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Probabilistic machine learning increasingly informs critical decisions in medicine, economics, politics, and beyond. To aid the development of trust in these decisions, we develop a taxonomy delineating where trust in an analysis can break down: (1) in the translation of real-world goals to goals on a particular set of training data, (2) in the translation of abstract goals on the training data to a concrete mathematical problem, (3) in the use of an algorithm to solve the stated mathematical problem, and (4) in the use of a particular code implementation of the chosen algorithm. We detail how trust can fail at each step and illustrate our taxonomy with two case studies. Finally, we describe a wide variety of methods that can be used to increase trust at each step of our taxonomy. The use of our taxonomy highlights steps where existing research work on trust tends to concentrate and also steps where building trust is particularly challenging. [This paper was published in "Science Advances."]

Investigating properties and characteristics of unary operations is shown to be facilitated by using calculators. Several avenues for instructional exploration are suggested and examples given. These include questions relating to relations, inverses, commutativity, distributivity, and iterations. A discussion of the calculator algorithm for exploring each question is included. (MP)

The sixth session of IT@EDU98 consisted of seven papers on the topic of the learning machine--Vietnamese based human-computer interface, and was chaired by Phan Viet Hoang (Informatics College, Singapore). "Knowledge Based Approach for English Vietnamese Machine Translation" (Hoang Kiem, Dinh Dien) presents the knowledge base approach, which consists of concepts such as things, actions, relations, and attributes, organized on the structure of inheritance hierarchy. "A Learning Algorithm for Feature Selection Based on Genetic Approach" (Nguyen Dinh Thuc, Le Hoai Bac) presents a genetic algorithm that chooses relevant features from a set of given features, for feature selection based on the correlation among the features and between every feature and given target curve. "Artificial Neural Network for Color Classification" (Tran Cong Toai) examines several neural network models, their learning schemes, and their effectiveness in color classification. "Synthesizing and Recognizing Vietnamese Speech" (Hoang Kiem, Nguyen Minh Triet, Vo Tuan Kiet, Thai Hung Van, Luu Duc Hien, Bui Tien Len) presents algorithms applied successfully in Vietnamese isolated word recognition and Vietnamese synthesis. "On-Line Character Recognition" (Nguyen Thanh Phuong) presents a real-time handwriting character recognition system based on a structural approach. "Data Mining and Knowledge Acquisition from a Database" (Hoang Kiem, Do Phuc) considers how to use multi-dimensional data model (MDDM) for mining rules in a large database. "Genetic Algorithm for Initiative of Neural Networks" (Nguyen Dinh Thuc, Tan Quang Sang, Le Ha Thanh, Tran Thai Son) describes a procedure for initiative of neural networks based on genetic algorithms, based on the correlation between every weight and error function. (SWC)

The present study was an exploratory study of the content-specific knowledge structures of three teacher educators (two in math and one in science). Pathfinder, a method for eliciting associative memory networks, was used to describe the knowledge structures of the teacher educators. Pathfinder was also used to determine changes in knowledge structures of students enrolled in a teaching methodology class taught by each educator. Finally, a measure of the correspondence between students' knowledge structures and those of the teacher educators was correlated with students' performances in the courses. For two teacher educators, students' knowledge structures corresponded more closely with that of the teacher educator after the course than before. For one teacher educator, students exhibited little change in knowledge structure correspondence. Also, students who corresponded most to teacher educators performed better in their respective courses. The findings point to the need for further study of the acquisition of knowledge in undergraduate students and the processes associated with the transmission of knowledge in math and science teacher-education programs. Contains 3 figures, and 19 references. (Author/SLD)

Describes shortcomings of computer science/engineering education and explains a new focus on informatics. Highlights include simulation, visualization, algorithmization, design of information processing models, parallel computing, a history of informatics, informatics versus physics and mathematics, and implications for education. (51 references) (LRW)

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and automatic classification) in an attempt to reduce the amount of searching for the irreducible factors of the polynomial. The approach taken to polynomial factorization is quite different from previous attempts because: (1) it is distinct from numerical techniques; (2) possibilities for terms in a factor are generated from the terms in the polynomial; and (3) a reclassification technique is used to allow the application of different sets of heuristics to a polynomial during factorization attempts on it. Data presented show the importance of learning to the efficiency of operation of the scheme. Factorization times of polynomials factored by both the scheme described in this paper and Wang's implementation of Berlekamp's algorithm are given and compared, and an analysis of avariance experiment provides an indication of the significant sources of variation influencing the factorization time. (Author/DGC)