Towards curricular coherence in integers and fractions: a study of the efficacy of a lesson sequence that uses the number line as the principal representational context

This paper reports a study of the efficacy of Learning Mathematics through Representations (LMR), an innovative curriculum unit designed to support upper elementary students’ understandings of integers and fractions. The unit supports an integrated treatment of integers and fractions through (a) the use of the number line as a cross-domain representational context, and (b) the building of mathematical definitions in classroom communities that become resources to support student argumentation, generalization, and problem solving. In the efficacy study, fourth and fifth grade teachers employing the same district curriculum (Everyday Mathematics) were matched on background indicators and then assigned to either the LMR experimental classrooms (n = 11) or the comparison group (n = 8 with 10 classrooms). During the fall semester, LMR teachers implemented the LMR unit on 19 days and district curriculum on other days of mathematics instruction. HLM analyses documented greater achievement for LMR students than Comparison students on both the end-of-unit and the end-of year assessments of integers and fractions knowledge; the growth rates of LMR students were similar regardless of entering ability level, and gains for LMR students occurred on item types that included number line representations and those that did not. The findings point to the efficacy of the LMR sequence in supporting teaching and learning in the domains of integers and fractions.     

DYNGA: a general purpose QM-MM-MD program. I. Application to water

We present a general purpose QM-MM-MD engine (DYNGA) designed to test alternative hybrid Hamiltonians geared towards the treatment of problems of interest in structural biology including the use of experimental data constraints. In this first presentation we use DYNGA to explore the behaviour of a traditional QM-MM approach in the treatment of the water—water interaction. We find the potential energy hypersurface for the water dimer computed with the HF 4–31G*/TIP3P hybrid Hamiltonian tends to be too flat. We also explore the effect of using traditional QM-MM techniques on proton wires and conclude there is a need for improvement, possibly addressed by using polarizable force fields.     

ConFlo III - an interface for high precision delta(13)C and delta(15)N analysis with an extended dynamic range

A newly developed interface coupling a CHN combustion device (elemental analyser 'EA') to an isotope ratio mass spectrometer is described and evaluated. The purpose of the device is to extend the dynamic range of delta(13)C and delta(15)N analysis from less than 2 orders of magnitude to more than 3 orders of magnitude. Carbon isotope ratio measurements of atropine as a model compound have been performed analysing between 1 μg to 5 mg C with acceptable to excellent precision (0.6 to 0.06 per thousand, delta-notation). The correction due to the blank signal is critical for sample amounts smaller than 4 μg C. The maximum sample weight is determined by the combustion capacity of the EA. Larger sample amounts are measured using dilution of a small part of the EA effluent with helium. The dilution mechanism works virtually free of isotope fractionation. Copyright 1999 John Wiley & Sons, Ltd.