This twentieth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 18. For each of the chapters in Unit 18, the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are given, answers to exercises are provided, and sample text questions are included. (DT)

Using the concepts of conditional probability, conditional expectation, and conditional independence, the main results of the classical test theory model can be derived in a very few steps with minimal assumptions. The present effort explores the possibility that present classical test theories can be further condensed. (Author/RC)

The present study used a two-choice spatial probability-learning situation (Bitterman, 1975; Wilson & Oscar, 1966) in order to explore the hypothesis that Korsakoff patients differ from control subjects in the way in which they respond to changes in reinforcement contingencies. (Author)

A case is made for a comprehensive curriculum that includes strong competencies with not only number ideas and computation, but also with other mathematical topics such as geometry, statistics, probability, and estimation. (MP)

The inclusion of probability in the school curriculum is argued to be justified on mathematical, psychological, and social grounds. Contemporary teaching approaches are suggested as sufficient. (MP)

Discusses scattering problems in continuous media, and presents a simple discrete model for scalar wave scattering from inhomogeneities on a lattice. Illustrates the relationships between the amplitude of the scattered wave and the characteristic function of the fluctuating motion of a point reflector in one dimension. (Author/GA)

The bias attributable to nonresponse in population estimates in the field of education was studied. Data were collected from responses to mathematics and science exercises administered by the National Assessment of Educational Progress to a probability sample of 17-year olds, as well as a probability sample selected from nonrespondents.…

The author gives a three dimensional analog of Pascal's Triangle as an exercise in heuristic thinking and an introduction to the multinomial theorem. The analog involves finding the number of shortest routes to various rooms in a cubical apartment house. (MN)

The contributions made by including probability theory in the primary grade curriculum are examined with respect to the day to day living of the developing child and his preparation for later life. In particular, language and decision making, misconceptions, research and systematic thinking, occupations, and the future are discussed. (MN)

The probabilities of six-card poker hands are derived and compared to those of the five-card poker hands. (JT)

E. Burns' (1984) attempt to explain the below average mean IQ scores reported for samples of learning dsabled (LD) students through the use of the bivariate normal probability distribution was examined. Alternative explanations which focus on issues related to the referral, identification, and placement of children are presented.(Author)

Three estimates of the probabilities of correct classification in predictive discriminant analysis were computed using mathematical formulas, resubstitution, and external analyses: (1) optimal hit rate; (2) actual hit rate; and (3) expected actual hit rate. Methods were compared using Monte Carlo sampling from two data sets. (Author/GDC)

One way in which a computer simulation can convince students of the validity of formulas for the density and distributive functions of the sum of two variables is described. Four computer program listings are included. (MNS)

A computer program simulated guessing on multiple-choice test items and calculated deviation IQ's from observed scores which contained a guessing component. Extensive variability in deviation IQ's due entirely to chance was found. (Author/LMO)

Solutions to a problem on seating arrangements and one on a box-office situation are discussed; a statistical approach is used. Four computer programs are included. (MNS)