Meanings of fractions as demonstrated by future primary teachers in the initial phase of teacher education

Fractions are a fundamental content of primary-level education and must therefore be included in the training courses for primary school teachers. Experts argue that deep understanding is required to improve primary school teachers’ knowledge of this mathematical concept (Ball, 1990; Cramer, Post & del Mas, 2002; Newton, 2008). Our study focuses on the part-whole relationship as a crucial foundation in working with fractions. This paper characterizes some of the meanings of this relationship for a group of future primary school teachers

Meaning of the part-whole relation and the concept of fraction for primary teachers

The part-whole relation is complex and raises questions that affect different disciplines. Researchers have proposed different interpretations of the notions of fraction and rational number (e.g., Behr, Lesh, Post & Silver, 1983; Kieren, 1976). We highlight three kinds of relations in the study of rational numbers—the part whole-relation, the part-part relation, and the functional relation—through which we organize the different subconstructs of rational number. We claim that the meaning of fractions should be understood through three components: their mathematical structure, their representations and their senses

Efecto de la sequía continua y la inmersión sobre la respuesta de eclosión de los huevos de Ochlerotatus albifasciatus (Diptera: Culicidae) almacenados a baja temperatura

Se estudió el rol de los factores ambientales sobre la eclosión de los huevos de O. albifasciatus (Macquart), simulando condiciones de invierno. La hipótesis planteada fue que la respuesta de eclosión de los huevos depende de: (1) tiempo de permanencia a baja temperatura, (2) condiciones de almacenamiento, y (3) tiempo de aclimatación. Los huevos fueron almacenados a 5º C en condiciones de sequía y sumergidos durante 7, 21, 35, 90 y 146 días; luego fueron aclimatados a 22º C durante 24, 72, y 168 horas y posteriormente inundados para inducir la eclosión. El porcentaje de huevos eclosionados se analizó con un Modelo Lineal Generalizado con distribución binomial. Los resultados mostraron que: (1) largos períodos de almacenamiento en frío y largos tiempos de aclimatación mejoran la respuesta de eclosión, (2) la condición de almacenamiento tiene un efecto moderado en la eclosión, siendo más marcada en los huevos almacenados en seco; (3) tiempos prolongados de aclimatación mejoran aún más las eclosiones de los huevos sumergidos, que los almacenados en seco; (4) largo tiempo en frío mejora la eclosión de los huevos almacenados en seco, que los sumergidos; (5) los huevos que permanecieron más tiempo en frío respondieron mejor cuando el tiempo de aclimatación fue prolongado.The role of environmental factors on the hatching response of O. albifasciatus (Macquart) eggs is studied by simulating winter conditions in the laboratory. The hypothesis tested was that hatching response is affected by: (1) time that eggs remain at low temperature, (2) storage conditions, and (3) acclimatization time. Eggs were stored at 5ºC in drought and immersion conditions during 7, 21, 35, 90 and 146 days, immediately after, they were acclimatized at 22ºC during 24, 72, and 168 hours, and then eggs were flooded to induce hatching. Percent of hatched eggs was analyzed with a Generalized Lineal Model with a binomial distribution. Results show that: (1) a long storage period at cold temperature and long acclimatization periods improve the hatching response; (2) storage conditions have a moderate effect on hatching, being more evident in eggs stored dry; (3) a long time of acclimatization favors the hatching response in submerged eggs more than in eggs stored dry; (4) long time at cold favors the hatching response in eggs stored dry more than in submerged eggs; (5) the hatching response of eggs that remain for a long time at low temperature is higher when the time of acclimatization is long.Fil: Sy, Victoria Elena. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Limnología ; ArgentinaFil: Campos, Raul Ernesto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Limnología ; ArgentinaFil: Castro, Luis Eduardo. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Spent Oyster Mushroom Substrate in a Mix with Organic Soil for Plant Pot Cultivation

Disposal of spent mushroom substrates can pose a problem to the environment. The reuse in crop production by its recycling as an ingredient of growing mixes would provide an environmentally safe disposition. We show the use of Pleurotus Pleurotus sp. spent substrate, sp. spent substrate, obtained after cultivation on a sunfl ower seed hulls based substrate and mixed with organic soil from local nurseries. Salvia offi cinalis Salvia offi cinalis was used to study plant growth in was used to study plant growth in pot cultivation under greenhouse conditions. Treatments were: C, control (soil used in a local nursery); T1, soil : Pleurotus Pleurotus spent substrate (2:1 v/v); and T2, equivalent to T1, but spent substrate (2:1 v/v); and T2, equivalent to T1, but using washed Pleurotus Pleurotus spent substrate in order to reduce its salt content. T1 substrate spent substrate in order to reduce its salt content. T1 substrate had 3.3 times higher electrical conductivity (7 mS cm-1) than that of the control, which is high for the growth of most plants. Air porosity was greater in T1 (7.4%) and T2 (10.2%) than the control (2.8%). The content of certain nutrients also increased with regard to the control, such as phosphorus and sulphur (T1 and T2 substrates), as well as potassium (T1 substrate). After growing 29 days on T1 substrate, plants showed a marked increase in biomass (ca. 21%, p < 0.05) and some minerals compared to the control. T2 plants grew poorly, possibly because of nitrogen defi cit. T1 substrate was adequate to sustain the growth of S. offi cinalis S. offi cinalis plants in pots, by improving air porosity and mineral content.Fil: López Castro, Ramón Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; ArgentinaFil: Delmastro, Silvia Elena. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; ArgentinaFil: Curvetto, Nestor Raul. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; Argentina. Universidad Nacional del Sur. Departamento de Agronomía; Argentin

Tekniset apuvälineet ikääntyneiden kotona selviytymisen tukena

Opinnäytetyön tarkoituksena oli selvittää, minkälaisia teknisiä apuvälineitä käytetään ikääntyneiden kotona asumisen tukena. Tavoitteena oli antaa lisää tietoa ikääntyneille sekä omaisille teknisistä apuvälineistä. Aineistona oli 5 kotimaista tutkimusta. Suomen väestö ikääntyy. Väestöpoliittisen ennusteen mukaan vuonna 2035 noin 25 prosenttia Suomen väestöstä on 65 vuotta täyttäneitä. Monet ikääntyneet haluavat asua kotona mahdollisimman pitkään. Harvat ikääntyneet selviytyvät kotona itsenäisesti, vaan he tarvitsevat tuekseen teknisiä apuvälineitä. Aineiston analysoin laadullisella sisällönanalyysilla teorialähtöisesti eli deduktiivisesti. Opinnäytetyössä oli kolme opinnäytetyön kysymystä, joihin pyrin löytämään vastaukset. Aineistona tässä työssä on käytetty viittä kotimaista tutkimusta vuosilta 1998-2008. Opinnäytetyön tulosten mukaan ilmeni, että tekniset apuvälineet voidaan jakaa kolmeen ryhmään, turvallisuutta lisääviin, sosiaalista vuorovaikutusta lisääviin sekä fyysistä toimintatukea tukeviin. Turvallisuutta lisääviä teknisiä apuvälineitä oli selkeästi eniten, kun taas fyysistä toimintatukea tukevia oli selkeästi vähiten. Opinnäytetyön tulosten tarkastelussa olen pohtinut mm. teknisten apuvälineiden käytettävyyttä, ikääntyneiden suhtautumista teknisiin apuvälineisiin sekä miten ikääntymisen tuomat rajoitteet vaikuttavat teknisten apuvälineiden käyttöön. Opinnäytetyön pohjalta löysin jatkotutkimushaasteita. Mielestäni olisi hyödyllistä haastatella omaisia ja kysyä heidän mielipiteitä ja käyttäjäkokemuksia, kokevatko he, että heidän omaisensa ovat turvassa teknisten apuvälineiden turvin, sillä sukulaiset saattavat asua eri kaupungeissa tai jopa eri puolella Suomea. Lisäksi olisi hyödyllistä tutkia ikääntyneiden mielipiteitä siitä, millaisia teknisten apuvälineiden pitäisi olla, ettei niitä koettaisi pelottaviksi ja vieraiksi esineiksi. Sekä olisi mielenkiintoista tietää miten ikääntynyt kokee ohjauksen ja perehdytyksen merkityksen.Technical auxiliaries for the old to support the living conditions at home The aim of the thesis was to find out, what kind of equipment are used to support the living conditions of the old at home. The purpose was also to gain more information to the old as well as to their relatives of the technical auxiliary tools. The study based on earlier data base research material that consists of five Finnish studies. The population in Finland is ageing. According to the social politic estimation in 2035 approximately 25 % of the population is over the age of 65 years. Many of the old like to live at home as long as possible. Few of the old manage at home independently without technical supportive equipment. The database was analysed according to the qualitative theoretical angle. The thesis includes three basic questions that are to be answered. Five domestic studies dating back to 1998-2008 have been used as the basis of the study. The results of the thesis indicate that technical auxiliaries may be divided into three groups accordingly: improved safety, social contacts and physical additional capability. The first of these was most emphasized whereas the last one was observed to come as least. Further analysis of the thesis I have clarified the usability of the technical equipment, the acting of the old to these equipment as well as the way, how the limitative effects due to ageing affect the use of these equipment. On the basis of the research I found some challenges for the additional study. I find it useful to interview the relatives and ask their opinions and experiences, whether they feel that their relatives are safe with the technical equipment. Their relatives may live in remote cities or even far away counties. In addition to this it may be useful to study the opinions of the old for what the auxiliaries should be like in order them not to be found frightening or strange obstacles. It would also be interesting to know how the old feel about the guidance orientation

Transverse Diagnostics For High Energy Hadron Colliders

The Large Hadron Collider (LHC) is a circular synchrotron accelerator that will explore new Physics at the higher energies ever achieved, aiming to find the Higgs boson. The LHC is being built at CERN and by 2007 it will be ready to produce head-on collisions of protons at a centre-of-mass energy of 14 TeV. The employment of superconducting magnets for achieving high energies, the high luminosity required for physics, the limited dynamic aperture and the large energy stored in the beams will make the machine very challenging to operate, especially during the injection process and the energy ramp. Two particular problems will be a high sensitivity to beam losses and a relatively poor field quality requiring the use of many types of magnetic correction elements. This may lead to the inclusion of certain beam measurements in feedback loops, making special demands on the control system. The injection and acceleration of the LHC proton beams without particle losses and emittance blow up will require an accurate control of the beam parameters. The value of the betatron tune is about 63 units and needs to be controlled to a level of $\Delta Q = ±0.003$. Orbit excursions should be limited to less than 0.5 mm. The linear chromaticity should be limited to some units (nominal value $Q'_HV = 2$). This Thesis will be focused on the improvement of new instrumentation for the measurement of beam parameters that is compatible with LHC high intens ity running. In this sense, the importance for the performance of the accelerator of terms such as tune or chromaticity will be pointed out. This work can be considered to be divided into two differentiated parts: the tests performed to a potentially beam diagnostics device and the improvement of the sensitivity of an already existing monitor. However, behind both subjects there is a common objective: the need of implementing new sensitive and non destructive methods for measuring parameters of major importance to keep the beam within the tight tolerances imposed to the superconducting and high energy accelerator LHC

Interpretación de diagramas de comparación multiplicativa por estudiantes de secundaria

Este trabajo se centra en procesos de traducción de problemas gráficos de comparación multiplicativa a representación verbal y simbólica. Pedimos a 89 estudiantes del primer curso de educación secundaria que inventaran un problema que se ajustara a un diagrama y que escribieran una ecuación que integrara las relaciones del diagrama. Los dos procesos de traducción se han mostrado difíciles para los estudiantes, provocando diversidad de respuestas. El análisis conjunto de las respuestas reveló que la competencia de los estudiantes en el proceso de invención no es independiente de la traducción algebraica