How does imposing a step-by-step solution method impact students’ approach to mathematical word problem solving?

This paper presents the second phase of a larger research program with the purpose of exploring the possible consequences of a gap between what is done in the classroom regarding mathematical word problem solving and what research shows to be effective in this particular field of study. Data from the first phase of our study on teachers’ self-proclaimed practices showed that one-third of elementary teachers from the region of Quebec require their students to follow a specific sequential problem-solving method, known as the ‘what I know, what I look for’ method. These results led us to hypothesize that the observed gap may have an impact on students’ comprehension of mathematical word problems. The use of this particular method was the foundation for us to study, in the second phase, the effect of the imposition of this sequential method on students’ literal and inferential understanding of word problems. A total of 278 fourth graders (9–10 years old) solved mathematical word problems followed by a test to assess their understanding of the word problems they had just solved. The results suggest that the use of this problem solving method does not seem to improve or impair students’ understanding. From a more fundamental point of view, our study led us to the conclusion that the way word problem solving is addressed in the mathematics classroom, through sequential and inflexible methods, does not help students develop their word problem solving competence.     

Micro-level reserving for general insurance claims using a long short-term memory network

Detailed information about individual claims are completely ignored when insurance claims data are aggregated and structured in development triangles for loss reserving. In the hope of extracting predictive power from the individual claims characteristics, researchers have recently proposed to use micro-level loss reserving approaches. We introduce a discrete-time individual reserving framework incorporating granular information in a deep learning approach named Long Short-Term Memory (LSTM) neural network. At each time period, the network has two tasks: first, classifying whether there is a payment or a recovery, and second, predicting the corresponding non-zero amount, if any. Based on a generalized Pareto model for excess payments over a threshold, we adjust the LSTM reserve prediction to account for extreme payments. We illustrate the estimation procedure on a simulated and a real general insurance dataset. We compare our approach with the chain-ladder aggregate method using the predictive outstanding loss estimates and their actual values.     

Assessing MS-based quantitation strategies for low-level impurities in peptide reference materials: application to angiotensin II

Analytical and Bioanalytical Chemistry - Identification and quantitation of related impurities is vital in obtaining corrected purity values for peptide certified reference materials. The...     

Purity assignment for peptide certified reference materials by combining qNMR and LC-MS/MS amino acid analysis results: application to angiotensin II

Analytical and Bioanalytical Chemistry - The purity value assignment of metrologically traceable peptide reference standards requires specialized primary methods. Conventionally, amino acid...     

Liquid chromatography-tandem mass spectrometry determination for multiclass pesticides from insect samples by microwave-assisted solvent extraction followed by a salt-out effect and micro-dispersion purification

The effects of phyto-pharmaceutic compounds (PPCs), such as neonicotinoids, on wildlife reproduction and survival are a rising concern. Yet, understanding the biological consequences of PPC use is particularly complex given the large diversity of PPCs and their derivatives to which wildlife can be exposed. Here, we present a simple and sensitive method for the simultaneous detection and quantification of multiclass PPCs (54 molecules) in single insect boluses (<0.05 g dry mass) by ultra-high pressure liquid chromatography coupled to a tandem mass spectrometer (LC-MS/MS). A key part of this new method is the use of a two-step extraction method combining (i) the high efficiency of a microwave-assisted solvent extraction (MAE) for extracting analytes that might be tightly bound to environmental matrices and (ii) the versatility of a salt-out effect adapted from the QuEChERS methodology allowing the extraction and purification of a wide array of analytes. This microwave-assisted salt-out extraction (MASOE) approach was compared to classical extraction methods including matrix solid phase dispersion (MSPD), microwave-assisted extraction (MAE), and the QuEChERS method. Average recoveries for 54 analytes ranged from 49% to 106%, (relative standard deviations <22%). The limits of detection (LODs) and quantification (LOQs) were in the ranges of 0.10–3.00 ng g⁻¹ and 0.40–7.00 ng g⁻¹, respectively. We applied this method to analyse 881 insect boluses collected from Tree Swallow (Tachycineta bicolour) nestlings along an agricultural intensification gradient in southern Québec (Canada). We detected 25 PPCs out of the 54 considered. We detected at least one PPC in 30% of samples and were able to quantify at least one of them in 17% of samples. Our study shows that the MASOE method should prove to be a powerful tool for studying the fate and impacts of PPCs on wildlife.