Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Mixing colours : an ICT tool based on a semiotic framework for mathematical meaning-making about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

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).

Porous PLGA microspheres effectively loaded with BSA protein by electrospraying combined with phase separation in liquid nitrogen

Polymer microspheres loaded with bioactive particles, biomolecules, proteins, and/or growth factors play important roles in tissue engineering, drug delivery, and cell therapy. The conventional double emulsion method and a new method of electrospraying into liquid nitrogen were used to prepare bovine serum albumin (BAS)-loaded poly(lactic-co-glycolic acid) (PLGA) porous microspheres. The particle size, the surface morphology and the internal porous structure of the microspheres were observed using scanning electron microscopy (SEM). The loading efficiency, the encapsulation efficiency, and the release profile of the BSA-loaded PLGA microspheres were measured and studied. It was shown that the microspheres from double emulsion had smaller particle sizes (3-50 m), a less porous structure, a poor loading efficiency (5.2 %), and a poor encapsulation efficiency (43.5%). However, the microspheres from the electrospraying into liquid nitrogen had larger particle sizes (400-600 m), a highly porous structure, a high loading efficiency (12.2%), and a high encapsulation efficiency (93.8%). Thus the combination of electrospraying with freezing in liquid nitrogen and subsequent freeze drying represented a suitable way to produce polymer microspheres for effective loading and sustained release of proteins.

Nitrogen and phosphorus transformations in fixed-film biofilters subjected to aeration/no-aeration cycles

Despite recent developments in fixed-film combined biological nutrients removal (BNR) technology; fixed-film systems (i.e., biofilters), are still at the early stages of development and their application has been limited to a few laboratory-scale experiments. Achieving enhanced biological phosphorus removal in fixed-film systems requires exposing the micro-organisms and the waste stream to alternating anaerobic/aerobic or anaerobic/anoxic conditions in cycles. The concept of cycle duration (CD) as a process control parameter is unique to fixed-film BNR systems, has not been previously investigated, and can be used to optimise the performance of such systems. The CD refers to the elapsed time before the biomass is re-exposed to the same environmental conditions in cycles. Fixed-film systems offer many advantages over suspended growth systems such as reduced operating costs, simplicity of operation, absence of sludge recycling problems, and compactness. The control of nutrient discharges to water bodies, improves water quality, fish production, and allow water reuse. The main objective of this study was to develop a fundamental understanding of the effect of CD on the transformations of nutrients in fixed-film biofilter systems subjected to alternating aeration I no-aeration cycles A fixed-film biofilter system consisting of three up-flow biofilters connected in series was developed and tested. The first and third biofilters were operated in a cyclic mode in which the biomass was subjected to aeration/no-aeration cycles. The influent wastewater was simulated aquaculture whose composition was based on actual water quality parameters of aquacuture wastewater from a prawn grow-out facility. The influent contained 8.5 - 9:3 mg!L a111monia-N, 8.5- 8.7 mg/L phosphate-P, and 45- 50 mg!L acetate. Two independent studies were conducted at two biofiltration rates to evaluate and confirm the effect of CD on nutrient transformations in the biofilter system for application in aquaculture: A third study was conducted to enhance denitrification in the system using an external carbon- source at a rate varying from 0-24 ml/min. The CD was varied in the range of0.25- 120 hours for the first two studies and fixed at 12 hours for the third study. This study identified the CD as an important process control parameter that can be used to optimise the performance of full-scale fixed-film systems for BNR which represents a novel contribution in this field of research. The CD resulted in environmental conditions that inhibited or enhanced nutrient transformations. The effect of CD on BNR in fixed-film systems in terms of phosphorus biomass saturation and depletion has been established. Short CDs did not permit the establishment of anaerobic activity in the un-aerated biofilter and, thus, inhibited phosphorus release. Long CDs resulted in extended anaerobic activity and, thus, resulted in active phosphorus release. Long CDs, however, resulted in depleting the biomass phosphorus reservoir in the releasing biofilter and saturating the biomass phosphorus reservoir in the up-taking biofilter in the cycle. This phosphorus biomass saturation/depletion phenomenon imposes a practical limit on how short or long the CD can be. The length of the CD should be somewhere just before saturation or depletion occur and for the system tested, the optimal CD was 12 hours for the biofiltration rates tested. The system achieved limited net phosphorus removal due to the limited sludge wasting and lack of external carbon supply during phosphorus uptake. The phosphorus saturation and depletion reflected the need to extract phosphorus from the phosphorus-rich micro-organisms, for example, through back-washing. The major challenges of achieving phosphorus removal in the system included: (I) overcoming the deterioration in the performance of the system during the transition period following the start of each new cycle; and (2) wasting excess phosphorus-saturated biomass following the aeration cycle. Denitrification occurred in poorly aerated sections of the third biofilter and generally declined as the CD increased and as the time progressed in the individual cycle. Denitrification and phosphorus uptake were supplied by an internal organic carbon source, and the addition of an external carbon source (acetate) to the third biofilter resulted in improved denitrification efficiency in the system from 18.4 without supplemental carbon to 88.7% when the carbon dose reached 24 mL/min The removal of TOC and nitrification improved as the CD increased, as a result of the reduction in the frequency of transition periods between the cycles. A conceptual design of an effective fixed-film BNR biofilter system for the treatment of the influent simulated aquaculture wastewater was proposed based on the findings of the study.

Nitrogen fertilizer rate management as a nitrous oxide mitigation strategy: Development of a nitrous oxide emission reduction protocol (NERP)

Nitrous oxide (N2O) is a potent agricultural greenhouse gas (GHG). More than 50% of the global anthropogenic N2O flux is attributable to emissions from soil, primarily due to large fertilizer nitrogen (N) applications to corn and other non-leguminous crops. Quantification of the trade–offs between N2O emissions, fertilizer N rate, and crop yield is an essential requirement for informing management strategies aiming to reduce the agricultural sector GHG burden, without compromising productivity and producer livelihood. There is currently great interest in developing and implementing agricultural GHG reduction offset projects for inclusion within carbon offset markets. Nitrous oxide, with a global warming potential (GWP) of 298, is a major target for these endeavours due to the high payback associated with its emission prevention. In this paper we use robust quantitative relationships between fertilizer N rate and N2O emissions, along with a recently developed approach for determining economically profitable N rates for optimized crop yield, to propose a simple, transparent, and robust N2O emission reduction protocol (NERP) for generating agricultural GHG emission reduction credits. This NERP has the advantage of providing an economic and environmental incentive for producers and other stakeholders, necessary requirements in the implementation of agricultural offset projects.

Nitrogen fertilizer management for nitrous oxide (N2O) mitigation in intensive corn (Maize) production: an emissions reduction protocol for US Midwest agriculture

Nitrous oxide (N2O) is a major greenhouse gas (GHG) product of intensive agriculture. Fertilizer nitrogen (N) rate is the best single predictor of N2O emissions in row-crop agriculture in the US Midwest. We use this relationship to propose a transparent, scientifically robust protocol that can be utilized by developers of agricultural offset projects for generating fungible GHG emission reduction credits for the emerging US carbon cap and trade market. By coupling predicted N2O flux with the recently developed maximum return to N (MRTN) approach for determining economically profitable N input rates for optimized crop yield, we provide the basis for incentivizing N2O reductions without affecting yields. The protocol, if widely adopted, could reduce N2O from fertilized row-crop agriculture by more than 50%. Although other management and environmental factors can influence N2O emissions, fertilizer N rate can be viewed as a single unambiguous proxy—a transparent, tangible, and readily manageable commodity. Our protocol addresses baseline establishment, additionality, permanence, variability, and leakage, and provides for producers and other stakeholders the economic and environmental incentives necessary for adoption of agricultural N2O reduction offset projects.

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.