It has often been claimed that children's mathematical understanding is based on their ability to reason logically, but there is no good evidence for this causal link. We tested the causal hypothesis about logic and mathematical development in two related studies. In a longitudinal study, we showed that (a) 6-year-old children's logical abilities and their working memory predict mathematical achievement 16 months later; and (b) logical scores continued to predict mathematical levels after controls for working memory, whereas working memory scores failed to predict the same measure after controls for differences in logical ability. In our second study, we trained a group of children in logical reasoning and found that they made more progress in mathematics than a control group who were not given this training. These studies establish a causal link between logical reasoning and mathematical learning. Much of children's mathematical knowledge is based on their understanding of its underlying logic.Logical relations lie at the heart of many fields of inquiry. Think of the relation known as transitivity, for example, if A ¼ B and B ¼ C, then A ¼ C. This relation is pertinent to the number of objects in a set, to length, to volume, to colour, to shape, to people's intelligence, to the matching of photographs of fingerprints, to the taste of orange juice etc. Transitivity is significant in the domains of number and measurement, but it is neither number nor measurement. Not all the relations are transitive: if A is the father of B and B is the father of C, it does not follow that A is the father of C. For this reason, Piaget (1950) argued that the pertinence of a logical relation is given meaning in a domain through experience.A similar argument was advanced by Simon and Klahr (1995;Klahr, 1982) about conservation. Transformations, they argued, have different effects on different quantities, and children learn about these differences by experience. If we add a jar of water at 208C to another jar of water also at 208C, the quantity of water (the * Correspondence should be addressed to Terezinha Nunes, 15 Norham Gardens, Oxford OX2 6PY, UK Reproduction in any form (including the internet) is prohibited without prior permission from the Society extensive quantity) increases, but the temperature (an intensive quantity) stays the same. Children must learn the domains where different logical relations (or axioms) apply.Children almost certainly need to understand the logical relations between quantities in order to learn how to represent numbers and arithmetic. These relations are not the same as arithmetic or the numeration system, but are relevant to them. One such relation is correspondence: if two sets contain the same number of objects, then the objects in one set are in one-to-one correspondence with those in the other. If set B is in two-to-one correspondence with set A, and C is in two-to-one correspondence with A, then B and C are equivalent.

This is a repository copy of Spatial variability in depositional reservoir quality of deep-water channel-fill and lobe deposits.

Recognition and interpretation of sedimentary structures is fundamental to understanding sedimentary processes. Banded sandstones are an enigmatic sedimentary facies comprising alternating mud-rich (as matrix and/or mud clasts) and cleaner sand layers. The juxtaposition of hydrodynamically different grain sizes contradicts established models of cleaner-sand bedform development. Here, outcrop, subsurface core, and petrographic data from three deep-water systems, with well-constrained paleogeographic contexts, are used to describe the range of sedimentary textures, bedform morphologies, and facies associations, and to quantify the mud content of banding. Banding can occur in any part of a bed (base, middle, or top), but it typically overlies a structureless basal sandstone or mud-clast conglomerate lag, and is overlain by clean parallel-laminated sandstone and/or ripple cross-lamination. Banding morphology ranges from sub-parallel to bedforms that comprise low-angle laminae with discontinuous lenses of mudstone, or asymmetric bedforms comprising steeply dipping foresets that transition downstream into low-amplitude bedwaves, or steeply dipping ripple-like bedforms with heterolithic foresets. This style of banding is interpreted as a range of bedforms that form progressively in the upper-stage plane-bed flow regime via tractional reworking beneath mud-laden transitional plug flows. The balance of cohesive and turbulent forces, and the rate of flow deceleration (aggradation rate), govern the style of deposit. Banded sandstones and linked debrites are rarely found juxtaposed together in the same bed because they are distributed preferentially in proximal and distal settings, respectively. Understanding the origins of banding in turbidite sandstones, the conditions under which it forms, and its distribution across deep-water systems and relationship to linked debrites, is important for it to be used effectively as a tool to interpret the geological record.

This is a repository copy of Topographic controls on the development of contemporaneous but contrasting basin-floor depositional architectures.

The topography of the seabed (orientation and gradient) and rheology of the flows greatly influences the character of basin-floor turbidity current deposits. Therefore, submarine fan pinchouts can help to constrain seabed topography and flow behavior at the time of deposition. Although the depositional architecture of submarine lobe pinchouts has been documented in various basin-fills, the quantification of the rates of change at pinchouts in different paleogeographic positions and basin configurations has not been attempted previously. Here, we utilize extensive outcrops and research boreholes from the oblique up-dip pinchout of Fans 3 and 4 and the lateral pinchout of Fan 3 in the Tanqua depocenter, Karoo Basin, South Africa, to compare sedimentary facies and to quantify the rates of change in gross interval thickness. At the oblique up-dip pinchout, Fan 3 thins abruptly at a rate of 12 m/km, while Fan 4 thins at a rate of 4 m/km. Marked differences between Fans 3 and 4 in sedimentary facies and architecture toward the up-dip pinchout, with termination of lobes in Fan 3 and a channel-lobe transition zone and external levee in Fan 4, suggests progradation of the system. The thinning rate of the lateral pinchout of Fan 3 is 2 m/km, with the presence of hybrid beds in the lower part of Fan 3, while the upper part is dominated by structured sandstones and thin-bedded heterolithics. The variations in facies suggest that lobe-scale frontal and lateral pinchouts are stacked at the lobe complex-scale lateral pinchout of Fan 3, highlighting the importance of a hierarchical understanding when studying basin-floor fan pinchouts. The quantified rates of change in fan thickness and sedimentology on the oblique up-dip and lateral fan pinchouts are markedly different. Contrasting pinchout architecture above slopes with subtle differences in gradient and orientation cautions against the simple definition of reservoir input parameters for stratigraphic traps in submarine fan systems.