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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
231

Costs of reproduction in a temperate-zone lizard, Elgaria coerulea

Rutherford, Pamela 02 November 2018 (has links)
Understanding why organisms possess certain combinations of life-history traits is important to our understanding of how natural selection operates. Combinations of life-history traits evolve in response to the costs of current reproduction to both survival and future reproduction. Reproductive costs have been broadly categorised into two types: 1) survival costs, and 2) potential fecundity costs. As a means of predicting and explaining variation in reproductive investment in lizards and snakes, Shine and Schwarzkopf (1992) attempted to determine the relative importance of the two kinds of costs to individual lifetime fitness (the SS model). They concluded that most lizard species are unlikely to make trade-offs between current and future reproduction (fecundity costs). In this study of a temperate-zone lizard, Elgaria coerulea, I have three main objectives: 1) to provide the first natural history data for a Canadian population of this species, 2) to describe life-history traits for this population, and 3) to formally test the predictions of the SS model and discuss its potential predictive power. Individual Elgaria coerulea occupy relatively small areas, thus minimising costs associated with a long-distance migration. In addition to having limited movement, Elgaria coerulea rely on hiding as one of their main anti-predator strategies, although there is sex-dependent variation in their retreat-site selection. Emergence patterns of male Elgaria coerulea did not change over their reproductive cycle. In contrast, the probability of capturing an adult female in the open steadily increased over the summer. These results suggest that the benefits of emerging from cover outweigh the costa in females, but not males. Annual survival rate of adult females was 44% and juvenile survival rate was 22%. The survival rate of adult males likely fell in between these values, but I was not able to estimate it directly because of small sample sizes. I infer from the female’s relatively high survival rate that the necessity for gravid females to spend more time in the open during gestation does not translate simply to increased mortality. Gravid females have reduced sprint speed and sprint speed was inversely related to the burden of the clutch. Therefore, gravid females presumably could reduce their predation risk by remaining closer to cover than males or juveniles. However, this is not the case; all northern alligator lizards remained close to cover. Thus, the lack of shift in anti-predator behaviour of gravid females may be a result of all Elgaria coerulea relying on crypsis rather than sprinting as an anti-predator defence. I did detect a difference in body coloration. Gravid females had more black pigmentation than males or juveniles. The black pigmentation may help females blend in with their background better than males, thereby reducing predation risk, or help increase their body temperature at a quicker rate. Another important anti-predator strategy in Elgaria coerulea is tail autotomy, and once again I measured variation in this trait between males and females. Gravid females never lose small parts of their tails, perhaps giving them extra time to escape from a predator. Furthermore, recent tail loss was not seen in gravid females during late gestation. By contrast, males were equally likely to autotomise at any time of the year. Females may be less likely than males to lose their tails because of the potential reproductive gain by females with intact tails. Females with intact tails had a higher probability of being reproductive and females with longer tails had larger newborn. Finally, I show that some Elgaria coerulea trade current reproduction for growth. Examination of reproductive costs in Elgaria coerulea revealed problems with incorporating cold-climate reptile species into the SS model. Because cold-climate species spend significant time in hibernation each year they have relatively short interclutch intervals. For these species the SS model predicts that trade-offs between current and future reproduction are more likely. The likelihood of fecundity costs also increases, even that concurrent growth and reproduction may be more prevalent than previously believed, as is evident in Elgaria coerulea. Both of these factors need to be incorporated into the SS model is increase our ability to make predictions about the evolution of reproductive effort in cold-climate species. / Graduate
232

Uma abordagem para aumentar a privacidade de localização assegurada por mix-zones em redes veiculadas

Carianha, Antônio Marcos Lopez Fernandez January 2011 (has links)
Submitted by LIVIA FREITAS (livia.freitas@ufba.br) on 2016-01-29T15:21:05Z No. of bitstreams: 1 Dissertação_Antônio_Carianha.pdf: 918883 bytes, checksum: 8f268850189f18efdff2b10f919f8f62 (MD5) / Approved for entry into archive by LIVIA FREITAS (livia.freitas@ufba.br) on 2016-03-17T15:46:28Z (GMT) No. of bitstreams: 1 Dissertação_Antônio_Carianha.pdf: 918883 bytes, checksum: 8f268850189f18efdff2b10f919f8f62 (MD5) / Made available in DSpace on 2016-03-17T15:46:28Z (GMT). No. of bitstreams: 1 Dissertação_Antônio_Carianha.pdf: 918883 bytes, checksum: 8f268850189f18efdff2b10f919f8f62 (MD5) / As redes veiculares consistem em sistemas de comunicação que possibilitam que nos veiculares possam interagir entre si e com uma infraestrutura de suporte existente ao longo do caminho percorrido por estes. Exemplos de possíveis aplicações para estas redes incluem prevenção de colisões e difusão de informações sobre condições de trafego e da pista. Um dos principais desafios para sua adoção em larga escala e garantir a privacidade de informações particulares dos seus usuários, tais como identidade do motorista, dinâmica de seus automóveis e percurso realizado rotineiramente. A ausência da garantia de privacidade pode inibir a participação dos usuários em redes veiculares, resultando no fracasso da implantação destas.Para proteger a privacidade de localização do usuário, este deve permanecer anonimo e não-rastreável durante seu percurso. Soluções recentes asseguram privacidade de localização por meio de “mix-zones”, regiões onde um no veicular pode mudar sua identidade anonima temporária (pseudônimo) sem ser rastreado. Embora as mix-zones evitem ataques provindos de fora da rede de comunicação veicular, elas são vulneráveis a ataques internos, pois dentro de uma mix-zone as mensagens são codificadas por meio de uma chave secreta de grupo. Para tratar de tal vulnerabilidade, este trabalho propõe novos mecanismos, de modo a contribuir para aumentar o nível de privacidade de localização proporcionado por tais regiões. Através da realização de simulações minuciosas, a abordagem proposta é avaliada e comparada a soluções existentes. Os resultados mostram que a solução proposta é viável e fornece maior nível de privacidade de localização.
233

Concentration-Discharge Relations in the Critical Zone: Implications for Resolving Critical Zone Structure, Function, and Evolution

Chorover, Jon, Derry, Louis A., McDowell, William H. 11 1900 (has links)
Critical zone science seeks to develop mechanistic theories that describe critical zone structure, function, and long-term evolution. One postulate is that hydrogeochemical controls on critical zone evolution can be inferred from solute discharges measured down-gradient of reactive flow paths. These flow paths have variable lengths, interfacial compositions, and residence times, and their mixing is reflected in concentration-discharge (C-Q) relations. Motivation for this special section originates from a U.S. Critical Zone Observatories workshop that was held at the University of New Hampshire, 20-22 July 2015. The workshop focused on resolving mechanistic CZ controls over surface water chemical dynamics across the full range of lithogenic (e.g., nonhydrolyzing and hydrolyzing cations and oxyanions) and bioactive solutes (e.g., organic and inorganic forms of C, N, P, and S), including dissolved and colloidal species that may cooccur for a given element. Papers submitted to this special section on concentration-discharge relations in the critical zone include those from authors who attended the workshop, as well as others who responded to the open solicitation. Submissions were invited that utilized information pertaining to internal, integrated catchment function (relations between hydrology, biogeochemistry, and landscape structure) to help illuminate controls on observed C-Q relations.
234

Geochemistry in the Critical Zone: limestone-shale and kimberlite weathering in the Flint Hills, Kansas, USA

Gura, Colleen Marie January 1900 (has links)
Master of Science / Department of Geology / Saugata Datta / Pamela Kempton / The Critical Zone is the realm where rocks meet life. This study examines the physicochemical interactions that occur when interbedded limestone-shale systems and kimberlitic rocks weather to form soils. Fast weathering processes with extensive soil loss have been a major environmental concern in the Flint Hills for decades. Knowledge of soil formation processes, rates of formation and subsequent loss, and understanding how these processes differ in different systems are critical for managing soil as a resource. Kimberlites are CO₂-rich igneous rocks that are high in Mg and Fe; they are compositionally distinct from the Paleozoic limestones and shales found throughout the rest of the region. This study will compare the geochemistry and mineralogy of the Stockdale Kimberlite in Riley county to that of interbedded limestone-shale system typical of the Flint Hills as sampled from Konza Prairie LTER. Bulk composition and mineralogy of the soils overlying these different bedrock types have been analyzed using X-Ray Fluorescence (XRF), X-Ray Diffraction (XRD), bulk elemental extractions, and particle size analyses. Results show that the kimberlitic soils have higher concentrations of Fe, Mg, Ca, K and some trace elements in greater proportions (e.g. Ti, Ni, Cu). The weathering products differ mineralogically as well, e.g. lizardite is abundant in kimberlitic soils and absent from the limestone terranes. Kimberlite derived soils also contain minerals as well such as kleberite (an alteration product of illminite), phlogopite, and magnetite. Kimberlite-sourced soils have different physical properties than the thin limestone-sourced soils surrounding them. Particle size analysis shows that the limestone-shale soils have different proportions of the clay size fraction in different core locations (~47% in highlands, ~51% at watershed base, ~41% in lowlands) whereas kimberlitic soils have a larger sand fraction than Konza (~19% vs. 10%). Clay minerals from the limestone-shale system reveals clay micas, kaolinite, and some expandable 2:1 layer silicates. Clay minerals from kimberlite-sourced soils are identified as primarily smectites with clay micas and kaolinites. Similarities between the kimberlite and limestone-shale soils are primarily seen in the shallower portions of the soil profile, suggesting that loess/wind-blown dust make a significant contribution to the soils in both areas. It could be concluded that kimberlite-sourced and limestone-shale-sourced soils produce weathering products that differ both chemically and mineralogically and could potentially have agricultural significance in terms of water retention as well as ionic and nutrient mobilities in these soils.
235

Swash zone dynamics of coarse-grained beaches during energetic wave conditions

Almeida, Luis Pedro January 2015 (has links)
Coarse-grained beaches, such as pure gravel (PG), mixed sand-gravel (MSG) and composite (CSG) beaches, can be considered as one of the most resilient non-cohesive morpho-sedimentary coastal environments to energetic wave forcing (e.g., storms). The hydraulically-rough and permeable nature of gravel (D50 > 2 mm), together with the steep (reflective) beach face, provide efficient mechanisms of wave energy dissipation in the swash zone and provide a natural means of coastal defence. Despite their potential for shore protection very little is known about the response of these environments during high energetic wave conditions. Field measurements of sediment transport and hydrodynamics on coarse-grained beaches are difficult, because there are few instruments capable of taking direct measurements in an energetic swash zone in which large clasts are moving, and significant morphological changes occur within a short period of time. Remote sensing methods emerge in this context as the most appropriate solution for these types of field measurement. A new remote sensing method, based around a mid-range (~ 50 m) 2D laser-scanner was developed, which allows the collection of swash zone hydrodynamics (e.g., vertical and horizontal runup position, swash depth and velocity) and bed changes on wave-by-wave time scale. This instrument allowed the complete coverage of the swash zone on several coarse-grained beaches with a vertical accuracy of approximately 0.015 m and an average horizontal resolution of 0.07 m. The measurements performed with this new methodology are within the accuracy of traditional field techniques (e.g. video cameras, ultrasonic bed-level sensors or dGPS). Seven field experiments were performed between March 2012 and January 2014 on six different coarse-grained beaches (Loe Bar, Chesil, Slapton, Hayling Island, Westward Ho! and Seascale), with each deployment comprising the 2D laser-scanner together with complementary in-situ instrumentation (e.g., pressure transducer, ADV current meter). These datasets were used to explore the hydrodynamics and morphological response of the swash zone of these different environments under different energetic hydrodynamic regimes, ranging from positive, to zero, to negative freeboard regimes. With reference to the swash zone dynamics under storms with positive freeboard regimes (when runup was confined to the foreshore) it was found that extreme runup has an inverse relationship with the surf scaling parameter (=2Hs /gTptan2). The highest vertical runup excursions were found on the steepest beaches (PG beaches) and under long-period swell, while lower vertical runup excursions where linked to short-period waves and beaches with intermediate and dissipative surf zones, thus demonstrating that the contrasting degree of wave dissipation observed in the different types of surf zones is a key factor that control the extreme runup on coarse-grained beaches. Contrasting morphological responses were observed on the different coarse-grained beaches as a result of the distinct swash\surf zone hydrodynamics. PG beaches with narrow surf zone presented an asymmetric morphological response during the tide cycle (accretion during the rising and erosion during the falling tide) as a result of beach step adjustments to the prevailing hydrodynamics. On dissipative MSG and CSG beaches the morphological response was limited due to the very dissipative surf zone, while on an intermediate CSG beach significant erosion of the beach face and berm was observed during the entire tide cycle as a result of the absence of moderate surf zone wave dissipation and beach step dynamics. Fundamental processes related to the link between the beach step dynamics and the asymmetrical morphological response during the tidal cycle were for the first time measured under energetic wave conditions. During the rising tide the onshore shift of the breaking point triggers the onshore translation of the step and favors accretion (step deposit development), while during the falling tide the offshore translation of the wave breaking point triggers retreat of the step and favours backwash sediment transport (erosion of the step deposit). Under zero and negative freeboard storm regimes (when runup exceeds the crest of the barrier or foredune), field measurements complimented by numerical modelling (Xbeach-G) provide clear evidence that the presence of a bimodal wave spectrum enhances the vertical runup and can increase the likelihood of the occurrence of overtopping and overwash events over a gravel barrier. Most runup equations (e.g., Stockdon et al., 2006) used to predict the thresholds for storm impact regime (e.g., swash, overtopping and overwash) on barriers lack adequate characterisation of the full wave spectra; therefore, they may miss important aspects of the incident wave field, such as wave bimodality. XBeach-G allows a full characterization of the incident wave field and is capable of predicting the effect of wave spectra bimodality on the runup, thus demonstrating that is a more appropriate tool for predicting the storm impact regimes on gravel barriers. Regarding the definition of storm impact regimes on gravel barriers, it was found that wave period and wave spectra bimodality are key parameters that can affect significantly the definition of the thresholds for these different regimes. While short-period waves dissipate most of their energy before reaching the swash zone (due to breaking) and produce short runup excursions, long-period waves arrive at the swash zone with enhanced heights (due to shoaling) and break at the edge of the swash, thus promoting large runup excursions. When offshore wave spectrum presents a bimodal shape, the wave transformation on shallow waters favours the long period peak (even if the short-period peak is the most energetic offshore) and large runup excursions occur. XBeach-G simulations show that the morphological response of fine gravel barriers is distinct from coarse gravel barriers under similar overtopping conditions. While on coarser barriers overtopping regimes are expected to increase the crest elevation and narrow the barrier, on fine barriers sedimentation occurs on the back of the barrier and in the lower beach face. Such different sedimentation patterns are attributed to the different hydraulic conductivity of the different sediment sizes which control the amount of flow dissipation (due to infiltration) and, therefore, the capacity of the flow to transport sediment across and over the barrier crest. The present findings have significantly improved our conceptual understanding of the response of coarse-grained beaches during storms. A new field technique to measure swash dynamics in the field was developed during this thesis and has great potential to become widely used in a variety of coastal applications.
236

A fast-track method for fatigue crack growth prediction with a cohesive zone model

Dahlan, Hendery January 2013 (has links)
An alternative point of view with regard to understanding the mechanism of energy transfer involved to create new surface is considered in this study. A combination of transport equation and cohesive element is presented. A practical demonstration in 1-D is presented to simulate the mechanism of energy transfer in a damage zone model for both elastic and elastic-plastic materials. The combination of transport and cohesion element shows the extent elastic energy plays to supply the energy required for crack growth. Meanwhile, plastic energy dissipation for an elastic-plastic material is shown to be well described by the transport approach. The cohesive zone model is one of many alternative approaches used to simulate fatigue crack growth. The model incorporates a relationship between cohesive traction and separation in the zone ahead of a crack tip. The model introduces irreversibility into the constitutive relationships by means of damage accumulation with cyclic loading. The traction-separation relationship underpinning the cohesive zone model is not required to follow a predetermined path, but is dependent on irreversibility introduced by decreasing a critical cohesive traction parameter. The approach can simulate fatigue crack growth without the need for re-meshing and caters for constant amplitude loading and single overloading. This study shows the retardation phenomenon occurring in elastic plastic-materials due to single overloading. Plastic materials can generate a significant plastic zone at the crack which is shown to be well captured by the cohesive zone model approach. In a cohesive zone model, fatigue crack growth involves the dissipation of separation energy released per cycle. The crack advance is defined by the total energy separation dissipated term equal to the critical energy release rate or toughness. The effect of varying toughness with the assumption that the critical traction remains fixed is investigated here. This study reveals that varying toughness does not significantly affect the stress distribution along the crack path. However, plastic energy dissipation can significantly increase with toughness. A new methodology called the fast-track method is introduced to accelerate the simulation of fatigue crack growth. The method adopts an artificial material toughness. The basic idea of the proposed method is to decrease the number of cycle for computation by reducing the toughness. By establishing a functional relationship between the number of cycles and variable artificial toughness, the real number of cycles can be predicted. The proposed method is shown to be an excellent agreement with the numerical results for both constant amplitude loading and single overloading. A new approach to predict fatigue crack growth curves is presented. The approach combines the fast-track method and an extrapolation methodology. The basic concept is to establish a function relationship using the curve fitting technique applied to data obtained from preliminary calculation of fast-track methodology. It is shown in this thesis that the new methodology provides excellent agreement with an empirical model. The methodology is limited to constant amplitude loading and small scale yielding conditions. It is shown in the thesis that fatigue crack growth curves for variable amplitude loading can be predicted by using the data set for fatigue crack growth rate for constant amplitude loading. A retardation parameter can be deduced from the number of cycles delayed using the cohesive zone model. The retardation parameter is established by performing calculation for different toughness. This methodology is shown to give good agreement with results from empirical models for different variable amplitude loading conditions.
237

The Yarlung suture mélange, Lopu Range, southern Tibet: Provenance of sandstone blocks and transition from oceanic subduction to continental collision

Metcalf, Kathryn, Kapp, Paul 08 1900 (has links)
With the aim of better understanding the history of ocean closure and suturing between India and Asia, we conducted a geologic investigation of a siliciclastic matrix tectonic melange within the western Yarlung suture zone of southern Tibet (Lopu Range region, similar to 50 km northwest of Saga). The siliciclastic matrix melange includes abundant blocks of ocean plate stratigraphy and sparse blocks of sandstone. Metapelite and metabasite blocks in the melange exhibit lower greenschist fades mineral assemblages, indicating that they were not deeply subducted. We obtained detrital zircon U-Pb geochronologic and sandstone petrographic data from sandstone blocks in the melange and sandstone beds from Tethyan Himalayan strata exposed to the south of the suture. The sandstones from both units are all similar in U-Pb detrital zircon age spectra and petrography to the nearby Tethyan Cretaceous-Paleocene Sangdanlin section, which records the earliest appearance (at similar to 59 Ma) of arc-affinity strata deposited conformably on Indian-affinity strata. Two Paleocene sandstones, one of which is a schistose block incorporated in the siliciclastic matrix melange, yielded indistinguishable maximum depositional ages of similar to 59 Ma. Mesozoic Asian-affinity sandstone blocks previously documented in the siliciclastic matrix melange 200-500 km along strike to the east are notably absent in the Lopu Range region. We documented a gradational transition in structural style from the block-in-matrix melange in the northeast to the south-vergent Tethyan thrust belt in the southwest. Blocks of Tethyan Himalayan strata increase in size and the volumetric proportion of matrix decreases from northeast to southwest. We conclude that no arc-affinity sandstone blocks were incorporated into the subduction complex until India-Asia collision at similar to 59 Ma when the Xigaze forearc basin became overfilled and Tethyan Himalayan strata entered the trench. As collision progressed, there was a gradual transition in structural style from block-in-matrix melange formation to imbricate-style thrust belt formation. (C) 2017 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.
238

Les pouvoirs de police administrative du préfet de zone de défense et de sécurité / The administrative police skill of the « préfet de zone de défense et de sécurité »

Capart, Rémi 09 January 2015 (has links)
Les zones de défense ont été créées par le décret n° 50-1189 du 29 septembre 1950 relatif à l'organisation de la défense en surface du territoire métropolitain. D'abord à vocation principalement militaire, elles sont devenues au fil du temps de véritables circonscriptions administratives placées sous l'autorité d'un préfet de zone de défense et de sécurité. Représentant de l'Etat dans sa zone, ce haut fonctionnaire est en particulier chargé de la préparation et de l'exécution des mesures de sécurité nationale. De fait, il est susceptible de traiter des situations de crise dont l'ampleur dépasse la compétence territoriale des préfets de département et nécessitant une gestion globale à l'échelle de la zone. Les mouvements sociaux générés par les crises financières, les pandémies ou bien les catastrophes technologiques et naturelles telle que la tempête Klaus sont autant de menaces contemporaines pour l'ordre public, non plus seulement appréhendé à l'échelon départemental, mais zonal et voire national. C'est à partir de ce constat que la commission Malet au travers du livre blanc sur la défense et la sécurité nationale et l'inspection générale de l'administration ont proposé en 2008 l'attribution d'un pouvoir de police administrative au préfet de zone de défense et de sécurité en complément de ceux dont il dispose par ailleurs. Ce projet de thèse ambitionne de définir le contenu et les limites des pouvoirs de police administrative du préfet de zone de défense et de sécurité. / The administrative police skill of the « préfet de zone de défense et de sécurité ».The defense and security area were created in France in 1950 by an a government's decree which concerned the organization of the territory defense. Their first vocation was mainly military. Afterward They became real administrative districts placed under the responsibility of an administrative authority : The "préfet de zone de défense et de sécurité". (There's no equivalent of that administrative authority in other countries). Representative of the central power, this state man is responsible for the preparation and for the execution of the national security measures. He is thus able to of handling crisis situations when these can't be manage by the lower statutory authority (the "préfet" of the department). Industrial or Natural disasters as storms which struck France, floods, etc. even the terrorist risk, are so many threats which concern the public order. The multiplicity of these protean phenomenons requires to adapt tools to their evolutions. This obligation to adapt the French device has these problems was realized in 2008 by a strategic document : "le livre blanc sur la défense et la sécurité nationale". Numerous pieces of the security instrument were modified, amplified, strengthened. The "préfet de zone de défense et de sécurité" saw her skills manifestly strengthened by the attribution of an administrative police power. The administrative police is a cardinal notion of the French organization. She allows to protect the public order and punish its disorder by administrative measures. This power now in the hands of the "prefet de zone de defense et de securité" and it's applied on her same named area. The potentialities offered by this power are immense but they must be understood to be mastered. It is the objective of this thesis : present the contents and the limits of administrative police skill of the "préfet de zone de défense et de sécurité".
239

Living Pedagogical Moments Between Curriculum as Lived and Curriculum as Plan: A Phenomenological Inquiry Into the Tensions of Teacher Education

Knowles, Kelsey January 2015 (has links)
This master’s research is a phenomenological inquiry into the pedagogical moment in teacher education. This phenomenon is explored through a conceptual lens that draws from the phenomenological pedagogical ideals that are intrinsic to the work of both Ted Aoki and Max van Manen. Following a comprehensive outline of the phenomenological methodology that guides this thesis, the pedagogical moment is described in terms of three phases: tension, opening and pulse. The phenomenon is further explored through several sub themes relating to the lifeworld existentials (time, body, space, relation to other). This research intertwines several phenomenological concepts (such as intentionality, embodiment, consciousness, pedagogy, and motion sensitive phenomenology), within the context of one “living” phenomenon as a way of shedding light on what it is like to experience a pedagogical moment from within the tensions of practicum teaching.
240

Things Kids Think With: The Role of the Physical Properties of Mathematical Tools in Children's Learning in the Context of Addition of Fractions

Abtahi, Yasaman January 2016 (has links)
This research was designed to examine the role of the physical properties of the mathematical tools, in children’s learning in the context of adding two fractions. My two research questions were: (1) How does the feedback from the mathematical tools play a mediating role between the physical actions of the child with respect to the mathematical affordances of the tools and the child’s thinking about and learning and knowing of solving addition of fractions problems? And (2) What role is played by mathematical tools in the emergence of a Zone of Proximal Development during the child’s solving of addition of fractions problems? To address these questions, I interviewed 13 grade 7 students in Ottawa, Ontario, in groups of two and in three rounds of 30-minute interviews per group. The results showed that the physical properties of the tools play a role in how children perceived the mathematical affordances of the tool, attached mathematical meaning to the tools, created mathematical artefacts and solved the addition of fractions problems. Moreover, the findings show that in children’s interactions with mathematical tools, at times, the Zone of Proximal Development (ZPD) emerged, with the guidance provided by the tools. I conclude that children’s interaction with the tools provided them the possibility of learning newer forms of reflections, expressions and actions in relation to adding two fractions. This learning was a result of a complex and intertwined relationship between the immediate physical properties and affordances of the tool, the traces of the thoughts of the designer of the tools, as well as the children’s previous knowing of fractions. With this study, I extend the Vygotskian notion of the more knowledgeable other within the ZPD to include not only agents (children and adults) but also tools.

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