World Transformation: Spherical Reasoning
 Spherical Reasoning
4 Jun 2004 @ 09:41, by ming

From Swanny the Tinker: Global vs. sequential

Global learners learn in layers. They prefer an overview of where they are going first before learning a complex process. They like having a map, knowing where they are headed and what they are working toward. For example, global learners learn phonics quicker if they are shown the result first--that they will be able to figure out unknown words. They enjoy having examples shown to them even if they aren't capable of imitating the skill yet.

Sequential learners find introductory overviews distracting and confusing. They expect to learn whatever they are shown immediately or they become frustrated because they don't have the ability of the global learner to see "the big picture." They prefer to proceed step-by-step, in an orderly way, to the end result. Sequential learners are in the majority, and most educational materials are laid out in a sequential rather than a global way.

These learning styles--concrete vs. abstract and global vs. sequential--are ways of thinking and learning that can affect a child across a variety of skills. Most people can be divided according to their tendency to be more concrete or abstract; more global or more sequential. Just because your child prefers one style over another does not mean he has a serious learning problem or a learning disability. Sometimes he may have difficulties with schoolwork, however, if his learning strengths don't match up with the teaching methods being used in his school. These learning styles are important to your child even when they don't reveal a serious learning problem. Any learner has an advantage when he knows what his strengths are and how to use them to his benefit.

The exception is that having weak sequential reasoning skills can be a significant barrier to learning and is dealt with in more depth in the next section. However, weak global reasoning skills usually means only that the individual is a sequential learner. The solution is typically as simple as choosing a sequential instructional method, something done in education already.

Global learners sometimes get confused by step-by-step instructions, especially if the steps are numerous and complex.

Effect on learning: These students get confused easily and lose sight of the point of the lesson during step-by-step instruction. When these students grow older, however, they will grasp important underlying concepts and theories more quickly than strongly sequential learners.

Strategies: Provide an overview, a clue of where the lesson is headed, before beginning instruction or review.

Examples: Global learners have an easier time with multi-step processes if they first understand what all the steps do. For example, they'll better grasp the purpose and uses of the imaginary lines on maps and globes such as longitude and latitude if they understand that those lines gave the first explorers a way to tell where they were in the ocean when they couldn't see land.

Biophysical Chemistry

New NMR Tools for Aqueous Systems

The essence of life is coordinated motion. From enzyme catalysis to muscle contraction, a molecular choreography of stupendous complexity is enacted in every biological cell and organism. Most of the players in this highly interconnected network of molecular processes are proteins. Protein motions take place on a vast range of time scales, but they are nearly always over-damped (rather than ballistic) and are therefore directly coupled to other motions in their, mostly aqueous, environment. The motions of water molecules are therefore essential to life.
To the NMR spectroscopist, water is not only the most abundant molecule in the biosphere (and therefore often a major constituent of NMR samples); this small molecule also has a surprisingly rich repertoire of NMR properties. For example, the water proton magnetization may relax via the direct nuclear magnetic dipole interaction, the electron-mediated scalar interaction, the isotropic or anisotropic parts of the interaction with the external magnetic field, and the interaction with the magnetic fields induced by molecular rotation or by unpaired electrons. The heading "New NMR Tools for Aqueous Systems" encompasses several projects where new methods for analyzing the structure and dynamics of molecular systems are developed by exploiting the NMR properties of water. Two examples of such projects are described here.

The unique physical properties of liquid water, including its thermal anomalies, can be traced back to the ability of water molecules to form transient three-dimensional networks of hydrogen bonds. Yet, remarkably little experimental information is available on the temperature-dependent hydrogen-bond geometry in water. Pair correlation functions derived from X-ray and neutron diffraction have provided important benchmarks for testing models of water structure but they can only give an isotropically averaged, one-dimensional projection of water structure. Information about the stretching and bending of hydrogen bons can be obtained from the water proton’s magnetic shielding tensor, an exquisitely sensitive probe of the local electronic environment. In liquid water, the shielding tensor is isotropically averaged by fast molecular tumbling so that only its isotropic average, É–iso, can be determined from the resonance frequency. To define the hydrogen bond geometry, the shielding anisotropy, ɢɖ, must be determined from its second-order contribution to the 1H spin relaxation rate. Although 1H spin relaxation in liquid water has been thoroughly studied over the past 50 years, the contribution from shielding anisotropy has escaped detection because, under normal conditions, 1H relaxation is heavily dominated by strong magnetic dipole fields from nearby protons. However, from relaxation measurements at variable magnetic field (2.35 – 18.8 T) on a sample of D2O doped with 1% H2O, we were able to determine ɢɖ with 1 % accuracy over a wide temperature range [Modig & Halle, JACS 124, 12031 (2002)]. The shielding anisotropy is surprisingly large, approaching 30 ppm at low temperatures, and its temperature dependence is four times stronger than that of É–iso (see figure).

To derive geometrical information, the dependence of ɖiso and ɢɖ on the nuclear configuration must be known. This was obtained by ab initio density functional shielding calculations (performed by Bernd Pfrommer) on liquid water configurations generated by ab initio molecular dynamics simulations. Intersections of the shielding surfaces along two intermolecular coordinates (see figure) show that ɢɖ is a more sensitive hydrogen bond probe than ɖiso.

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