Hasil untuk "Mathematics"

P. H. Leslie

Lieut.-Col A G M, Kendrick

R. Skemp

J. Carlson, Stefan M¨uller-Stach, C. Peters et al.

E. Fennema, T. P. Carpenter, M. Franke et al.

This study examined changes in the beliefs and instruction of 21 primary grade teachers over a 4-year period in which the teachers participated in a CGI (Cognitively Guided Instruction) teacher development program that focused on helping the teachers understand the development of children's mathematical thinking by interacting with a specific research-based model. Over the 4 years, there were fundamental changes in the beliefs and instruction of 18 teachers such that the teachers' role evolved from demonstrating procedures to helping children build on their mathematical thinking by engaging them in a variety of problem-solving situations and encouraging them to talk about their mathematical thinking. Changes in the instruction of individual teachers were directly related to changes in their students' achievement. For every teacher, class achievement in concepts and problem solving was higher at the end of the study than at the beginning. In spite of the shift in emphasis from skills to concepts and problem solving, there was no overall change in computational performance. The findings suggest that developing an understanding of children's mathematical thinking can be a productive basis for helping teachers to make the fundamental changes called for in current reform recommendations.

N. Bourbaki

J. Hoffman, Claes Johnson, A. Logg

R. Gersten, Nancy C. Jordan, Jonathan R. Flojo

D. Stipek, Karen B. Givvin, Julie M. Salmon et al.

A. Arcavi

I. Holloway, D. Ansari

C. Clark, V. Pritchard, L. Woodward

E. Spelke

Mansureh Kebritchi, Atsusi Hirumi, Haiyan Bai

Amy Devine, Kayleigh Fawcett, Dénes Szűcs et al.

Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys’ mathematics performance is more negatively affected by MA than girls’ performance is. The aim of the current study was to measure girls’ and boys’ mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies. Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on ‘online’ mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in the mathematics classroom, particularly because there is evidence that MA develops during the primary school years. Furthermore, our study showed no gender difference in mathematics performance, despite girls reporting higher levels of MA. These results might suggest that girls may have had the potential to perform better than boys in mathematics however their performance may have been attenuated by their higher levels of MA. Longitudinal research is needed to investigate the development of MA and its effect on mathematics performance.

M. Ashcraft, A. Moore

J. Harackiewicz, Christopher S. Rozek, Chris S. Hulleman et al.

Jianjun Cao, Bailing An, Enran Hou et al.

This study presents a novel local meshless approach for solving one-dimensional Fisher’s equation, combining a local scheme, Gaussian radial basis functions (G-RBF), and a collocation technique. The method leverages the Gaussian basis’s nonlinear fitting capability, the sparsity of the local scheme to avoid ill-conditioned matrices, and the simplicity of collocation. After time discretization using a finite difference scheme, the method constructs local approximations at each collocation point using G-RBFs over small subsets of neighboring nodes. Numerical experiments confirm its effectiveness in solving Fisher-type problems, with errors decreasing smoothly as collocation points increase and maintaining stable accuracy over time. The proposed method demonstrates computational efficiency, robustness, and potential for handling large-scale reaction-diffusion systems.

Luma F. Ali, Hussein Togun, Abdellatif M. Sadeq

Practical applications such as solar power energy systems, electronic cooling, and the convective drying of vented enclosures require continuous developments to enhance fluid and heat flow. Numerous studies have investigated the enhancement of heat transfer in L-formed vented cavities by inserting heat-generating components, filling the cavity with nanofluids, providing an inner rotating cylinder and a phase-change packed system, etc. Contemporary work has examined the thermal performance of L-shaped porous vented enclosures, which can be augmented by using metal foam, using nanofluids as a saturated fluid, and increasing the wall surface area by corrugating the cavity’s heating wall. These features are not discussed in published articles, and their exploration can be considered a novelty point in this work. In this study, a vented cavity was occupied by a copper metal foam with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>P</mi><mi>I</mi><mo>=</mo><mn>10</mn></mrow></semantics></math></inline-formula> and saturated with a copper–water nanofluid. The cavity walls were well insulated except for the left wall, which was kept at a hot isothermal temperature and was either non-corrugated or corrugated with rectangular waves. The Darcy–Brinkman–Forchheimer model and local thermal non-equilibrium models were adopted in momentum and energy-governing equations and solved numerically by utilizing commercial software. The influences of various effective parameters, including the Reynolds number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>20</mn><mo>≤</mo><mi>R</mi><mi>e</mi><mo>≤</mo><mn>1000</mn></mrow></semantics></math></inline-formula>), the nanoparticle volume fraction (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>%</mo><mo>≤</mo><mi>φ</mi><mo>≤</mo><mn>20</mn><mo>%</mo></mrow></semantics></math></inline-formula>), the inflow and outflow vent aspect ratios (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.1</mn><mo>≤</mo><mrow><mrow><mi>D</mi></mrow><mo>/</mo><mrow><mi>H</mi></mrow></mrow><mo>≤</mo><mn>0.4</mn></mrow></semantics></math></inline-formula>), the rectangular wave corrugation number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>5</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>10</mn></mrow></semantics></math></inline-formula>), and the corrugation dimension ratio (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>R</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>R</mi><mo>=</mo><mn>0.5</mn></mrow></semantics></math></inline-formula>) were determined. The results indicate that the flow field and heat transfer were affected mainly by variations in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><mi>D</mi></mrow><mo>/</mo><mrow><mi>H</mi></mrow></mrow></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi></mrow></semantics></math></inline-formula> for a non-corrugated left wall; they were additionally influenced by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>R</mi></mrow></semantics></math></inline-formula> when the wall was corrugated. The fluid- and solid-phase temperatures of the metal foam increased with an increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><mi>D</mi></mrow><mo>/</mo><mrow><mi>H</mi></mrow></mrow></mrow></semantics></math></inline-formula>. The fluid-phase Nusselt number near the hot left sidewall increased with an increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi></mrow></semantics></math></inline-formula> by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced separators="|"><mrow><mn>25</mn><mo>–</mo><mn>60</mn></mrow></mfenced><mo>%</mo></mrow></semantics></math></inline-formula>, while the solid-phase Nusselt number decreased by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced separators="|"><mrow><mn>10</mn><mo>–</mo><mn>30</mn></mrow></mfenced><mo>%</mo></mrow></semantics></math></inline-formula>, and these numbers rose by around <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.5</mn></mrow></semantics></math></inline-formula> times when the Reynolds number increased from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>20</mn></mrow></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1000</mn></mrow></semantics></math></inline-formula>. For the corrugated hot wall, the Nusselt numbers of the two metal foam phases increased with an increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> and decreased with an increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><mi>D</mi></mrow><mo>/</mo><mrow><mi>H</mi></mrow></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>R</mi></mrow></semantics></math></inline-formula>, or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi></mrow></semantics></math></inline-formula> by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>10</mn><mo>%</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>19</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>37</mn><mo>%</mo></mrow></semantics></math></inline-formula>. The original aspect of this study is its use of a thermal, non-equilibrium, nanofluid-saturated metal foam in a corrugated L-shaped vented cavity. We aimed to investigate the thermal performance of this system in order to reinforce the viability of applying this material in thermal engineering systems.

Roberto Montemanni, Sara Ceschia, Andrea Schaerf

Home healthcare has become more and more central in the last decades, due to the advantages it can bring to both healthcare institutions and patients. Planning activities in this context, however, presents significant challenges related to route planning and mutual synchronization of caregivers.In this paper we propose a new compact model for the combined optimization of scheduling (of the activities) and routing (of the caregivers) characterized by fewer variables and constraints when compared with the models previously available in the literature. The new model is solved by a constraint programming solver and compared experimentally with the exact and metaheuristic approaches available in the literature on the common datasets adopted by the community. The results show that the new model provides improved lower bounds for the vast majority of the instances, while producing at the same time high quality heuristic solutions, comparable to those of tailored metaheuristics, for small/medium size instances.