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).

Bioactive mesopore-glass microspheres with controllable protein-delivery properties by biomimetic surface modification

Microsphere systems with the ideal properties for bone regeneration need to be bioactive, and at the same time possess the capacity for controlled protein/drug-delivery; however, the current crop of microsphere system fails to fulfill these properties. The aim of this study was to develop a novel protein-delivery system of bioactive mesoporous glass (MBG) microspheres by a biomimetic method through controlling the density of apatite on the surface of microspheres, for potential bone tissue regeneration. MBG microspheres were prepared by using the method of alginate cross-linking with Ca2+ ions. The cellular bioactivity of MBG microspheres was evaluated by investigating the proliferation and attachment of bone marrow stromal cell (BMSC). The loading efficiency and release kinetics of bovine serum albumin (BSA) on MBG microspheres were investigated after coprecipitating with biomimetic apatite in simulated body fluids (SBF). The results showed that MBG microspheres supported BMSC attachment and the Si containing ionic products from MBG microspheres stimulated BMSCs proliferation. The density of apatite on MBG microspheres increased with the length of soaking time in SBF. BSA-loading efficiency of MBG was significantly enhanced by co-precipitating with apatite. Furthermore, the loading efficiency and release kinetics of BSA could be controlled by controlling the density of apatite formed on MBG microspheres. Our results suggest that MBG microspheres are a promising protein-delivery system as a filling material for bone defect healing and regeneration.

Bioactive inorganic materials/alginate composite microspheres with controllable drug-delivery ability

Alginate microspheres are considered a promising material as a drug carrier in bone repair due to excellent biocompatibility, but their main disadvantage is low drug entrapment efficiency and non-controllable release. The aim of this study was to investigate the effect of incorporating mesoporous bioglass (MBG), non-mesoporous bioglass (BG) or hydroxyapatite (HAp) into alginate microspheres on their drug-loading and release properties. X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and atomic emission spectroscopy (AES) were used to analyse the composition, structure and dissolution of bioactive inorganic materials and their microspheres. Dexamethasone (DEX)-loading and release ability of four microspheres were tested in phosphate buffered saline with varying pHs. Results showed that the drug-loading capacity was enhanced with the incorporation of bioactive inorganic materials into alginate microspheres. The MBG/Alginate microspheres had the highest drug loading ability. DEX release from alginate microspheres correlated to the dissolution of MBG, BG and HAp in PBS, and that the pH was an efficient factor in controlling the DEX release; a high pH resulted in greater DEX release, whereas a low pH delayed DEX release. In addition, MBG/alginate, BG/alginate and HAp/alginate microspheres had varying apatite-formation and dissolution abilities, which indicate that the composites would behave differently with respect to bioactivity. The study suggests that microspheres made of a composite of bioactive inorganic materials and alginate have a bioactivity and degradation profile which greatly improves their drug delivery capacity, thus enhancing their potential applications as bioactive filler materials for bone tissue regeneration.

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.

The effect of rhBMP-2 on canine osteoblasts seeded onto 3D bioactive polycaprolactone scaffolds

Our strategy entails investigating the influence of varied concentrations (0, 10, 100 and 1000 ng/ml) of human recombinant bone morphogenetic protein-2 (rhBMP-2) on the osteogenic expression of canine osteoblasts, seeded onto poly-caprolactone 20% tricalcium phosphate (PCL-TCP) scaffolds in vitro. Biochemical assay revealed that groups with rhBMP-2 displayed an initial burst in cell growth that was not dose-dependent. However, after 13 days, cell growth declined to a value similar to control. Significantly less cell growth was observed for construct with 1000 ng/ml of rhBMP-2 from 20 days onwards. Confocal microscopy confirmed viability of osteoblasts and at day 20, groups seeded with rhBMP-2 displayed heightened cell death as compared to control. Phase contrast and scanning electron microscopy revealed that osteoblasts heavily colonized surfaces, rods and pores of the PCL-TCP scaffolds. This was consistent for all groups. Finally, Von Kossa and osteocalcin assays demonstrated that cells from all groups maintained their osteogenic phenotype throughout the experiment. Calcification was observed as early as four days after stimulation for groups seeded with rhBMP-2. In conclusion, rhBMP-2 seems to enhance the differentiated function of canine osteoblasts in a non-dose dependent manner. This resulted in accelerated mineralization, followed by death of osteoblasts as they underwent terminal differentiation. Notably, PCL-TCP scaffolds seeded only with canine osteoblasts could sustain excellent osteogenic expression in vitro. Hence, the synergy of PCL with bioactive TCP and rhBMP-2 in a novel composite scaffold, could offer an exciting approach for bone regeneration.

Bioactive SrO–SiO2 glass with well-ordered mesopores : characterization, physiochemistry and biological properties

For a biomaterial to be considered suitable for bone repair it should ideally be both bioactive and have a capacity for controllable drug delivery; as such, mesoporous SiO2 glass has been proposed as a new class of bone regeneration material by virtue of its high drug-loading ability and generally good biocompatibility. It does, however, have less than optimum bioactivity and controllable drug delivery properties. In this study, we incorporated strontium (Sr) into mesoporous SiO2 in an effort to develop a bioactive mesoporous SrO–SiO2 (Sr–Si) glass with the capacity to deliver Sr2+ ions, as well as a drug, at a controlled rate, thereby producing a material better suited for bone repair. The effects of Sr2+ on the structure, physiochemistry, drug delivery and biological properties of mesoporous Sr–Si glass were investigated. The prepared mesoporous Sr–Si glass was found to have an excellent release profile of bioactive Sr2+ ions and dexamethasone, and the incorporation of Sr2+ improved structural properties, such as mesopore size, pore volume and specific surface area, as well as rate of dissolution and protein adsorption. The mesoporous Sr–Si glass had no cytotoxic effects and its release of Sr2+ and SiO44− ions enhanced alkaline phosphatase activity – a marker of osteogenic cell differentiation – in human bone mesenchymal stem cells. Mesoporous Sr–Si glasses can be prepared to porous scaffolds which show a more sustained drug release. This study suggests that incorporating Sr2+ into mesoporous SiO2 glass produces a material with a more optimal drug delivery profile coupled with improved bioactivity, making it an excellent material for bone repair applications. Keywords: Mesoporous Sr–Si glass; Drug delivery; Bioactivity; Bone repair; Scaffolds