Mechanistic studies on the degradation of gasoline oxygenates by advanced oxidation technologies and the reaction of 4-methyl-1,2,4-triazoline-3,5-dione with tetracyclopropylethylene

Gasoline oxygenates (MTBE, methyl tert-butyl ether; DIPE, di-isopropyl ether; ETBE, ethyl tert-butyl ether; TAME, tert-amyl ether) are added to gasoline to boost octane and enhance combustion. The combination of large scale use, high water solubility and only minor biodegradability has now resulted in a significant gasoline oxygenate contamination occurring in surface, ground, and drinking water systems. Combination of hydroxyl radical formation and the pyrolytic environment generated by ultrasonic irradiation (665 kHz) leads to the rapid degradation of MTBE and other gasoline oxygenates in aqueous media. ^ The presence of oxygen promotes the degradation processes by rapid reaction with carbon centered radicals indicating radical processes involving O 2 are significant pathways. A number of the oxidation products were identified. The formation of products (alcohols, ketones, aldehydes, esters, peroxides, etc) could be rationalized by mechanisms which involve hydrogen abstraction by OH radical and/or pyrolysis to form carboncentered radicals which react with oxygen and follow standard oxidation chain processes. ^ The reactions of N-substituted R-triazolinediones (RTAD; R = CH 3 or phenyl) have attracted considerable interest because they exhibit a number of unusual mechanistic characteristics that are analogous to the reactions of singlet oxygen (1O2) and offer an easy way to provide C-N bond(s) formation. The reactions of triazolinedione with olefins have been widely studied and aziridinium imides are generally accepted to be the reactive intermediates. ^ We observed the rapid formation of an unusual intermediate upon mixing tetracyclopropylethylene with 4-methyl-1,2,4-triazoline-3,5-dione in CDCl 3. Detailed characterization by NMR (proton, 13C, 2-D NMRs) indicates the intermediate is 5,5,6,6-tetracyclopropyl-3-methyl-5,6-dihydro-oxazolo[3,2- b][1,2,4]-triazolium-2-olate. Such products are extremely rare and have not been studied. Upon warming the intermediate is converted to 2 + 2 diazetidine (major) and ene product (minor). ^ To further explore the kinetics and dynamics of the reaction activation energies were obtained using Arrhenius plots. Activation energies for the formation of the intermediate from reactants, and 2+2 adduct from the intermediate were determined as 7.48 kcal moll and 19.8 kcal mol−1 with their pre-exponential values of 2.24 × 105 dm 3 mol−1 sec−1 and 2.75 × 108 sec−1, respectively, meaning net slow reactions because of low pre-exponential values caused by steric hindrance. ^

Origin of the Grande Ronde Formation flows, Columbia River flood basalt group

Lavas belonging to the Grande Ronde Formation (GRB) constitute about 63% of the Columbia River Basalt Group (CRBG), a flood basalt province in the NW United States. A puzzling feature is the lack of phenocrysts (< 5%) in these chemically evolved lavas. Based mainly on this observation it has been hypothesized that GRB lavas were nearly primary melts generated by large-scale melting of eclogite. Another recent hypothesis holds that GRB magmas were extremely hydrous and rose rapidly from the mantle such that the dissolved water kept the magmas close to their liquidi. I present new textural and chemical evidence to show that GRB lavas were neither primary nor hydrous melts but were derived from other melts via efficient fractional crystallization and mixing in shallow intrusive systems. Texture and chemical features further suggest that the melt mixing process may have been exothermic, which forced variable melting of some of the existing phenocrysts. ^ Finally, reported here are the results of efforts to simulate the higher pressure histories of GRB using COMAGMAT and MELTS softwares. The intent was to evaluate (1) whether such melts could be derived from primary melts formed by partial melting of a peridotite source as an alternative to the eclogite model, or if bulk melting of eclogite is required; and (2) at what pressure such primary melts could have been in equilibrium with the mantle. I carried out both forward and inverse modeling. The best fit forward model indicates that most primitive parent melts related to GRB could have been multiply saturated at ∼1.5--2.0 GPa. I interpret this result to indicate that the parental melts last equilibrated with a peridotitic mantle at 1.5--2.0 GPa and such partial melts rose to ∼0.2 GPa where they underwent efficient mixing and fractionation before erupting. These models suggest that the source rock was not eclogitic but a fertile spinel lherzolite, and that the melts had ∼0.5% water. ^

Phosphorus Biogeochemistry and the Impact of Phosphorus Enrichment: Why Is the Everglades so Unique?

The Florida Everglades is extremely oligotrophic and sensitive to small increases in phosphorus (P) concentrations. P enrichment is one of the dominant anthropogenic impacts on the ecosystem and is therefore a main focus of restoration efforts. In this review, we synthesize research on P biogeochemistry and the impact of P enrichment on ecosystem structure and function in the Florida Everglades. There are clear patterns of increased P concentrations and altered structure and processes along nutrient-enrichment gradients in the water, periphyton, soils, macrophytes, and consumers. Periphyton, an assemblage of algae, bacteria, and associated microfauna, is abundant and has a large influence on phosphorus cycling in the Everglades. The oligotrophic Everglades is P-starved, has lower P concentrations and higher nitrogen–phosphorus (N:P) ratios, and has oxidized to only slightly reduced soil profiles compared to other freshwater wetland ecosystems. Possible general causes and indications of P limitation in the Everglades and other wetlands include geology, hydrology, and dominance of oxidative microbial nutrient cycling. The Everglades may be unique with respect to P biogeochemistry because of the multiple causes of P limitation and the resulting high degree of limitation.

Effects of invasive Africanized honey bees (Apis mellifera scutellata) on native stingless bee populations (Meliponinae) and traditional Mayan beekeeping in central Quintana Roo, Mexico

The Maya of the Yucatan region have a long history of keeping the native stingless bees (subfamily Meliponinae). However, market forces in the last few decades have driven the Maya to favor the use of invasive Africanized honey bees (Apis mellifera scutellata) for producing large quantities of high quality honey that has an international market. Furthermore, the native bees traditionally used by the Maya are now disappearing, along with the practice of keeping them. ^ An interdisciplinary approach was taken in order to determine the social factors behind the decrease in stingless beekeeping and the ecological driving forces behind their disappearance from the wild. Social research methods included participant observation with stingless beekeepers, Apis beekeepers, and marketing intermediaries. Ecological research methods included point observations of commonly known melliferous and polliniferous plants along transects in three communities with different degrees of human induced ecosystem disturbance. ^ The stingless bee species most important to the Maya, Melipona beecheii, has become extremely rare, and this has caused a breakdown of stingless beekeeping tradition, compounded with the pressure of the market economy, which fuels Apis beekeeping and has lessened the influence of traditional practices. The community with the heaviest amount of human induced ecosystem disturbance also had the highest degree of dominance of Apis mellifera, while the area with the most intact ecosystem had the highest diversity of stingless bees, though Apis mellifera was still the dominant species. Aggressive competitive behavior involving physical attacks by Apis mellifera against stingless bees was observed on several occasions, and this is a new observation previously unreported by science. ^

Holocene Mg/Ca, alkenones, and light stable isotope measurements on the outer North Iceland shelf, sediment core MD99-2269

We present new Holocene century to millennial-scale proxies for the well-dated piston core MD99-2269 from Húnaflóadjúp on the North Iceland Shelf. The core is located in 365 mwd and lies close to the fluctuating boundary between Atlantic and Arctic/Polar waters. The proxies are: alkenone-based SST°C, and Mg/Ca SST°C estimates and stable d13C and d18O values on planktonic and benthic foraminifera. The data were converted to 60 yr equi-spaced time-series. Significant trends in the data were extracted using Singular Spectrum Analysis and these accounted for between 50% and 70% of the variance. A comparison between these data with previously published climate proxies from MD99-2269 was carried out on a data set which consisted of 14-variable data set covering the interval 400-9200 cal yr BP at 100 yr time steps. This analysis indicated that the 1st two PC axes accounted for 57% of the variability with high loadings clustering primarily into "nutrient" and "temperature" proxies. Clustering on the 100 yr time-series indicated major changes in environment at ~6350 and ~3450 cal yr BP, which define early, mid- and late Holocene climatic intervals. We argue that a pervasive freshwater cap during the early Holocene resulted in warm SST°s, a stratified water column, and a depleted nutrient supply. The loss of the freshwater layer in the mid-Holocene resulted in high carbonate production, and the late Holocene/neoglacial interval was marked by significantly more variable sea surface conditions.

Ethnogenesis and Craniofacial Change in Japan from the Perspective of Nonmetric Traits

To examine population affinities in light of the ‘dual structure model’, frequencies of 21 nonmetric cranial traits were analyzed in 17 prehistoric to recent samples from Japan and five from continental northeast Asia. Eight bivariate plots, each representing a different bone or region of the skull, as well as cluster analysis of 21-trait mean measures of divergence using multidimensional scaling and additive tree techniques, revealed good discrimination between the Jomon-Ainu indigenous lineage and that of the immigrants who arrived from continental Asia after 300 BC. In Hokkaido, in agreement with historical records, Ainu villages of Hidaka province were least, and those close to the Japan Sea coast were most, hybridized with Wajin. In the central islands, clines were identified among Wajin skeletal samples whereby those from Kyushu most resembled continental northeast Asians, while those from the northernmost prefectures of Tohoku apparently retained the strongest indigenous heritage. In the more southerly prefectures of Tohoku, stronger traces of Jomon ancestry prevailed in the cohort born during the latest Edo period than in the one born after 1870. Thus, it seems that increased inter-regional mobility and gene flow following the Meiji Restoration initiated the most recent episode in the long process of demic diffusion that has helped to shape craniofacial change in Japan.

Moral Emotions in Palliative Care: Empirical Insights from Austria and Canada

Research aims: Moral emotions as one specific group of emotions play a vital role in delivering palliative care as e.g. ethical issues and moral distress belong to daily routine.
Moral emotions are oriented to the welfare of other persons or the society as a whole. To better understand moral emotions in Palliative Care the aims of the presented study are to ana- lyze care situations from Austria and Canada in different care settings and identify families of moral emotions on one hand and describe influencing contextual factors on the other hand. Methods: Within a qualitative study design a reanalysis of Austrian narratives on ethical issues and Canadian narra- tives on moral distress were conducted. Data in Austria encompass 36 narratives that were generated through qual- itative questionnaires in nursing homes. Canadian data are based on qualitative interviews with home care palliative specialists and encompass 47 critical incidents. The reanal- ysis of data was conducted with narrative analysis. Results: Preliminary results show that moral emotions in palliative care can be found in families around “empathy and relatedness”, “sadness, isolation and bereavement”, “anger, frustration and powerlessness”, “guilt and shame” and “being touched and feel close”. Contextual factors influencing moral emotions can be summarized as “suffer- ing and decline of client”, “expectations and dynamics of family”, “structural conflicts and power issues” and “lack of resources and information”.
Conclusion: The diversity of moral emotions reflects the everyday experiences in palliative care. It became obvious that most of the moral emotions that have been expressed appear to be interconnected within a bundle of other emo- tions. Contextual factors influencing moral emotions in pal- liative care are relatively independent of care settings. In Palliative Care moral emotions and their contextual factors constitute an important source of insight for reflection in organizational ethics.

Phylum-wide transcriptome analysis of oogenesis and early embryogenesis in selected nematode species

Oogenesis is a prerequisite for embryogenesis in Metazoa. During both biological processes important decisions must be made to form the embryo and hence ensure the next generation: (1) Maternal gene products (mRNAs, proteins and nutrients) must be supplied to the embryo. (2) Polarity must be established and axes must be specified. While incorporation of maternal gene products occurs during oogenesis, the time point of polarity establishment and axis specification varies among species, as it is accomplished either prior, during, or after fertilisation. But not only the time point when these events take place varies among species but also the underlying mechanisms by which they are triggered. For the nematode model Caenorhabditis elegans the underlying pathways and gene regulatory networks (GRNs) are well understood. It is known that there the sperm entry point initiates a primary polarity in the 1-celled egg and with it the establishment of the anteroposterior axis. However, studies of other nematodes demonstrated that polarity establishment can be independent of sperm entry (Goldstein et al., 1998; Lahl et al., 2006) and that cleavage patterns, symmetry formation and cell specification also differ from C. elegans. In contrast to the studied Chromadorea (more derived nematodes including C. elegans), embryos of some marine Enoplea (more basal representatives) even show no discernible early polarity and blastomeres can adopt variable cell fates (Voronov and Panchin 1998). The underlying pathways controlling the obviously variant embryonic processes in non-Caenorhabditis nematodes are essentially unknown. In this thesis I addressed this issue by performing a detailed unbiased comparative transcriptome analysis based on microarrays and RNA sequencing of selected developmental stages in a variety of nematodes from different phylogenetic branches with C. elegans as a reference system and a nematomorph as an outgroup representative. In addition, I made use of available genomic data to determine the presence or absence of genes for which no expression had been detected. In particular, I focussed on components of selected pathways or GRNs which are known to play essential roles during C. elegans development and/or other invertebrate or vertebrate model systems. Oogenesis must be regulated differently in non-Caenorhabditis nematodes, as crucial controlling components of Wnt and sex determination signaling are absent in these species. In this respect, I identified female-specific expression of potential polarity associated genes during gonad development and oogenesis in the Enoplean nematode Romanomermis culicivorax. I could show that known downstream components of the polarity complexes PAR-3/-6/PKC-3 and PAR-1/-2 are absent in non-Caenorhabditis species. Even PAR-2 as part of the polarity complex does not exist in these nematodes. Instead, transcriptomes of nematodes (including C. elegans), show expression of other polarity-associated complexes such as the Lgl (Lethal giant larvae) complex. This result could pose an alternative route for nematodes and nematomorphs to initiate polarity during early embryogenesis. I could show that crucial pathways of axis specification, such as Wnt and BMP are very different in C. elegans compared to other nematodes. In the former, Wnt signaling, for instance, is mediated by four paralogous beta-catenins, while other Chromadorea have fewer and Enoplea only one beta-catenin. The transcriptomes of R. culicivorax and the nematomorph show that regulators of BMP (e.g. Chordin), are specifically expressed during early embryogenesis only in Enoplea and the close outgroup of nematomorphs. In conclusion, my results demonstrate that the molecular machinery controlling oogenesis and embryogenesis in nematodes is unexpectedly variable and C. elegans cannot be taken as a general model for nematode development. Under this perspective, Enoplean nematodes show more similarities with outgroups than with C. elegans. It appears that certain pathway components were lost or gained during evolution and others adopted new functions. Based on my findings I can conjecture, which pathway components may be ancestral and which were newly acquired in the course of nematode evolution.

Dynamic Workload Parallelization and System Calibration on Single-Chip Cloud Computer

Many-core systems are emerging from the need of more computational power and power efficiency. However there are many issues which still revolve around the many-core systems. These systems need specialized software before they can be fully utilized and the hardware itself may differ from the conventional computational systems. To gain efficiency from many-core system, programs need to be parallelized. In many-core systems the cores are small and less powerful than cores used in traditional computing, so running a conventional program is not an efficient option. Also in Network-on-Chip based processors the network might get congested and the cores might work at different speeds. In this thesis is, a dynamic load balancing method is proposed and tested on Intel 48-core Single-Chip Cloud Computer by parallelizing a fault simulator. The maximum speedup is difficult to obtain due to severe bottlenecks in the system. In order to exploit all the available parallelism of the Single-Chip Cloud Computer, a runtime approach capable of dynamically balancing the load during the fault simulation process is used. The proposed dynamic fault simulation approach on the Single-Chip Cloud Computer shows up to 45X speedup compared to a serial fault simulation approach. Many-core systems can draw enormous amounts of power, and if this power is not controlled properly, the system might get damaged. One way to manage power is to set power budget for the system. But if this power is drawn by just few cores of the many, these few cores get extremely hot and might get damaged. Due to increase in power density multiple thermal sensors are deployed on the chip area to provide realtime temperature feedback for thermal management techniques. Thermal sensor accuracy is extremely prone to intra-die process variation and aging phenomena. These factors lead to a situation where thermal sensor values drift from the nominal values. This necessitates efficient calibration techniques to be applied before the sensor values are used. In addition, in modern many-core systems cores have support for dynamic voltage and frequency scaling. Thermal sensors located on cores are sensitive to the core's current voltage level, meaning that dedicated calibration is needed for each voltage level. In this thesis a general-purpose software-based auto-calibration approach is also proposed for thermal sensors to calibrate thermal sensors on different range of voltages.

Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Small bowel pseudomelanosis and oral iron therapy

Small bowel pseudomelanosis is a rarely reported clinical entity characterized by brown pigmentation of small bowel mucosa. The authors describe two cases, both with iron deficiency anemia, one of an 81-year-old female patient submitted for capsule endoscopy that revealed a brown pigmentation of all small bowel mucosa and another of an 81-year-old male whose retrograde double-balloon enteroscopy revealed a diffuse brown pattern of small bowel mucosa. Ileal biopsies confirmed intense iron deposition in the macrophages of the lamina propria. Both patients were on oral iron therapy and the second one had a previous double-balloon enteroscopy, 2 years earlier, which revealed only ileal angiodysplasias. These two cases demonstrate the importance of two new endoscopic methods for diagnosis of small bowel pseudomelanosis, the rarity of such an entity and its close relation with oral iron therapy.

An auditory, acoustic, articulatory and sociophonetic study of Swedish Viby-i

The study investigates the acoustic, articulatory and sociophonetic properties of the Swedish /iː/ variant known as 'Viby-i' in 13 speakers of Central Swedish from Stockholm, Gothenburg, Varberg, Jönköping and Katrineholm. The vowel is described in terms of its auditory quality, its acoustic F1 and F2 values, and its tongue configuration. A brief, qualitative description of lip position is also included. Variation in /iː/ production is mapped against five sociolinguistic factors: city, dialectal region, metropolitan vs. urban location, sex and socioeconomic rating. Articulatory data is collected using ultrasound tongue imaging (UTI), for which the study proposes and evaluates a methodology. The study shows that Viby-i varies in auditory strength between speakers, and that strong instances of the vowel are associated with a high F1 and low F2, a trend which becomes more pronounced as the strength of Viby-i increases. The articulation of Viby-i is characterised by a lowered and backed tongue body, sometimes accompanied by a double-bunched tongue shape. The relationship between tongue position and acoustic results appears to be non-linear, suggesting either a measurement error or the influence of additional articulatory factors. Preliminary images of the lips show that Viby-i is produced with a spread but lax lip posture. The lip data also reveals parts of the tongue, which in many speakers appears to be extremely fronted and braced against the lower teeth, or sometimes protruded, when producing Viby-i. No sociophonetic difference is found between speakers from different cities or dialect regions. Metropolitan speakers are found to have an auditorily and acoustically stronger Viby-i than urban speakers, but this pattern is not matched in tongue backing or lowering. Overall the data shows a weak trend towards higher-class females having stronger Viby-i, but these results are tentative due to the limited size and stratification of the sample. Further research is needed to fully explore the sociophonetic properties of Viby-i.

Salted-Fish industry in Roman Lusitania: Trade Memories between Oceanus and Mare Nostrum

Initiated by Augustus, Rome’s Atlantic policy seems to have been consolidated in the age of Claudius, with the acknowledgement of the economic potential offered by the Atlantic region. It is in this context that we must understand the development of the salted-fish industry in Lusitania. In the same geographical contexts, and in close relationship with fish-processing factories, are known about 20 pottery centres producing amphorae, located in the regions of Peniche, Sado and Tejo valleys, and the coasts of Alentejo and Algarve. This production extended in time beyond the end of the Western Roman Empire and up to the end of the 5th and 6th centuries, according to the archaeological data of some amphora kilns and fish-processing sites. The identification of Lusitanian amphorae in distant consuming centres and several shipwrecks in the Mediterranean basin confirm the long-distance commerce and the total integration of this “peripheral” region into the trade routes of the Roman Empire.

The interpersonal and mental health implications of the coherence of coming out narratives for a sample of gay men in committed romantic relationships

The coming out process has been conceptualized as a developmental imperative for those who will eventually accept their same-sex attractions. It is widely accepted that homophobia, heterosexism, and homonegativity are cultural realities that may complicate this developmental process for gay men. The current study views coming out as an extra-developmental life task that is at best a stressful event, and at worst traumatic when coming out results in the rupture of salient relationships with parents, siblings, and/or close friends. To date, the minority stress model (Meyer, 1995; 2003) has been utilized as an organizing framework for how to empirically examine external stressors and mental health disparities for lesbians, gay men, and bisexual individuals in the United States. The current study builds on this literature by focusing on the influence of how gay men make sense of and represent the coming out process in a semi-structured interview, more specifically, by examining the legacy of the coming out process on indicators of wellness. In a two-part process, this study first employs the framework well articulated in the adult attachment literature of coherence of narratives to explore both variation and implications of the coming out experience for a sample of gay men (n = 60) in romantic relationships (n = 30). In particular, this study employed constructs identified in the adult attachment literature, namely Preoccupied and Dismissing current state of mind, to code a Coming Out Interview (COI). In the present study current state of mind refers to the degree of coherent discourse produced about coming out experiences as relayed during the COI. Multilevel analyses tested the extent to which these COI dimensions, as revealed through an analysis of coming out narratives in the COI, were associated with relationship quality, including self-reported satisfaction and observed emotional tone in a standard laboratory interaction task and self-reported symptoms of psychopathology. In addition, multilevel analyses also assessed the Acceptance by primary relationship figures at the time of disclosure, as well as the degree of Outness at the time of the study. Results revealed that participant’s narratives on the COI varied with regard to Preoccupied and Dismissing current state of mind, suggesting that the AAI coding system provides a viable organizing framework for extracting meaning from coming out narratives as related to attachment relevant constructs. Multilevel modeling revealed construct validity of the attachment dimensions assessed via the COI; attachment (i.e., Preoccupied and Dismissing current state of mind) as assessed via the Adult Attachment Interview (AAI) was significantly correlated with the corresponding COI variables. These finding suggest both methodological and conceptual convergence between these two measures. However, with one exception, COI Preoccupied and Dismissing current state of mind did not predict relationship outcomes or self-reported internalizing and externalizing symptoms. However, further analyses revealed that the degree to which one is out to others moderated the relationship between COI Preoccupied and internalizing. Specifically, for those who were less out to others, there was a significant and positive relationship between Preoccupied current state of mind towards coming out and internalizing symptoms. In addition, the degree of perceived acceptance of sexual orientation by salient relationship figures at the time of disclosure emerged as a predictor of mental health. In particular, Acceptance was significantly negatively related to internalizing symptoms. Overall, the results offer preliminary support that gay men’s narratives do reflect variation as assessed by attachment dimensions and highlights the role of Acceptance by salient relationship figures at the time of disclosure. Still, for the most part, current state of mind towards coming out in this study was not associated with relationship quality and self-reported indicators of mental health. This finding may be a function of low statistical power given the modest sample size. However, the relationship between Preoccupied current state of mind and mental health (i.e., internalizing) appears to depend on degree of Outness. In addition, the response of primary relationships figures to coming out may be a relevant factor in shaping mental health outcomes for gay men. Limitations and suggestions for future research and clinical intervention are offered.

Connecting the dots: Examining the role of parental beliefs and preschoolers’ affect and engagement in predicting parent-child number exploration during a meaningful math experience

The current study examined the frequency and quality of how 3- to 4-year-old children and their parents explore the relations between symbolic and non-symbolic quantities in the context of a playful math experience, as well as the role of both parent and child factors in this exploration. Preschool children’s numerical knowledge was assessed while parents completed a survey about the number-related experiences they share with their children at home, and their math-related beliefs. Parent-child dyads were then videotaped playing a modified version of the card game War. Results suggest that parents and children explored quantity explicitly on only half of the cards and card pairs played, and dyads of young children and those with lower number knowledge tended to be most explicit in their quantity exploration. Dyads with older children, on the other hand, often completed their turns without discussing the numbers at all, likely because they were knowledgeable enough about numbers that they could move through the game with ease. However, when dyads did explore the quantities explicitly, they focused on identifying numbers symbolically, used non-symbolic card information interchangeably with symbolic information to make the quantity comparison judgments, and in some instances, emphasized the connection between the symbolic and non-symbolic number representations on the cards. Parents reported that math experiences such as card game play and quantity comparison occurred relatively infrequently at home compared to activities geared towards more foundational practice of number, such as counting out loud and naming numbers. However, parental beliefs were important in predicting both the frequency of at-home math engagement as well as the quality of these experiences. In particular, parents’ specific beliefs about their children’s abilities and interests were associated with the frequency of home math activities, while parents’ math-related ability beliefs and values along with children’s engagement in the card game were associated with the quality of dyads’ number exploration during the card game. Taken together, these findings suggest that card games can be an engaging context for parent-preschooler exploration of numbers in multiple representations, and suggests that parents’ beliefs and children’s level of engagement are important predictors of this exploration.