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This experiment examined decisions made by teachers using only status data with those made by teachers using growth and status data. Middle school math teachers from five schools within a single school division located in Virginia participated in the study. Participants were randomly assigned to either the status only or growth and status group. They were then asked to analyze a sample set of class data and complete a survey in which they rated the success of four types of students, identified teacher strengths and weaknesses, and rated their confidence in and the usefulness of the data received. Teachers with access to growth and status data differed significantly in their ratings of three of the four types of students. Students with high growth/low achievement were rated more favorably by teachers with growth and status data (p < .05). Students with low growth/high achievement and those with low growth/low achievement were rated less favorably by teachers with access to growth and status data (p < .05). Teachers with access to growth and status data also chose different strengths and weaknesses than those with access to only status data. Teachers did not differ significantly in their confidence in the data or the perceived usefulness of the data, although limitations may have influenced this finding.

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A mathematical model has been developed to describe the growth of trees in stands of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) from age ten to age 100 years. An initial square pattern of spacing was assumed. At age ten years the trees were assumed to be open-grown, that is, growing in diameter at breast height at a maximum rate. A regression of d.b.h. on age was obtained from eighteen open-grown, Douglas fir trees measured on the Saanich Peninsula, Vancouver Island. The relationship derived from these data agreed with further data collected elsewhere in the coastal regions of British Columbia and Washington and in the interior of British Columbia. The d.b.h. growth of individual trees was predicted by five-year periods. Relationships between crown width and d.b.h. were calculated from data on 426 open-grown, Douglas fir trees. There was a close correlation between crown width and root spread for open-grown trees. A multiple regression equation was obtained for height of 869 trees on d.b.h. and basal area per acre. All regression equations calculated for use in the model, were highly significant statistically. The model is initiated with a matrix of 15 x 15 trees (or tree "locations”). The initial d.b.h. of each tree is specified and, from the crown width/d.b.h. regressions, the crown width of each tree is calculated. As long as the tree remains free of competition, this calculated crown width is reduced by 40 per cent by the reduction factor "REDFAC", to give the "competitive" crown width. This was because it was found that, in young Douglas fir plantations, there could be considerable overlapping of the crowns before d.b.h. growth was reduced. As soon as competition sets in the original 40 per cent reduction is systematically reduced. The proportion of the circumference of each tree that is occupied by the crowns of surrounding competitors is then calculated. This proportion indicates the amount of competition to which the tree is being subjected and varies between zero, if the tree is open-grown, and one or more, if the tree is completely enclosed by the surrounding competitors. If the reduction is sufficiently great, continued survival of the tree is considered unlikely, and the tree is assumed to have died. The periodic d.b.h. growth of the surviving trees is calculated at five-year intervals to age 100 years. All calculations are performed using am I.B.M. 7090 electronic computer. A summary of the structure of the stand can be printed out at the end of each five-year period if required. Height growth can be described by modifying the stand model by including an appropriate regression equation. Similarly, volume growth can be estimated by modifying the basic stand model. The mathematical model developed here satisfactorily describes the growth of Douglas fir stands on an individual tree basis, over a wide range of site conditions, stand densities, amounts and distributions of mortality and thinning regimes. Field data cannot be secured to evaluate the accuracy of all the tests made. However, there are no gross errors in absolute values and results are accurate proportionately. The model described here can aid the forester in managing Douglas fir stands in the Pacific Northwest. By simulating the growth of his stands from age ten to age 100 years in a few minutes he can study questions that would otherwise require several human generations to evaluate. / Forestry, Faculty of / Graduate

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