The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

Examining the potential application of childhood stature in assessing adolescent overweight and obesity

Background: Increasing Overweight and Obesity (OwOb) prevalence in pediatric populations is becoming a public health concern in many countries. The purpose of this study was to determine if childhood stature components, particularly the Leg Length Index (LLI = [height - sitting height]! height), were useful in assessing risk of OwOb in adolescence. Methods: Data was from a longitudinal study conducted in south Ontario since 2004. Approximately 2360 students had body composition measurements including sitting height and standing height at baseline. Among them, 1167 children (573 girls, 594 boys) who had weight and height measured at the 5 th year follow-up, were included in this analysis. OwOb was defined using age and sex specific BMI (kg!m 2 ) cut-off points corresponding to adults' BMI ~ 25. Results: Overall, 34% (n=298) of adolescents were considered as OwOb. The results from logistic regression analysis indicated that with 1 unit increase in LLI the odds of OwOb decreased 24% (Odds Ratio, [95% Confidence Interval], 0.76, [0.66-0.87]) after adjusted for age, sex and baseline waist circumference. Further adjusting for birth weight, birth order, breastfeeding, child's physical activity, maternal smoking, education, mother's age at birth and mother's BMI, did not change the relationship. Our results also indicated that mother's smoking status is associated with LLI. Discussion: Although LLI measured at childhood in this study is related to OwOb risk in adolescents, the underlying mechanism is unclear and further study is needed.

Application of thermal ion-molecule reactions in tackling spectroscopic inferences in inductively coupled plasma mass spectrometry

Part I: Ultra-trace determination of vanadium in lake sediments: a performance comparison using O2, N20, and NH3 as reaction gases in ICP-DRC-MS Thermal ion-molecule reactions, targeting removal of specific spectroscopic interference problems, have become a powerful tool for method development in quadrupole based inductively coupled plasma mass spectrometry (ICP-MS) applications. A study was conducted to develop an accurate method for the determination of vanadium in lake sediment samples by ICP-MS, coupled with a dynamic reaction cell (DRC), using two differenvchemical resolution strategies: a) direct removal of interfering C10+ and b) vanadium oxidation to VO+. The performance of three reaction gases that are suitable for handling vanadium interference in the dynamic reaction cell was systematically studied and evaluated: ammonia for C10+ removal and oxygen and nitrous oxide for oxidation. Although it was able to produce comparable results for vanadium to those using oxygen and nitrous oxide, NH3 did not completely eliminate a matrix effect, caused by the presence of chloride, and required large scale dilutions (and a concomitant increase in variance) when the sample and/or the digestion medium contained large amounts of chloride. Among the three candidate reaction gases at their optimized Eonditions, creation of VO+ with oxygen gas delivered the best analyte sensitivity and the lowest detection limit (2.7 ng L-1). Vanadium results obtained from fourteen lake sediment samples and a certified reference material (CRM031-040-1), using two different analytelinterference separation strategies, suggested that the vanadium mono-oxidation offers advantageous performance over the conventional method using NH3 for ultra-trace vanadium determination by ICP-DRC-MS and can be readily employed in relevant environmental chemistry applications that deal with ultra-trace contaminants.Part II: Validation of a modified oxidation approach for the quantification of total arsenic and selenium in complex environmental matrices Spectroscopic interference problems of arsenic and selenium in ICP-MS practices were investigated in detail. Preliminary literature review suggested that oxygen could serve as an effective candidate reaction gas for analysis of the two elements in dynamic reaction cell coupled ICP-MS. An accurate method was developed for the determination of As and Se in complex environmental samples, based on a series of modifications on an oxidation approach for As and Se previously reported. Rhodium was used as internal standard in this study to help minimize non-spectral interferences such as instrumental drift. Using an oxygen gas flow slightly higher than 0.5 mL min-I, arsenic is converted to 75 AS160+ ion in an efficient manner whereas a potentially interfering ion, 91Zr+, is completely removed. Instead of using the most abundant Se isotope, 80Se, selenium was determined by a second most abundant isotope, 78Se, in the form of 78Se160. Upon careful selection of oxygen gas flow rate and optimization ofRPq value, previous isobaric threats caused by Zr and Mo were reduced to background levels whereas another potential atomic isobar, 96Ru+, became completely harmless to the new selenium analyte. The new method underwent a strict validation procedure where the recovery of a suitable certified reference material was examined and the obtained sample data were compared with those produced by a credible external laboratory who analyzed the same set of samples using a standardized HG-ICP-AES method. The validation results were satisfactory. The resultant limits of detection for arsenic and selenium were 5 ng L-1 and 60 ng L-1, respectively.