416 research outputs found

    Conceptual Models for Integer Addition and Subtraction

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    In this article, we report the findings of a study conducted with 6 Grade 8 students in the United States. The students posed stories for open number sentences involving addition and subtraction of integers. We analysed the stories posed by the students to build models that describe the conceptual structures behind these posed stories – the conceptual models for integer addition and subtraction. These four conceptual models for thinking about and using integer addition and subtraction include Bookkeeping, Counterbalance, Relativity, and Translation, and are generated from the students’ posed stories. We also provide profiles of conceptual model use for two of the 6 students that describe how the students posed stories to accommodate conceptual model use, such as posing unconventional or unrealistic stories or changing the structure of the number sentences. The conceptual models and descriptions of how the students used them provide perspective into student thinking about integers and contexts, highlighting the mathematics of the students, and calling for a re-examination of contexts used in school mathematics

    Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem

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    Previous research has documented that preservice teachers (PSTs) struggle with under- standing fraction concepts and operations, and misconceptions often stem from their understanding of the referent whole. This study expands research on PSTs’ understanding of wholes by investigating pictorial strategies that 85 PSTs constructed for a multistep fraction task in a multiplicative context. The results show that many PSTs were able to construct valid pictorial strategies, and the strategies were widely diverse with respect to how they made sense of an unknown referent whole of a fraction in multiple steps, how they represented the wholes in their drawings, in which order they did multiple steps, and which type of model they used (area or set). Based on their wide range of pictorial strategies, we discuss potential benefits of PSTs’ construction of their own representations for a word problem in developing problem solving skills

    What Does It Take to Be a Fox? New Horizons for Communities of Practice

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    In this theoretical research report we reflect on the challenges of becoming more fox-like in mathematics education work. Using a communities of practice motivating theoretical lens, we compare and discuss the differences in defining, creating, and accessing knowledge between virtual and scholarly communities of practice in mathematics education. We present four claims that virtual communities of practice in mathematics education are inherently foxy work. As part of our claims, we discuss how scholarly communities of practices are inherently hedgehog work. We conclude with a list of recommendations of those within the scholarly communities of practice in mathematics education. These recommendations include looking toward the successful fox-like attributes of the virtual communities in mathematics education

    Growth factors for clinical-scale expansion of human articular chondrocytes : Relevance for automated bioreactor systems

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    The expansion of chondrocytes in automated bioreactors for clinical use requires that a relevant number of cells be generated, starting from variable initial seeding densities in one passage and using autologous serum. We investigated whether the growth factor combination transforming growth factor beta 1/fibroblast growth factor 2/platelet-derived growth factor BB (TFP), recently shown to enhance the proliferation capacity of human articular chondrocytes (HACs), allows the efficiency of chondrocyte use to be increased at different seeding densities and percentages of human serum (HS). HACs were seeded at 1,000, 5,000, and 10,000 celIS/cm(2) in medium containing 10 bovine serum or 10,000 cells/cm(2) with 1 chondrogenic capacity of post-expanded HACs was then assessed in pellet cultures. Expansion with TFP allowed a sufficient number of HACs to be obtained in one passage even at the lowest seeding density and HS percentage and variability in cartilage-forming capacity of HACs expanded under the different conditions to be reduced. Instead, larger variations and insufficient yields were found in the absence of TFP. By allowing large numbers of cells to be obtained, starting from a wide range of initial seeding densities and HS percentages, the use of TFP may represent a viable solution for the efficient expansion of HACs and addresses constraints of automated clinical bioreactor systems

    Componentes menores y estabilidad a la oxidación mediante DSC de aceite de colza fraccionado y estructurado mediante catálisis con lipasa

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    Natural fats and oils can be modified by various methods to prepare products with desired physical, chemical and nutritional properties. The enrichment and retention of the minor lipid components, the incorporation of capric acid and oxidative stability in low temperature fractionated rapeseed oil (RSO) in acetone were assessed in this study. The fractionated liquid part (L-RSO), the solid part (S-RSO) and the RSO were transesterified with capric acid (CA) at different mole ratios using lipase. The yields of L-RSO and S-RSO were 30 and 70 g per 100 g, respectively. The L-RSO contained higher levels of linoleic acid and linolenic acid, and a lower level of oleic acid compared to the S-RSO. The S-RSO contained a higher amount of total sterols than the RSO and the L-RSO. In contrast, the L-RSO contained a higher amount of total tocopherols than the RSO and the S-RSO. The incorporation of CA was ideal at a mole ratio of 1:3. The content of sterols and tocopherols gradually decreased with an increased mole ratio for the CA incorporation. The oxidative stability shown as onset temperature, determined by DSC, of the S-RSO was higher compared to those of the L-RSO and RSO.Las grasas y aceites naturales pueden ser modificados mediante diversos métodos para preparar productos con propiedades físicas, químicas y nutricionales deseadas. El enriquecimiento y la retención de componentes lipídicos menores, la incorporación de ácido cáprico y estabilidad a la oxidación a baja temperatura de aceites de colza (RSO) fraccionado en acetona, se evaluaron en este estudio. La fracción líquida (L-RSO), la fracción sólida (S-RSO) y el RSO son transesterificados con ácido cáprico (CA) en diversas relaciones molares utilizando lipasa. Los rendimientos de las fracciones L-RSO y RSO-S fueron de 30 y 70 g por 100 g, respectivamente. La fracción líquida L-RSO contenía un mayor nivel de los ácidos linoleico y linolénico, y un menor nivel de ácido oleico en comparación con la fracción sólida S-RSO. La fracción sólida S-RSO tiene mayor contenido total de esteroles que RSO y que L-RSO. En contraste, la fracción L-RSO contenía mayor contenido de tocoferoles totales que RSO y que S-RSO. La incorporación de CA fue excelente con una relación molar de 1:3. El contenido de esteroles y tocoferoles disminuyó gradualmente con un incremento de la relación molar de la incorporación de CA. La estabilidad oxidativa muestra cómo la temperatura de inicio, determinada mediante DSC, de la fracción S-RSO fue mayor en comparación con la de la L-RSO y RSO
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