Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Guillermo Gómez-Peña : a "new age shaman” in a bohemian theme park

The Marquis de Sade was declared, “the fist commandment of art is ‘never to bore,’” and perhaps no other artist of his generation has embodied this sentiment more than Guillermo Gómez- Peña, the Mexican-born performance artist and cultural theorist living in San Francisco. Since the early 1980s Gómez-Peña, along with his performance troupe La Pocha Nostra, have been engaged in “reverse anthropology” staging “postcolonial” performances that foreground race and intervene in our cultural fears and desires by focusing on our obsession with the exotic. He deftly navigates the “post-multicultural” world – accelerated by globalization and nation branding – by using elaborate performative and interactive elements that expose (to the audience) their deeply embedded cultural stereotypes and desires for the other.

Conflict and seduction in the public sphere

In a critical but sympathetic reading of Habermas’s work (1984, 1987a, 1987b, 2003), Luke Goode (2005) recently sought to rework his theory of deliberative democracy in an age of mediated and increasingly digital public spheres. Taking a different approach, Alan McKee (2005) challenged the culture- and class-bound strictures of Habermasian rationalism, instead pursuing a more radically pluralist account of postmodern public spheres. The editors of this special section of Media, Culture & Society invited us to discuss our differing approaches to the public sphere. Goode holds that the institutional bases of contemporary public spheres (political parties, educational institutions or public media) remain of critical importance, albeit in the context of a kaleidoscopic array of unofficial and informal micro-publics, both localized and de-territorialized. In contrast, McKee sustains a ‘hermeneutics of suspicion’ toward the official, hegemonic institutions of the public sphere since they tend to exclude and delegitimize discourses and practices that challenge their polite middle-class norms. McKee’s recent research has focused on sexual cultures, particularly among youth (McKee, 2011). Goode’s recent work has examined new social media spaces, particularly in relation to news and public debate (e.g. Goode, 2009; Goode et al., 2011). Consequently, our discussion turned to a domain which links our interests: after Goode discussed some of his recent research on (in)civility on YouTube as a new media public sphere, McKee challenged him to consider the case of pornographic websites modelled on social media sites.1 He identifies a greater degree of ‘civility’ in these pornographic sibling sites than on YouTube, requiring careful consideration of what constitutes a ‘public sphere’ in contemporary digital culture. Such sites represent an environment that shatters the opposition of public and private interest, affording public engagement on matters of the body, of intimacy, of gender politics, of pleasure and desire – said by many critics to be ruled out of court in Habermasian theory. Such environments also trouble traditional binaries between the cognitive and the affective, and between the performative and the deliberative. In what follows we explore the differences between our approaches in the form of a dialogue. As is often the case, our approaches seemed less at odds after engaging in conversation than may have initially appeared. But important differences of emphasis remain.

The relationship between CFH and ARMS2 genotypes and neuroretinal function in persons without age-related macular degeneration

Purpose: To determine whether neuroretinal function differs in healthy persons with and without common risk gene variants for age- related macular degeneration (AMD) and no ophthalmoscopic signs of AMD, and to compare those findings in persons with manifest early AMD. Methods and Participants: Neuroretinal function was assessed with the multifocal electroretinogram (mfERG) (VERIS, Redwood City, CA,) in 32 participants (22 healthy persons with no clinical signs of AMD and 10 early AMD patients). The 22 healthy participants with no AMD were risk genotypes for either the CFH (rs380390) and/or ARMS2 (rs10490920). We used a slow flash mfERG paradigm (3 inserted frames) and a 103 hexagon stimulus array. Recordings were made with DTL electrodes; fixation and eye movements were monitored online. Trough N1 to peak P1 (N1P1) response densities and P1-implicit times (IT) were analysed in 5 concentric rings. Results: N1P1 response densities (mean ± SD) for concentric rings 1-3 were on average significantly higher in at-risk genotypes (ring 1: 17.97 nV/deg2 ± 1.9, ring 2: 11.7 nV/deg2 ±1.3, ring 3: 8.7 nV/deg2 ± 0.7) compared to those without risk (ring 1: 13.7 nV/deg2 ± 1.9, ring 2: 9.2 nV/deg2 ±0.8, ring 3: 7.3 nV/deg2 ± 1.1) and compared to persons with early AMD (ring 1: 15.3 nV/deg2 ± 4.8, ring 2: 9.1 nV/deg2 ±2.3, ring 3 nV/deg2: 7.3± 1.3) (p<0.5). The group implicit times, P1-ITs for ring 1 were on average delayed in the early AMD patients (36.4 ms ± 1.0) compared to healthy participants with (35.1 ms ± 1.1) or without risk genotypes (34.8 ms ±1.3), although these differences were not significant. Conclusion: Neuroretinal function in persons with normal fundi can be differentiated into subgroups based on their genetics. Increased neuroretinal activity in persons who carry AMD risk genotypes may be due to genetically determined subclinical inflammatory and/or histological changes in the retina. Assessment of neuroretinal function in healthy persons genetically susceptible to AMD may be a useful early biomarker before there is clinical manifestation of AMD.

Eyes on 3D-Current 3D biomimetic disease concept models and potential applications in age-related macular degeneration

Three dimensional cellular models that mimic disease are being increasingly investigated and have opened an exciting new research area into understanding pathomechanisms. The advantage of 3D in vitro disease models is that they allow systematic and in-depth studies of physiological and pathophysiological processes with less costs and ethical concerns that have arisen with animal models. The purpose of the 3D approach is to allow crosstalk between cells and microenvironment, and with cues from the microenvironment, cells can assemble their niche similar to in vivo conditions. The use of 3D models for mimicking disease processes such as cancer, osteoarthritis etc., is only emerging and allows multidisciplinary teams consisting of tissue engineers, biologist biomaterial scientists and clinicians to work closely together. While in vitro systems require rigorous testing before they can be considered as replicates of the in vivo model, major steps have been made, suggesting that they will become powerful tools for studying physiological and pathophysiological processes. This paper aims to summarize some of the existing 3D models and proposes a novel 3D model of the eye structures that are involved in the most common cause of blindness in the Western World, namely age-related macular degeneration (AMD).

25 million years to break a continent : early to middle Miocene rifting and syn-extensional magmatism in the southern Gulf of California

Cenozoic extension in western Mexico has been divided into two episodes separated by the change from convergence to oblique divergence at the plate boundary. The Gulf Extensional Province is thought to have started once subduction ended at ~12.5 Ma whereas early extension is classified as Basin and Range. Mid-Miocene volcanism of the Comondú group has been considered as a subduction-related arc, whereas post ~12.5 Ma volcanism would be extension-related. Our new integration of the continental onshore and offshore geology of the south-east Gulf region, backed by tens of Ar-Ar and U-Pb ages and geochemical studies, document an early-mid Miocene rifting and extension-related bimodal to andesitic magmatism prior to subduction termination. Between ~21 and 11 Ma a system of NNW-SSE high-angle extensional faults rifted the western side of the Sierra Madre Occidental (SMO) ignimbrite plateau. In Nayarit, rhyolitic domes and some basalts were emplaced along this extensional belt at 18-17 Ma. These rocks show strong antecrystic inheritance but an absence of Mesozoic and older xenocrysts, suggesting a genesis in the mid-upper crust triggered by extension-induced basaltic influx. In Sinaloa, large grabens were floored by huge dome complexes at ~21-17 Ma and filled by continental sediments with interlayered basalts dated at 15 Ma. Mid-Miocene volcanism, including the largely volcaniclastic Comondú strata in Baja California, was thus emplaced in rift basins and appears associated to decompression melting rather than subduction. Along the coast, flat-lying basaltic lava flows dated at 11-10 Ma are exposed just above the present sea level. Here crustal thickness is 25-20 Km, almost half that in the core of the SMO, implying significant lithosphere stretching before ~11 Ma. This mafic pulse, with relatively high Ti but still clear Nb-Ta negative spikes, may be related to the detachment of the lower part of the subducted slab, allowing asthenosphere to flow into parts of the mantle previously fluxed by subduction fluids. Very uniform OIB-like lavas appear in late Pliocene and Pleistocene, only 18 m.y. after the onset of rifting and ~9 m.y. after the end of subduction. Our study shows that rifting began much earlier than Late Miocene and progressively overwhelmed subduction in generating magmatism.

Late Oligocene to middle Miocene rifting and syn-extensional magmatism in the southwestern Sierra Madre occidental, Mexico: the beginning of the Gulf of California rift

Although Basin and Range style extension affected several areas of western Mexico since the Late Eocene, extension in the Gulf of California region (the Gulf Extensional Province GEP) is thought to have started as subduction waned and ended at ~14 12.5 Ma. A general consensus also exists in considering the mid Miocene Comondú group as a suprasubduction volcanic arc. Our new integration of the geology of the south east Gulf region, backed by 43 new Ar Ar and U Pb mineral ages and geochemical studies, document a widespread phase of extension in the southern GEP between latest Oligocene and Early Miocene that subsequently focused in the region of the future Gulf in the Middle Miocene. Upper Oligocene to Lower Miocene rocks across the southern Sierra Madre Occidental (SMO)(northern Nayarit and southern Sinaloa) were affected by major ~N S to NNW striking normal faults prior to ~21 Ma. Then, between ~21 and 11 Ma, a system of NNW-SSE high angle extensional faults continued extending the southwestern side of the SMO. Rhyolitic domes, shallow intrusive bodies, and lesser basalts were emplaced along this extensional belt at 20-17 Ma. In northern Sinaloa, large grabens were floored by huge dome complexes at ~21-17 Ma and filled by continental sediments with interlayered basalts dated at 15-14 Ma, a setting and timing very similar to Sonora. Early to Middle Miocene volcanism, including the largely volcaniclastic Comondú strata in Baja California Sur, was thus emplaced in rift basins and was likely associated to decompression melting of upper mantle (inducing crustal partial melting) rather than to fluxing by fluids from the young subducting plate. Along the Nayarit and Sinaloa coast, flatlying basaltic lava flows dated at 11-10 Ma are exposed just above the present sea level. Here, crustal thickness is almost half that in the unextended core of the SMO, implying significant lithosphere stretching before ~11 Ma. Our study shows that rifting began much earlier than Late Miocene and provided a fundamental control on the style and composition of volcanism from at least 30 Ma. We envision a sustained period of lithospheric stretching and magmatism during which the pace and breadth of extension changed at ~20-18 Ma to be narrower and likely more rapid, and again at ~12.5 Ma, when the kinematics of rifting became more oblique.

Injuries leading to hospitalisation in the first year of life : analysis by trimester of age using coded data and textual description

Objective: To describe unintentional injuries to children aged less than one year, using coded and textual information, in three-month age bands to reflect their development over the year. Methods: Data from the Queensland Injury Surveillance Unit was used. The Unit collects demographic, clinical and circumstantial details about injured persons presenting to selected emergency departments across the State. Only injuries coded as unintentional in children admitted to hospital were included for this analysis. Results: After editing, 1,082 children remained for analysis, 24 with transport-related injuries. Falls were the most common injury, but becoming proportionately less over the year, whereas burns and scalds and foreign body injuries increased. The proportion of injuries due to contact with persons or objects varied little, but poisonings were relatively more common in the first and fourth three-month periods. Descriptions indicated that family members were somehow causally involved in 16% of injuries. Our findings are in qualitative agreement with comparable previous studies. Conclusion: The pattern of injuries varies over the first year of life and is clearly linked to the child's increasing mobility. Implications: Injury patterns in the first year of life should be reported over shorter intervals. Preventive measures for young children need to be designed with their rapidly changing developmental stage in mind, using a variety of strategies, one of which could be opportunistic developmentally specific education of parents. Injuries in young children are of abiding concern given their immediate health and emotional effects, and potential for long-term adverse sequelae. In Australia, in the financial year 2006/07, 2,869 children less than 12 months of age were admitted to hospital for an unintentional injury, a rate of 10.6 per 1,000, representing a considerable economic and social burden. Given that many of these injuries are preventable, this is particularly concerning. Most epidemiologic studies analyse data in five-year age bands, so children less than five years of age are examined as a group. This study includes only those children younger than one year of age to identify injury detail lost in analyses of the larger group, as we hypothesised that the injury pattern varied with the developmental stage of the child. The authors of several North American studies have commented that in dealing with injuries in pre-school children, broad age groupings are inadequate to do justice to the rapid developmental changes in infancy and early childhood, and have in consequence analysed injuries in shorter intervals. To our knowledge, no similar analysis of Australian infant injuries has been published to date. This paper describes injury in children less than 12 months of age using data from the Queensland Injury Surveillance Unit (QISU).

Older drivers' crashes in Queensland, Australia

Background: The growing proportion of older adults in Australia is predicted to comprise 23% of the population by 2030. Accordingly, an increasing number of older drivers and fatal crashes of these drivers could also be expected. While the cognitive and physiological limitations of ageing and their road safety implications have been widely documented, research has generally considered older drivers as a homogeneous group. Knowledge of age-related crash trends within the older driver group itself is currently limited. Objective: The aim of this research was to identify age-related differences in serious road crashes of older drivers. This was achieved by comparing crash characteristics between older and younger drivers and between sub-groups of older drivers. Particular attention was paid to serious crashes (crashes resulting in hospitalisation and fatalities) as they place the greatest burden on the Australian health system. Method: Using Queensland Crash data, a total of 191,709 crashes of all-aged drivers (17–80+) over a 9-year period were analysed. Crash patterns of drivers’ aged 17–24, 25–39, 40–49, 50–59, 60–69, 70–79 and 80+ were compared in terms of crash severity (e.g., fatal), at fault levels, traffic control measures (e.g., stop signs) and road features (e.g., intersections). Crashes of older driver sub-groups (60–69, 70–79, 80+) were also compared to those of middle-aged drivers (40–49 and 50–59 combined, who were identified as the safest driving cohort) with respect to crash-related traffic control features and other factors (e.g., speed). Confounding factors including speed and crash nature (e.g., sideswipe) were controlled for. Results and discussion: Results indicated that patterns of serious crashes, as a function of crash severity, at-fault levels, road conditions and traffic control measures, differed significantly between age groups. As a group, older drivers (60+) represented the greatest proportion of crashes resulting in fatalities and hospitalisation, as well as those involving uncontrolled intersections and failure to give way. The opposite was found for middle-aged drivers, although they had the highest proportion of alcohol and speed-related crashes when compared to older drivers. Among all older drivers, those aged 60–69 were least likely to be involved in or the cause of crashes, but most likely to crash at interchanges and as a result of driving while fatigued or after consuming alcohol. Drivers aged 70–79 represented a mid-range level of crash involvement and culpability, and were most likely to crash at stop and give way signs. Drivers aged 80 years and beyond were most likely to be seriously injured or killed in, and at-fault for, crashes, and had the greatest number of crashes at both conventional and circular intersections. Overall, our findings highlight the heterogeneity of older drivers’ crash patterns and suggest that age-related differences must be considered in measures designed to improve older driver safety.

Prediction of age at menopause from assessment of ovarian reserve may be improved by using body mass index and smoking status

Objective: Menopause is the consequence of exhaustion of the ovarian follicular pool. AMH, an indirect hormonal marker of ovarian reserve, has been recently proposed as a predictor for age at menopause. Since BMI and smoking status are relevant independent factors associated with age at menopause we evaluated whether a model including all three of these variables could improve AMH-based prediction of age at menopause. Methods: In the present cohort study, participants were 375 eumenorrheic women aged 19–44 years and a sample of 2,635 Italian menopausal women. AMH values were obtained from the eumenorrheic women. Results: Regression analysis of the AMH data showed that a quadratic function of age provided a good description of these data plotted on a logarithmic scale, with a distribution of residual deviates that was not normal but showed significant leftskewness. Under the hypothesis that menopause can be predicted by AMH dropping below a critical threshold, a model predicting menopausal age was constructed from the AMH regression model and applied to the data on menopause. With the AMH threshold dependent on the covariates BMI and smoking status, the effects of these covariates were shown to be highly significant. Conclusions: In the present study we confirmed the good level of conformity between the distributions of observed and AMH-predicted ages at menopause, and showed that using BMI and smoking status as additional variables improves AMH-based prediction of age at menopause.

The relationship between anti-mullerian hormone in women receiving fertility assessments and age at menopause in subfertile women : evidence from large population studies

Context: Anti-Müllerian hormone (AMH) concentration reflects ovarian aging and is argued to be a useful predictor of age at menopause (AMP). It is hypothesized that AMH falling below a critical threshold corresponds to follicle depletion, which results in menopause. With this threshold, theoretical predictions of AMP can be made. Comparisons of such predictions with observed AMP from population studies support the role for AMH as a forecaster of menopause. Objective: The objective of the study was to investigate whether previous relationships between AMH and AMP are valid using a much larger data set. Setting: AMH was measured in 27 563 women attending fertility clinics. Study Design: From these data a model of age-related AMH change was constructed using a robust regression analysis. Data on AMP from subfertile women were obtained from the population-based Prospect-European Prospective Investigation into Cancer and Nutrition (Prospect- EPIC) cohort (n � 2249). By constructing a probability distribution of age at which AMH falls below a critical threshold and fitting this to Prospect-EPIC menopausal age data using maximum likelihood, such a threshold was estimated. Main Outcome: The main outcome was conformity between observed and predicted AMP. Results: To get a distribution of AMH-predicted AMP that fit the Prospect-EPIC data, we found the critical AMH threshold should vary among women in such a way that women with low age-specific AMH would have lower thresholds, whereas women with high age-specific AMH would have higher thresholds (mean 0.075 ng/mL; interquartile range 0.038–0.15 ng/mL). Such a varying AMH threshold for menopause is a novel and biologically plausible finding. AMH became undetectable (�0.2 ng/mL) approximately 5 years before the occurrence of menopause, in line with a previous report. Conclusions: The conformity of the observed and predicted distributions of AMP supports the hypothesis that declining population averages of AMH are associated with menopause, making AMH an excellent candidate biomarker for AMP prediction. Further research will help establish the accuracy of AMH levels to predict AMP within individuals.

Critical Literacy in the Early Years : Emergence and Sustenance in an Age of Accountability

The work of early childhood educators in facilitating young children’s literacy acquisition has never received more attention than in the new millennium. Media hype about literacy crises, falling standards, teacher quality and government promises of minimum standards for all children have simultaneously increased the ‘visibility’ of literacy and the stakes for school performance. Indeed the last two decades could be seen as an age of pronouncements with respect to literacy, with politicians internationally promising to cure supposed low literacy with standardized tests and mandated programmes. As the rhetoric around literacy intensifies many late-capitalist economies are experiencing shifts that have increased the gaps between rich and poor, changed the very nature of work, and fundamentally altered the cultural mix of their populations. More and more children attending schools where English is the language of instruction speak it as a second or third language. Many children have experienced the effects of war, terrorism, migration and poverty. Many live in fractured, fragmented and changing families. Teacher populations are changing too. In some places aging teacher workforces mean that there is already a shortage of qualified teachers. Literacy is also changing as the impact of digital technologies on global and local communication, economies and knowledges begins to bite in everyday and working lives. It is challenging to think about how spaces for the emergence and sustenance of critical literacy in early childhood education might be created.

Video-based road commentary training improves hazard perception of young drivers in a dual task

This study used a video-based hazard perception dual task to compare the hazard perception skills of young drivers with middle aged, more experienced drivers and to determine if these skills can be improved with video-based road commentary training. The primary task required the participants to detect and verbally identify immediate hazard on video-based traffic scenarios while concurrently performing a secondary tracking task, simulating the steering of real driving. The results showed that the young drivers perceived fewer immediate hazards (mean = 75.2%, n = 24, 19 females) than the more experienced drivers (mean = 87.5%, n = 8, all females), and had longer hazard perception times, but performed better in the secondary tracking task. After the road commentary training, the mean percentage of hazards detected and identified by the young drivers improved to the level of the experienced drivers and was significantly higher than that of an age and driving experience matched control group. The results will be discussed in the context of psychological theories of hazard perception and in relation to road commentary as an evidence-based training intervention that seems to improve many aspects of unsafe driving behaviour in young drivers.

Board age and gender diversity : a test of competing linear and curvilinear predictions

We test competing linear and curvilinear predictions between board diversity and performance. The predictions were tested using archival data on 288 organizations listed on the Australian Securities Exchange. The findings provide additional evidence on the business case for board gender diversity and refine the business case for board age diversity.