Investigating Elementary Teachers' Conceptions of Animal Classification

Numerous studies have been conducted regarding alternative conceptions about animal diversity and classification, many of which have used a cross‐age approach to investigate how students' conceptions change over time. None of these studies, however, have investigated teachers' conceptions of animal classification. This study was intended to augment the findings of past research by exploring the conceptions that elementary teachers possess about animal classification. Using interviews and written items, we documented teachers' conceptions about animal classification and compared them with student conceptions identified in previous research studies. Many of the teachers' conceptions observed in this study were similar to students' conceptions in that they were often too limited or too general compared with scientifically accepted conceptions. Also, the teachers in this study frequently used “non‐defining” characteristics, such as locomotion and habitat, to classify animals. As a result, several misclassifications were observed in the teachers' responses to the written items. Notably, the results of our study demonstrate that teachers often have the same alternative conceptions about animal classification as students. We explore some possible explanations for these alternative conceptions and discuss the instructional implications of the findings.     

Strategic planning of transportation services for petroleum products An application of capacitated gravity models

Strategic planning of physical facilities and pricing of services for the distribution of petroleum products require a comprehensive consideration of the alternative means by which the products can be shipped to consumers from refineries, a mechanism for estimating the percentage of volumes that would be shipped via each alternative, and an assessment of the financial impact of changes in physical configurations and tariff structures of the distribution networks. Capacitated gravity models were created by adapting multiplicative competitive interaction (MCI) models for market share to accommodate capacity constraints at individual facilities and the aggregate capacity of groups of facilities served by the same pipeline segment. Procedures for calibrating the models were developed to cope with the problem of having only partial information about competitors' deliveries. Described in this paper are the structure of the models, calibration procedures, and their application to corporate planning in a large independent pipeline company which serves the midcontinental U.S. as a common carrier of refined petroleum products.     

Approximate solution to the diffusion equation and its application to seepage-related problems

Effective dam safety procedures require pore pressure measurements to be interpreted as soon as possible after readings have been taken. Direct interpretations based on partial differential equations are not appropriate. Here, we took a different approach which consisted in applying the impulse response function concept to a dam site. Consequently, two models were designed so that their parameters matched the temporal moments of Green’s function of the associated parabolic problem. These models were compared with closed-form solutions. The first model was the exponential decay model, which gave good results, but did not account for high loading harmonics. The second model, based on the fundamental solution of a parabolic problem, was surprisingly accurate. As an example problem we considered monitoring data obtained from a zoned earth dam. The results show that the main aspects of the processes reflected in most cell recordings can be described in a linear framework, and that they are accounted for by both models.     

A revised theorization of the relationship between teachers’ conceptions of mathematics and its teaching

We assembled the ideas about mathematics and about its teaching which were expressed by mathematicians and mathematics educators into two pairs of ‘official’ (collective) conceptions: mathematics is either static or dynamic, and mathematics teaching is either closed or open. These polar conceptions produce a 4-pair relationship between the conceptions of mathematics and its teaching. The adherence to official conceptions was tapped by a questionnaire encompassing 176 Israeli high school mathematics teachers, aimed at examining the relationship between their conceptions of mathematics and its teaching. The majority of these teachers either hold a single conception in one of the domains or do not adhere to any conception, and a quarter of them hold either the static-closed or dynamic-open pairs of conceptions that prevail among teachers in other countries. Consequently, we define a conception of an entity as a comprehensive and homogenous set of ideas about a particular characteristic or feature of that entity. Reality is that teachers practice their profession without adhering to any official conception, and perhaps are (/to be?/) praised for their reluctance to blindly adopt the clear-cut rigid official conceptions of mathematics and its teaching while maintaining their individual and independent blends of ideas.     

夜盘交易对我国贵金属期货市场的影响研究

对比了我国贵金属期货市场推出夜盘交易制度前后流动性、波动性与联动性的变化,并研究了该交易制度带来的长期与短期不同的影响。首先,采用经过修正的流动性比率衡量市场流动性,并引入虚拟变量纳入回归模型,进一步研究夜盘交易对市场流动性的贡献;接下来,将每日收益率分解为隔夜收益率和日内收益率,通过建立EGARCH模型,分别考察夜盘交易对隔夜波动率和日内波动率长期与短期的影响;最后,通过建立VAR-BEKK-GARCH模型,从均值和方差两个层面研究了国内外贵金属期货市场间的联动性。研究发现:我国推出的夜盘交易制度显著提高了贵金属期货市场的流动性,降低了贵金属期货市场的波动性,尤其是降低了隔夜收益率的波动性,日内收益率的波动性并没有显著减弱;夜盘交易的推出同时增强了国内外期货市场之间的联动性,提升了我国贵金属期货市场对信息的吸收与传递效率。     

Evidence of Rote Learning of Science by Spanish University Students

The purpose of this investigation was to test for alternative conceptions of students enrolled in a second course of sciences at the Teacher Training School in Pamplona, Spain, regarding a geological topic (silicates) which had been studied in previous educational levels. The investigation also proposed to test the efficiency of Novak's concept mapping technique as a method of knowing the cognitive structure of the students. Students' concept maps showed the existence of a large number of alternative conceptions and the persistence and tenacity of these misconceptions after a period of instruction on the topic, even in the case of so-called “good” students.     

Beyond realistic considerations: modeling conceptions and controls in task examples with simple word problems

Using simple word problems, we analyze possible teacher conceptions on the process of problem solving, its goals and the choices that a problem solver can make in problem mathematization. We identify several possible teacher conceptions that would be responsible for the different didactical contracts that teachers create in the mathematics class. Using especially chosen and designed task examples, we demonstrate the diagnosis of teacher own controls in solving problems and in evaluating problem solutions. We also discuss characteristics of task examples that might promote a shift from a problem solving perspective to a modeling perspective that goes beyond merely accepting alternative solutions due to realistic considerations. This shift in perspective would be exhibited through a new understanding of the process of fitting mathematical models in problem situations.     

Crop planning optimization model: the validation and verification processes

Each optimization problem in the area of natural resources claims for a specific validation and verification (V&V) procedures which, for overwhelming majority of the models, have not been developed so far. In this paper we develop V&V procedures for the crop planning optimization models in agriculture when the randomness of harvests is considered and complex crop rotation restrictions must hold. We list the criteria for developing V&V processes in this particular case, discuss the restrictions given by the data availability and suggest the V&V procedures. To show its relevance, they are applied to recently constructed stochastic programming model aiming to serve as a decision support tool for crop plan optimization in South Moravian farm. We find that the model is verified and valid and if applied in practice—it thus offers a plausible alternative to standard decision making routine on farms which often leads to breaking the crop rotation rules.     

Binariness and rational choice

The concept of numerical representability of preferences together with maximality is at the heart of the concept of rationality embodied in classical optimization models. The difficulty of representing social preferences arises from inherent intransitivities thrown up by democratic voting procedures and by non-binary choice rules which need to be adopted to cope with these intransitivities. An alternative (weaker) concept of representability is developed and it is shown that this concept can partially accommodate intransitivity and non-binariness. ‘Weak transitivity’ and ‘weak binaries’ conditions are provided and it is shown that these conditions are necessary and sufficient for ‘weak representability’. While the weak transitivity condition would be violated by social aggregation procedures, the non-binary functions used by social choice theorists do indeed satisfy the condition of ‘weak binariness’.     

Understanding of Earth and Space Science Concepts: Strategies for Concept‐Building in Elementary Teacher Preparation

This research is concerned with preservice teacher understanding of six earth and space science concepts that are often taught in elementary school: the reason for seasons, phases of the moon, why the wind blows, the rock cycle, soil formation, and earthquakes. Specifically, this study examines the effect of readings, hands‐on learning stations, and concept mapping in improving conceptual understanding. Undergraduates in two sections of a science methods course (N= 52) completed an open‐ended survey, giving explanations about the above concepts three times: as a pretest and twice as posttests after various instructional interventions. The answers, scored with a three point rubric, indicated that the preservice teachers initially had many misconceptions (alternative conceptions). A two way ANOVA with repeated measures analysis (pretest/posttest) demonstrated that readings and learning stations are both successful in building preservice teacher's understanding and that benefits from the hands‐on learning stations approached statistical significance. Concept mapping had an additive effect in building understanding, as evident on the second posttest. The findings suggest useful strategies for university science instructors to use in clarifying science concepts while modeling activities teachers can use in their own classrooms.     

UTA-poly and UTA-splines: Additive value functions with polynomial marginals

Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the alternative on the different criteria of the decision problem. The score of an alternative is determined by a marginal value function that evolves monotonically as a function of the performance of the alternative on this criterion. Determining the shape of the marginals is not easy for a decision maker. It is easier for him/her to make statements such as “alternative a is preferred to b”. In order to help the decision maker, UTA disaggregation procedures use linear programming to approximate the marginals by piecewise linear functions based only on such statements. In this paper, we propose to infer polynomials and splines instead of piecewise linear functions for the marginals. In this aim, we use semidefinite programming instead of linear programming. We illustrate this new elicitation method and present some experimental results.     

Teachers' Conceptions of Integrated Mathematics Curricula

In this qualitative research study, we sought to understand teachers' conceptions of integrated mathematics. The participants were teachers in the first year of implementation of a state‐mandated, high school integrated mathematics curriculum. The primary data sources for this study included focus group and individual interviews. Through our analysis, we found that the teachers had varied conceptions of what the term integrated meant in reference to mathematics curricula. These varied conceptions led to the development of the Conceptions of Integrated Mathematics Curricula Framework describing the different conceptions of integrated mathematics held by the teachers. The four conceptions—integration by strands, integration by topics, interdisciplinary integration, and contextual integration—refer to the different ideas teachers connect as well as the time frame over which these connections are emphasized. The results indicate that even when teachers use the same integrated mathematics curriculum, they may have varying conceptions of which ideas they are supposed to connect and how these connections can be emphasized. These varied conceptions of integration among teachers may lead students to experience the same adopted curriculum in very different ways.     

Large-scale geodetic least-squares adjustment by dissection and orthogonal decomposition

Very large-scale matrix problems currently arise in the context of accurately computing the coordinates of points on the surface of the earth. Here geodesists adjust the approximate values of these coordinates by computing least-squares solutions to large sparse systems of equations which result from relating the coordinates to certain observations such as distances or angles between points. The purpose of this paper is to suggest an alternative to the formation and solution of the normal equations for these least-squares adjustment problems. In particular, it is shown how a block-orthogonal decomposition method can be used in conjunction with a nested dissection scheme to produce an algorithm for solving such problems which combines efficient data management with numerical stability. The approach given here parallels somewhat the development of the natural factor formulation, by Argyris et al., for the use of orthogonal decomposition procedures in the finite-element analysis of structures. As an indication of the magnitude that these least-squares adjustment problems can sometimes attain, the forthcoming readjustment of the North American Datum in 1983 by the National Geodetic Survey is discussed. Here it becomes necessary to linearize and solve an overdetermined system of approximately 6,000,000 equations in 400,000 unknowns—a truly large scale matrix problem.     

Regression based reserving models and partial information

We consider a class of distribution-free regression models only defined in terms of moments, which can be used to model separate reported but not settled reserves, and incurred but not reported reserves. These regression models can be estimated using standard least squares and method of moments techniques, similar to those used in the distribution-free chain-ladder model. Further, these regression models are closely related to double chain-ladder type models, and the suggested estimation techniques could serve as alternative estimation procedures for these models. Due to the simple structure of the models it is possible to obtain Mack-type mean squared error of prediction estimators. Moreover, the analysed regression models can be used on different levels of detailed data, and by using the least squares estimation techniques it is possible to show that the precision in the reserve predictor is improved by using more detailed data. These regression models can be seen as a sequence of linear models, and are therefore also easy to bootstrap non-parametrically.     

Zero duality gap in surrogate constraint optimization: A concise review of models

Surrogate constraint relaxation was proposed in the 1960s as an alternative to the Lagrangian relaxation for solving difficult optimization problems. The duality gap in the surrogate relaxation is always as good as the duality gap in the Lagrangian relaxation. Over the years researchers have proposed procedures to reduce the gap in the surrogate constraint. Our aim is to review models that close the surrogate duality gap. Five research streams that provide procedures with zero duality gap are identified and discussed. In each research stream, we will review major results, discuss limitations, and suggest possible future research opportunities. In addition, relationships between models if they exist, are also discussed.     

Convergence and formal manipulation in the theory of series from 1730 to 1815

In the early calculus mathematicians used convergent series to represent geometrical quantities and solve geometrical problems. However, series were also manipulated formally using procedures that were the infinitary extension of finite procedures. By the 1720s results were being published that could not be reduced to the original conceptions of convergence and geometrical representation. This situation led Euler to develop explicitly a more formal approach which generalized the early theory. Formal analysis, which was predominant during the second half of the 18th century despite criticisms of it by some researchers, contributed to the enlargement of mathematics and even led to a new branch of analysis: the calculus of operations. However, formal methods could not give an adequate treatment of trigonometric series and series that were not the expansions of elementary functions. The need to use trigonometric series and introduce nonelementary functions led Fourier and Gauss to reject the formal concept of series and adopt a different, purely quantitative notion of series.     

Nonparametric regression estimation with general parametric error covariance

The asymptotic distribution for the local linear estimator in nonparametric regression models is established under a general parametric error covariance with dependent and heterogeneously distributed regressors. A two-step estimation procedure that incorporates the parametric information in the error covariance matrix is proposed. Sufficient conditions for its asymptotic normality are given and its efficiency relative to the local linear estimator is established. We give examples of how our results are useful in some recently studied regression models. A Monte Carlo study confirms the asymptotic theory predictions and compares our estimator with some recently proposed alternative estimation procedures.     

Short Term Forecasting: Horses for Courses

Within the British Gas Corporation the Headquarters Operational Research Department has assisted various clients with a range of short term forecasting problems. As a result, over the years considerable experience has been gained with the use of alternative forecasting procedures. The authors felt that it would be interesting to compare the usefulness of these alternative approaches, not as usual by their forecasting performance measured in terms of some statistical parameter, but rather in terms of some qualitative factors. Amongst these we identify the objectives of the forecaster, nature of the environment, ease of use and nature of the time series itself. Such factors we believe may well be more important than the forecasting performance as determined by strictly statistical measures. This paper discusses, in these terms, our experience of using alternative forecasting models for appliance sales and gas sendout forecasting problems.