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.

Leaf blade quantitative anatomy of sugarcane cultivars and clones

The objective of this study was to make a quantitative assess of the anatomic characteristics of leaf blade of the sugarcane cultivars RB855113, SP80-1842, SP80-1816, RB867515 and clone RB957689 presenting different sensitivity to the mixture of sodium trifloxysulfuron + ametryn herbicides. Compared to the other cultivars assessed, RB855113 cultivar, considered more sensitive to the herbicide mixture, presented relevant differences such as greater proportion of bulliform cells, greater tissue proportion in the transverse section of the leaf blade, greater stomata and trichome density on both surfaces, thinner epidermis on the adaxial surface and length of stomata on both surfaces. The external paraclinal wall of the bulliform cells was thinner than in the common epidermis cells in all the genotypes on the adaxial and abaxial surfaces. Multivariate analysis of the data on the variables considered most relevant to explain the herbicide penetration singled out the sensitive RB855113 from the other materials. Such characteristics can explain the greater penetration, and consequently, greater sensitivity of this cultivar to the sodium trifloxysulfuron + ametryn mixture.

Quantitative variables applied to phenological studies of Sargassum vulgare C. Agardh (Phaeophyceae - Fucales) from Ilha Grande Bay, State of Rio de Janeiro

The suitability of quantitative variables for phenological studies was evaluated in a population of the brown seaweed Sargassum vulgare from "Praia das Gordas", Angra dos Reis, Ilha Grande Bay, state of Rio de Janeiro. From June 1998 to May 1999, twenty adult individuals were randomly sampled at bimonthly intervals. Fifteen variables related to the vegetative and reproductive development of perennial and non-perennial parts of the individuals were quantified. Variables related to the non-perennial parts were more useful than those related to the perennial parts, because they showed a clear variation over the year. Vegetative development declined from June to October, and increased from October to February, when maximum median values of thallus height, total dry mass, non-perennial parts dry mass, and degree of branching were reached. This pattern coincided with those described for other species of the genus from warm temperate regions. Thallus height, a usually employed character in other phenological studies of Sargassum, showed lower coefficient of variation (53.2%) than those related to dry mass (72.0% to 182.3%). Peak of reproduction occurred from June to August, according to the following variables: fertile primary lateral branches number and dry mass and receptacles dry mass. Non-perennial parts dry mass and receptacles dry mass are recommended for phenological studies of S. vulgare. This methodological procedure avoids the sampling of the whole individual and warrants its regeneration from the perennial parts.

Quantitative Analysis of Novel Prostate Cancer Markers in Tissue

Prostate cancer is a heterogeneous disease affecting an increasing number of men all over the world, but particularly in the countries with the Western lifestyle. The best biomarker assay currently available for the diagnosis of the disease, the measurement of prostate specific antigen (PSA) levels from blood, lacks specificity, and even when combined with invasive tests such as digital rectal exam and prostate tissue biopsies, these methods can both miss cancers, and lead to overdiagnosis and subsequent overtreatment of cancers. Moreover, they cannot provide an accurate prognosis for the disease. Due to the high prevalence of indolent prostate cancers, the majority of men affected by prostate cancer would be able to live without any medical intervention. Their latent prostate tumors would not cause any clinical symptoms during their lifetime, but few are willing to take the risk, as currently there are no methods or biomarkers to reliably differentiate the indolent cancers from the aggressive, lethal cases that really are in need of immediate medical treatment. This doctoral work concentrated on validating 12 novel candidate genes for use as biomarkers for prostate cancer by measuring their mRNA expression levels in prostate tissue and peripheral blood of men with cancer as well as unaffected individuals. The panel of genes included the most prominent markers in the current literature: PCA3 and the fusion gene TMPRSS2-ERG, in addition to BMP-6, FGF-8b, MSMB, PSCA, SPINK1, and TRPM8; and the kallikrein-related peptidase genes 2, 3, 4, and 15. Truly quantitative reverse-transcription PCR assays were developed for each of the genes for the purpose, time-resolved fluorometry was applied in the real-time detection of the amplification products, and the gene expression data were normalized by using artificial internal RNA standards. Cancer-related, statistically significant differences in gene transcript levels were found for TMPRSS2-ERG, PCA3, and in a more modest scale, for KLK15, PSCA, and SPINK1. PCA3 RNA was found in the blood of men with metastatic prostate cancer, but not in localized cases of cancer, suggesting limitations for using this method for early cancer detection in blood. TMPRSS2-ERG mRNA transcripts were found more frequently in cancerous than in benign prostate tissues, but they were present also in 51% of the histologically benign prostate tissues of men with prostate cancer, while being absent in specimens from men without any signs of prostate cancer. PCA3 was shown to be 5.8 times overexpressed in cancerous tissue, but similarly to the fusion gene mRNA, its levels were upregulated also in the histologically benign regions of the tissue if the corresponding prostate was harboring carcinoma. These results indicate a possibility to utilize these molecular assays to assist in prostate cancer risk evaluation especially in men with initially histologically negative biopsies.

Quantitative features of Cedrela odorata L. wood (Meliaceae)

Cedrela odorata L. (Meliaceae) occurs in the Atlantic forest, Amazon rain forest, riparian forest of the country, and wetlands, which demand species adapted to their water conditions. Studies in ecological wood anatomy demonstrated that weather factors' variations have direct influence on the wood anatomical structure and that the fragmentation of the natural habitats is a direct cause of the edge effect which alters the abiotic aspects of the location, interfering consequently in its vegetation. A comparative analysis of 20 anatomical quantitative features of the wood structure was performed in populations of Cedrela odorata growing inside and on the edge of the swamp forest and granulometric analysis was made on the soil. The quantitative data were submitted to the Mann-Whitney's nonparametric test, presenting a statistically significant value decrease in the eleven wood features mean for the specimens growing in the edge of swamp forest.

Mating system in Myracrodruon urundeuva (Anarcadiaceae): implications for conservation genetics

The aims of this study were to investigate the mating system of a fragmented population of the dioecious tropical tree Myracrodruon urundeuva Allemão, using five microsatellite loci and the mixed mating and correlated mating models. The study was conducted in the Estação Ecológica de Paulo de Farias (436 ha), where the population occupies about 142 ha. The mating system was estimated using 514 open-pollinated offspring, collected from 30 seed-trees. Estimates of the multilocus outcrossing rate confirm that the species is dioecious (t m = 1.0). Low levels of mating among relatives were detected in the population (1 - t s = 0.020). The estimate of paternity correlation (r p(m)) indicated that offsprings were composed of mixtures of half-sibs and full-sibs, with the latter occurring at a low frequency (average of 0.148). The estimated coancestry coefficient within families (Θ = 0.147) was larger and the effective population size (Ne(v)) was lower (Ne(v) = 2.98) than expected in progenies from panmictic populations (Θ = 0.125, Ne(v) = 4, respectively). In terms of conservation, the results indicate that to retain an effective population size of 150, is necessary to collect seeds from at least 50 seed-trees.

Microphotometric scanning of chromatid gaps and breaks induced by AluI and BamHI in Chinese hamster ovary cells

Chromatid gaps and breaks induced by the restriction endonucleases AluI and BamHI in the long arm of chromosome 1 of Chinese hamster ovary cells were microphotometrically scanned and mapped to a quantitative G-band map. More than 50% of chromatid breaks appeared as chromatin losses of greater than 5% of the total arm length. The majority of chromatid gaps and breaks as well as chromatin losses induced by both restriction endonucleases were non-randomly located in a region from 0.35 to 0.65 relative length units of the long arm of chromosome 1. We suggest that the access of these endonucleases to chromosomal DNA depends on the local organization of the chromatin.

Family names and the length of the Y chromosome in Brazilian blacks

The variability of the lengths of the heterochromatic and euchromatic segments of the human Y chromosome was studied by a quantitative method of densitometric measurement in 60 normal and unrelated black individuals (30 with and 30 without devotional surnames), living in Salvador, Bahia, northeastern Brazil. Thirty normal and unrelated Caucasian individuals of European origin, living in Curitiba, Paraná, south Brazil, were included as controls. The heterochromatic segment and total Y chromosome lengths were greater in caucasians than in blacks without devotional surnames, and these were greater than in blacks with devotional surnames. These findings are in agreement with previous reports of a higher percentage of black ancestry in blacks carrying devotional surnames than those carrying non-devotional ones.

Genetics of resistance to the fungus Helminthosporium sativum in wheat: use of culture filtrates in tissue culture

Six wheat genotypes and their F1 and F2 generations were exposed to the action of Helminthosporium sativum culture filtrates to examine the genetics of hexaploid wheat resistance. The objective was to improve the efficiency of breeding programs by identifying the action and number of genes involved in the resistance. The varied response of the tested genotypes to the culture filtrates allowed division of the genotypes into four groups: resistant, moderately resistant, moderately susceptible and susceptible. This variability was detected in the progeny, suggesting that the parents have distinct genetic constitutions. Additive gene action predominated and genetic gain was shown to be possible through selection. The genetic control of the resistance trait seems to be complex because of the presence of gene interaction and the difficulty of eliminating the environmental effects. The inheritance seems to be oligogenic

Predicting variety composite means without diallel crossing

Prediction of variety composite means was shown to be feasible without diallel crossing the parental varieties. Thus, the predicted mean for a quantitative trait of a composite is given by: Yk = a1 sigmaVj + a2sigmaTj + a3 - a4, with coefficients a1 = (n - 2k)/k²(n - 2); a2 = 2n(k - 1)/k²(n - 2); a3 = n(k - 1)/k(n - 1)(n - 2); and a4 = n²(k - 1)/k(n - 1)(n - 2); summation is for j = 1 to k, where k is the size of the composite (number of parental varieties of a particular composite) and n is the total number of parent varieties. Vj is the mean of varieties and Tj is the mean of topcrosses (pool of varieties as tester), and and are the respective average values in the whole set. Yield data from a 7 x 7 variety diallel cross were used for the variety means and for the "simulated" topcross means to illustrate the proposed procedure. The proposed prediction procedure was as effective as the prediction based on Yk = - ( -)/k, where and refer to the mean of hybrids (F1) and parental varieties, respectively, in a variety diallel cross. It was also shown in the analysis of variance that the total sum of squares due to treatments (varieties and topcrosses) can be orthogonally partitioned following the reduced model Yjj’ = mu + ½(v j + v j’) + + h j+ h j’, thus making possible an F test for varieties, average heterosis and variety heterosis. Least square estimates of these effects are also given

Quantitative receptor radioautography in the study of receptor-receptor interactions in the nucleus tractus solitarii

The nucleus tractus solitarii (NTS) in the dorsomedial medulla comprises a wide range of neuropeptides and biogenic amines. Several of them are related to mechanisms of central blood pressure control. Angiotensin II (Ang II), neuropeptide Y (NPY) and noradrenaline (NA) are found in the NTS cells, as well as their receptors. Based on this observation we have evaluated the modulatory effect of these peptide receptors on a2-adrenoceptors in the NTS. Using quantitative receptor radioautography, we observed that NPY and Ang II receptors decreased the affinity of a2-adrenoceptors for their agonists in the NTS of the rat. Cardiovascular experiments agreed with the in vitro data. Coinjection of a threshold dose of Ang II or of the NPY agonists together with an ED50 dose of adrenergic agonists such as NA, adrenaline and clonidine counteracted the depressor effect produced by the a2-agonist in the NTS. The results provide evidence for the existence of an antagonistic interaction between Ang II at1 receptors and NPY receptor subtypes with the a2-adrenoceptors in the NTS. This receptor interaction may reduce the transduction over the a2-adrenoceptors which can be important in central cardiovascular regulation and in the development of hypertension

Quantitative studies of the vasculature of the carotid body in the chronically hypoxic rat

The carotid bodies of rats made chronically hypoxic by breathing 12% O2 in a normobaric chamber (inspired PO2 91 mmHg) were compared with those of controls. Serial 5-µm sections of the organs were examined using an interactive image analysis system. The total volume of the carotid bodies was increased by 64%. The total vascular volume rose by 103% and was likely due to an increase in size of the large vessels (>12 µm lumen diameter) because the small vessel (5-12 µm lumen diameter) volume did not increase significantly while the small vessel density tended to decrease. The extravascular volume was increased by 57%. Expressed as a percentage of the total volume of the organ, the total vascular volume did not change, but the small vessel volume was significantly decreased from 7.83 to 6.06%. The large vessel volume must therefore have been increased. The proportion occupied by the extravascular volume was virtually unchanged (84 vs 82%). In accordance with these findings, the small vessel endothelial surface area per unit carotid body volume was diminished from 95.2 to 76.5 mm-1, while the extravascular area per small vessel was increased from 493 to 641 µm2 or by 30%. In conclusion, the enlargement of the carotid body in chronic hypoxia is most likely due to an increase in total vascular volume, mainly involving the "large" vessels, and to an increase in extravascular volume. This is in contrast to our previously published findings indicating that in the spontaneous insulin-dependent diabetic rat the enlargement of the carotid body is due solely to an increase in extravascular volume.