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.

A salutogenic approach to healing following child sexual assault

Decades of research has now produced a rich description of the destruction child sexual assault (CSA) can cause in an individual’s life. Post-Traumatic Stress Disorder (PTSD), Dissociative Identity Disorder, Borderline Personality Disorder, depression, anxiety, Panic Disorder, intimacy issues, substance abuse, self-harm, and suicidal ideation and attempts, are some of the negative outcomes that have been attributed to this type of traumatic experience. Psychology's tendency to dwell within a pathological paradigm, along with popular media who espouse a similar rhetoric, would lead to the belief that once exposed to CSA, an individual is forever at the mercy of dealing with a massive array of accompanying negative effects. While the possibility of these outcomes in those who have experienced CSA is not at all denied, it is also timely to consider an alternative paradigm that up until now has received a paucity of attention in the sexual assault literature. That is to say, not only do people have the ability to work through the painful and personal impacts of CSA, but for some people the process of recovery may provide a catalyst for positive life changes that have been termed post-traumatic growth (Tedeschi & Calhoun, 1995). To begin with in this chapter, the negative sequale’ of childhood sexual assault it discussed initially. Inherent to this discussion are questions of measurement and definitions of sexual assault. The chapter highlights ways in which the term CSA has been defined and hence operationalised in research, and the myriad problems, confusions, and inconclusive findings that have plagued the sexual assault literature. Following this is a review of the sparse literature that has conceptualised CSA from a more salutogenic (Antonovsky, 1979) theoretical orientation. It is argued that a salutogenic approach to intervention and to research in this area, provides a more useful way of promoting healing and the gaining of wisdom, but importantly does not negate the very real distress that may accompany growth. This chapter will then present a case study to elucidate the theoretical and empirical literature discussed using the words of a survivor. Finally, the chapter concludes with implications for therapeutic practice, which includes some practical ways in which to promote adaptation to life within the context of having survived this insidious crime.

A comparison of Chinese and Australian early childhood mathematics

In the 21st century mathematics proficiency is synonymous with a numerate citizenry. In the past few decades young children’s ability to reason mathematically and develop mathematical proficiencies has been recognised. This paper explores the history of early childhood mathematics (ECME) that may explicate differences in Chinese and Australian contexts. Results of this review established that China and Australia are diametrically positioned in ECME. Influencing each countries philosophies and practices are their cultural beliefs. ECME in China and Australia must be culturally sustainable to achieve excellent outcomes for young children. Ongoing critique and review is necessary to ensure that ECME is meeting the needs of all teachers and children in their particular context. China and Australia with their rich contrasting philosophies can assist each other in their journeys to create exemplary ECME for the 21st century.

Exploring the process of meaning making in healing after childhood sexual assault : a case study approach

Childhood sexual assault (CSA) is one of the most devastating of all traumatic experiences with population studies documenting survivors experiencing higher levels of pathology than general trends in survivors of other traumatic experiences. Yet recent research has demonstrated that far from being permanently crippled by their experiences, many adult survivors of CSA manage to heal and move forward in their lives to experience a rich and fulfilling existence. In this paper two case studies are presented to provide a detailed account of how a person who has experienced CSA may find a pathway to healing. Moreover, data demonstrates that meaning making, spiritual or otherwise, is a pivotal part of acceptance of CSA and ensuing growth. The case studies highlight the unique journeys of two women and the underlying similarities in their pathway to healing. Clinical implications of the research are discussed and specific strategies for encouraging healing and growth are outlined.

Evidence supporting exercise interventions for persons in early-stage Alzheimer’s disease

The purpose of this article is to grade research evidence supporting exercise-based interventions for persons with early-stage dementias and to report the recommendations of a consensus panel. The search produced 11 data based articles testing the effects of exercise interventions on a variety of outcomes. The body of evidence to support exercise interventions in the prevention and treatment of Alzheimer’s disease is growing and has potential as a treatment modality following translational studies in recreation therapy and other fields.

Sustainability initiatives in early years settings

Children bring much knowledge about sustainability issues into the early childhood classroom. In recent times, I have overheard children as young as three years of age discuss events such as the BP Oil Spill in American waters and extreme weather patterns. While aspects of these events can be overwhelming, responding to children's existing knowledge allows for an educative approach to sustainability issues, and a focus on the multitude of ways individuals and communities are working to create positive change.

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.

Early-mid Cretaceous tectonic evolution of eastern Gondwana : from silicic LIP magmatism to continental rupture

The Early–mid Cretaceous marks the confluence of three major continental-scale events in eastern Gondwana: (1) the emplacement of a Silicic Large Igneous Province (LIP) near the continental margin; (2) the volcaniclastic fill, transgression and regression of a major epicontinental seaway developed over at least a quarter of the Australian continent; and (3) epeirogenic uplift, exhumation and continental rupturing culminating in the opening of the Tasman Basin c. 84 Ma. The Whitsunday Silicic LIP event had widespread impact, producing both substantial extrusive volumes of dominantly silicic pyroclastic material and coeval first-cycle volcanogenic sediment that accumulated within many eastern Australian sedimentary basins, and principally in the Great Australian Basin system (>2 Mkm3 combined volume). The final pulse of volcanism and volcanogenic sedimentation at c. 105–95 Ma coincided with epicontinental seaway regression, which shows a lack of correspondence with the global sea-level curve, and alternatively records a wider, continental-scale effect of volcanism and rift tectonism. Widespread igneous underplating related to this LIP event is evident from high paleogeothermal gradients and regional hydrothermal fluid flow detectable in the shallow crust and over a broad region. Enhanced CO2 fluxing through sedimentary basins also records indirectly, large-scale, LIP-related mafic underplating. A discrete episode of rapid crustal cooling and exhumation began c. 100–90 Ma along the length of the eastern Australian margin, related to an enhanced phase of continental rifting that was largely amagmatic, and probably a switch from wide–more narrow rift modes. Along-margin variations in detachment fault architecture produced narrow (SE Australia) and wide continental margins with marginal, submerged continental plateaux (NE Australia). Long-lived NE-trending cross-orogen lineaments controlled the switch from narrow to wide continental margin geometries.

Paleomagnetic data support Early Permian age for the Abor Volcanics in the lower Siang Valley, NE India; significance for Gondwana-related break-up models

Confusion exists as to the age of the Abor Volcanics of NE India. Some consider the unit to have been emplaced in the Early Permian, others the Early Eocene, a difference of ∼230 million years. The divergence in opinion is significant because fundamentally different models explaining the geotectonic evolution of India depend on the age designation of the unit. Paleomagnetic data reported here from several exposures in the type locality of the formation in the lower Siang Valley indicate that steep dipping primary magnetizations (mean = 72.7 ± 6.2°, equating to a paleo-latitude of 58.1°) are recorded in the formation. These are only consistent with the unit being of Permian age, possibly Artinskian based on a magnetostratigraphic argument. Plate tectonic models for this time consistently show the NE corner of the sub-continent >50°S; in the Early Eocene it was just north of the equator, which would have resulted in the unit recording shallow directions. The mean declination is counter-clockwise rotated by ∼94°, around half of which can be related to the motion of the Indian block; the remainder is likely due local Himalayan-age thrusting in the Eastern Syntaxis. Several workers have correlated the Abor Volcanics with broadly coeval mafic volcanic suites in Oman, NE Pakistan–NW India and southern Tibet–Nepal, which developed in response to the Cimmerian block peeling-off eastern Gondwana in the Early-Middle Permian, but we believe there are problems with this model. Instead, we suggest that the Abor basalts relate to India–Antarctica/India–Australia extension that was happening at about the same time. Such an explanation best accommodates the relevant stratigraphical and structural data (present-day position within the Himalayan thrust stack), as well as the plate tectonic model for Permian eastern Gondwana.

Epistemic beliefs and beliefs about teaching practices for moral learning in the early years of school : relationships and complexities

While investment in young children is recognised as important for the development of moral values for a cohesive society, little is known about early years teaching practices that promote learning of moral values. This paper reports on observations and interviews with 11 Australian teachers, focusing on their epistemic beliefs and beliefs about teaching practices for moral education with children aged 5 to 8 years. The analysis revealed three main patterns of thinking about moral education: following others, reflecting on points of view, and informing reflection for action. These patterns suggest a relationship between epistemic beliefs and beliefs about teaching practices for moral learning which have implications for teacher professional development concerning experiences in moral education.

Gifted early adolescents’ negotiating identity : A case study of self-presentation theory

Academically gifted students are recognised as possessing considerable achievement potential. Yet many fail to perform at a level commensurate with their ability. Often gifted students in early adolescence are faced with a forced choice between fulfilment of potential and achieving stable positive relationships with peers. This choice can affect their achievement and may have far-reaching personal and social costs. This case study explored the viability of self-presentation theory to explain students' ways of negotiating their sense of self whilst developing public identity and the concomitant affects on achievement and the fulfilment of potential. It examined how gifted students moderate their images in their learning and extra-curricular environments. Further, the study identifies those self-presentation strategies adopted that either facilitate or hinder achievement. This study may assist parents, educators and school counsellors to provide greater support for gifted adolescents.

A vibrational spectroscopic study of the so-called ‘healing’ mineral papagoite CaCuAlSi2O6(OH)3

Papagoite is a silicate mineral named after an American Indian tribe and was used as a healing mineral. Papagoite CaCuAlSi2O6(OH)3 is a hydroxy mixed anion compound with both silicate and hydroxyl anions in the formula. The structural characterization of the mineral papagoite remains incomplete. Papagoite is a four-membered ring silicate with Cu2+ in square planar coordination. The intense sharp Raman band at 1053 cm−1 is assigned to the ν1 (A 1g) symmetric stretching vibration of the SiO4 units. The splitting of the ν3 vibrational mode offers support to the concept that the SiO4 tetrahedron in papagoite is strongly distorted. A very intense Raman band observed at 630 cm−1 with a shoulder at 644 cm−1 is assigned to the ν4 vibrational modes. Intense Raman bands at 419 and 460 cm−1 are attributed to the ν2 bending modes. Intense Raman bands at 3545 and 3573 cm−1 are assigned to the stretching vibrations of the OH units. Low-intensity Raman bands at 3368 and 3453 cm−1 are assigned to water stretching modes. It is suggested that the formula of papagoite is more likely to be CaCuAlSi2O6(OH)3 · xH2O. Hence, vibrational spectroscopy has been used to characterize the molecular structure of papagoite.

Early stage start-ups : evidence from the Comprehensive Australian Study of Entrepreneurial Emergence (CAUSEE)

In this chapter, the picture of Australian small business is supplemented by using data from the Comprehensive Australian Study of Entrepreneurial Emergence (CAUSEE) . This data tracks large numbers of on-going business start-ups over time. The Australian Centre of Entrepreneurship Research at Queensland University of Technology collected data in four annual waves. (Wave 1 to Wave 4) from 2007 to 2011. CAUSEE allows the analysis of entrepreneurial entrants at two stages of development, i.e. nascent and young firms. Nascent firms are defined as firms in the process of being created, but not yet established in the market, and young firms are defined as having been operational for up to four years. An analysis of nascent firms provides unique insights, as no other known Australian database captures and follows the development of business start-ups at the pre-operational stage. In addition, the project captured judgment over samples of high-potential start-ups.

Early adolescents’ helping behaviours when a friend is injured in a fight : the role of an extended Theory of Planned Behavior

This paper examines the role of first aid training in increasing adolescent helping behaviours when taught in a school-based injury prevention program, Skills for Preventing Injury in Youth (SPIY). The research involved the development and application of an extended Theory of Planned Behaviour (TPB), including “behavioural willingness in a fight situation,” “first aid knowledge” and “perceptions of injury seriousness”, to predict the relationship between participation in SPIY and helping behaviours when a friend is injured in a fight. From 35 Queensland high schools, 2500 Year 9 students (mean age = 13.5, 40% male) completed surveys measuring their attitudes, perceived behavioural control, subjective norms and behavioural intention, from the TPB, and added measures of behavioural willingness in a fight situation, perceptions of injury seriousness and first aid knowledge, to predict helping behaviours when a friend is injured in a fight. It is expected that the TPB will significantly contribute to understanding the relationship between participation in SPIY and helping behaviours when a friend is injured in a fight. Further analyses will determine whether the extension of the model significantly increases the variance explained in helping behaviours. The findings of this research will provide insight into the critical factors that may increase adolescent bystanders’ actions in injury situations.