The film begins with a talk by a representative of the Ford Motor Company. The emphasis in this introduction is on the role research has played in making possible many remarkable ad vances in science. The introductory remarks are followed up by scenes depicting research results being used by technicians.

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- Author or Editor: Arthur F. Coxford x

### Arthur F. Coxford

The film makes effective use of points, color, a metronome, and different-sized arrows to demonstrate the physical principles at work as forces act upon bodies in space. The points are the bodies, the arrows are forces, and the metronome marks equal time intervals. Several scenes in the film reminded this viewer of a billiard game where the points were the balls and the arrows were cue sticks.

### Arthur F. Coxford Jr.

How many times in teaching geometry have you come to the days before Christmas or Easter vacation knowing that very little would be accomplished in that time? And yet, not wishing to waste the time entirely, you sought something that would be worthwhile, but also different, in order to capture the fancy of your students.

### Arthur F. Coxford

This film is an excellent introduction to the fundamental concepts of probability. A simple probability scale from 0 to 1 is used to illustrate the probabilities of events that are certain to occur and those whose occurrence is impossible. The formula for the probability of an event is defined to be the ratio of “those events which interest us” to “the total events in the sample space.” This formula is developed with several clearly illustrated examples involving coins and dice. Two more examples, only slightly more complicated, further strengthen this develop ment. One of these, on the effectiveness of a vaccine, shows how a sample space may be created by experiments.

### Arthur F. Coxford

*Of Stars and Men* employs animated charac ters and a beautiful music track (Bach) in ex plaining man's position in the universe, That man, not the lion, is king of the animals is as serted in the initial phase of the film. But as man begins to probe the universe in which he lives, he finds that he is not the center.

### Edited by Arthur F. Coxford

*Thinking in Sets* is the first in a series of films entitled, “Pathways to Modern Mathematics,” The basic ideas of sets such as the meaning of set, symbols for writing sets, the empty set, universe, and the four relations of sets (disjoint, “overlapping,” equal, and proper subset) are developed in the film, Finally, the idea of set is applied to geometry.

### Edited by Arthur F. Coxford

In developing the idea of intersection, the meanings of set, member of a set, subset, and null or empty set are discussed. These ideas are first related to a baseball team and the specta tors in the bleachers. As the film progresses, the principles are discussed in relation to numerals, points on the number line, and the diagrams illustrating these ideas. Venn diagrams are in troduced early and used generously throughout the film. The symbols for subset, intersection, and null set are also used.

### Arthur F. Coxford Jr

For approximately forty years the French psychologist Jean Piaget and his various collaborators have been producing volumes dealing with the formation of concepts in children. He has intensively studied the concepts of number, geometry, physical causality, space, the world, and reality; also the moral judgment, reasoning, language, and thought of the child. He has published a total of twenty-five books on these subjects, four teen of which are now in English.

### Arthur F. Coxford

The release of the *International Study of Achievement in Mathematics* evoked strong criticism in leading American news media of the mathematical education provided United States' students (see The *New York Times*, March 12, 1967; Time, March 17, 1967; Education U.S.A., March 13 and 20, 1967).

### Arthur F. Coxford Jr.

In his book, *The Child's Conceplion of Number*, Jean Piaget stated that the concept of number has three basic aspects: cardinal number, ordinal number, and unit. He has given criteria for determining when a child understands each of the basic concepts. A child understands cardinal number when he is able' to construct a one-to-one correspondence between two sets of objects and to conserve this corrspondcnce when it is no longer perceptually obvious.