Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

Soil management effects on organic carbon in isolated fractions of a Gray Luvisol

Agricultural management affects soil organic matter, which is important for sustainable crop production and as a greenhouse gas sink. Our objective was to determine how tillage, residue management and N fertilization affect organic C in unprotected, and physically, chemically and biochemically protected soil C pools. Samples from Breton, Alberta were fractionated and analysed for organic C content. As in previous report, N fertilization had a positive effect, tillage had a minimal effect, and straw management had no effect on whole-soil organic C. Tillage and straw management did not alter organic C concentrations in the isolated C pools, while N fertilization increased C concentrations in all pools. Compared with a woodlot soil, the cultivated plots had lower total organic C, and the C was redistributed among isolated pools. The free light fraction and coarse particulate organic matter responded positively to C inputs, suggesting that much of the accumulated organic C occurred in an unprotected pool. The easily dispersed silt-sized fraction was the mineral-associated pool most responsive to changes in C inputs, whereas the microaggregate-derived silt-sized fraction best preserved C upon cultivation. These findings suggest that the silt-sized fraction is important for the long-term stabilization of organic matter through both physical occlusion in microaggregates and chemical protection by mineral association.

Acid hydrolysis of easily dispersed and microaggregate-derived silt- and clay-sized fractions to isolate resistant soil organic matter

The current paradigm in soil organic matter (SOM) dynamics is that the proportion of biologically resistant SOM will increase when total SOM decreases. Recently, several studies have focused on identifying functional pools of resistant SOM consistent with expected behaviours. Our objective was to combine physical and chemical approaches to isolate and quantify biologically resistant SOM by applying acid hydrolysis treatments to physically isolated silt- and clay-sized soil fractions. Microaggegrate-derived and easily dispersed silt- and clay-sized fractions were isolated from surface soil samples collected from six long-term agricultural experiment sites across North America. These fractions were hydrolysed to quantify the non-hydrolysable fraction, which was hypothesized to represent a functional pool of resistant SOM. Organic C and total N concentrations in the four isolated fractions decreased in the order: native > no-till > conventional-till at all sites. Concentrations of non-hydrolysable C (NHC) and N (NHN) were strongly correlated with initial concentrations, and C hydrolysability was found to be invariant with management treatment. Organic C was less hydrolysable than N, and overall, resistance to acid hydrolysis was greater in the silt-sized fractions compared with the clay-sized fractions. The acid hydrolysis results are inconsistent with the current behaviour of increasing recalcitrance with decreasing SOM content: while %NHN was greater in cultivated soils compared with their native analogues, %NHC did not increase with decreasing total organic C concentrations. The analyses revealed an interaction between biochemical and physical protection mechanisms that acts to preserve SOM in fine mineral fractions, but the inconsistency of the pool size with expected behaviour remains to be fully explained.

Impact of soil texture on the distribution of soil organic matter in physical and chemical fractions

Previous research on the protection of soil organic C from decomposition suggests that soil texture affects soil C stocks. However, different pools of soil organic matter (SOM) might be differently related to soil texture. Our objective was to examine how soil texture differentially alters the distribution of organic C within physically and chemically defined pools of unprotected and protected SOM. We collected samples from two soil texture gradients where other variables influencing soil organic C content were held constant. One texture gradient (16-60% clay) was located near Stewart Valley, Saskatchewan, Canada and the other (25-50% clay) near Cygnet, OH. Soils were physically fractionated into coarse- and fine-particulate organic matter (POM), silt- and clay-sized particles within microaggregates, and easily dispersed silt-and clay-sized particles outside of microaggregates. Whole-soil organic C concentration was positively related to silt plus clay content at both sites. We found no relationship between soil texture and unprotected C (coarse- and fine-POM C). Biochemically protected C (nonhydrolyzable C) increased with increasing clay content in whole-soil samples, but the proportion of nonhydrolyzable C within silt- and clay-sized fractions was unchanged. As the amount of silt or clay increased, the amount of C stabilized within easily dispersed and microaggregate-associated silt or clay fractions decreased. Our results suggest that for a given level of C inputs, the relationship between mineral surface area and soil organic matter varies with soil texture for physically and biochemically protected C fractions. Because soil texture acts directly and indirectly on various protection mechanisms, it may not be a universal predictor of whole-soil C content.

Land use effects on soil carbon fractions in the southeastern United States. II. changes in soil carbon fractions along a forest to pasture chronosequence

Since land use change can have significant impacts on regional biogeochemistry, we investigated how conversion of forest and cultivation to pasture impact soil C and N cycling. In addition to examining total soil C, we isolated soil physiochemical C fractions in order to understand the mechanisms by which soil C is sequestered or lost. Total soil C did not change significantly over time following conversion from forest, though coarse (250-2,000 mum) particulate organic matter C increased by a factor of 6 immediately after conversion. Aggregate mean weight diameter was reduced by about 50% after conversion, but values were like those under forest after 8 years under pasture. Samples collected from a long-term pasture that was converted from annual cultivation more than 50 years ago revealed that some soil physical properties negatively impacted by cultivation were very slow to recover. Finally, our results indicate that soil macroaggregates turn over more rapidly under pasture than under forest and are less efficient at stabilizing soil C, whereas microaggregates from pasture soils stabilize a larger concentration of C than forest microaggregates. Since conversion from forest to pasture has a minimal impact on total soil C content in the Piedmont region of Virginia, United States, a simple C stock accounting system could use the same base soil C stock value for either type of land use. However, since the effects of forest to pasture conversion are a function of grassland management following conversion, assessments of C sequestration rates require activity data on the extent of various grassland management practices.

Land use effects on soil carbon fractions in the southeastern United States. I. Management-intensive versus extensive grazing

Changes in grassland management intended to increase productivity can lead to sequestration of substantial amounts of atmospheric C in soils. Management-intensive grazing (MiG) can increase forage production in mesic pastures, but potential impacts on soil C have not been evaluated. We sampled four pastures (to 50 cm depth) in Virginia, USA, under MiG and neighboring pastures that were extensively grazed or bayed to evaluate impacts of grazing management on total soil organic C and N pools, and soil C fractions. Total organic soil C averaged 8.4 Mg C ha(-1) (22%) greater under MiG; differences were significant at three of the four sites examined while total soil N was greater for two sites. Surface (0-10 cm) particulate organic matter (POM) C increased at two sites; POM C for the entire depth increment (0-50 cm) did not differ significantly between grazing treatments at any of the sites. Mineral-associated C was related to silt plus clay content and tended to be greater under MiG. Neither soil C:N ratios, POM C, or POM C:total C ratios were accurate indicators of differences in total soil C between grazing treatments, though differences in total soil C between treatments attributable to changes in POM C (43%) were larger than expected based on POM C as a percentage of total C (24.5%). Soil C sequestration rates, estimated by calculating total organic soil C differences between treatments (assuming they arose from changing grazing management and can be achieved elsewhere) and dividing by duration of treatment, averaged 0.41 Mg C ha(-1) year(-1) across the four sites.

Cell density alters matrix accumulation in two distinct fractions and the mechanical integrity of alginate-chondrocyte constructs

Chondrocyte density in articular cartilage is known to change with the development and growth of the tissue and may play an important role in the formation of a functional extracellular matrix (ECM). The objective of this study was to determine how initial chondrocyte density in an alginate hydrogel affects the matrix composition, its distribution between the cell-associated (CM) and further removed matrix (FRM) fractions, and the tensile mechanical properties of the developing engineered cartilage. Alginate constructs containing primary bovine chondrocytes at densities of 0, 4, 16, and 64 million cells/ml were fabricated and cultured for 1 or 2 weeks, at which time structural, biochemical, and mechanical properties were analyzed. Both matrix content and distribution varied with the initial cell density. Increasing cell density resulted in an increasing content of collagen and sulfated-glycosaminoglycan (GAG) and an increasing proportion of these molecules localized in the CM. While the equilibrium tensile modulus of cell-free alginate did not change with time in culture, the constructs with highest cell density were 116% stiffer than cell-free controls after 2 weeks of culture. The equilibrium tensile modulus was positively correlated with total collagen (r2 = 0.47, p < 0.001) and GAG content (r2 = 0.68, p < 0.001), and these relationships were enhanced when analyzing only those matrix molecules in the CM fraction (r2 = 0.60 and 0.72 for collagen and GAG, respectively, each p < 0.001). Overall, the results of this study indicate that initial cell density has a considerable effect on the developing composition, structure, and function of alginate–chondrocyte constructs.