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1
Gordon, Lisa Lande. "Children's understanding of basic number concept." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186857.
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Three experiments were completed in this study in order to explore gist/verbatim independence/dependence. The first experiment was interested in developmental differences in verbatim memory performance, while the second and third experiments were concerned with developmental differences in verbatim memory and in relationships between verbatim and separate forms of gist memories. Extant data have demonstrated that accurate performance on reasoning tasks does not rely on accurate verbatim memory. However, how separate gists interact with each other, and each in relation to verbatim memory, has previously received scant attention. Results from Experiments 2 and 3 revealed stochastic independence between gists, and between separate gists and verbatim memory. In addition, distinct developmental patterns were uncovered. Younger subjects appear to have performed most accurately on nominal gist, while second grade subjects performed worst on nominal probes. Similarly, second graders responded most accurately on relational probes, while preschoolers performed poorest on relational probes. Additionally, consistent with recent literature on memory development that finds verbatim-reasoning independence, verbatim probes were not found to yield the highest rate of accuracy. If performance accuracy on reasoning tasks was dependent on accurate verbatim encoding, memory would have been better for verbatim information than for both relational and nominal. Experiment 3 explored the effects of training on gist extraction. Although training was not found to generate a statistically significant difference in performance for either age relative to the control groups' performance, indirect support for its impact on performance was found, and reviewed. Relative to those in the control group, the preschoolers in the experimental group seemed to benefit from training and demonstrated a performance pattern comparable to that of the second graders', although significance was not determined in these experiments. In summary, clear evidence of verbatim-gist independence was found, and indicates that separate gists may also function as distinct and individual processes. Additionally, there was some indication that training may elicit comparable gist performance patterns between age-groups, but the subject pool in these experiments appears to have been too small to exploit a training impact.
2
Chan, Wai-lan Winnie. "An investigation into two-digit number processing among Chinese children and adults." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B42841495.
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Anderson, Ursula Simone. "Color, shape, and number identity-nonidentity responding and concept formation in orangutans." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42740.
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The ability to recognize sameness among objects and events is a prerequisite for abstraction and forming concepts about what one has learned; thus, identity and nonidentity learning can be considered the backbone of higher-order human cognitive abilities. Discovering identity relations between the constituent properties of objects is an important ability that often characterizes the comparisons that humans make so it is important to devote attention to understanding how nonhuman primates process and conceptualize part-identity as well as whole-identity. Because the ability to generalize the results of learning is to what concepts ultimately reduce, the series of experiments herein first investigated responding to part-identity and -nonidentity and whole-identity and -nonidentity and then explored the generality of such learning to the formation of concepts about color, shape, and cardinal number.
The data from Experiments 1, 2, and 3 indicated that the two orangutans learned to respond concurrently to color whole-identity and -nonidentity and they responded faster to color whole-identity. Additionally, both subjects learned to respond concurrently to color and shape part- and whole-identity and for the most part, it was easier for them to do so with color part- and whole-identity problems than shape part- and whole-identity problems. Further, their learned responses to color and shape part- and whole-identity fully transferred to novel color part-identity problems for both subjects and fully transferred to novel color and shape whole-identity problems for one orangutan. The data from Experiments 4, 5, and 6 showed that one subject learned to judge numerical identity when both irrelevant dimensions were cue-constant, but the subject did not do the same when one or more irrelevant dimensions were cue-ambiguous. Further, the subject's accuracy was affected by the numerical distance and the numerical total of comparisons during acquisition of the conditional discrimination. The subject subsequently formed a domain-specific concept about numerical identity as evinced by the transfer of learning to novel numerosities instantiated with novel, cue-constant element colors and shapes and novel numerosities instantiated with cue-constant, familiar element colors and shapes.
Given the adaptive significance of using concepts, it is important to investigate if and how nonhuman primates form identity concepts for which they categorize or classify the stimuli around them. This dissertation provided evidence about the extent to which orangutans learned to respond to color, shape, and number identity and nonidentity and subsequent concept formation from such learning. The findings from this study will help in understanding the convergence and divergence in the expression abstraction in the primate phylogeny, thus, informing our understanding about the origins and mechanisms of cognition in human and nonhuman primates.
4
Cock, Josephine Judy. "Implicit learning : number rules and invariant features." Thesis, University of Reading, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320132.
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Wynn, M. Karen (Margaret Karen). "The development of counting and the concept of number." Thesis, Massachusetts Institute of Technology, 1990. http://hdl.handle.net/1721.1/13719.
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Chan, Wai-lan Winnie, and 陳偉蘭. "An investigation into two-digit number processing among Chinese children and adults." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B42841495.
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Safi, Farshid. "Exploring the Understanding of Whole Number Concepts and Operations: A Case Study Analysis of Prospective Elementary School Teachers." Doctoral diss., Orlando, Fla. : University of Central Florida, 2009. http://purl.fcla.edu/fcla/etd/CFE0002811.
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Roy, George J. "Prospective teachers' development of whole number concepts and operations during a classroom teaching experiment." Orlando, Fla. : University of Central Florida, 2008. http://purl.fcla.edu/fcla/etd/CFE0002398.
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Lunken, Eugene Jonah. "Is subitizing simply canonical pattern matching." Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/29426.
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Gea, Luis Daniel. "Genetic diversity and gain : the concept of a status number." Thesis, University of Canterbury. Forestry, 1997. http://hdl.handle.net/10092/7197.
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A trade-off always tends to exist involving genetic gains and selection intensity, on the one hand, and the remaining effective population size (usually known as Ne), on the other. A new approach is presented and analysed for different breeding situations, using stochastic simulations, in terms of mating designs and subline sizes, guiding breeders through a new concept of status number (Ns) and its trade-off with gain.
Status number is defined as half the inverse of the average coancestry and depicts the current state of the population. The status number concept can easily be applied to deployment of different genotypes with unequal representation.
Breeding schemes with small breeding groups are slightly more efficient in preserving status number through multiple generations than breeding schemes with large groups. Medium- to large-size breeding groups showed a comparatively small reduction in aggregated status number over generations but showed greater increases in gain compared with small groups. Inbreeding in small elites becomes so great that it is likely to cause fertility problems and disturb selection considerably. Small breeding groups will probably not be useful for a sustainable long-term breeding strategy. Substantial benefits on status number for subdividing the population into small breeding groups will only be seen after numerous generations.
Selection schemes that maximise gain by unrestricted combined index selection will result in rapid inbreeding, and may not be sustainable in the long term. Selection procedures that place less emphasis on family information would best meet long-term diversity targets. However, gains may be too low for mating systems and selection procedures that do not include a between-family component, especially with low heritabilities. This is a good reason for using a large number of families as founders of the breeding population.
Going from selection within only 0.5 or 1 available cross per parent per generation (made equivalent to within-family selection) to 2.5 crosses per parent (restricting the number of individuals chosen per full-sib family) resulted in substantial increases in genetic gain, depending on heritability. However, increasing the number of crosses per parent up to 2.5 does carry a modest penalty of increased coefficient of inbreeding and reduced status number.
Higher levels of gain per unit of status number loss are obtained with a conservative within family selection strategy but to reach the same level of gain more cycles of breeding will be required.
Effects of departures from assumptions (zero inbreeding coefficient and coancestry for the founders, genes being independently assorted, no mutation and interactions, or combinations from departures of the neutrality assumption) , singly and in various combinations will occur, meaning that calculations and predictions based on pedigrees will be biased. Future work will require modelling the effects for departures from the idealised assumptions and laboratory-based quantification of departures from some key assumptions.
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Lan, Shasha. "Teaching and learning of number concept in Chinese primary classroom." Master's thesis, University of Cape Town, 2017. http://hdl.handle.net/11427/27302.
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The research investigated the practices of the teaching and learning of number concept and primary mathematics broadly, within a classroom context in China's Inner Mongolia province. Informed by Vygotsky's cultural historical theoretical framework, and using an ethnographic approach - with triangulated data collection methods, the research examined a teacher's approaches to teaching primary mathematical concepts. The research explored the teacher's rationale and understanding underpinning her classroom practices in order to uncover sociocultural contingencies and influences on the part of both the teacher's and learners' framing of the teaching and learning of mathematics in a Chinese Grade 1 classroom. The findings suggest that the teaching of mathematics, specifically number concept, has been and is undergoing changes, as policy regulations within the Chinese schooling system also undergo transformation. The findings further suggest that the introduction of learner-centred teaching into the Chinese curriculum policy framework has not significantly, if at all, supplanted teacher-controlled approaches in the classroom under investigation. While the emphasis placed by the teacher on precision and efficacy appears to have enabled learners to acquire the necessary skills and procedures to carry out the number operations, the concurrent lack of emphasis on individual, or authentic learner-centred approaches that engage learners in problem-based exploration of knowledge, appears to have inhibited the development amongst learners of independent and critical problem-solving skills.
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Alghamdi, Abdulwahab. "Evaluation of acid fracturing based on the "acid fracture number" concept." Texas A&M University, 2006. http://hdl.handle.net/1969.1/3835.
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Acid fracturing is one of the preferred methods to stimulate wells in carbonate
reservoirs. It consists of injecting an acid solution at high enough pressure to break
down the formation and to propagate a two-wing crack away from the wellbore. The
acid reacts with the carbonate formation and this causes the etching of the fracture
surfaces. After the treatment, the created etched surfaces do not close perfectly and that
leaves behind a highly conductive path for the hydrocarbons to be produced. We
distinguish the issue of treatment sizing (that is the determination of the volume of acid
to be injected) and the issue of creating optimum fracture dimensions given the size of
the treatment. This is reasonable because the final cost of a treatment is determined
mainly by the volume of acid injected and our goal should be to achieve the best
performance of the treated well. The well performance depends on the created fracture
dimensions and fracture conductivity and might change with time due to various reasons.
This research evaluates two field cases from Saudi Aramco where acid fracturing
treatment has been used to stimulate a carbonate formation. I investigated the following issues: a) how effective was the treatment to restoring the initial productivity, b) how did
the productivity of the well change with time; c) what are the possible reasons for the
change in performance, d) what are our options to improve acid fracture design in the
future?
Based on our research work both near-well liquid drop-out and fractureconductivity
deterioration can impact the production in different proportion. Moreover,
the fracturing model tends to overestimate the fracture conductivity in some cases as
shown in SA-2. Also, the ÂAcid fracture Number concept proves to be an effective way
to evaluate the acid fracturing treatment. Several recommendations were made based on
this research work as described in the last part of my thesis.
13
Cheung, Siu-pun. "The effective use of number sense for assisting students with learning difficulties." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/hkuto/record/B40039924.
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Vermeulen, Cornelis Franz. "Senior primere leerlinge se begrip van sekere algemene getaleienskappe, met besondere verwysing na die distributiewe eienskap." Thesis, Stellenbosch : Stellenbosch University, 1991. http://hdl.handle.net/10019.1/69396.
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ENGLISH ABSTRACT: Number properties, amongst others the commutative, associative and distributive properties
and general rearrangement principles, form the building blocks of manipulative algebra.
Research and observation have shown that sec~mdary school pupils do not sufficiently
master manipulative algebra, i.e. they do not possess sufficient mastery towards the nature,
meaning, functionality and logic of algebraic manipulations. They are hence not aware that
algebraic manipulations are based on the number properties, on the one hand because they
were not given sufficient opportunity to experience algebra as generalised arithmetic when
they were introduced to algebra, and on the other hand because the number properties,
about which young children possess intuitive knowledge, were never explicated for them.
This study investigates the level of awareness of several number properties present in senior
primary (especially standard 3) pupils, and utilises a few activities to attempt to lead pupils
towards a higher level of awareness. In addition this study attempts to determine whether
pupils who follow the experimental primary mathematics curriculum (project pupils)
possess a higher level of awareness than pupils who follow the traditional curriculum (nonproject
pupils). As part of the latter effort, two investigation methods are utilised with
regards to specifically the distributive property, i.e. clinical interviews and questionnaires.
This also serves as part of a wider effort to design a measuring instrument with which
possible differences between the learning outcomes of project and non-project pupils can be
measured ..
From the results of this study, it seems to appear that the large majority of pupils are
explicitly aware of the commutative properties of addition and multiplication and the
general rearrangement principles, to a lesser extent with regards to a minus sign before
brackets, and that there does not exist a significant difference about the level of awareness
towards these properties between project and non-project pupils.
With regards to the distributive property, there appears to exist a considerable amount of
difference in the level of awareness between project and non-project pupils, the first
mentioned being the higher. However, the opinion is expressed that the level of awareness
among project pupils is not high enough, and that project pupils must be given sufficient
opportunity in (at least standards 4 and 5) to explicate this property for themselves.
Finally, a model of the levels of awareness, based on results of this study, is proposed.AFRIKAANSE OPSOMMING: Getaleienskappe, waaronder die kommutatiewe, assosiatiewe en distributiewe eienskappe en algemene herrangskikkingsbeginsels, vorm die boustene van manipulatiewe algebra. Navorsing en waarneming het aan die lig gebring dat hoerskoolleerlinge manipulatiewe algebra nie na behore beheers nie, dit wil se hulle beskik nie oor voldoende beheersing ten opsigte van die aard, betekenis, funksionalteit en logika van algebraise manipulasies nie. Hulle is dus nie daarvan bewus dat algebraiese manipulasies op die getaleienskappe berus nie, enersyds omdat hulle nie tydens die kennismaking met manipulatiewe algebra genoegsaam in die geleentheid gestel is om algebra as veralgemeende rekenkunde te ervaar nie, en andersyds omdat die getaleienskappe, waaroor jong kinders intuitiewe kennis besit, nooit vir hulle geeksplisiteer is nie. Hierdie studie stel ondersoek in na senior primere (hoofsaaklik standerd 3) leerlinge se vlak van bewustheid van enkele getaleienskappe, en benut enkele aktiwiteite om leerlinge na 'n hoer vlak van bewustheid daarvan te probeer lei. Hierbenewens word probeer om vas te stel of daar by leerlinge wat die eksperimentele primere wiskunde-kurrikulum volg (projekleerlinge) 'n hoer vlak van bewustheid aanwesig is as by leerlinge wat die tradisionele kurrikulum volg (nie-projekleerlinge). As· deel van laasgenoemde poging, word twee ondersoekmetod~s gevolg ten opsigte van spesifiek die distributiewe eienskap, naamlik kliniese onderhoude en vraelyste. Dit dien ook as deel van 'n breer poging om 'n meetinstrument te ontwerp waarmee moontlike verskille tussen die leeruitkomste van projek- en nie-projekleerlinge gemeet kan word. Dit wil uit die bevindinge van hierdie studie voorkom asof die oorgrote meerderheid leertinge eksplisiet bewus is van die kommutatiewe eienskappe ten opsigte van optelling en vermenigvuldiging en die algemene herrangskikkingsbeginsels, in 'n mindere mate ten opsigte van die minusteken voor hakies, en dat daar nie 'n noemenswaardige verskil in die vlak van bewustheid oor hierdie eienskappe by projek- en nie-projekleerlinge bestaan nie. Sover dit die distributiewe eienskap betref, lyk dit asof daar 'n redelike verskil in die vlak van bewustheid by projek- en nie-projekleerlinge is met eersgenoemde die hoogste. Tog word die mening uitgespreek dat die vlak van bewustheid by projekleerlinge nie hoog genoeg is nie, en dat hulle in minstens standerd 4 en 5 in die geleentheid gestel moet word om hierdie getaleienskap vir hulself te eksplisiteer.
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Waxman, Natalie. "Counting and sequential processing in children with Down Syndrome and typically developing children." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=100218.
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The development of numerical skills in children with Down syndrome is an area of research that has been neglected in the literature despite overwhelming evidence of its importance, both pedagogically, and for everyday functioning. The present study examines two important sub-skills of numeracy. Twelve boys with Down syndrome were compared to 24 typically developing boys (matched on verbal mental age and on chronological age) on two novel, computerized tasks designed to measure sequential processing and counting. Boys with Down syndrome performed comparably to both groups of typically matched controls on the sequential task. However, differences emerged when boys with Down syndrome were required to point and attribute meaning to each step on the counting task. These findings offer novel insights into the development of number skills and provide important data that can aid in the creation of syndrome-specific education strategies to maximize the potential of children with Down syndrome.
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ADEY, KYM LLEWELLYN. "PRESCHOOLER UNDERSTANDING OF PRINCIPLES GOVERNING COUNTING." Diss., The University of Arizona, 1987. http://hdl.handle.net/10150/184106.
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This dissertation sought to explore dimensions of preschooler conceptual awareness of the principles of counting. The study derived its focus from the research of Rochel Gelman and, in particular, the principles of counting she purports are implicitly understood by young children. Their frequent inability to manifest this awareness in their counting performances is explained as resulting from their susceptibility to task demands. This study explores this position by seeking to facilitate performance in order that conceptual understanding might be more apparent. The sample for this study consisted of 40 children (20 aged 3 years 3 months-3 years 9 months; 20 aged 4 years 3 months-4 years 9 months) selected randomly from a cross section of preschool and day-care centers in Adelaide, South Australia. Phase 1 of the study explored the impact of a procedure which allowed for children to receive both visual and tactile feedback on their counting behavior on array sizes ranging from 2 to 19. The results show conclusively that this self-monitoring technique significantly improved counting performances for both age groups. In doing so it lends support to the Gelman hypothesis that conceptual awareness of the 'how-to' count principles can be masked by task demands. Phase 2 of the study looked at the complex 'order-irrelevance' principle. The results suggest that preschoolers understand that items can be counted in any order before they appreciate that this has no impact on cardinal value. The extreme susceptibility of preschoolers to variations in task demands necessitates further exploration of design and analysis parameters.
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Nason, Rodney Allan, and mikewood@deakin edu au. "Production system model of children's development of number concepts." Deakin University. School of Education, 1988. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051110.152425.
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The purpose of the present research study was to produce a global, cumulative model of number concept development for children between the ages of two and eight years old.
The theoretical and methodological orientation of this study was greatly influenced by Richard Young's production system analysis of seriation by young children (Young, 1971, 1976) and by Newell's (1973) seminal paper, You can't play twenty questions with nature and win. The methodology used in this investigation thus was as follows. A series of complex number tasks encompassing many aspects of the concept of number were developed. Five children aged between three and seven years then were videotaped while performing some of these complex number tasks. From a detailed protocol analysis of the video-recordings, computer simulation models written in the production system language PSS3 (Ohlsson, 1979) were produced.
Specific production system models were produced for each of following aspects of the children's number knowledge:
(i) sharing of discrete quantities;
(ii) comparison of shares; and
(iii) conservation/addition/subtraction of number.
These domain-specific models were based on the converging experimental evidence obtained from each of the childrens responses to variants of the complex number tasks. Each child thus received a different set of problems which were chosen systematically in order to clarify particular features of the child's abilities. After a production system model for each child had been produced within a domain, these models were compared and contrasted. From this analysis, developmental trends within the domain were identified and discussed. The research and educational implications of these developmental trends then were discussed.
In the concluding parts of this study, the children's domain-specific production system models were cumulated into global, comprehensive models which accurately represented their behaviour in a variety of number tasks. These comprehensive models were compared and contrasted and general developmental trends in young children's number knowledge were identified and discussed.
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Foster, Robin. "Children's use of apparatus in the development of the concept of number." Thesis, University of Warwick, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.288541.
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Furlong, Ellen Elizabeth. "Number Cognition and Cooperation." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1216999104.
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Broadway, James Michael. "SNARC and SNAAC: spatial-numeric association of response codes and attentional cuing." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44708.
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Two event-related potential (ERP) experiments were conducted to investigate spatial-numeric associations of response codes (SNARC) and attentional cuing (SNAAC). In the SNARC effect, people respond faster when making a left-hand response to report that a number is small, and when making a right-hand response to report that a number is large. Experiment 1 examined effects of SNARC-compatibility and prior response-probability in a number comparison task. Lateralized readiness potentials (LRPs) showed that SNARC-compatibility influenced an intermediate stage of response-selection, and prior response-probability influenced both earlier and later stages. The P300 ERP component was also modulated by SNARC-compatibility and prior response-probability, suggesting parietal involvement in the SNARC effect. In the SNAAC effect, attention is directed to left-side regions of space upon viewing small-magnitude numbers, and to right-side regions of space upon viewing large-magnitude numbers. Experiment 2 investigated whether ERPs evoked by peripheral visual probes would be enhanced when probes appeared in the left hemifield after small-magnitude digits and when they appeared in the right hemifield after large-magnitude digits. ERPs to peripheral probes were not modulated by numerical magnitude of digit pre-cues.
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Leung, Yun-hing. "The relationship between numerical estimation and number sense in students' learning of mathematics." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/hkuto/record/B40040173.
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Wong, Tin-yau, and 王天佑. "The roles of the approximate number system and number-numerosity mapping on the mathematics achievement in normally- and low-achieving children and children with mathematics learning disability." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/207200.
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Humans are born with a basic sense of number. This number sense, which is now called the Approximate Number System (ANS), allows us to represent numerosity without the use of symbols. There has been a debate on whether this nonsymbolic ANS contributes to our symbolic mathematics skills, and the recent findings are inclined to support the link between the two. However, what remains unclear is the mechanism underlying the relationship between the ANS and our mathematics skills, and whether children with Mathematics Learning Disabilities (MLD) suffer from a defective ANS. The present thesis aimed at addressing the above issues in two studies. Study 1 aimed at identifying the mechanism of how the ANS contributes to children’s mathematics skills. A group of 210 kindergarteners were tested on their ANS acuity, number-numerosity mapping skills (measured by counting and estimation tasks), and their arithmetic skills. They were then re-tested twice when they were in Grade 1.Using Structural Equation Modeling, it was found that children’s ANS acuity in kindergarten predicted their arithmetic skills one year later, and the relationship was mediated by their number-numerosity mapping skills. This suggested that ANS may contribute to mathematics learning by enabling more precise mapping between number symbols and the corresponding numerosity representation, hence making numbers meaningful. Studies 2A and 2B aimed at verifying whether children with MLD suffered from deficits in their ANS as well as their number-numerosity mapping skills. The same group of participants was followed one more time in Grade 2. Using the standard low-achievement method (Study 2A) and a more data-driven method known as the latent class growth analysis(Study 2B), two groups of children with MLD were identified. Both groups of children had deficits in both the ANS and their number-numerosity mapping skills as compared with their normally-achieving peers. Other groups of low-achieving children were also identified, and their difficulties seemed to be contributed by factors other than their ANS. While one of the low-achieving groups seemed to have deficit lying mainly on the number-numerosity mapping skills, the other low-achieving group did not show any cognitive deficits but had much lower SES compared to other groups. The relationship between the ANS and children’s mathematics achievement was supported and elaborated in the present study. The findings not only articulated a potential mechanism of how children learned about mathematics, but they also allowed educators to have better understanding of the cognitive profiles of children with MLD, thus facilitating early identification and intervention. The different profiles of the low-achieving groups also highlighted the need for differential intervention for different groups of low-achieving children.published_or_final_version
Psychology
Doctoral
Doctor of Philosophy
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Chaturvedula, Sri Ramya. "Designing multi-core architecture using folded torus concept to minimize the number of switches." Thesis, Wichita State University, 2011. http://hdl.handle.net/10057/5163.
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A multi-core system provides improved performance/power ratio than a single-core one. However, multi-core architecture suffers from thermal constraint and data inconsistency. Current multi-core system is not adequate to increase memory-level parallelism and cache performance due to its poor core-to-core interconnection topology. In some architecture, like MIT Raw, each node/core has computing and switching components. Switching component of such a node consumes power while the node is only computing and vice versa. In this paper, we propose a design methodology to reduce the number of switches in multi-core architecture without compromising the performance. According to this method, nodes are separated between computing cores and network switches. Using folded torus topology, we develop a scheme to connect the components (cores and switches) in the multi-core architecture. We use multi-core architectures with various numbers of nodes (cores and switches) to evaluate the proposed methodology. Using synthetic workload, we obtain the core-to-core communication delay and total power consumption for MIT RAW, Triplet Based Architecture (TriBA), Logic-Based Distributed Routing (LBDR), and the proposed architecture. Experimental results show that the proposed architecture outperforms Raw, TriBA, and LBDR by cutting down the need for the number of switches significantly. According to the results, proposed architecture reduces total power consumption approximately by 77% and average delay by 54%. Power reduction comes from the fact that number of switches is cut down. Average delay is decreased as each switch provides adequate communicate channels.Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science.
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JUNIOR, WALTER GOMIDE DO NASCIMENTO. "THE INFINITE COUNTED BY GOD: A DEDEKINDIAN INTERPRETATION OF CANTOR S TRANSFINITE ORDINAL NUMBER CONCEPT." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2006. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=9031@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOSubjacente à teoria dos números ordinais transfinitos de Cantor, há uma perspectiva finitista. Segundo tal perspectiva, Deus pode bem ordenar o infinito usando, para tanto, de procedimentos similares ao ato de contar, entendido como o ato de bem ordenar o finito. Desta maneira, um diálogo natural entre Cantor e Dedekind torna-se possível, dado que Dedekind foi o primeiro a tratar o ato de contar como sendo, em sua essência, uma forma de bem ordenar o mundo espáciotemporal pelos números naturais. Nesta tese, o conceito de número ordinal transfinito, de Cantor, é entendido como uma extensão do conceito dedekindiano de número natural.
Underlying Cantor s transfinite ordinal numbers theory, there is a finistic perspective. Accordingly that perspective, God can well order the infinite using, for that, similar procedures to the act of counting, understood as the act of well order the finite. That s why a natural dialog between Cantor and Dedekind becomes possible, since Dedekind was the first to consider the act of counting as being, in its essence, a way of well order the spatial-temporal world by natural numbers. In this thesis, the concept of Cantor´s transfinite ordinal number is understood as an extension of dedekindian concept of natural number.
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Le, Grange Lynn Louise. "The development of the number concept in Grade R: a case study of a school in the Wellington area." University of the Western Cape, 2014. http://hdl.handle.net/11394/4397.
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Magister Educationis - MEdSystemic evaluation undertaken by the Department of Basic Education as part of the Literacy and Numeracy Strategy 2006 – 2016 posed a serious challenge in South African schools. The numeracy and mathematics results in 2009 stated that 35% of learners in Grade 3 achieved the required level of competence in Mathematics. This has, however, improved to 48.3% in 2010 but dropped to 47.6% in 2011. The development of early number concept in countries such as the Netherlands, Singapore and Helsinki has shown that early intervention is essential for reaching mathematical success in schooling. The Curriculum and Assessment Policy Statement (CAPS) integrates the three learning programmes: Literacy, Numeracy and Life Skills for Grade R into a daily programme of activities. Within this daily programme it specifies that 35% of each day must be used towards Numeracy. The Grade R method of teaching emphasizes the fact that teaching must take place informally but planned formally. The purpose of this study is to examine how early mathematics is taught in an integrated and informal setting to improve number concept. The theoretical framework underpinning this study is based on the constructivist views of Piaget and Vygotsky and how these theories lay the foundation for the development of number concept in Grade R. Number skills to develop number concept were identified in nine lessons to underpin the content area 1, Numbers, Operations and Relationships as determined by the Grade R Mathematics Curriculum and Assessment Policy Statement (CAPS). The methodology employed to answer the research question were video-recordings, observations and interviews. The findings identified number skills such as emergent number concepts: distinguishing numerosity, imitating resultative counting and symbolizing by using fingers as well as growing number concepts: discovering different meanings of numbers, oral counting, one- to- one correspondence, rote counting, perceptual subitising, resultative counting, representing and symbolizing numbers, ordinality, place value, emergent object-based counting and calculating and golden moments. The discussion of the findings focused on the CAPS content area and how these number skills were used to achieve the demands of the content area 1. The major findings of this study presented a case of the utilization of number skills to achieve the development of number concept in Grade R, how mathematics should be made fun, and how incidental learning, “golden moments” can be used to introduce key mathematical concepts informally. This study has implications for teachers of Grade R and for the training of pre-service Grade R teachers at tertiary level.
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Cheung, Siu-pun, and 張兆斌. "The effective use of number sense for assisting students with learningdifficulties." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B40039924.
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Mathews, Elizabeth Leigh. "Improving a Second Grade Student's Number Sense: An Instructional Intervention." MSSTATE, 2007. http://sun.library.msstate.edu/ETD-db/theses/available/etd-04082007-162641/.
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The purpose of this qualitative case study was to help a second grade student, who struggled with mathematics but excelled in reading, to develop a conceptual understanding of number sense, using a teacher researcher-created intervention. The five-step, one-on-one intervention included the following: (1) use trade books to build mathematical knowledge and vocabulary (2) teacher modeling of concepts, (3) guided practice with manipulatives, (4) review using games and a ?Fact Pack?, and (5) journal writing to explain concepts. The Early Mathematics Assessment-3 (TEMA-3) was used as a pre- and post-test assessment the student?s mathematical knowledge. Other data included transcriptions of audio taped intervention sessions, notes from video-taped intervention sessions, fieldnotes, and artifacts from the classroom and intervention sessions. Data sources were triangulated. On the TEMA-3 Pretest, the student scored at the first grade, fourth month (1.4) level. After 13 Lessons covered in 22 sessions (approximately 11 hours of one-on-one instruction), the student scored at the second grade, second month (2.2) level. She also scored Proficient on the state curriculum test in mathematics. Four aspects of the intervention seem to help the student most in her development of number sense. They included the use of (1) a number line; (2) a number structure, which visually depicted the value of numbers; (3) trade books to provide an anchor for each skill and a memorable context; and (4) journaling. In addition, the data revealed that once the student understood the concept of ten?s and one?s, her ability to count and add extended to include numbers 1 to 100. Recommendations for students who excel in reading and writing, but struggle with mathematics, include the following: the use of trade books and writing may help them better understand mathematics concepts; review of mathematical concepts through enjoyable, meaningful games and the use of a Fact Pack are useful; the use a horizontal number line and number structure, which is consistent with left-to-right directionality of reading and writing, may help students better understand the concepts of more, less, before, and after; and consistent use of vocabulary during instruction may help students better understand number concepts.
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Mntunjani, Lindiwe. "The use of mathematical resources to teach number concepts in the foundation phase." Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2494.
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Thesis (MEd (Education))--Cape Peninsula University of Technology, 2016.The poor performance of learners in mathematics has long been a matter of concern in South Africa. One certain fact from the Annual National Assessment (ANA) results is that the problem starts in the Foundation Phase (FP) with number concepts. The aim of this study was to explore how five Foundation Phase teachers located in challenging socio-economic school contexts in the Western Cape used mathematical resources to promote teaching for understanding of the important number concept area in CAPS. These resources included humans, materials, culture and time. The research was located within the interpretive qualitative research paradigm and used a case study approach. The participants in the study included five FP teachers teaching Grades 1 to 3 at two schools in the Western Cape. Data was collected through lesson plan analysis, lesson observations and semi-structured interviews. The data collected was then analysed through the lens of Vygotsky’s socio-cultural theory. Socio-cultural theory maintains that knowledge is best acquired if it is mediated by language, more knowledgeable others and physical tools. Vygotsky believed that knowledge is first acquired interpersonally, then intrapersonally, as learners first learn from others, then internalise or individualise knowledge while going through the four stages of the Zone of Proximal Development (ZPD). The findings of this study revealed that teaching for understanding was often compromised by teaching to enable learners to pass assessments. Teachers understood the importance of using resources to teach number concepts in the Foundation Phase, but inclined to rote teaching with work drills in preparation for assessments such as the Annual National Assessment (ANA) and the systemic assessment. Resources were often used when learners struggled to understand concepts and as calculation tools. This study supports the view from the literature that the way in which resources are used affects the teaching and learning of number concepts. It recommends that teachers should read and follow the CAPS mathematics document, as it clearly states what resources to use and how. This study further recommends that more research on the use of resources to teach mathematics in other content areas should be done.
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Kaminski, Eugene. "A program to promote the development of number sense and reflective practice with pre-service teacher education students." Thesis, Queensland University of Technology, 1996.
Find full textAbstract:
This thesis documents the development, implementation and partial evaluation of a number sense program within a mathematics education unit in the Bachelor of Teaching
course at the Australian Catholic University (McAuley campus). The program aimed to promote the development of primary pre-service student teachers' number sense,
their understanding of, and reflective practice in, mathematics. The conceptual framework, which guided the study, drew upon research and literature on number sense, on undergraduate student teacher development and on reflective practice. The following became the research questions for the study.
Question 1. (a) How do student teachers in a pre-service teacher education course use, at the commencement of a semester, number sense in their understanding of,
and calculating in, mathematics? (b) What aspects of student teachers' experiences in mathematics have contributed to their approaches to, and views of, mathematics?
Question 2.
How does a number sense program within a mathematics education unit assist pre-service teacher education students iri their understanding and use of mathematics?
Question 3.
How do pre-service teacher education students' experiences, in a number sense program within a mathematics education unit, promote the development of reflective practice in mathematics? The research methodology, interpretive in nature, drew on a number of perspectives in order to more effectively investigate the research questions. It incorporated elements of case study and illuminative evaluation perspectives, and utilised a multiple methods
approach, including participant observation, for the collection of data. During the investigation, it appeared that student teachers had little past experience with activities which promoted either number sense development or reflective practice in mathematics. Many of the student teachers' views of, beliefs and assumptions in, mathematics were seldom challenged in the past, and opportunities to justify and defend their mathematical thinking,particularly to their peers, were limited.
It was concluded that student teachers' experiences in developing number sense, when using socio-cognitive, constructivist and reflective approaches, assisted in developing them beyond technical rationality levels of reflectivity and beyond basic duality epistemic levels.
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Chan, Wai-lan Winnie, and 陳偉蘭. "Strategic counting: a novel assessment of place-value understanding." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B49617916.
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Children’s counting strategies, such as counting from one or by groups of tens, reflect how much they understand the place-value structure of numbers. In a novel task for assessing place-value concept, namely the strategic counting task, children were asked to count small squares, which were arranged with or without correspondence to the base-ten number structure. The counting strategies of kindergarteners and first graders revealed that children developed from perceiving number as an undivided entity to seeing it as a collection of independent groups of tens, indicating a trend of increasing place-value understanding. First graders’ strategic counting task scores at the end of fall semester predicted their mathematical achievement at the end of spring semester, over and above age, intelligence, and measures of simple counting, number representation, place-value understanding, and arithmetic calculation. Based on item analysis, a brief version containing only five items was developed for more user-friendly classroom administration. First graders’ scores in the brief version uniquely predicted their mathematical achievement even at the end of second grade. Growth curve modeling revealed that children who were low mathematics achievers at the end of second grade had already shown poor performance in the brief version in early first grade and remained lagging behind their peers over the 18 months. Early poor understanding of place-value concept, then, seems to persist to upper grade and impede mathematical development. Implications for early support to children with difficulties in place-value concept were discussed.published_or_final_version
Psychology
Doctoral
Doctor of Philosophy
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Rendell, Gerard Vincent Alfred. "An integrated modeling framework for concept formation : developing number-sense, a partial resolution of the learning paradox." Thesis, Kingston University, 2012. http://eprints.kingston.ac.uk/27841/.
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The development of mathematics is foundational. For the most part in early childhood it is seldom insurmountable. Various constructions exhibit conceptual change in the child, which is evidence of overcoming the learning paradox. If one tries to account for learning by means of mental actions carried out by the learner, then it is necessary to attribute to the learner a prior structure , one that is as advanced or as complex as the one to be acquired, unless there is emergence. This thesis reinterprets Piaget's theory using research from neurophysiology, biology, machine learning and demonstrates a novel approach to partially resolve the learning paradox for a simulation that experiences a number line world, exhibiting emergence of structure using a model of Drosophila. In doing so, the research evaluates other models of cognitive development against a real-world, worked example of number-sense from childhood mathematics. The purpose is to determine if they assume a prior capacity to solve problems or provide parallel assumptions within the learning process as additional capabilities not seen in children. Technically, the research uses an artificial neural network with reinforcement learning to confirm the emergence of permanent object invariants. It then evaluates an evolved dialectic system with hierarchical finite state automata within a reactive Argos framework to confirm the reevaluated Piagetian developmental model against the worked example. This research thesis establishes that the emergence of new concepts is a critical need in the development of autonomous evolvable systems that can act, learn and plan in novel ways, in noisy situations.
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Dias, Marisa da Silva. "Reta real: conceito imagem e conceito definição." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11162.
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The study investigated concept image and concept definition related to the properties of the number line, and particularly the notion of density. The subjects were 45 teachers of secondary school mathematics (students aged 11-16 years) from São Paulo (Brazil). It was hypothesised that the teachers conceptions would match those of students in the age range that they teach. In order to validate this hypothesis, a diagnostic test was developed and the results of the teachers were compared with results obtained in both national and international studies of students conceptions. Analysis confirmed the hypothesis and indicated that both the concept image and concept definition used by the teachers were not coherent with formal. A sub-set of four teachers also participated in interviews developed with the aim of creating situations in which potential conflict factors would become cognitive conflict factors. Teachers reactions during these interviews indicated that these situations helped them to enhance to a higher intellectual stages in their reasoning about the number line
Esta pesquisa investigou conceito imagem e conceito definição relacionados às propriedades da reta real e, particularmente, à noção de densidade. Os sujeitos foram 45 professores de matemática do ensino fundamental e médio de São Paulo (Brasil). A hipótese foi que concepções dos professores seriam as mesmas apresentadas por estudantes, desse mesmo segmento de ensino. Para validarmos esta hipótese, desenvolvemos um teste diagnóstico e comparamos os resultados dos professores com os obtidos em pesquisas nacionais e internacionais sobre as concepções de estudantes. A investigação confirmou a hipótese e evidenciou a existência de conceitos imagem e definição não coerentes com o formal. Um grupo de quatro professores também participou de entrevistas desenvolvidas com o objetivo de criar situações nas quais fatores de conflito potencial tornassem fatores de conflito cognitivo. As reações dos professores durante essas entrevistas indicaram que essas situações possibilitam-lhes alcançar estágios intelectuais mais elevados em relação à reta real
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Cogan, Donavan. "The aerodynamic design and development of an urban concept vehicle through CFD analysis." Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2386.
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Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2016.This work presents the computational uid dynamics (CFD) analysis of a light road vehicle. Simulations are conducted using the lattice Boltzmann method (LBM) with the wall adapting local eddy (WALE) turbulence model. Simulations include and compare the use of a rolling road, rotating wheels, adaptive re nement as well as showing comparison with a Reynolds-averaged Navier-Stokes (RANS) solver and the Spalart- Allmaras (SA) turbulence model. The lift coe cient of the vehicle for the most part was seen to show a much greater di erence and inconsistencies when compared to drag from the comparisons of solvers, turbulence models, re nement and the e ect of rolling road. Determining the drag of a road vehicle can be easily achieved and veri ed using multiple solvers and methods, however, the lift coe cient and its validation require a greater understanding of the vehicle ow eld as well as the solvers, turbulence models and re nement levels capable of correctly simulating the turbulent regions around a vehicle. Using the presented method, it was found that the optimisation of vehicle aerodynamics can easily be done alongside the design evolution from initial low-drag shapes to the nal detail design, ensuring aerodynamic characteristics are controlled with aesthetic change.
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Russell, Kelly A. "Children's prenumerical quantification of time." Birmingham, Ala. : University of Alabama at Birmingham, 2008. https://www.mhsl.uab.edu/dt/2008p/russell.pdf.
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Thesis (Ph. D.)--University of Alabama at Birmingham, 2008.Additional advisors: Jerry Aldridge, Lois Christensen, Lynn Kirkland, Maryann Manning. Description based on contents viewed Oct. 7, 2008; title from PDF t.p. Includes bibliographical references (p. 66-68).
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Leung, Yun-hing, and 梁潤興. "The relationship between numerical estimation and number sense in students' learning of mathematics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B40040173.
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Swarner, Joyce Carroll. "Ordinal size scaling in preschool children." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184584.
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Young children are limited in their usage of comparative adjectives and ordinal numbers, typical ways of describing ordinal relationships. However, research in a number of areas suggests the possibility of a precursor level of ordinal concept. To facilitate the search for precursor ordinal skills, ordinal ability was defined in ordinal measurement terms. Only "greater than - less than," asymmetric judgements were required. Additionally, linguistic demands were reduced by using family-role terms as size designators. Experimental manipulations included variations in scale size and in the complexity level of ordinal conceptualization. Solution strategies based on "good form" and on "pairwise comparison" were precluded by using pictures of randomly placed objects which could not be manipulated by the child. Ninety-six 3-6 year old children pointed to "Daddy," "Mommy," "Big boy/girl," "Little boy/girl," and "Baby" when shown sets of 3 to 5 circles or squares which differed only in size. Tasks were of three types: Identification, mapping labels onto a single set of objects; Coordination, mapping labels onto two identical sets of objects in which corresponding "family members" are the same size; and Transposition, mapping labels onto two separate sets in which corresponding family members are of different sizes. Data were analyzed in an Age (3), by Scale Size (3), by Complexity Level (3), by Shape (2) mixed design ANOVA, and significant main effects were obtained for all variables. Tasks became more difficult with increases in scale size, and in complexity level. Square objects were slightly more difficult than circular, and older children were more proficient than younger ones. Post hoc tests generally supported the obtained main effects. Finer grained analysis using Latent Trait procedures supported the global ANOVA results, and supported the hypothesis that the end points of a scale are easier than the central positions. Response patterns indicated that errors were size-related, and suggested transitional levels of performance. The present study demonstrates that children as young as three can demonstrate a precursor ordinal concept when the task is framed in familiar terms and is placed in a context which is meaningful for them.
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Scholtz, Marie-Louise. "A critical analysis of the teaching and learning of number concept in a Grade 2 class in the Western Cape." Thesis, Cape Peninsula University of Technology, 2012. http://hdl.handle.net/20.500.11838/2137.
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Thesis (MTech (Education))--Cape Peninsula University of Technology, 2012.This action research case study focussed on the teaching and learning of number concept development. The research was conducted in an English Grade 2 class in a primary school in a lower socio-economic community in Manenberg on the Cape Flats, The research is based on the constructivist theories of Piaget, Vygotsky and Feuerstein and was conducted in the paradigm of praxis. The focus of the research was six learners in a class of 43 who were identified by the class educator through the process of continued assessment as needing intervention. Initial data collection was conducted utilising a questionnaire. This instrument was chosen to allow for a gentle introduction and a less threatening means of collecting information from a fellow colleague. I entered the classroom initially as observer and later as participant-observer. I observed how the class teacher taught the superordinate and subordinate concepts of number concept. Some observation sessions were video-recorded to allow for richer data collection. Followup interviews with the class teacher to discuss observations made as well as introduce new teaching methods were audio-recorded. Data were analysed using the process of discourse analysis. I found that the teacher used a variety of different teaching methods, but tended to gravitate to rote teaching with transcription and drill work to develop and consolidate number concept. The learners acquired number concept by implementing previously taught methods without any real understanding. During intervention, it was noted that the focus group fared better when allowed to use concrete equipment.
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Mak, Yee-nei, and 麥伊妮. "What are the differences in conceptual and procedural knowledge of fractions between high and low ability learners?" Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B45589355.
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VanBrackle, Anita S. "The relationship of unmanipulated self-reports of children's internalized representation of numbers to mathematics achievement." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39925.
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Tracanella, Aline Tafarelo. "O Sistema de Numeração Decimal: um estudo sobre o valor posicional." Pontifícia Universidade Católica de São Paulo, 2018. https://tede2.pucsp.br/handle/handle/21279.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
As soon as children begin their school life, they already carry with them an idea about the numbers and operation of the Decimal Number System (DNS). However, this knowledge need to be systematized, extended and deepened appropriately in order to assist in the construction of other mathematical concepts. Given this problem, the present research aims to investigate the mobilized knowledge of the positional value in the DNS and the understanding of the characteristics of number zero in the same system by students of the fourth year of Elementary School. Therefore, it is done a brief historical context to rescue how the development of this kind of knowledge by ancient people has developed over time. As theoretical contributions, it is used the researches of Piaget & Szeminska, and of Kamii on the constructions of the number concept by the students. Regarding to the acquisition of the properties of the DNS, it is discussed the researches of Fayol, Lerner & Sadovsky as well as Zunino, who also studies the issue of the number zero in this system. To achieve the research objective, it is adopted the qualitative methodology, since the focus of it is on the mobilized knowledge by the students in the search for a solution to proposed activities. It was also developed an instrument with six exercises involving the positional value and the number zero, based on the proposed sequence in the Brandt version. One week after an application of the instrument, it was conducted a semistructured interview, which was of very important to understand the answers provided by the students. In the analysis and discussion of the obtained data, it is understand that the students mobilized knowledge about the numerical sequence and the criteria of comparison pointed out by Lerner & Sadovsky. In addition to these mobilized knowledge, the participants also used the contextualization of activities to justify their responses, using a comparison with everyday situations, such as, for example, age observation among children. Regarding the number zero, it was analyzed the meanings attributed to this number by the students during interviews. During the research phases, all students stated that zero “worth nothing”, but they have provided justifications that meet the historical facts pointed out in the brief contextualization carried out in the third chapter of the research. It is also noted that the participants are building their knowledge about DNS, presenting an unstable knowledge that changes according to the question asked regarding the proposed situation. The results found in this research indicate that the work with DNS needs to be continuous throughout the initial years of Elementary School, as the students continue to build their knowledge about DNS and expand their understanding of the number zero in the years after the literacy cycle
Assim que as crianças iniciam sua vida escolar, já carregam consigo alguma ideia sobre os números e sobre o funcionamento do Sistema de Numeração Decimal (SND). Todavia esses conhecimentos precisam ser sistematizados, ampliados e aprofundados adequadamente, para auxiliar na construção de outros conceitos matemáticos. Diante dessa problemática, a presente pesquisa tem por objetivo investigar que conhecimentos são mobilizados por alunos do quarto ano do Ensino Fundamental acerca do valor posicional no SND e sobre a compreensão do número zero nesse mesmo sistema. Para isso, buscamos em uma breve contextualização histórica resgatar como se deu o desenvolvimento desses saberes por povos antigos no decorrer do tempo. Como aportes teóricos, nos baseamos nas pesquisas de Piaget e Szeminska e de Kamii sobre a construção do conceito de número pelos alunos. Com relação à aquisição das propriedades do SND, discorremos sobre as pesquisas de Fayol e de Lerner e Sadovsky, bem como de Zunino, que aborda também a questão do número zero nesse sistema. Para atender ao objetivo da pesquisa, adotamos a metodologia de cunho qualitativo, pois o foco da investigação está nos conhecimentos mobilizados pelos educandos na busca por uma solução para as atividades propostas. Elaboramos um instrumento com seis exercícios envolvendo o valor posicional e o número zero, baseado na sequência proposta na tese de Brandt. Uma semana após a aplicação do instrumento, realizamos uma entrevista semiestruturada, que foi de suma importância para compreender com maior clareza as respostas fornecidas pelos alunos. Na análise e discussão dos dados obtidos, compreendemos que os estudantes mobilizaram conhecimentos acerca da sequência numérica e dos critérios de comparação apontados por Lerner e Sadovsky. Além desses conhecimentos mobilizados, os participantes também recorreram à contextualização das atividades para justificar suas respostas, usando a comparação com situações cotidianas, como, por exemplo, a observação da idade entre crianças. Com relação ao número zero, analisamos os significados atribuídos a esse número pelos alunos durante as entrevistas. Durante as fases da pesquisa, todos os educandos afirmaram que o zero “não vale nada”, mas trouxeram justificativas que vão ao encontro dos fatos histórico apontados na breve contextualização realizada no primeiro capítulo da investigação. Notamos também que os participantes estão construindo seus conhecimentos acerca do SND, apresentando um conhecimento não estável, ou seja, que se altera de acordo com a pergunta feita referente à situação proposta. Os resultados encontrados nessa pesquisa apontam que o trabalho com o SND precisa ser contínuo, durante todos os anos iniciais do Ensino Fundamental, pois os alunos continuam construindo seus conhecimentos acerca do SND e ampliando sua compreensão sobre o número zero nos anos posteriores ao ciclo de alfabetização
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Dias, Marisa da Silva. "Formação da imagem conceitual da reta real: um estudo do desenvolvimento do conceito na perspectiva lógico - histórica." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-10102007-145627/.
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O trabalho constitui-se na formação da imagem conceitual do professor, na inter-relação indivíduo-coletividade, a fim de compreender a relação da imagem conceitual com o desenvolvimento da reta real na perspectiva lógico-histórica desse conceito. Os procedimentos metodológicos fundamentam-se nas contribuições teóricas da pesquisa-ação, cujo problema social se configura no campo do ensino e da aprendizagem da matemática. Os sujeitos são educadores matemáticos: pesquisadora e professores do Ensino Fundamental e Médio. O desenvolvimento da imagem conceitual e aspectos de seu ensino realizou-se por meio de um curso de formação contínua para professores organizado sob os pressupostos da atividade orientadora de ensino e da perspectiva lógico-histórica do conceito. O curso abordou a transição de um campo numérico a outro, com foco na reta real, partindo da formulação do sistema de numeração posicional e a transição para o número natural, seguindo a fração como número racional, o irracional resultante da incomensurabilidade e o contínuo numérico - a reta real - como a captação numérica do movimento. Os aportes teórico-metodológicos do materialismo dialético e da atividade contribuíram para a compreensão do movimento da imagem conceitual. A análise da imagem conceitual orientou-se pela reprodução dos principais nexos conceituais no desenvolvimento do pensamento numérico. A intertextualidade, como recurso que proporciona evidenciar o movimento da imagem conceitual dos sujeitos na exposição e análise dos dados, possibilitou perceber que a dialética do pensamento numérico transita entre discreto-denso-contínuo, comensurável-incomensurável, finito-infinito, cardinalidade-ordenação. Neste movimento do pensamento revelam-se dilemas, a negação de um conhecimento, negação da negação, lógica dialética e lógica formal e as categorias dialéticas: forma e conteúdo, aparência e essência, análise e síntese, empírico e teórico, lógico e histórico, intuição e dedução. Conclui-se que o desenvolvimento da imagem conceitual individual de conceito matemático, ocorre na relação indivíduo-coletividade e, pode ser coerente com o significado científico elaborado historicamente por meio da realização de uma atividade orientadora de ensino fundamentada em pressupostos lógico-históricos do conceito.This work consists of a study of the formation teachers\' concept image by the individualcollective inter-relation, in order to understand the relation of concept image with the development of the number line in a logical-historical perspective of the concept. The methodological procedures are based on the action research theoretical contribution, whose social problem appears in the mathematics teaching and learning field. The subjects are mathematics educators: the researcher and secondary school teachers. The development of the concept image and its teaching aspects were achieved during a teacher continuous training course, which was organized according to the teaching oriented activity contributions and the logical-historical perspective of the concept. One approach of this training course was the transition from one numerical field to another; a special attention was focussed on the number line, beginning with the formulation of the positional number system and the transition to the natural number, regarding the fraction as a rational number, the irrational number as a result of the incommensurability. Other approach was the arithmetic continuity - as the numerical capitation of the movement. The theoretical and methodological basis of the dialectical materialism and the activity theory contribute to the understanding of the concept image movement. The concept image analysis was guided by the reproduction of the main internal connections of numerical thought development. The intertextuality, as a resource which highlights the subjects\' concept image in the exposition and in the data analysis, made possible to realize that the dialectic of the numerical thought oscillates between the discreet- dense-continuous, the incommensurable and the commensurable, the finite and the infinite, the cardinality and the ordinance. Dilemmas, negation of knowledge, negation of negation, dialectical and formal logic and dialectical categories: form and content, appearance and essence, analysis and synthesis, empirical and theoretical, logical and historical, intuition and deduction, are revealed in this movement. In conclusion, the individual concept image\'s development of the mathematical concept takes place in the individual-collective relations and it can be coherent with the historically elaborated scientific meaning by performing a teaching oriented activity based on the logical-historical concept assumptions.
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Fausset, Cara Bailey. "Comprehension of health risk probabilities: the roles of age, numeracy, format, and mental representation." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44832.
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Probabilities, an essential dimension of risk communication, can be presented in various formats including frequencies (e.g., 1 in 10), percentages (e.g., 10%), or verbal phrases (e.g., unlikely); the literature is mixed concerning which format best supports comprehension. Additionally, it is not well understood how people who vary in their level of numeracy understand those probabilities. The goal of the present three-phase within-participant study was to understand how the factors of format and numeracy influence comprehension and mental representations of probabilities for younger and older adults. Overall, the results of this research clearly indicated that comprehension and mental representation of health risk probabilities are influenced by format, age, and numeracy. To best support comprehension and comparison of health risk probabilities for younger adults and healthy older adults with varying numeracy, percent format should be used.
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De, Ford D. "Scale-up of bioreactors : The concept of bioreactor number and its relation to the physiology of industrial micro-organisms at different scales." Thesis, Teesside University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380694.
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Gomes, Rodrigo Rafael [UNESP]. "A noção de função em Frege." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/91131.
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gomes_rr_me_rcla.pdf: 970847 bytes, checksum: f1f63ef47745a8d3404205c27335f1b1 (MD5)Neste trabalho apresentamos e analisamos o conceito fregiano de função, presente nos três livros de Frege: Begriffsschrift, Os Fundamentos da Aritmética e Leis Fundamentais da Aritmética. Discutimos ao longo dele o que Frege entendia por função e argumento, as modificações conceituais que tais noções sofreram no período de publicação de seus livros e a importância dessas noções para a sua filosofia. Para tanto, analisamos a linguagem artificial do primeiro livro, a definição de número do segundo, e os casos particulares de funções que são definidos no terceiro, bem como as considerações contidas em outros escritos do filósofo alemão. Verificamos uma caracterização puramente sintática de função em Begriffsschrift, uma distinção entre o sinal de uma função e aquilo que ele denota em Os Fundamentos da Aritmética, e a associação de dois elementos distintos a uma expressão funcional em Leis Fundamentais da Aritmética: o seu sentido e a sua referência. Finalmente, constatamos que a originalidade do sistema fregiano reside na possibilidade de considerar esse ou aquele termo de uma proposição como o argumento (ou os argumentos) de uma função.
In this work we present and analyze the fregean concept of function, present in the three books by Frege: Begriffsschrift, The Foundations of the Arithmetic and Fundamental Laws of the Arithmetic. We discuss what Frege understood by function and argument, the conceptual modifications that such notions suffered in the period of publication of those books and the importance of these notions for his philosophy. For so much, we analyze the artificial language of the first book, the definition of number in the second, and the particular cases of functions that are defined in the third, as well as the considerations contained in other works by the philosopher. We verify a purely syntactic characterization of function in Begriffsschrift, a distinction between the sign of a function and what it denotes in The Foundations of the Arithmetic, and the association of two different elements to a functional expression in Fundamental Laws of the Arithmetic: its sense and its reference. Finally, we verify that the originality of the Frege´s system is based on the possibility of considering one or other term of a proposition as the argument (or the arguments) of a function.
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Dalung, Emma, and Mikael Johansson. "Kvalitetssäkring av monteringsmoment vid Fasta Motorers F11-montering utifrån en process-, felläges- och effektanalys." Thesis, Högskolan Väst, Institutionen för ingenjörsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:hv:diva-4257.
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I detta examensarbete har möjligheten att kvalitetssäkra en monteringsbana vid Parker Hannifin Manufacturing Sweden AB:s anläggning i Trollhättan utretts. Syftet med studien var att förbättra kvalitetssäkringen vid Fasta Motorers F11-montering och arbetet baserades på en tidigare utarbetad felläges- och effektanalys. För att styrka kundperspektivet genomfördes en undersökning av vad kunderna reklamerar, i form av PQP-anmälningar samt NCMR-rapporter. Genom att därefter identifiera kritiska monteringsmoment i felläges- och effektanalysen, PQP-anmälningar och NCMR-rapporter, var en prioritering möjlig att utföra. Prioriteringen resulterade i att feltyperna felvridet lagerhus, felplock av material samt kuggfel ansågs vara de mest kritiska att kvalitetssäkra. Målet med arbetet var att reducera det totala risktalsvärdet, vilket var möjligt genom en konceptgenerering samt ett konceptval för de specifika prioriteringarna. I samband med konceptgenereringen undersöktes, genom intervjuer med berörd personal, specifika kundbehov. Dessa kundbehov omarbetades därefter till målspecifikationer för att underlätta genereringen av koncept. Då informativa koncept var framtagna återstod ett val av det bäst lämpade konceptet. Valet utfördes med två olika metoder, screening och scoring samt 3P, för att ytterligare säkerställa att rätt koncept valts. Det var därmed möjligt att uppdatera felläges- och effektanalysen med de valda åtgärderna och då påvisa att syftet var uppnått. Syftet med kvalitetssäkringen uppnåddes genom att sänka det totala risktalsvärdet med 47,5 procent mot det tidigare risktalsvärdet, 6415.In this thesis an investigation has been made in order to find possibilities to assure the quality at an assembly line at Parker Hannifin Manufacturing Sweden AB:s facility in Trollhättan. The purpose with the study was to improve the quality assurance at Fixed Motors F11-assembly line, where the work was based on an already conducted process-FMEA. In order to verify and further investigate the customer perspective, an inquiry was also done to see what customers complained about, this with help of PQP, Product Quality Problems, and NCMR, Nonconformance reports. By analyzing the process-FMEA, PQP and NCMR reports an identification and prioritization of critical failures were made. The result from these steps was three failures, incorrect positioning of the bearing house, picking of incorrect material and incorrect gear timing. These three were considered to be the most critical failures to quality assure. The aim with the quality work were set to reduce the total RPN, Risk Priority Number, of the process-FMEA, which was rendered by applying a concept generation and a concept selection for the specific failures. In relation with the concept selection, interviews were made with staff that was considered important and vital for the project. This was made to identify specific customer needs regarding solutions to the three failures. From these needs a target specification was developed to ease the generation of concepts. After generating a number of well specified concepts, a concept selection was made using the two methods screening and scoring and an additional Parker method called 3P to further establish that the right concepts was chosen. Further it was then possible to update the process-FMEA with the chosen concept solutions and by doing that reaching the project aim. By implementing the solutions it was possible to reduce total RPN, 6415, with 47,5 percent.
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Gomes, Rodrigo Rafael. "A noção de função em Frege /." Rio Claro : [s.n.], 2009. http://hdl.handle.net/11449/91131.
Full textAbstract:
Orientador: Irineu BicudoBanca: Itala Maria Loffredo D'Otaviano
Banca: Paulo Isamo Hiratsuka
Resumo: Neste trabalho apresentamos e analisamos o conceito fregiano de função, presente nos três livros de Frege: Begriffsschrift, Os Fundamentos da Aritmética e Leis Fundamentais da Aritmética. Discutimos ao longo dele o que Frege entendia por função e argumento, as modificações conceituais que tais noções sofreram no período de publicação de seus livros e a importância dessas noções para a sua filosofia. Para tanto, analisamos a linguagem artificial do primeiro livro, a definição de número do segundo, e os casos particulares de funções que são definidos no terceiro, bem como as considerações contidas em outros escritos do filósofo alemão. Verificamos uma caracterização puramente sintática de função em Begriffsschrift, uma distinção entre o sinal de uma função e aquilo que ele denota em Os Fundamentos da Aritmética, e a associação de dois elementos distintos a uma expressão funcional em Leis Fundamentais da Aritmética: o seu sentido e a sua referência. Finalmente, constatamos que a originalidade do sistema fregiano reside na possibilidade de considerar esse ou aquele termo de uma proposição como o argumento (ou os argumentos) de uma função.
Abstract: In this work we present and analyze the fregean concept of function, present in the three books by Frege: Begriffsschrift, The Foundations of the Arithmetic and Fundamental Laws of the Arithmetic. We discuss what Frege understood by function and argument, the conceptual modifications that such notions suffered in the period of publication of those books and the importance of these notions for his philosophy. For so much, we analyze the artificial language of the first book, the definition of number in the second, and the particular cases of functions that are defined in the third, as well as the considerations contained in other works by the philosopher. We verify a purely syntactic characterization of function in Begriffsschrift, a distinction between the sign of a function and what it denotes in The Foundations of the Arithmetic, and the association of two different elements to a functional expression in Fundamental Laws of the Arithmetic: its sense and its reference. Finally, we verify that the originality of the Frege's system is based on the possibility of considering one or other term of a proposition as the argument (or the arguments) of a function.
Mestre
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Louange, Jemmy E. "An examination of the relationships between teaching and learning styles, and the number sense and problem solving ability of Year 7 students." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2007. https://ro.ecu.edu.au/theses/306.
Full textAbstract:
Independent studies of teaching for number sense and problem solving have revealed that teaching for either of them separately poses a great challenge for the teacher. Yet research focusing on the relationship between number sense and problem solving was virtually non-existent, although the relationship between students' number ·sense and problem solving ability was becoming more and more evident through various modes and endeavours. This study sought to explore what sort of relationships exist between students' number sense and their problem solving ability, and the contribution of the teacher's teaching style and the students' learning style towards students' performance in these two respective areas.
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Silva, Ana Paula Perovano dos Santos. "A concepção de professores dos anos iniciais do ensino fundamental sobre a construção do conceito de número pela criança." Pontifícia Universidade Católica de São Paulo, 2012. https://tede2.pucsp.br/handle/handle/10909.
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Previous issue date: 2012-03-19Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The present study aims to investigate concepts that are present when teachers proposes work the concept of number with students from 1st and 2nd years of elementary school of the Jequié BA. For both, we theoretical uses a framework that allows us to analize the number perspective: Mathematics Education emphasizing the ideas of Piaget and Kamii and Public Policy, translated in this work for the official documents, PCN, RCNEI and Curriculum Guidelines of the State of Bahia. To treat the optical of the teacher we add to this reflection, knowledge and conceptions of knowledge teachers. Developed research in a descriptive qualitative approach in with participated as subjects 13 teachers of the early years of elementary school for three scholls in the city of Jequié BA. Data collection was made though a questionnaire and semistructured interview. As a results of this process of reflection, it appears that the teachers have the idea that number is synonymous with the numeral, perform, too empirical evidence of design, trends and approaches of classical and formalistic socioetnocultural. That confusion may be reflected upon education implying a limition of teaching, restricting the number to work with the activities of reading and writing numerals. Hope helpin bringing ideas to teachers in relation to the construction of the concept of number for the child
O presente estudo tem por objetivo investigar que concepções estão presentes quando professores se propõe trabalhar o conceito de número com alunos do 1º e 2º anos do Ensino Fundamental de Jequié BA. Para tanto, buscamos aporte teórico recorre a um referencial teórico que permite analisar o número sob a perspectiva: da Educação Matemática enfatizando as ideias de Piaget e Kamii e das Políticas Públicas traduzidas neste trabalho pelos documentos oficiais PCN, RCNEI e Diretrizes Curriculares do Estado da Bahia. Para tratar a ótica do professor agregamos a essa reflexão, os conhecimentos, saberes e concepções dos professores.Desenvolvemos uma pesquisa na abordagem qualitativa de cunho descritivo em que participaram como sujeitos 13 professoras dos anos iniciais do Ensino Fundamental de três escolas da Cidade de Jequié BA. A coleta dos dados foi efetuada por meio de questionário e entrevista semiestruturada. Como resultado desse processo de reflexão, constata-se que as professoras têm a concepção de que número é sinônimo de numeral; percebemos, também, indícios da concepção empirista, e aproximações das tendências formalista clássica e socioetnocultural.Tal confusão pode se refletir no momento do ensino implicando numa limitação do trabalho docente, restringindo o trabalho com os número às atividades de leitura e escrita de numerais.Esperamos contribuir no sentido de trazer reflexões aos professores, em relação à construção do conceito de número pela criança
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Silva, Rosania Maria da. "Diferentes usos da variável por alunos do ensino fundamental." Pontifícia Universidade Católica de São Paulo, 2009. https://tede2.pucsp.br/handle/handle/11400.
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Previous issue date: 2009-05-22Secretaria da Educação do Estado de São Paulo
This report refers to a case study that aimed to check the understanding and usage of the variable for students of eighth grade, in questions that involving their symbolization, interpretation and manipulation. Thus, we used a tool called the theoretical and methodological the three uses of variable model (3UV), presented by Trigueros and Ursini (2001). This model relates the skills necessary to understanding the three main uses of the variable in school algebra: unknown number, general number and variables in functional relationship. As a methodological tool it was used to design a questionnaire to identify the meanings and uses of the variable by seventeen students of a public school in the city of São Paulo. Besides the application of the questionnaire, which was attended by an observer, were used in audio recordings and semi-structured interviews as tools for collecting information. The set of data was analyzed taking as references the Model 3UV and aspects that, according Caraça (1954) summarize the concept of variable: the symbolic and substantial. The results show the difficulty of symbolization, especially when it should be variable of roles in general number or functional relationship. The interpretation, these students, when questioned, citing the variable as a representative of any values, but not always referring to all that it represents, but also its coefficient. In procedures for manipulation, indicating a lack of interpretation of the variable in algebraic sentences, showing the predominance of the use of algorithms for the resolution and lack of understanding of the solutions obtained, even when used correctly. The results also show that the symbolic and substantive issues stand out, separately, depending on what the question requires
Este relatório se refere a um estudo de caso que teve por objetivo verificar a compreensão e os usos da variável por alunos de oitava série, em questões que envolvem sua simbolização, interpretação e manipulação. Para tal, foi utilizada uma ferramenta teórico-metodológica denominada Modelo dos três usos da variável (3UV), apresentada por Trigueros e Ursini (2001). Tal modelo relaciona as habilidades necessárias ao entendimento dos três principais usos da variável na álgebra escolar: incógnita, número genérico e variáveis em relação funcional. Como ferramenta metodológica foi utilizado na elaboração de um questionário para identificar os significados e usos da variável por dezessete alunos de uma escola da rede estadual da grande São Paulo. Além da aplicação do questionário, que contou com a presença de um observador, foram utilizadas gravações em áudio e entrevistas semi-estruturadas como instrumentos de coleta de informações. O conjunto de dados obtido foi analisado tomando como referências o Modelo 3UV e os aspectos que, segundo Caraça (1954) sintetizam o conceito de variável: o simbólico e o substancial. Os resultados mostram a dificuldade de simbolização, principalmente quando deve ser por variáveis nos papéis de número genérico ou em relacionamento funcional. Quanto à interpretação, esses alunos, quando questionados, citam a variável como representante de quaisquer valores, porém, nem sempre se referindo ao conjunto que ela representa, mas também ao seu coeficiente. Em procedimentos de manipulação, indicam a falta de interpretação da variável nas sentenças algébricas, mostrando o predomínio do uso de algoritmos para a resolução e a falta de entendimento das soluções obtidas, mesmo quando foram utilizados corretamente. Os resultados também apontam que os aspectos simbólico e substancial se destacam, separadamente, dependendo do que requer a questão
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BOCCARDO, GIULIO. "Experimental and numerical investigation of a high boost and high injection pressure Diesel engine concept for heavy duty applications." Doctoral thesis, Politecnico di Torino, 2018. http://hdl.handle.net/11583/2709722.
Full textAbstract:
The upcoming European Stage V emissions regulation for Non-Road Heavy Duty Diesel Engines will force OEMs to adopt Diesel Particulate Filters, adding a further degree of complexity to the aftertreatment system, which in several cases already includes specific devices for NOx reduction. Since complex aftertreatment systems can rise packaging problems as well as reliability issues, a project in collaboration with Kohler, Politecnico di Torino, Ricardo and Denso, has been carried out to explore the feasibility of a Stage V compliant SCR-free architecture for a 90kW Non Road Diesel engine. To this scope a prototype engine based on the Kohler KDI3404, was equipped with a low-pressure Exhaust Gas Recirculation system, a two-stage turbocharger and a 3000 bar injection pressure-capable Fuel Injection System.
This thesis focuses on the experimental and numerical assessment of emissions and performances of this engine architecture over the Stage V certification procedure. It will be shown how the high-pressure Fuel Injection System is the key technology to meet the stringent requirements, demonstrating how increasing the injection pressure from 2000 to 3000 bar can dramatically improve the NOx-Soot and NOx-Particulate Number trade-off, together with engine efficiency, without adversely affecting the emission of nanoparticles. Moreover, the use of extremely high injection pressures in conjunction with after injection as a soot reduction technique, was found to be capable of achieving up to 50% smoke reduction with a more than acceptable engine efficiency degradation.
Thanks to a dedicated steady state and transient calibration, the engine was able to run a compliant NRSC and NRTC with more than 10% margin on NOx and a level of particulate matter and particulate number which can be easily managed by the DOC+DPF aftertreatment system. However, some components of the tested engine, such as the turbochargers, were found to be far from the optimal, thus resulting into relatively poor efficiency figures.
Therefore, a 1D-CFD model featuring predictive combustion and emissions models was developed in order to assess the full potentials of this architecture on a kind of “virtual test rig”, on which different components could be easily evaluated.
The model results proved that, with a better design of the exhaust and EGR line, and with a slightly higher performance turbocharger, consistent engine efficiency improvements could be obtained, making the SCR-free solution as a valuable alternative to the SCR architecture to meet the Stage V emissions regulations.