Spontaneous Focusing on Quantitative Relations and the Development of Rational Number Conceptual Knowledge

The aim of the present set of studies was to explore primary school children’s Spontaneous Focusing On quantitative Relations (SFOR) and its role in the development of rational number conceptual knowledge. The specific goals were to determine if it was possible to identify a spontaneous quantitative focusing tendency that indexes children’s tendency to recognize and utilize quantitative relations in non-explicitly mathematical situations and to determine if this tendency has an impact on the development of rational number conceptual knowledge in late primary school. To this end, we report on six original empirical studies that measure SFOR in children ages five to thirteen years and the development of rational number conceptual knowledge in ten- to thirteen-year-olds. SFOR measures were developed to determine if there are substantial differences in SFOR that are not explained by the ability to use quantitative relations. A measure of children’s conceptual knowledge of the magnitude representations of rational numbers and the density of rational numbers is utilized to capture the process of conceptual change with rational numbers in late primary school students. Finally, SFOR tendency was examined in relation to the development of rational number conceptual knowledge in these students. Study I concerned the first attempts to measure individual differences in children’s spontaneous recognition and use of quantitative relations in 86 Finnish children from the ages of five to seven years. Results revealed that there were substantial inter-individual differences in the spontaneous recognition and use of quantitative relations in these tasks. This was particularly true for the oldest group of participants, who were in grade one (roughly seven years old). However, the study did not control for ability to solve the tasks using quantitative relations, so it was not clear if these differences were due to ability or SFOR. Study II more deeply investigated the nature of the two tasks reported in Study I, through the use of a stimulated-recall procedure examining children’s verbalizations of how they interpreted the tasks. Results reveal that participants were able to verbalize reasoning about their quantitative relational responses, but not their responses based on exact number. Furthermore, participants’ non-mathematical responses revealed a variety of other aspects, beyond quantitative relations and exact number, which participants focused on in completing the tasks. These results suggest that exact number may be more easily perceived than quantitative relations. As well, these tasks were revealed to contain both mathematical and non-mathematical aspects which were interpreted by the participants as relevant. Study III investigated individual differences in SFOR 84 children, ages five to nine, from the US and is the first to report on the connection between SFOR and other mathematical abilities. The cross-sectional data revealed that there were individual differences in SFOR. Importantly, these differences were not entirely explained by the ability to solve the tasks using quantitative relations, suggesting that SFOR is partially independent from the ability to use quantitative relations. In other words, the lack of use of quantitative relations on the SFOR tasks was not solely due to participants being unable to solve the tasks using quantitative relations, but due to a lack of the spontaneous attention to the quantitative relations in the tasks. Furthermore, SFOR tendency was found to be related to arithmetic fluency among these participants. This is the first evidence to suggest that SFOR may be a partially distinct aspect of children’s existing mathematical competences. Study IV presented a follow-up study of the first graders who participated in Studies I and II, examining SFOR tendency as a predictor of their conceptual knowledge of fraction magnitudes in fourth grade. Results revealed that first graders’ SFOR tendency was a unique predictor of fraction conceptual knowledge in fourth grade, even after controlling for general mathematical skills. These results are the first to suggest that SFOR tendency may play a role in the development of rational number conceptual knowledge. Study V presents a longitudinal study of the development of 263 Finnish students’ rational number conceptual knowledge over a one year period. During this time participants completed a measure of conceptual knowledge of the magnitude representations and the density of rational numbers at three time points. First, a Latent Profile Analysis indicated that a four-class model, differentiating between those participants with high magnitude comparison and density knowledge, was the most appropriate. A Latent Transition Analysis reveal that few students display sustained conceptual change with density concepts, though conceptual change with magnitude representations is present in this group. Overall, this study indicated that there were severe deficiencies in conceptual knowledge of rational numbers, especially concepts of density. The longitudinal Study VI presented a synthesis of the previous studies in order to specifically detail the role of SFOR tendency in the development of rational number conceptual knowledge. Thus, the same participants from Study V completed a measure of SFOR, along with the rational number test, including a fourth time point. Results reveal that SFOR tendency was a predictor of rational number conceptual knowledge after two school years, even after taking into consideration prior rational number knowledge (through the use of residualized SFOR scores), arithmetic fluency, and non-verbal intelligence. Furthermore, those participants with higher-than-expected SFOR scores improved significantly more on magnitude representation and density concepts over the four time points. These results indicate that SFOR tendency is a strong predictor of rational number conceptual development in late primary school children. The results of the six studies reveal that within children’s existing mathematical competences there can be identified a spontaneous quantitative focusing tendency named spontaneous focusing on quantitative relations. Furthermore, this tendency is found to play a role in the development of rational number conceptual knowledge in primary school children. Results suggest that conceptual change with the magnitude representations and density of rational numbers is rare among this group of students. However, those children who are more likely to notice and use quantitative relations in situations that are not explicitly mathematical seem to have an advantage in the development of rational number conceptual knowledge. It may be that these students gain quantitative more and qualitatively better self-initiated deliberate practice with quantitative relations in everyday situations due to an increased SFOR tendency. This suggests that it may be important to promote this type of mathematical activity in teaching rational numbers. Furthermore, these results suggest that there may be a series of spontaneous quantitative focusing tendencies that have an impact on mathematical development throughout the learning trajectory.

Interaction between the mineral content and the occurrence number of aquatic fungi in leaves submerged in a stream in the Atlantic rainforest, São Paulo, Brazil

Leaves of Ficus microcarpa L. f., Quercus robur L., and Alchornea triplinervia (Spreng.) Muell. Arg., submerged in a stream of the Atlantic rainforest in the "Reserva Biológica do Alto da Serra de Paranapiacaba", State of São Paulo, Brazil, were collected monthly, from April to November 1990, in order to determine the number of fungal occurrences (zoosporic fungi and aquatic Hyphomycetes), and the content of total N (%), total P (%), K+ (%), Ca+2 (%), Mg+2 (%), S+3 (%), Fe+3 (ppm), Cu+3 (ppm), Mn+2 (ppm), Zn+2 (ppm), Bo (ppm), Na+2 (ppm) and Al+3 (ppm). According to the tests of Kruskal-Wallis, Mann-Whitney and Wilcoxon, the means of the mineral content of the three types of leaves were significantly different, except for Mg+2 (%), Mn+2 (ppm), Zn+2 (ppm) and Na+2 (ppm). On comparing the mineral content with the number of fungal occurrence, an independence test showed a positive correlation between the presence of zoosporic fungi on the leaves of A. triplinervia and the total nitrogen, phosphorus and S+3 content, whereas the aquatic Hyphomycetes depended on the amount of Ca+2 available. Regarding leaves of F. microcarpa, the occurrence of zoosporic fungi was linked to the S+3 level, and the presence of aquatic Hyphomycetes, to the content of K+, Ca+2, S+3 and Bo. On Q. robur leaves, zoosporic fungi showed a positive correlation with the Ca+2 content, but a negative one with Fe+3 and Al+3 levels, while the occurrence of aquatic Hyphomycetes was influenced by the content of Ca+2, Mg+2, Fe+3, Al+3, Mn+2, Zn+2 and Na+2. The correlation between the occurrence number of aquatic Hyphomycetes and a high mineral content indicates that their nutritional requirements may be more complex than those of zoosporic fungi. Further studies are still required to understand the implications of this tendency on the diversity of aquatic native mycota.

Number of buried seeds and seedlings emergence in cerradão, cerrado and gallery forest soils at Pedregulho, Itirapina (SP), Brazil

This study was carried out at the site named Pedregulho in the "Estação Experimental de Itirapina", Itirapina, state of São Paulo, Brazil. Soil samples were collected in the rainy and in the dry season at three depths in the gallery forest, cerrado and cerradão. The total number of seeds was counted after being separated from the soil by wet sieving and the number of viable seeds was determined by emergence of seedlings in soil samples in a greenhouse. The number of seeds and of emerged seedlings decreases as soil samples become deeper. The number of seeds was much larger in the cerrado in the dry season than in the rainy season, but it was lower in the dry than in the rainy season in the gallery forest. The number of seeds in the cerradão was similar in both seasons. There was a heavy discrepancy between the total number of seeds and that of emerged seedlings.

Intrapopulational chromosome number variation in Zephyranthes sylvatica Baker (Amaryllidaceae: Hippeastreae) from Northeast Brazil

Zephyranthes Herb. is a taxonomically complex and cytologically variable group, with about 65 species of Neotropical distribution. Chromosome number variability in 32 individuals of a Zephyranthes sylvatica population from Northeast Brazil was investigated. Three cytotypes were found: 2n = 12 (one metacentric, four submetacentric and one acrocentric pairs), in 24 individuals; 2n = 12 + 1B, in five and three individuals with 2n = 18, a triploid cytotype. All diploid individuals showed chromosomes with polymorphism in pair one and two, while in triploids this polymorphism was observed in all chromosome triplets, generally with two homomorphic chromosomes and a higher or lower heteromorphic chromosome. All individuals had reticulated interfasic nucleus and a slightly asymmetric chromosome complement, with one metacentric chromosome pair and the others more submetacentric to acrocentric. These data confirm the cytological variability previously registered for the genus. Mechanisms involved in karyotypic evolution in this population are discussed.

Chromosome number in germplasm accessions of Paspalum notatum (Gramineae)

Chromosome numbers are reported for 127 germplasm accessions of Paspalum notatum maintained by EMBRAPA (Empresa Brasileira de Pesquisa Agropecuária) in two research centers in Brazil. Most accessions were collected in their natural habitats in Southern Brazil. Tetraploidy (2n = 40 chromosomes) was predominant (91% of the accessions studied), confirming previous reports for the species. Eleven accessions with 2n = 20 chromosomes, although collected in the wild, are possibly derived from 'Pensacola' bahiagrass, commonly cultivated in the area since its introduction from the United States in the 60's, for the establishment of permanent pastures.

Chromosome number and secondary constriction variation in 51 accessions of a citrus germplasm bank

The mitotic chromosomes of 51 citrus accessions from the Centro Nacional de Pesquisa em Mandioca e Fruticultura Tropical, Cruz das Almas, BA, Brazil, were analyzed. The sample included representatives of 20 Citrus species, one of Poncirus and seven hybrids. All accessions showed 2n = 18 without any evidence of numerical variation. The most clearly variable karyotype feature was the number and position of secondary constrictions (SECs). In 19 accessions the SECs were not identified, mainly due to the degree of chromatin condensation. In the remainder they varied in number from one to three per karyotype. They were found in the proximal region of one of the three largest chromosome pairs, in the terminal/subterminal region of a smaller chromosome or, more seldom, terminally in a larger chromosome. Only in a few cases were such constrictions observed simultaneously in both homologues of the same chromosome pair. The high variability of this karyotype feature may be due to the activation of this region in the previous interphase but may also indicate a high structural variability and heterozygosity of citrus germplasms

Spreading depression is facilitated in adult rats previously submitted to short episodes of malnutrition during the lactation period

Lactating rat dams were submitted to short episodes (1, 2 or 3 weeks) of nutritional restriction by receiving the "regional basic diet" (RBD, with 8% protein) of low-income human populations of Northeast Brazil. Their pups were then studied regarding the developmental effects on body and brain weights. When the rats reached adulthood, cortical susceptibility to the phenomenon of spreading depression (SD) was evaluated by performing electrophysiological recordings on the surface of the cerebral cortex. SD was elicited at 20-min intervals by applying 2% KCl for 1 min to a site on the frontal cortex and its occurrence was monitored at 2 sites in the parietal region by recording the electrocorticogram and the slow potential change of SD. When compared to control rats fed a commercial diet with 23% protein, early malnourished rats showed deficits in body and brain weights (10% to 60% and 3% to 15%, respectively), as well as increases in velocity of SD propagation (10% to 20%). These effects were directly related to the duration of maternal dietary restriction, with pups malnourished for 2 or 3 weeks presenting more intense weight and SD changes than those malnourished for 1 week. The effects of 1-week restrictions on SD were less evident in the pups malnourished during the second week of lactation and were more evident in pups receiving the RBD during the third week. The results indicate that short episodes of early malnutrition during the suckling period can affect body and brain development, as well as the cortical susceptibility to SD during adulthood. The data also suggest that the third week of lactation is the period during which the brain is most sensitive to malnutrition, concerning the effects on SD

Aversive stimulation during the stress-hyporesponsive period does not affect the number of corticotroph cells in neonatal male rats

Immunohistochemistry was used to evaluate the effects of neonatal handling and aversive stimulation during the first 10 days of life on the number of corticotrophs in the anterior lobe of the pituitary of 11-day-old male Wistar rats. Since adult rats handled during infancy respond with reduced corticosterone secretion in response to stressors and with less behavior inhibition in novel environments, we assumed that neonatal stimulation could affect pituitary morphology during this critical period of cell differentiation. Three groups of animals were studied: intact (no manipulation, N = 5), handled (N = 5) and stimulated (submitted to 3 different aversive stimuli, N = 5). The percentage of ACTH-immunoreactive cells in the anterior lobe of the pituitary (number of ACTH-stained cells divided by total number of cells) was determined by examining three slices per pituitary in which a minimum of 200 cells were counted by two independent researchers. Although animals during the neonatal period are less reactive to stress-like stimulation in terms of ACTH and corticosterone secretion, results showed that the relative number of ACTH-stained cells of neonatal handled (0.25 ± 0.01) and aversive stimulated (0.29 ± 0.03) rats was not significantly different from intact (0.30 ± 0.03) animals. Neonatal stimulation may have a differential effect on the various subpopulations of corticotroph cells in the anterior pituitary

Postnatal development of rats exposed to fluoxetine or venlafaxine during the third week of pregnancy

The aim of the present study was to compare the toxic effects of fluoxetine (F) (8 and 16 mg/kg) and venlafaxine (V) (40 and 80 mg/kg) administered during the third week of pregnancy on early development of rats. Both antidepressants were administered by gavage on pregnancy days 15 to 20 to groups of 10 to 12 animals each. Duration of gestation, food and water consumption, number of live pups and birth weight were recorded. Litters were culled to six pups at birth (day 1) and followed for growth until weaning (day 25). On day 60, a male and a female from each litter were injected with the 5-HT1 agonist, 5-methoxy-N,N-dimethyltryptamine (6 mg/kg, ip) and the serotonergic syndrome was graded. Fluoxetine but not venlafaxine reduced the duration of pregnancy when compared to the control (C) group (F = 21.1 days and C = 21.6 days, mean, P<0.02; maximum = 22 days and minimum = 21 days in both groups). The highest doses of both fluoxetine, 16 mg/kg (F16), and venlafaxine, 80 mg/kg (V80), reduced the food intake of pregnant rats, resulting in different rates of body weight gain during treatment (from pregnancy day 15 to day 20): F16 = 29.0 g, V80 = 28.7 g vs C = 39.5 g (median). Birth weight was influenced by treatment and sex (P<0.05; two-way ANOVA). Both doses of fluoxetine or venlafaxine reduced the body weight of litters; however, the body weight of litters from treated dams was equal to the weight of control litters by the time of weaning. At weaning there was no significant difference in weight between sexes. There was no difference among groups in number of live pups at birth, stillbirths, mortality during the lactation period or in the manifestation of serotonergic syndrome in adult rats. The occurrence of low birth weight among pups born to dams which did not show reduced food ingestion or reduction of body weight gain during treatment with lower doses of fluoxetine or venlafaxine suggests that these drugs may have a deleterious effect on prenatal development when administered during pregnancy. In addition, fluoxetine slightly but significantly affected the duration of pregnancy (about half a day), an effect not observed in the venlafaxine-treated groups.

Perinatal development and adult blood pressure

A growing body of evidence supports the concept of fetal programming in cardiovascular disease in man, which asserts that an insult experienced in utero exerts a long-term influence on cardiovascular function, leading to disease in adulthood. However, this hypothesis is not universally accepted, hence animal models may be of value in determining potential physiological mechanisms which could explain how fetal undernutrition results in cardiovascular disease in later life. This review describes two major animal models of cardiovascular programming, the in utero protein-restricted rat and the cross-fostered spontaneously hypertensive rat. In the former model, moderate maternal protein restriction during pregnancy induces an increase in offspring blood pressure of 20-30 mmHg. This hypertensive effect is mediated, in part, by fetal exposure to excess maternal glucocorticoids as a result of a deficiency in placental 11-ß hydroxysteroid dehydrogenase type 2. Furthermore, nephrogenesis is impaired in this model which, coupled with increased activity of the renin-angiotensin system, could also contribute to the greater blood pressure displayed by these animals. The second model discussed is the cross-fostered spontaneously hypertensive rat. Spontaneously hypertensive rats develop severe hypertension without external intervention; however, their adult blood pressure may be lowered by 20-30 mmHg by cross-fostering pups to a normotensive dam within the first two weeks of lactation. The mechanisms responsible for this antihypertensive effect are less clear, but may also involve altered renal function and down-regulation of the renin-angiotensin system. These two models clearly show that adult blood pressure is influenced by exposure to one of a number of stimuli during critical stages of perinatal development.

A priori estimation of accuracy and of the number of wells to be employed in limiting dilution assays

The use of limiting dilution assay (LDA) for assessing the frequency of responders in a cell population is a method extensively used by immunologists. A series of studies addressing the statistical method of choice in an LDA have been published. However, none of these studies has addressed the point of how many wells should be employed in a given assay. The objective of this study was to demonstrate how a researcher can predict the number of wells that should be employed in order to obtain results with a given accuracy, and, therefore, to help in choosing a better experimental design to fulfill one's expectations. We present the rationale underlying the expected relative error computation based on simple binomial distributions. A series of simulated in machina experiments were performed to test the validity of the a priori computation of expected errors, thus confirming the predictions. The step-by-step procedure of the relative error estimation is given. We also discuss the constraints under which an LDA must be performed.

Influence of the test situation on pup retrieval behavior of normal and undernourished lactating rats

Undernutrition of dams and pups disrupts the retrieval efficiency of mothers. However, if the mothers are assessed in their home cages, they spend more time with their litters. In the present study the effect of test conditions on pup retrieval behavior of mothers receiving a 25% (well-nourished group) and 8% casein diet (undernourished group) was examined. In agreement with previous studies, undernourished mothers spent more time with their litters than well-nourished dams as lactation proceeded. Pup retrieval behavior varied with test conditions. In the first experiment, the maternal behavior of dams was assessed by the standard procedure (pups were separated from their mother and scattered over the floor of the home cage). The mother was then returned and the number of retrieved pups was recorded. From day 3 to 8, the retrieval efficiency of undernourished dams decreased, while the retrieval efficiency of well-nourished mothers did not vary. In the second experiment, mothers were subjected to a single retrieval test (on day 9 of lactation) using the procedure described for experiment 1. No difference between well-nourished and undernourished mothers was observed. In the third experiment, seven-day-old pups were separated from the mothers and returned individually to a clean home cage. Dietary treatment did not affect the retrieval efficiency. However, undernourished dams reconstructed the nest more slowly than did well-nourished dams. Taken together, these results suggest that pup retrieval behavior of the undernourished mother is not impaired by dietary restriction when the maternal environment is disturbed minimally.

Plasma and testicular testosterone levels, volume density and number of Leydig cells and spermatogenic efficiency of rabbits

Plasma and tissue testosterone concentrations were determined by radioimmunoassay in 12 eight-month-old sexually mature New Zealand White rabbits and evaluated for possible associations with spermatogenic efficiency as well as with volume density and number of Leydig cells. Testicular tissue was processed histologically and histometry was performed in order to quantify germ cells, Sertoli cells and Leydig cells. Spermatogenic efficiency, reported as the ratios among germ cells (spermatogonia, primary spermatocytes and round spermatids) and by the ratio of germ cells to Sertoli cells, was not associated with testosterone levels. However, Leydig cell parameters such as number of Leydig cells per gram of testis, total number of Leydig cells per testis and percent cell volume of Leydig cell nuclei were correlated significantly with testosterone levels. The statistically significant correlation (r = 0.82, P<0.05) observed between testosterone levels and the number of Leydig cells per gram of testis suggests that, in the rabbit, the latter parameter can serve as a criterion for monitoring testosterone levels in this species under normal conditions.

Malnutrition during lactation as a metabolic imprinting factor inducing the feeding pattern of offspring rats when adults: The role of insulin and leptin

The aim of the present study was to determine the impact of malnutrition during early postnatal life and the feeding pattern of rat offspring when adults (2 months and 1 year old). In comparison with rats normally fed during lactation, we observed that adult offspring displayed a faster process of feeding reduction when a protein-free diet was offered. In addition, we studied the concentration of insulin and leptin in the lactating pups (10 days) and when these offspring became adult after the onset of a new feeding pattern induced by the protein-free diet. When the diet was changed at 60 days, the offspring malnourished during lactation displayed, after 3 days, a food intake reduction around 41.4 vs 14.2% of the control group. At 10 days of life, plasma leptin and insulin were higher in the malnourished pups when compared with normally fed rats (leptin: 4.6 ± 0.8 vs 2.25 ng/ml; insulin: 0.73 ± 0.12 vs 0.22 ± 0.03 ng/ml) while at 60 days they showed reduction of both hormones when compared with the control group (leptin: 1.03 ± 0.25 vs 1.43 ± 0.5 ng/ml; insulin: 0.54 ± 0.3 vs 0.61 ± 0.4 ng/ml). Despite the different food intake reductions, the malnourished and control rats displayed a similar reduction of insulin and leptin after 3 days of protein-free diet (from 60 to 63 days). The data suggest that the high concentration of insulin and leptin found at 10 days in the malnourished pups may elicit a sustained long-term and unique feeding pattern.

Dermal dendritic cell number correlates with serum autoantibody titers in Brazilian pemphigus foliaceus patients

Pemphigus foliaceus (PF) is an autoimmune bullous disease endemic in Brazil. Since serum IL-12 is increased in patients with PF and Langerhans cells (LC) produce IL-12, we titrated serum autoantibodies by indirect immunofluorescence, and quantified epidermal dendritic cells, known as LC, and dermal dendritic cells (DC). Biopsies of blistering lesions were obtained from 22 patients, 13 of whom were submitted to biopsy of both injured and of apparently healthy skin. The control groups consisted of skin from 8 cadavers and from 12 women submitted to breast plastic surgery. LC and DC were identified with anti-CD1a antibody and quantified by morphometric analysis. LC number in the lesion and in apparently healthy skin from PF patients was similar to that of both control groups. DC number in the injured skin (median = 0.94 DC/mm basement membrane) was higher than that of the cadaver group (median = 0.13 DC/mm basement membrane). In the 13 patients with biopsies of both injured and apparently healthy skin, LC and DC were present in larger numbers in the lesion. There was a direct correlation between DC number in the lesion of the PF group and serum autoantibody titers. This correlation was not observed for LC number. The increased number of DC in the lesion, as well as its direct correlation with serum autoantibody titers suggest the participation of DC in the pathogenesis of PF. The relationship between increased DC number and IL-12 in PF needs to be clarified.