Characteristics of Mathematical Problems Posed by Teachers

Background: In science, posing problems is considered as important as solving them, however, school has explored little this type of activity. Objective: To examine the features of mathematical problems posed by elementary school teachers, analysing aspects related to the statement of the problems and the types of problems formulated. Design: Descriptive, qualitative research. Setting and participants: Eighty-seven teachers (45 teaching 1st and 2nd grades, and 42 teaching 3rd, 4th, and 5th grades of elementary school) attending a teacher education course promoted by the Municipal Secretary of Education of Curitiba. Data collection and analysis: The teachers were asked to formulate four problems involving addition, subtraction, multiplication, and division. The types of the quantities involved, the necessary information, the number of steps required for solving the problems, and the types of problems from the theory of conceptual fields were analysed. Results: The problems presented a clear language, sufficient information, required a single operation for their solution, involved discrete quantities, and presented few challenges. The problems of addition and subtraction involved situations of composition and transformation, those of multiplication were of simple proportion, and those of division were of partitive problems. Conclusions: The results suggest that the teachers have a limited conception about the formulation of problems, emphasising the need to promote teacher training courses that develop a greater understanding of the properties of the mathematical concept involved in the problems to be formulated and about resolution procedures to be adopted

ANÁLISIS DE LA ESTRUCTURA DE SITUACIONES PROBLEMÁTICAS ELABORADAS POR DOCENTES EN UN PROCESO FORMATIVO

El objetivo principal de este artículo es analizar la estructura de las situaciones problemáticas que dan sentido a los conceptos de proporción simple, clase uno para muchos, desarrollada por docentes desde el comienzo de la escuela primaria, durante un proceso formativo. Para alcanzar este objetivo, nos apoyamos en la Teoría de Campos Conceptuales y la Formulación de Problemas. En este estudio participaron cuatro docentes que trabajaron en el segundo ciclo de escuela primaria y participaron de un proceso formativo en el ámbito del Programa Observatorio de la Educación. Los instrumentos utilizados para la recolección de datos fueron: elaboración inicial y final de situaciones problemáticas y audios de las reuniones formativas. Para el análisis se utilizaron categorías y subcategorías que surgieron de los marcos teóricos y los datos. Los resultados indican que, al inicio del proceso formativo, más de la mitad de las situaciones presentaban falta de información y el resto, aunque suficientes, contenían errores de puntuación, ortografía y regencia verbal. Al final del proceso formativo, se observó una reducción de situaciones con ausencia de información, especialmente en aquellas que no especificaron la división, lo que puede estar relacionado con las discusiones brindadas en la capacitación sobre la necesidad de observar la estructura del enunciado de una situación. problema, buscando presentar información clara que facilite la comprensión durante la resolución.Palabras clave: Proporción simple. Elaboración de situaciones problemáticas. Educación primaria. Formación de profesores.ANALYSIS OF THE STRUCTURE OF PROBLEM SITUATIONS ELABORATED BY TEACHERS IN A FORMATIVE PROCESSAbstractThis article has as main objective to analyze the structure of the problem situations that give meaning to the concepts of simple proportion, class one for many, elaborated by teachers of the early years of elementary school, during a formative process. To reach this goal, we contribute in Conceptual Field Theory and Problem Formulation. Four teachers who worked in the second cycle of basic education took part in this study and participated in a training process within the scope of the Education Observatory Program. The instruments used for data collection were: initial and final elaboration of problem situations and audios of the formative meetings. For the analysis, categories and subcategories that emerged from the theoretical frameworks and data were used. The results indicate that, at the beginning of the training process, more than half of the situations presented lack of information and the rest, although sufficient, contained errors in punctuation, spelling and verbal regency. At the end of the training process, there was a reduction in situations with an absence of information, especially in those that did not specify the division, which may be related to the discussions provided in the training on the need to observe the structure of the statement of a problem situation, seeking to present clear information that facilitates understanding during resolution.Key words: Simple proportion. Elaboration of problem situations. Elementary School. Teacher training.ANÁLISE DA ESTRUTURA DE SITUAÇÕES-PROBLEMA ELABORADAS POR PROFESSORES EM UM PROCESSO FORMATIVOResumoEste artigo tem como objetivo principal analisar a estrutura das situações-problema que dão sentido aos conceitos de proporção simples, classe um para muitos, elaboradas por professores dos anos inicias do ensino fundamental, durante um processo formativo. Para alcançar esse objetivo, aportamo-nos na Teoria dos Campos Conceituais e na Formulação de Problemas. Fizeram parte deste estudo quatro professores que atuavam no segundo ciclo do ensino fundamental e participaram de um processo formativo no âmbito do Programa Observatório da Educação. Os instrumentos utilizados para a coleta de dados foram: inicial e final de elaboração de situações-problema e áudios dos encontros formativos. Para a análise, foram utilizadas categorias e subcategorias que emergiram dos referenciais teóricos e dos dados. Os resultados indicam que, no início do processo formativo, mais da metade das situações apresentavam ausência de informações e, as demais, embora sendo suficientes, continham erros de pontuação, ortografia e regência verbal. No fim do processo formativo, houve uma redução das situações com ausência de informações, em especial, naquelas que não especificavam a divisão, o que pode ter relação com as discussões oportunizadas na formação sobre a necessidade se observar a estrutura do enunciado de uma situação-problema, buscando apresentar informações claras que facilitem a compreensão durante a resolução.Palavras-chave: Proporção simples. Elaboração de situações-problema. Ensino fundamental. Formação de professores.

EFFECT OF CASUALIZATION ON WORKERS PERFORMANCE IN ORGANIZATIONS

Casualization of labour in the world and indeed Nigeria is against the tenets of labour and this has caused continuous conflict between workers, labour unions, and employers across organizations in Nigeria and the world over. It is even more appalling to note that casual workers are barred from unionizing (trade union), denying them access to certain benefits in the organization. This is the essence to which the paper undertakes to examine the “impact of casualization on workers’ performance”. The objective of this study is to examine if casualization of work affects the productivity and output of casual workers. Descriptive survey research design was adopted in this study, the population of the study was from Coca-cola Bottling company (food and beverages), and Lolitta Manufacturing company makers of X-pression Hair product (Cosmestics industry) selected using simple proportion and random sampling techniques. The sample size was 152 respondents. Data was collected using structured questionnaire. Correlation and Regression tools were used to analyze the data. Results shows that casualization policy (absence of leave and leave allowance, absence of injury compensations and other social benefits) affects performance and effectiveness of casual workers. The study recommends stringent measures to ensure compliance with the provisions of the Casualization Prohibition Bill, 2010 leading to equal rights to all workers. This study further suggest a maximum period of six (6) month probation upon which all casual workers are converted to permanent staffs across organizations in Nigeria. The study also suggest that defaulting organizations are made to face the penalty irrespective of the status of the organization or owners. This way, organizations in Nigeria will attain acceptable human resources practices status as stated by ILO.

Estimates of Minimum Population Size for Walrus near Southeast Baffin Island, Nunavut

To support management objectives in Canada and Greenland, joint research between the Department of Fisheries and Oceans and Greenland Institute of Natural Resources was begun in 2005. Direct counts were used to determine the Minimum Counted Population (MCP) in summer around SE Baffin Island. Aerial surveys examined the coast from roughly the Saddleback Island in northern Hudson Strait to Isabella Bay on eastern Baffin Island but concentrated on the area between Loks Land and Cape Dyer. The maximum count was obtained on 3–4 September 2007 during boat surveys. The MCP ranged from 716 (in 2006) to 1,056 (2007). Using the largest MCP adjusted with published maximum estimates of the proportion of walrus hauled out concurrently, we estimated 1,420 (95% CI: 1,219–1,622) walrus were present. In addition, four walrus had been fitted with satellite relayed data logger tags prior to the maximum counts in 2007. Using the simple proportion of ‘tags dry’ on 3 September to adjust counts on 3 and 4 September 2007 provided an estimate of 2,102 (CI = MCP-4,482). Using the proportion of time dry immediately preceding the survey to adjust the maximum count produced an estimate of 2,502 (CI = 1,660–3,345) walrus were present in Hoare Bay. We conclude approximately 2,100–2,500 walrus were present in Hoare Bay in late summer 2007. This number is a negatively biased estimator of the population of walrus around SE Baffin Island and in the Hudson Bay–Davis Strait stock as a whole. Broader survey coverage in a short period and more detailed information on the movement of walrus between Greenland and Canada and the summer dispersal of these animals within Canada are required to improve population estimates.

Sequential and Temporal Properties of Behavior Induced By a Schedule of Periodic Food Delivery

I. Five hungry rats were exposed to a schedule of periodic food presentation, receiving a single pellet every 30 sec., in an apparatus that permitted drinking, running, and other activities. The development, extinction, and structure of behavior sequences under this regimen was studied in three experiments. 2. All the rats developed a stable pattern of behavior after twenty or so half-hour sessions. The modal pattern was drinking early in the interfood interval, running in the middle, and food anticipation at the end. This temporal pattern was associated with different sequential patterns in different individuals. 3. Elimination of opportunity to engage in one or more activities resulted in an increase in other activities, but the increase was not in simple proportion to their frequency under baseline conditions. 4. In the steady state the sequence of behaviors in each interval appeared to be determined by two main factors: (a) post-eating time, and (b) the "momentum" associated with an ongoing activity. Differences among individual rats appeared to be due largely to differences in the second factor.

Variation of Florisil Activity: Simple Method for Measuring Adsorbent Capacity and Its Use in Standardizing Florisil Columns

Sodium sulfate content was found to be the principal cause of variation of adsorbancy between batches of Florisil. A rapid method was developed for determining the adsorptive capacity of Florisil based on the absorption of lauric acid from hexane solution. An excess of lauric acid is used and the amount not adsorbed is measured by alkali titration. Lauric acid adsorbed (mg/g Florisil) is used to calculate, by simple proportion, equivalent quantities of Florisil from batches having different adsorptive capacities.

Sodium Regulation in the Crayfish Astacus Fluviatilis

1. In external sodium concentrations of up to 100 mM./l. the blood sodium concentration of Astacus is only slightly increased. As the external level approaches or exceeds the normal blood sodium concentration of 200 mM./l. so the increase becomes more marked. Similarly, there is an increase in urine sodium concentration. This net gain of sodium is accompanied by a considerable rise in sodium outflux as shown by 22Na. At external concentrations exceeding 300 mM./l., blood and urine concentrations rise to a similar level and active sodium movements appear to cease. 2. With increased blood sodium concentration the level in the muscles rises also. This relationship is not one of simple proportion and at high concentrations there is relatively more sodium in the muscles. 3. In artificial tap water animals with a high blood concentration lose sodium until the normal level is regained. This net loss is due to influx being much lower and outflux much higher than normal. Of the outflux, up to 70% is initially due to renal losses and losses over the body surface are higher than normal due to the excess sodium in the blood. 4. From the results given in this and previous papers the way in which sodium balance may be achieved under normal conditions is discussed.

The Relation between Scale Diameter and Body Length of Kamloops Trout, Salmo gairdneri kamloops

The scale/body relationship for Kamloops trout is very close to direct proportion for fish larger than 4.5 cm. fork length. The resultant plot on a double logarithmic grid is linear with a slope not significantly different from 1.00 (45°). Calculations of lengths of trout from scales at ages previous to that of capture can be made on the basis of simple proportion in two ways, (1) by use of a constant slope (45°) on a double logarithmic plot, or (2) by use of a constant zero-zero intercept on an arithmetic plot.Growth of the scales of the young is characterized by relatively rapid increase from time of scale formation, 3.5 cm. fork length up to 4.5 cm. At about 4.5 cm. fork length there is a sharp break (inflection) in the relative growth curve toward isometric growth of scales and body. Reliable estimates of the length of trout may be obtained from scales alone, using the diameter of the first circulus of the scale, the slopes and inflection of the relative scale/body plot and total diameter of the scale at time of capture.Marked Kamloops trout of known size were released in 1953. Subsequent recaptures both in 1953 and 1954 substantiated the accuracy of the method of estimating lengths of trout at ages previous to that of capture.Observations on the steelhead trout, Salmo gairdneri gairdneri, and on the coastal cutthroat trout, Salmo clarki clarki, suggest that an isometric scale/body relationship may exist among those species also.

THEORY AND MEASUREMENT OF VISUAL MECHANISMS

Measurements of ΔI as a function of retinal area illuminated have been obtained at various levels of standard intensity I1, using "white" light and light of three modal wave-lengths (λ465, 525, 680), for monocular stimulation and for simultaneous excitation of the two eyes ("binocular"), using several methods of varying (rectangular) area and retinal location, with control of exposure time. For data homogeneous with respect to method of presentation, log ΔIm = -Z log A + C, where ΔI = Ĩ2 – I1, A is area illuminated, and C is a terminal constant (= log ΔIm for A = 1 unit) depending on the units in which ΔI and A are expressed, and upon I1. The equation is readily deduced on dimensional grounds, without reference to specific theories of the nature of ΔI or of retinal area in terms of its excitable units. Z is independent of the units of I and A. Experimentally it is found to be the same for monocular and binocular excitations, as is to be expected. Also as is expected it is not independent of λ, and it is markedly influenced by the scheme according to which A is varied; it depends directly upon the rate at which potentially excitable elements are added when A is made to increase. For simultaneous excitation of the two eyes (when of very nearly equivalent excitability), ΔĪB is less than for stimulation of either eye alone, at all levels of I1, A, λ. The mean ratio (ΔĪL + ΔĪR)/2 to ΔIB was 1.38. For white light, doubling A on one retina reduces ΔIm in the ratio 1.21, or a little less than for binocular presentation under the same conditions. These facts are consistent with the view that the properties of ΔI are quantitatively determined by events central to the retina. The measure σ1ΔI of organic variation in discrimination of intensities and ΔIm are found to be in simple proportion, independent of I1, A, λ (and exposure time). Variability (σ1ΔI) is not a function of the mode of presentation, save that it may be slightly higher when both retinas are excited, and its magnitude (for a given level of ΔIm) is independent of the law according to which the adjustable intensity I2 is instrumentally controlled.

On the coefficient of viscous traction and its relation to that of viscosity

When experiments are made on the viscous flow of pitch and other substances of similar character, in the form of rods or cylinders, by the torsional method, it is found that the rate of turning under torsion of these rods is not strictly proportional to the driving couple. Thus the rate of flow of the material under shearing stress cannot be in simple proportion to stress. If it is wished to investigate the exact law connecting the rate of flow with the shearing forces, by means of the torsional method, a complication is at once met with, arising from the fact that the rate of flow in a twisting rod is not of the same value everywhere, but necessarily varies from nothing at the centre to a maximum at the surface of the rod. With the view of developing a more suitable way of investigating the phenomenon, trials were made with different methods of observing the flow of such bodies, under conditions in which the said objection does not apply. The results obtained in these ways exhibit the same departures from linearity as was suggested by the results obtained by the method of torsion.