Children's representation of symbolic and nonsymbolic magnitude examined with the priming paradigm

How people process and represent magnitude has often been studied using number comparison tasks. From the results of these tasks, a comparison distance effect (CDE) is generated, showing that it is easier to discriminate two numbers that are numerically further apart (e.g., 2 and 8) compared with numerically closer numbers (e.g., 6 and 8). However, it has been suggested that the CDE reflects decisional processes rather than magnitude representation. In this study, therefore, we investigated the development of symbolic and nonsymbolic number processes in kindergartners and first, second, and sixth graders using the priming paradigm. This task has been shown to measure magnitude and not decisional processes. Our findings revealed that a priming distance effect (PDE) is already present in kindergartners and that it remains stable across development. This suggests that formal schooling does not affect magnitude representation. No differences were found between the symbolic and nonsymbolic PDE, indicating that both notations are processed with comparable precision. Finally, a poorer performance on a standardized mathematics test seemed to be associated with a smaller PDE for both notations, possibly suggesting that children with lower mathematics scores have a less precise coding of magnitude. This supports the defective number module hypothesis, which assumes an impairment of number sense.     

A review of: “Philosophy and psychotherapy”

E. Erwin (1997) Philosophy and Psychotherapy, London: Sage, pp. 192, $37.50 (hb), $12.95 (pb)     

A review of: “Suicide: The tragedy of hopelessness”

David Aldridge (1997) Suicide: the Tragedy of Hopelessness, London: Jessica Kingsley, $15.95     

Concurrent validity of approximate number sense tasks in adults and children

Reasoning with non-symbolic numerosities is suggested to be rooted in the Approximate Number System (ANS) and evidence pointing to a relationship between the acuity of this system and mathematics is available. In order to use the acuity of this ANS as a screening instrument to detect future math problems, it is important to model ANS acuity over development. However, whether ANS acuity and its development have been described accurately can be questioned. Namely, different tasks were used to examine the developmental trajectory of ANS acuity and studies comparing performances on these different tasks are scarce. In the present study, we examined whether different tasks designed to measure the acuity of the ANS are comparable and lead to related ANS acuity measures (i.e., the concurrent validity of these tasks). We contrasted the change detection task, which is used in infants, with tasks that are more commonly used in older children and adults (i.e., comparison and same-different tasks). Together, our results suggest that ANS acuity measures obtained with different tasks are not related. This poses serious problems for the comparison of ANS acuity measures derived from different tasks and thus for the establishment of the developmental trajectory of ANS acuity.     

What can the same–different task tell us about the development of magnitude representations?

We examined the development of magnitude representations in children (Exp 1: kindergartners, first-, second- and sixth graders, Exp 2: kindergartners, first-, second- and third graders) using a numerical same-different task with symbolic (i.e. digits) and non-symbolic (i.e. arrays of dots) stimuli. We investigated whether judgments in a same-different task with digits are based upon the numerical value or upon the physical similarity of the digits. In addition, we investigated whether the numerical distance effect decreases with increasing age. Finally, we examined whether the performance in this task is related to general mathematics achievement. Our results reveal that a same-different task with digits is not an appropriate task to study magnitude representations, because already late kindergarteners base their responses on the physical similarity instead of the numerical value of the digits. When decisions cannot be made on the basis of physical similarity, a similar numerical distance effect is present over all age groups. This suggests that the magnitude representation is stable from late kindergarten onwards. The size of the numerical distance effect was not related to mathematical achievement. However, children with a poorer mathematics achievement score seemed to have more difficulties to link a symbol with its corresponding magnitude.     

The Effects of Kenyan Child-Raising Practices on Adult Life

The study investigated the effects on adult behavior of child-raising practices in Nairobi, Kenya. The research sample consisted of 11 adult men and women from polygamous (five), monogamous (five) and single parent (one) backgrounds. Additionally, the sample included adult participants from 9 social situations and, 42 clinical interviews from a counseling center and also from participant observation. Child-rearing practices significantly impacted personal qualities in Kenyan adults. The positive effects were: respect, diligence, determination, resilience, perseverance and tolerance in relationships. Among the negative effects were: perfectionism, poor self-image, underlying anger, fear and mistrust.     

The reliability of and the relation between non-symbolic numerical distance effects in comparison, same-different judgments and priming

The development of number processing is generally studied by examining the performance on basic number tasks (comparison task, same-different judgment, and priming task). Using these tasks, so-called numerical distance effects are obtained. All these effects are generally explained by assuming a magnitude representation related to a mental number line: magnitudes are represented from left to right with partially overlapping representations for nearby numbers. In this study, we compared the performance of adults on these different tasks using non-symbolic stimuli. First, we investigated whether the effects obtained in these behavioral tasks are reliable. Second, we examined the relation between the three different effects. The results showed that the observed effects in the case of the comparison task and the same-different task proved to be reliable. The numerical distance effect obtained in the priming task, however, was not reliable. In addition, a correlation was found between the distance effects in the comparison task and the same-different task. The priming distance effect did not correlate with the other two effects. These results suggest important differences between distance effects obtained under automatic and intentional task instructions regarding the use of them as indices of mathematical ability.