Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.

Bridging STEM in a real-world problem

Engineering-based modeling activities provide a rich source of meaningful situations that capitalize on and extend students’ routine learning. By integrating such activities within existing curricula, students better appreciate how their school learning in mathematics and science applies to problems in the outside world...

Investigating the effectiveness of an ecological approach to learning design in a first year mathematics for engineering unit

This paper reports on the results of a project aimed at creating a research-informed, pedagogically reliable, technology-enhanced learning and teaching environment that would foster engagement with learning. A first-year mathematics for engineering unit offered at a large, metropolitan Australian university provides the context for this research. As part of the project, the unit was redesigned using a framework that employed flexible, modular, connected e-learning and teaching experiences. The researchers, interested in an ecological perspective on educational processes, grounded the redesign principles in probabilistic learning design (Kirschner et al., 2004). The effectiveness of the redesigned environment was assessed through the lens of the notion of affordance (Gibson, 1977,1979, Greeno, 1994, Good, 2007). A qualitative analysis of the questionnaire distributed to students at the end of the teaching period provided insight into factors impacting on the successful creation of an environment that encourages complex, multidimensional and multilayered interactions conducive to learning.

Problem solving in a 21st century mathematics curriculum

Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

An investigation into the effectiveness of sensory modulation in reducing seclusion within an acute mental health unit

In this paper we report the findings from an evaluation of the introduction of sensory modulation (SM) in an acute mental health inpatient unit. It was expected that SM could be used to help settle patients experiencing high levels of disturbance and that as a result, there would be less need for use of more restrictive seclusion practices. The evaluation took place in a hospital in south-east Queensland, Australia. SM was introduced in one acute unit while the other served as a control. The evaluation comprised two studies. In the first study we aimed to determine whether SM reduced the level of disturbance among patients given the opportunity to use it. In the second study we aimed to find out whether the introduction of SM reduced the frequency and duration of seclusion. In study 1, we found that most patients reported marked reduction in disturbance after using SM and there was a very large effect size for the group as a whole. In study 2, we found that frequency of seclusion dropped dramatically in the unit that introduced SM but rose slightly in the unit that did not have access to SM. The change in seclusion rate was highly significant (χ2 = 49.1, df = 1, p < 0.001). Results are discussed, having reference to the limitations inherent in a naturalistic study.

What triggers problem recognition? An exploration on young Australian male problematic online gamers

Help-seeking is a complex decision-making process that first begins with problem recognition. However, little is understood about the conceptualisation of the helpseeking process and the triggers of problem recognition. This research proposes the use of the Critical Incident Technique (CIT) to examine and classify incidents that serve as key triggers of problem recognition among young Australian male problematic online gamers. The research provides a classification of five different types of triggers that will aid social marketers into developing effective early detection, prevention and treatment focused social marketing interventions.

Postglacial Early Permian (late Sakmarian-early Artinskian) shallow-marine carbonate deposition along a 2000 km transect from Timor to west Australia

Late Sakmarian to early Artinskian (Early Permian) carbonate deposition was widespread in the marine intracratonic rift basins that extended into the interior of Eastern Gondwana from Timor in the north to the northern Perth Basin in the south. These basins spanned about 20° of paleolatitude (approximately 35°S to 55°S). This study describes the type section of the Maubisse Limestone in Timor-Leste, and compares this unit with carbonate sections in the Canning Basin (Nura Nura Member of the Poole Sandstone), the Southern Carnarvon Basin (Callytharra Formation) and the northern Perth Basin (Fossil Cliff Member of the Holmwood Shale). The carbonate units have no glacial influence and formed part of a major depositional cycle that, in the southern basins, overlies glacially influenced strata and lies a short distance below mudstone containing marine fossils and scattered dropstones (perhaps indicative of sea ice). In the south marine conditions became more restricted and were replaced by coal measures at the top of the depositional sequence. In the north, the carbonate deposits are possibly bryozoan–crinoidal mounds; whereas in the southern basins they form laterally continuous relatively thin beds, deposited on a very low-gradient seafloor, at the tops of shale–limestone parasequences that thicken upward in parasequence sets. All marine deposition within the sequence took place under very shallow (inner neritic) conditions, and the limestones have similar grain composition. Bryozoan and crinoidal debris dominate the grain assemblages and brachiopod shell fragments, foraminifera and ostracod valves are usually common. Tubiphytes ranged as far south as the Southern Carnarvon Basin, albeit rarely, but is more common to the north. Gastropod and bivalve shell debris, echinoid spines, solitary rugose corals and trilobite carapace elements are rare. The uniformity of the grain assemblage and the lack of tropical elements such as larger fusulinid foraminifera, colonial corals or dasycladacean algae indicate temperate marine conditions with only a small increase in temperature to the north. The depositional cycle containing the studied carbonate deposits represents a warmer phase than the preceding glacially influenced Asselian to early Sakmarian interval and the subsequent cool phase of the “mid” Artinskian that is followed by significant warming during the late Artinskian–early Kungurian. The timing of cooler and warmer intervals in the west Australian basins seems out-of-phase with the eastern Australian succession, but this may be a problem of chronostratigraphic miscorrelation due to endemic faunas and palynofloras.

Medical free-text to concept mapping as an information retrieval problem

Concept mapping involves determining relevant concepts from a free-text input, where concepts are defined in an external reference ontology. This is an important process that underpins many applications for clinical information reporting, derivation of phenotypic descriptions, and a number of state-of-the-art medical information retrieval methods. Concept mapping can be cast into an information retrieval (IR) problem: free-text mentions are treated as queries and concepts from a reference ontology as the documents to be indexed and retrieved. This paper presents an empirical investigation applying general-purpose IR techniques for concept mapping in the medical domain. A dataset used for evaluating medical information extraction is adapted to measure the effectiveness of the considered IR approaches. Standard IR approaches used here are contrasted with the effectiveness of two established benchmark methods specifically developed for medical concept mapping. The empirical findings show that the IR approaches are comparable with one benchmark method but well below the best benchmark.

Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via cal- culation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases,the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN : decoys are able to block binding sites on PTEN mRNAs, thereby educing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations

Implementing a context-based environmental science unit in the middle years: Teaching and learning at the creek

Engaging middle-school students in science continues to be a challenge in Australian schools. One initiative that has been tried in the senior years but is a more recent development in the middle years is the context-based approach. In this ethnographic study, we researched the teaching and learning transactions that occurred in one 9th grade science class studying a context-based Environmental Science unit that included visits to the local creek for 11 weeks. Data were derived from field notes, audio and video recorded conversations, interviews, student journals and classroom documents with a particular focus on two selected groups of students. This paper presents two assertions that highlight pedagogical approaches that contributed to learning. Firstly, spontaneous teaching episodes created opportunities for in-the-moment questioning by the teacher that led to students’ awareness of environmental issues and the scientific method; secondly, group work using flip cameras afforded opportunities for students to connect the science concepts with the context. Furthermore, students reported positively about the unit and expressed their appreciation for the opportunity to visit the creek frequently. This findings from this study should encourage teachers to take students into the real-world field for valuable teaching and learning experiences that are not available in the formal classroom.

Communicating consequences with costs: A commentary on Corso et al's cost of injury

Estimating the economic burden of injuries is important for setting priorities, allocating scarce health resources and planning cost-effective prevention activities. As a metric of burden, costs account for multiple injury consequences—death, severity, disability, body region, nature of injury—in a single unit of measurement. In a 1989 landmark report to the US Congress, Rice et al1 estimated the lifetime costs of injuries in the USA in 1985. By 2000, the epidemiology and burden of injuries had changed enough that the US Congress mandated an update, resulting in a book on the incidence and economic burden of injury in the USA.2 To make these findings more accessible to the larger realm of scientists and practitioners and to provide a template for conducting the same economic burden analyses in other countries and settings, a summary3 was published in Injury Prevention. Corso et al reported that, between 1985 and 2000, injury rates declined roughly 15%. The estimated lifetime cost of these injuries declined 20%, totalling US$406 billion, including US$80 billion in medical costs and US$326 billion in lost productivity. While incidence reflects problem size, the relative burden of injury is better expressed using costs.

Palliative care problem severity score: Reliability and acceptability in a national study

Background The Palliative Care Problem Severity Score is a clinician-rated tool to assess problem severity in four palliative care domains (pain, other symptoms, psychological/spiritual, family/carer problems) using a 4-point categorical scale (absent, mild, moderate, severe). Aim To test the reliability and acceptability of the Palliative Care Problem Severity Score. Design: Multi-centre, cross-sectional study involving pairs of clinicians independently rating problem severity using the tool. Setting/participants Clinicians from 10 Australian palliative care services: 9 inpatient units and 1 mixed inpatient/community-based service. Results A total of 102 clinicians participated, with almost 600 paired assessments completed for each domain, involving 420 patients. A total of 91% of paired assessments were undertaken within 2 h. Strength of agreement for three of the four domains was moderate: pain (Kappa = 0.42, 95% confidence interval = 0.36 to 0.49); psychological/spiritual (Kappa = 0.48, 95% confidence interval = 0.42 to 0.54); family/carer (Kappa = 0.45, 95% confidence interval = 0.40 to 0.52). Strength of agreement for the remaining domain (other symptoms) was fair (Kappa = 0.38, 95% confidence interval = 0.32 to 0.45). Conclusion The Palliative Care Problem Severity Score is an acceptable measure, with moderate reliability across three domains. Variability in inter-rater reliability across sites and participant feedback indicate that ongoing education is required to ensure that clinicians understand the purpose of the tool and each of its domains. Raters familiar with the patient they were assessing found it easier to assign problem severity, but this did not improve inter-rater reliability.

An Approximate Solution Of One-Dimensional Piston Problem

A new theory of shock dynamics has been developed in the form of a finite number of compatibility conditions along shock rays. It has been used to study the growth or decay of shock strength for accelerating or decelerating piston starting with a nonzero piston velocity. The results show good agreement with those obtained by Harten's high resolution TVD scheme.

A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

Synthesis of macrocyclic diacyl/dialkyl glycerols containing disulfide tether and studies of their effects upon incorporation in DPPC membranes. Implications in the design of phospholipase A(2) modulators

A general method for the preparation of novel disulfide-tethered macrocyclic diacylglycerols (DAGs) has been described. Overall synthesis involved stepwise protection, acylation, and deprotection to yield the bis(omega-bromoacyl) glycerols. In the crucial macrocyclization step, a unique reagent, benzyltriethylammonium tetrathiomolybdate (BTAT), has been used to convert individual bis(omega-bromoacyl) glycerols to their respective macrocyclic disulfides. DAG 6, which had ether linkages between hydrocarbon chains and the glycerol backbone, was also synthesized from an appropriate precursor using a similar protocol. One of the DAGs (DAG 5) had a carbon-carbon tether instead of a disulfide one and was synthesized using modified Glaser coupling. Preparation of alpha-disulfide-tethered DAG (DAG 4) required an alternative method, as treatment of the bisbromo precursor with BTAT gave a mixture of several compounds from which separation of the target molecule was cumbersome. To avoid this problem, the bisbromide was converted to its corresponding dithiocyanate, which on further treatment with BTAT yielded the desired DAG (DAG 4) in good yield. Upon treatment with the reducing agent dithiothreitol (DTT), the DAGs that contain a disulfide tether could be quantitatively converted to their "open-chain" thiol analogues. These macrocyclic DAGs and their reduced "open-chain" analogues have been incorporated in DPPC vesicles to study their effect on model membranes. Upon incorporation of DAG 1 in DPPC vesicles, formation of new isotropic phases was observed by P-31 NMR, These isotropic phases disappeared completely on opening the macrocyclic ring by a reducing agent. The thermotropic properties of DPPC bilayers having DAGs (1-6) incorporated at various concentrations were studied by differential scanning calorimetry. Incorporation of DAGs in general reduced the cooperativity unit (CU) of the vesicles. Similar experiments with reduced "open-chain" DAGs incorporated in a DPPC bilayer indicated a recovery of CU with respect to their macrocyclic "disulfide" counterparts. The effect of inclusion of these DAGs on the activity of phospholipase A(2) (PLA(2)) was studied in vitro. Incorporation of DAC 1 in DPPC membranes potentiated both bee venom and cobra venom PLA(2) activities.