Although genetics has led to new ways of thinking about many problems in dentistry, there are others for which the concept of a particulate gene has failed to provide a clearcut solution. Interest in dentistry is not only in those discrete differences that may be attributed to a single gene substitution but also in such compound characters as arch shape, tooth morphology, or facial bone relationships that differ among individuals. Study of the variation in such quantitative dental characters has been limited largely to twin studies' 2 and to the comparison of mean values among groups of individuals.3-6 In these studies several or many different measurements of dental characters were made and were treated as independent of each other, although it was generally recognized that such treatment disregards the correlations resulting from those common causative agents that affect the various examined characters. It is clear that such analyses cannot provide a true picture of the relationships among the different groups under study.During recent years the analysis of intercorrelated compound variables has attracted the attention of many statisticians. Powerful analytical methods have been devised for comparing and for testing the significance of differences between multivariate distributions and for examining and describing the interrelationships among the variables contributing to such distributions. Until recently, these methods have been used in anthropologic and biologic research by comparatively few workers. Both biologists and statisticians have, however, recognized the necessity of working together toward the construction of suitable models and for the solution of such complex problems. Both the need and the desirability of co-operative effort are evidenced by the current support of training in mathematical biology and by the many conferences on biology and mathematics that have been held during the past few years. This paper will discuss several multivariate methods that may be used in the analysis of dental data, illustrating the methodology with some data from families and from a dental growth study, and will outline some additional problems in dental research to which such statistical methods may be applicable.The observations of Wylie7 and Stein, Kelley, and Wood' suggest that, with respect to several cranio-facial dimensions, daughters and fathers are more alike than are daughters and mothers, and, conversely, sons appear to be more similar to their mothers. It is impossible to derive from these observations a hypothesis consistent with the theorems of
Current approaches to teaching mathematics in English primary schools pay little attention to the kind of mathematics which children engage in outside of school. This paper attempts to redress the balance by describing the nature and characteristics of children’s out-of-school mathematics, and looking at how connections might be made between in-school and out-of-school mathematics. At home, mathematics is frequently encountered during play and games, and in authentic household activities such as cooking and shopping. There are also more school-like mathematical activities such as homework and commercially available maths schemes. The paper argues that it is important for connections to be made between home and school mathematics, but this is often impaired by teachers’ lack of knowledge about home mathematics and by parents’ lack of knowledge about school mathematics. One solution to this problem lies in knowledge exchange activities, and examples are provided of activities which operate in both the school-to-home and home-to-school directions. The main implications for teachers and educational psychologists are to pay much greater attention to children’s out-of-school mathematics, and to develop further ways of linking home and school mathematics.
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