hong Kong revealed that teachers in the higher achieving regions (Hong Kong and Japan) used reliably more linking gestures concurrent with verbal linkages than did U.S. teachers. Further, they were significantly more likely to tailor their gesture use to the recency of students’ experiences with source than U.S. teachers. The overall data align with growing evidence that U.S. teachers may not systematically capitalize on pedagogical opportunities to draw linkages between representations and that gestures may play a key role in doing so.

Developing structured representations

Leech et al.s model proposes representing relations as primed transformations rather than as structured representations (explicit representations of relations and their roles dynamically bound to fillers). However, this renders the model unable to explain several developmental trends (including relational integration and all changes not attributable to growth in relational knowledge). We suggest looking to an alternative computational model that learns structured representations from examples.

Working memory predicts children’s analogical reasoning

Analogical reasoning is the cognitive skill of drawing relationships between representations, often between prior knowledge and new representations, that allows for bootstrapping cognitive and language development. Analogical reasoning proficiency develops substantially during childhood, although the mechanisms underlying this development have been debated, with developing cognitive resources as one proposed mechanism. We explored the role of executive function (EF) in supporting childrens analogical reasoning development, with the goal of determining whether predicted aspects of EF were related to analogical development at the level of individual differences. We assessed 5- to 11-year-old childrens working memory, inhibitory control, and cognitive flexibility using measures from the National Institutes of Health Toolbox Cognition battery. Individual differences in childrens working memory best predicted performance on an analogical mapping task, even when controlling for age, suggesting a fundamental interrelationship between analogical reasoning and working memory development. These findings underscore the need to consider cognitive capacities in comprehensive theories of childrens reasoning development.