Exemplifying a model-eliciting task for primary school pupils

Mathematical modelling is a field that is gaining prominence recently in mathematics educaiton research and has generated interests in schools as well.  In Singapore, modelling and applications are included as process componens in revised 2007 curriculum document (MOE, 2007) as keeping to reform efforst. In Indonesia, efforts to place stronger emphasis on connecting school mathematics with real-world contexts and applications have started in Indonesian primary schools with the Pendidikan Matematika Realistik Indonesia (PMRI) movement a decade ago (Sembiring, Hoogland, Dolk, 2010). Amidst others, modeling activities are gradually introduced in Singapore and Indonesian schools to demonstrte the relevance of school mathematics with real-world problems. However, on order for it to find a place in the mathematics classroom, ther eis a need for teacher-practitioners to know what mathematical modelling and what a modelling task is. This paper sets out to exemplify a model-eliciting task that has been designed and used in both a Singapore and Indonesian mathematics classroom. Mathematical modelling, the features of a model-eliciting task, and its potential and advice on implementation are discussed. 

Assessing the uncertainties of model estimates of primary productivity in the tropical Pacific Ocean

Depth-integrated primary productivity (PP) estimates obtained from satellite ocean color-based models (SatPPMs) and those generated from biogeochemical ocean general circulation models (BCGCMs) represent a key resource for biogeochemical and ecological studies at global as well as regional scales. Calibration and validation of these PP models are not straightforward, however, and comparative studies show large differences between model estimates. The goal of this paper is to compare PP estimates obtained from 30 different models (21 SatPPMs and 9 BOGCMs) to a tropical Pacific PP database consisting of similar to 1000 C-14 measurements spanning more than a decade (1983-1996). Primary findings include: skill varied significantly between models, but performance was not a function of model complexity or type (i.e. SatPPM vs. BOGCM); nearly all models underestimated the observed variance of PR specifically yielding too few low PP (< 0.2 g Cm-2 d(-1)) values; more than half of the total root-mean-squared model-data differences associated with the satellite-based PP models might be accounted for by uncertainties in the input variables and/or the PP data; and the tropical Pacific database captures a broad scale shift from low biomassnormalized productivity in the 1980s to higher biomass-normalized productivity in the 1990s, which was not successfully captured by any of the models. This latter result suggests that interdecadal and global changes will be a significant challenge for both SatPPMs and BOGCMs. Finally, average root-mean-squared differences between in situ PP data on the equator at 140 degrees W and PP estimates from the satellite-based productivity models were 58% lower than analogous values computed in a previous PP model comparison 6 years ago. The success of these types of comparison exercises is illustrated by the continual modification and improvement of the participating models and the resulting increase in model skill. (C) 2008 Elsevier BY. All rights reserved.

An evaluation of ocean color model estimates of marine primary productivity in coastal and pelagic regions across the globe

Nearly half of the earth's photosynthetically fixed carbon derives from the oceans. To determine global and region specific rates, we rely on models that estimate marine net primary productivity (NPP) thus it is essential that these models are evaluated to determine their accuracy. Here we assessed the skill of 21 ocean color models by comparing their estimates of depth-integrated NPP to 1156 in situ C-14 measurements encompassing ten marine regions including the Sargasso Sea, pelagic North Atlantic, coastal Northeast Atlantic, Black Sea, Mediterranean Sea, Arabian Sea, subtropical North Pacific, Ross Sea, West Antarctic Peninsula, and the Antarctic Polar Frontal Zone. Average model skill, as determined by root-mean square difference calculations, was lowest in the Black and Mediterranean Seas, highest in the pelagic North Atlantic and the Antarctic Polar Frontal Zone, and intermediate in the other six regions. The maximum fraction of model skill that may be attributable to uncertainties in both the input variables and in situ NPP measurements was nearly 72%. on average, the simplest depth/wavelength integrated models performed no worse than the more complex depth/wavelength resolved models. Ocean color models were not highly challenged in extreme conditions of surface chlorophyll-a and sea surface temperature, nor in high-nitrate low-chlorophyll waters. Water column depth was the primary influence on ocean color model performance such that average skill was significantly higher at depths greater than 250 m, suggesting that ocean color models are more challenged in Case-2 waters (coastal) than in Case-1 (pelagic) waters. Given that in situ chlorophyll-a data was used as input data, algorithm improvement is required to eliminate the poor performance of ocean color NPP models in Case-2 waters that are close to coastlines. Finally, ocean color chlorophyll-a algorithms are challenged by optically complex Case-2 waters, thus using satellite-derived chlorophyll-a to estimate NPP in coastal areas would likely further reduce the skill of ocean color models.

The use of polylactic and polyglycolic copolymer biomaterial in a pre-clinical model of compromised primary stability

Aim Primary implant stability can be compromised by overdrilling of the implant bed. Filling the gap between the implant and the bone with a highly viscous copolymer of polylactic and polyglycolic acid (PLA/PGA) might stabilize the implant and thus supply osseointegration. The aim of this study was to evaluate implants installed in overdrilled beds associated with PLA/PGA in rats tibia model by means of removal torque test and fluorochrome analysis. Materials and methods For this experiment two groups were selected: in the test group 0.4 mm overdrilled defects (2.0 in diameter and 3 mm long ) were produced in the right tibia of seven rats and implants were placed covered with PLA/PGA biomaterial to fill the gap; the control group was not overdrilled and the implants were placed without the biomaterial. Implants of 1.6 mm in diameter and 3 mm long where placed into all defects. Calcein, alizarin and oxytetracyclin were injected at 7, 15 and 21 postoperative days, respectively, and the animals were sacrificed at 35 postoperative day. Results The results showed that all the implants achieved osseointegration. There were no statistical significance differences in torque-reverse and fluorocrome analysis (P>0.05). Conclusion We can conclude that overdrilled defects filled with PLA/PGA did not disturb osseointegration in this experimental model. © ARIESDUE.

An in vitro triple cell co-culture model with primary cells mimicking the human alveolar epithelial barrier

A triple cell co-culture model was recently established by the authors, consisting of either A549 or 16HBE14o- epithelial cells, human blood monocyte-derived macrophages and dendritic cells, which offers the possibility to study the interaction of xenobiotics with those cells. The 16HBE14o- containing co-culture model mimics the airway epithelial barrier, whereas the A549 co-cultures mimic the alveolar type II-like epithelial barrier. The goal of the present work was to establish a new triple cell co-culture model composed of primary alveolar type I-like cells isolated from human lung biopsies (hAEpC) representing a more realistic alveolar epithelial barrier wall, since type I epithelial cells cover >93% of the alveolar surface. Monocultures of A549 and 16HBE14o- were morphologically and functionally compared with the hAEpC using laser scanning microscopy, as well as transmission electron microscopy, and by determining the epithelial integrity. The triple cell co-cultures were characterized using the same methods. It could be shown that the epithelial integrity of hAEpC (mean ± SD, 1180 ± 188 Ω cm(2)) was higher than in A549 (172 ± 59 Ω cm(2)) but similar to 16HBE14o- cells (1469 ± 156 Ω cm(2)). The triple cell co-culture model with hAEpC (1113 ± 30 Ω cm(2)) showed the highest integrity compared to the ones with A549 (93 ± 14 Ω cm(2)) and 16HBE14o- (558 ± 267 Ω cm(2)). The tight junction protein zonula occludens-1 in hAEpC and 16HBE14o- were more regularly expressed but not in A549. The epithelial alveolar model with hAEpC combined with two immune cells (i.e. macrophages and dendritic cells) will offer a novel and more realistic cell co-culture system to study possible cell interactions of inhaled xenobiotics and their toxic potential on the human alveolar type I epithelial wall.

Studying Effects of Primary Care Physicians and Patients on the Trade-Off Between Charges for Primary Care and Specialty Care Using a Hierarchical Multivariate Two-Part Model

Objective. To examine effects of primary care physicians (PCPs) and patients on the association between charges for primary care and specialty care in a point-of-service (POS) health plan. Data Source. Claims from 1996 for 3,308 adult male POS plan members, each of whom was assigned to one of the 50 family practitioner-PCPs with the largest POS plan member-loads. Study Design. A hierarchical multivariate two-part model was fitted using a Gibbs sampler to estimate PCPs' effects on patients' annual charges for two types of services, primary care and specialty care, the associations among PCPs' effects, and within-patient associations between charges for the two services. Adjusted Clinical Groups (ACGs) were used to adjust for case-mix. Principal Findings. PCPs with higher case-mix adjusted rates of specialist use were less likely to see their patients at least once during the year (estimated correlation: –.40; 95% CI: –.71, –.008) and provided fewer services to patients that they saw (estimated correlation: –.53; 95% CI: –.77, –.21). Ten of 11 PCPs whose case-mix adjusted effects on primary care charges were significantly less than or greater than zero (p < .05) had estimated, case-mix adjusted effects on specialty care charges that were of opposite sign (but not significantly different than zero). After adjustment for ACG and PCP effects, the within-patient, estimated odds ratio for any use of primary care given any use of specialty care was .57 (95% CI: .45, .73). Conclusions. PCPs and patients contributed independently to a trade-off between utilization of primary care and specialty care. The trade-off appeared to partially offset significant differences in the amount of care provided by PCPs. These findings were possible because we employed a hierarchical multivariate model rather than separate univariate models.

Experimental ovine model of primary venous valve incompetence: a pilot study

PURPOSE: To compare two techniques used to create a larger animal model of venous valve incompetence. MATERIALS AND METHODS: To achieve vein dilatation as the primary cause of valve incompetence, common carotid jugular vein (JV) fistulas were created and optional filters were placed into the JV of sheep. Altogether, nine inferior vena cava filters were placed in three sheep in two stages. Six filters were placed caudal to the most caudal JV valve in three sheep and removed 6 weeks later. Then, three filters were placed across the most caudal valve in two sheep with competent valves and removed 3 weeks later. A common carotid artery-JV fistula was created in three sheep and followed-up for 1-3 weeks. Ascending and descending venograms were obtained to determine the JV sizes and function of their valves. The JVs removed at necropsy were studied with venoscopy. RESULTS: Only one of the six JVs with filters caudal to the most caudal valve had incompetent valves after filter removal at 6 weeks. In addition, only one of three JVs with the filter across the valve had incompetent valves after filter removal at 3 weeks. At 1-3-week follow-up of the group with common carotid artery-JV fistula, all three JVs had incompetent valves in the cephalad vein portion, but only one JV had an incompetent valve in its caudal portion. At venoscopy, the incompetent valves showed various degrees of damage ranging from shortening to the destruction of valve leaflets. CONCLUSION: Dilation of the valve annulus with a removable vena cava filter failed to produce valve incompetence. The promising results with the common carotid artery-JV fistula justify further detailed research.

Cytotoxic effects of camptothecin and cisplatin combined with tumor necrosis factor-related apoptosis-inducing ligand (Apo2L/TRAIL) in a model of primary culture of non-small cell lung cancer

The cytokine tumor-necrosis factor-related apoptosis-inducing ligand (Apo2L/TRAIL) has been shown to preferentially induce apoptosis in cancer cells. A previous study of our group demonstrated that non-small cell lung cancer cell lines can be sensitized to Apo2L/TRAIL-induced apoptosis by chemotherapeutic agents. The aim of the present study was the evaluation of these results in a model of primary culture of non-small cell lung cancer.

The cranial bone window model: studying angiogenesis of primary and secondary bone tumors by intravital microscopy

The successful treatment of primary and secondary bone tumors in a huge number of cases remains one of the major unsolved challenges in modern medicine. Malignant primary bone tumor growth predominantly occurs in younger people, whereas older people predominantly suffer from secondary bone tumors since up to 85% of the most frequently occurring malignant solid tumors, such as lung, mammary, and prostate carcinomas, metastasize into the bone. It is well known that a tumor's course may be altered by its surrounding tissue. For this reason, reported here is the protocol for the surgical preparation of a cranial bone window in mice as well as the method to implant tumors in this bone window for further investigations of angiogenesis and other microcirculatory parameters in orthotopically growing primary or secondary bone tumors using intravital microscopy. Intravital microscopy represents an internationally accepted and sophisticated experimental method to study angiogenesis, microcirculation, and many other parameters in a wide variety of neoplastic and nonneoplastic tissues. Since most physiologic and pathophysiologic processes are active and dynamic events, one of the major strengths of chronic animal models using intravital microscopy is the possibility of monitoring the regions of interest in vivo continuously up to several weeks with high spatial and temporal resolution. In addition, after the termination of experiments, tissue samples can be excised easily and further examined by various in vitro methods such as histology, immunohistochemistry, and molecular biology.

An empirical model to estimate the demand for primary care in urban settings

Objective. To measure the demand for primary care and its associated factors by building and estimating a demand model of primary care in urban settings.^ Data source. Secondary data from 2005 California Health Interview Survey (CHIS 2005), a population-based random-digit dial telephone survey, conducted by the UCLA Center for Health Policy Research in collaboration with the California Department of Health Services, and the Public Health Institute between July 2005 and April 2006.^ Study design. A literature review was done to specify the demand model by identifying relevant predictors and indicators. CHIS 2005 data was utilized for demand estimation.^ Analytical methods. The probit regression was used to estimate the use/non-use equation and the negative binomial regression was applied to the utilization equation with the non-negative integer dependent variable.^ Results. The model included two equations in which the use/non-use equation explained the probability of making a doctor visit in the past twelve months, and the utilization equation estimated the demand for primary conditional on at least one visit. Among independent variables, wage rate and income did not affect the primary care demand whereas age had a negative effect on demand. People with college and graduate educational level were associated with 1.03 (p < 0.05) and 1.58 (p < 0.01) more visits, respectively, compared to those with no formal education. Insurance was significantly and positively related to the demand for primary care (p < 0.01). Need for care variables exhibited positive effects on demand (p < 0.01). Existence of chronic disease was associated with 0.63 more visits, disability status was associated with 1.05 more visits, and people with poor health status had 4.24 more visits than those with excellent health status. ^ Conclusions. The average probability of visiting doctors in the past twelve months was 85% and the average number of visits was 3.45. The study emphasized the importance of need variables in explaining healthcare utilization, as well as the impact of insurance, employment and education on demand. The two-equation model of decision-making, and the probit and negative binomial regression methods, was a useful approach to demand estimation for primary care in urban settings.^