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Utah County, Utah, and more particularly the Utah Valley area, has undergone an enormous change during the last forty years. Rapid growth and urbanization brings with it the problems of urban sprawl. Controlling this sprawl is determined often times by an effective growth policy. Mapping and analyzing growth patterns and trends is a useful method in determining the effectiveness of the "growth towards the cities" policy of Utah County. Research was conducted by using maps, air photos, and field work in locating the growth history of the county.Growth has been influenced by several factors among which are the physical, climatic, and economic make up of the county. It has also been influenced by policies directed to control the growth, not necessarily as to numbers but as to location. These policies have been successful in locating the majority of the increasing urbanization within the cities where services can be provided more economically. Since the county and the cities can grow only where water is available, the major factor in the location of future growth will be the location of water.

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Acompanha: Material manipulável e manipulável virtual para o ensino de estimativa de proporção populacional na formação inicial de professores / O presente trabalho teve como objetivo principal avaliar como os acadêmicos do 3º ano de um curso de Licenciatura em Matemática veem a utilização de material manipulável e manipulável virtual para o Ensino de Estimativa de Proporção Populacional. Na intenção de alcançar tal objetivo, foi desenvolvida uma pesquisa aplicada de natureza qualitativa organizada em quatro etapas: 1-Levantamento do referencial teórico, na perspectiva de verificar situações do Ensino de conteúdos da Estatística na Educação Básica; 2-Busca por materiais para o Ensino de Estimativa de Proporção Populacional, na qual se encontrou o material manipulável elaborado pela professora Lisbeth Kaiserlian Cordani e pela falta de recursos tecnológicos existentes, a pesquisadora desenvolveu um manipulável virtual, em parceria com um acadêmico do curso de Ciência da Computação da Universidade Estadual do Norte do Paraná; 3 -Intervenção ou aplicação da pesquisa, em se referindo ao momento da aplicação dos materiais ditos na etapa 2, em uma turma do 3º ano de um curso de Licenciatura em Matemática em que foi realizada a coleta dos dados; 4 -Análise dos dados coletados, em que se utilizou a Análise Textual Discursiva embasada em Moraes e Galiazzi (2016). Após a análise dos dados, pôde-se observar que os acadêmicos aprovam a utilização de material manipulável e manipulável virtual para o Ensino de Estimativa de Proporção Populacional, constatado que: os materiais são vistos como estímulos para a Aprendizagem, é considerado uma inovação para o Ensino, proporcionam uma ligação entre o conhecimento teórico e o prático e somam positivamente na formação dos professores de Matemática, quando estes passam a conhecer esses materiais, ainda durante o curso de formação, estimulando-os a desenvolver o conteúdo futuramente na Educação Básica. / This work aimed to evaluate how the 3rdgrade students in a Mathematics Degree course judge, conceptualize or qualify the use of manipulable material and virtual manipulable for the Population Proportion Estimate Teaching. In order to meet this target, an applied qualitative research was developed and then organized in 4 steps: 1-Theoretical framework production to verify situations of Statistics contents Teaching in the Basic Education; 2-Search for materials for the Population Proportion Estimate Teaching, in which the manipulable material elaborated by the professor Lisbeth Kaiserlian Cordani was found and for the lack of existent technological resources the researcher developed a virtual manipulable in partnership with a student of the Computer Science course of Universidade Estadual do Norte do Paraná; 3-Intervention or application of the research, it refers to the application moment ofthe materials mentioned on the step 2 in a 3rdgrade class of a Mathematics Degree course where data were collected, 4-Data collection analysis, in which the Discursive Textual Analysis based upon Moraes and Galiazzi (2016) was used. Through data analysis, it was possible to observe that the students approve the use of manipulable material and virtual manipulable for the Population Proportion Estimate Teaching, beacuse: they help the teacher in the teaching process, they facilitate a contextualized teaching applied to the students’ reality, they provide a connection between the theoretical and practical knowledge and they contribute positively to the graduation of mathematics teachers when these ones get to know these materials still during the graduation course, stimulating them to develop the content futurely in the Basic Education.

The problem of the study was related to the asymptotic and relative efficiencies of the conventional biserial correlation coefficients and the two modified biserial correlation coefficients proposed by Brogden (1) and Lord-Clemans (2; 15). These were determined under some selected cutting points (p), and various sizes of samples (n) randomly drawn from the; simulated bivariate populations of four different shapes—normal, lognormal, double exponential, and the contaminated normal, and of various degrees in population parameter (p).

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