An eye for relations: eye-tracking indicates long-term negative effects of operational thinking on understanding of math equivalence

Prior knowledge in the domain of mathematics can sometimes interfere with learning and performance in that domain. One of the best examples of this phenomenon is in students’ difficulties solving equations with operations on both sides of the equal sign. Elementary school children in the U.S. typically acquire incorrect, operational schemata rather than correct, relational schemata for interpreting equations. Researchers have argued that these operational schemata are never unlearned and can continue to affect performance for years to come, even after relational schemata are learned. In the present study, we investigated whether and how operational schemata negatively affect undergraduates’ performance on equations. We monitored the eye movements of 64 undergraduate students while they solved a set of equations that are typically used to assess children’s adherence to operational schemata (e.g., 3 + 4 + 5 = 3 + __). Participants did not perform at ceiling on these equations, particularly when under time pressure. Converging evidence from performance and eye movements showed that operational schemata are sometimes activated instead of relational schemata. Eye movement patterns reflective of the activation of relational schemata were specifically lacking when participants solved equations by adding up all the numbers or adding the numbers before the equal sign, but not when they used other types of incorrect strategies. These findings demonstrate that the negative effects of acquiring operational schemata extend far beyond elementary school.     

Continuity in Representation Between Children and Adults: Arithmetic Knowledge Hinders Undergraduates' Algebraic Problem Solving

This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184) solved addition facts or participated in one of several control conditions. Those who solved addition facts were less likely to solve prealgebra equations (e.g., 6 + 8 +4 = 7 + __) correctly under speeded conditions. In a fourth experiment, the negative effects of solving arithmetic problems extended to undergraduates (N = 74) solving algebra problems with no time pressure. Taken together, results suggest that arithmetic activates knowledge that hinders performance on algebra problems. Thus, an operational view of equations, which is prevalent in children, does not seem to be revised or abandoned, even after years of experience with algebra.     

The Role of Non-Numerical Stimulus Features in Approximate Number System Training in Preschoolers from Low-Income Homes

Recent findings have suggested that adults’ and children’s approximate number system (ANS) acuity may be malleable through training, but research on ANS acuity has largely been conducted with adults and children who are from middle- to high-income homes. We conducted 2 experiments to test the malleability of ANS acuity in preschool-aged children from low-income homes and to test how non-numerical stimulus features affected performance. In Experiment 1, mixed-effects models indicated that children significantly improved their ratio achieved across training. Children’s change in probability of responding correctly across sessions was qualified by an interaction with surface area features of the arrays such that children improved their probability of answering correctly across sessions on trials in which numerosity conflicted with the total surface area of object sets significantly more than on trials in which total surface area positively correlated with numerosity. In Experiment 2, we found that children who completed ANS acuity training performed better on an ANS acuity task compared with children in a control group, but they only did so on ANS acuity trials in which numerosity conflicted with the total surface area of object sets. These findings suggest that training affects ANS acuity in children from low-income homes by fostering an ability to focus on numerosity in the face of conflicting non-numerical stimulus features.     

Effects of pain acceptance and pain control strategies on physical impairment in individuals with chronic low back pain

Psychosocial treatments for chronic pain are effective. There is a need, however, to understand the processes involved in determining how these treatments contribute to behavior change. Control and acceptance strategies represent two potentially important processes involved in treatment, although they differ significantly in approach. Results from laboratory-based studies suggest that acceptance-oriented strategies significantly enhance pain tolerance and behavioral persistence, compared with control-oriented strategies. There is a need, however, to investigate processes of acceptance and control directly in clinical settings. The present study investigated the effects of three brief instructional sets (pain control, pain acceptance, continued practice) on demonstrated physical impairment in 74 individuals with chronic low back pain using an analogue experimental design. After controlling for baseline performance, the pain acceptance group demonstrated greater overall functioning on a set of 7 standardized physical tasks relative to the other two groups, which did not differ from one another. Further, the acceptance group exhibited a 16.3% improvement in impairment, whereas the pain control group worsened by 8.3% and the continued practice group improved by 2.5%. These results suggest that acceptance may be a key process involved in behavior change in individuals with chronic pain.     

The impact of parental divorce on the attainment of the developmental tasks of young adulthood

The purpose of this study was to assess the impact of parental divorce on young adult development. One hundred twenty-five participants provided demographic information and completed the PAFS-Q (college version) and the conflict subscale of the Family Environment Scale. Results indicate that parental divorce and family conflict significantly affect developmental task attainment. The interactions between sex and age and family structure (i.e., single-parent or stepfamily) were also significant predictors of post-divorce task attainment. Implications of these results for therapists as well as recommendations for future research are provided.This is a revised version of a paper presented at the annual conference of the American Psychological Association, Los Angles, California, August 1994.     

Components of dental fear in adults?

The functional relatedness between dental fear and multiple other fears was studied in a normative sample of 285 undergraduates. Rachman and Lopatka's work on the inter-dependence of multiple fears within individuals, as well as Lang's bioinformational theory of emotion, provided a theoretical background for this investigation. Fears about social contact, pain, mutilation (e.g. injury, blood, disfigurement), and being closed-in were assessed within the realm of verbal report; they were studied as possible components and/or concomitants of the dental fear construct. Multiple regression analyses with these variables utilized the Dental Fear Survey total score as a criterion variable. Fear of pain was found to be the most significant predictor of dental fear in both males and females. For females only, mutilation fear was the next strongest determinant. Fear of being closed-in was an additional significant dental fear predictor for both sexes. The possible role of social fears in the manifestation of dental fear was not confirmed and awaits further investigation. Results were consistent with the idea that there may often be a moderate degree of functional dependence between dental fear and the other fears identified here.