Learning to Solve Mathematical Application Problems: A Design Experiment With Fifth Graders

Recent research has shown that many upper elementary school children do not master the skill of solving mathematical application problems. In this design experiment, a learning environment for teaching and learning how to model and solve mathematical application problems was developed and tested in 4 classes of 5th graders. Pupils were taught a series of heuristics embedded in an overall metacognitive strategy for solving mathematical application problems. Meanwhile, pupils of 7 control classes followed regular mathematics classes. The implementation and effectiveness of the experimental learning environment were tested in a study with a pretest-posttest-retention test design with an experimental and a control group. The results indicate that the intervention had a positive effect on different aspects of pupils' mathematical modeling and problem-solving abilities.     

Instability of elastic bodies

The study of the equilibrium of systems constitutes an important chapter of applied mechanics. Since Euler’s works on beam buckling, in 1774, many eminent specialists studied the problem of the elastic instability of structures.An examination of many works published in this field shows a large number of approaches or criteria adopted by various authors. The objective of this study is to show through a classical example the link between the different approaches to provide a multi-level basis and to propose a valid global approach for conservative as well as nonconservative systems.     

Observations sur le mémoire précédent

Sans résuméExtrait d'une lettre à M. D. D. Kosambi.     

Practical enantiospecific syntheses of (+) erythro-9- (2s-hydroxy-3r-nonyl) adenine.

Three enantiospecific syntheses of 1S (2S-benzyloxethyl) oxirane (9) from L-ascorbic acid, L(+) tartaric acid, and Z-butene 1,4-diol are reported. The conversion of 9 to 2S-hydroxy-3R-nonylamine (19) is also described.     

Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach

We consider the optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the constant coefficients Black and Scholes model and we consider a general class of utility functions. On an infinite time horizon, Elie and Touzi (Preprint, [2006]) provided the value function as well as the optimal consumption and investment strategy in explicit form. In a more realistic setting, we consider here an agent optimizing its consumption-investment strategy on a finite time horizon. The value function interprets as the unique discontinuous viscosity solution of its corresponding Hamilton-Jacobi-Bellman equation. This leads to a numerical approximation of the value function and allows for a comparison with the explicit solution in infinite horizon.     

A New and Efficient Synthesis of α-Amino Cycloalkyl-Phosphonic Acids via Electrophilic Azidation of Cycloalkylphosphonates

α-Amino cyclobutyl-, cyclopentyl-and cyclohexylphosphonic acids (13) were efficiently prepared from the related unsubstituted cycloalkylphosphonates (5), in three steps including electrophilic azidation of the corresponding lithiated carbanions, catalytic hydrogenation of the intermediate α-azido cycloalkyl-phosphonates (10) and acidic hydrolysis of the resulting α-amino cycloalkyl-phosphonates (12).     

Toward a structure-activity relationship for apoptolidin: selective functionalization of the hydroxyl group array

[reaction: see text] To investigate the structural basis for the exceptional selectivity and activity of apoptolidin (1), a strategy has been devised that allows for selective functionalization of seven of its eight hydroxyl groups based on progressive silyl protection, derivatization, and deprotection. The syntheses of these derivatives and their ability to inhibit F(0)F(1)-ATPase are reported.     

Elastic scattering of 1-GeV protons by nuclei

The calculated elastic scattering of 1.04-GeV protons by ²⁰⁸Pb, ⁵⁸Ni, and ⁴⁰Ca is compared with experiment. The effects of the spin-orbit potential, Pauli and short-range correlations, variations in the ratio of the real to the imaginary part of the nucleon-nucleon scattering amplitude at 0° are found to have similar effects. Further experiments are required before these effects can be disentangled. Changes of the neutron density compared to the proton density can be distinguished. The proton polarization by elastic scattering by ²⁰⁸Pb and ⁴⁰Ca is calculated omitting the effects of correlations.