EDUCATION
Computers Used as Tool to Teach Mathematics High school students apply such principles as Boolian algebra to computer programing Computers can be used as tools for teaching advanced mathematics to high school students. Results of two summer programs (institutes) at the schools of engineering at the University of Pennsylvania, Philadelphia, show that students are interested in learning such topics as symbolic logic, Boolian algebra, and the Euclidian algorithm when these principles are applied to computer programing. The aim of the computer-mathematics institutes at the University of Pennsylvania is to give superior students a chance to use scientific and mathematical skills to solve real problems, according to William Petrecca, assistant to the vice president for engineering affairs at the university. Mathematical topics not normally covered in high school courses (or even in most undergraduate curriculums), such as numerical analysis, probability theory, formal mathematical logic, and number theory, are presented in the context of computer programing, he explains. Institute. Last summer, 49 students from Philadelphia area high schools were selected to participate in the eight-week institute. Prerequisites are senior high school standing and two years of algebra and one year of geometry. More important, Mr. Petrecca says, is that the students have a strong interest in science and mathematics and a willingness to undertake the intensive program. Students get three hours of lecture daily with supplementary problem sessions. Classes are divided into small teams, each having a minimum of 12 hours' computer time a week for projects. This much time is unprecedented for high school students, Mr. Petrecca says. 50
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Besides a basic course for students who had had no previous computer experience, an advanced course (taught by Richard Wexelblat, instructor at the Moore School of Electrical Engineering) was given for 18 of the students who had previous training in computer fundamentals. Some of these advanced students were participants in the previous summer's informal program organized by Andries van Dam, a Ph.D. candidate in the Moore School of Electrical Engineering. Mr. van Dam taught 29 high school students on Saturdays in the summer of 1962 to use computers such as General Precision's RPC-4000 digital computer. "I wasn't interested in making programers out of the students," Mr. van Dam says, "but rather to show how a computer is a very useful tool in solving many kinds of problems/' Students need an appreciation of the power and limitations of a modern computer, an instrument which is playing an increasingly important role in many areas, he adds. For example, lawyers
and research workers in all sciences will need to use computers for information retrieval. Business majors and even English students need to be aware of the usefulness of computers to their area of interest and to society in general, Mr. van Dam believes. Programers. Several of the "graduates" of the first summer's program are using their knowledge of computers in research while attending college, according to Mr. van Dam. Some have found employment in university laboratories during the summer as authentic programers, and are invited to continue research at the university during the academic year. Such problems as production scheduling, inventory control, coulomb scattering along a particle track, and the study of rheological characteristics of mucus (important in the study of respiratory ailments such as cystic fibrosis) are among the research topics available to the students. The university plans to expand the program in the summer of 1964 to take
PROGRAMING. Daniel Ashler (center) instructs students in basic computer program for generating random sentences. A computer, given rules of English grammar and a limited vocabulary, forms grammatically correct sentences
new interested students as well as to offer more advanced work for those who took part in earlier programs. High Schools. The number of high schools and colleges using computers as teaching aids is increasing. For ex ample, several high schools in the Philadelphia area have purchased com puters for use in their mathematics, sci ence, and business curriculums. Infor mation Systems Groups (ISG) of General Precision Inc., Burbank, Calif., sells their model LGP-30 to high schools for $18,000. According to ISG, this particular model has ad vantages which make it ideal for high school teaching.
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CHEMICAL
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• It has 16 simple commands. • Some parts of the memory system can be locked in; thus, a program can't be destroyed by student error.
PHYSICAL FUNCTIONS
• The LGP-30 has a storage capacity of 36,000 characters. • It does not need special rooms, air conditioning, or special wiring. In spite of the cost of servicing these instruments (about $2500 each year), the schools using them believe that the addition of computer programing to their curriculum helps prepare students for the time when much of the func tions in business and industry will be done by computers.
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Students at Haverford College (Haverford, Pa.) now take their modern chemistry courses in modern surround ings. A new $2 million science build ing, which houses the chemistry, mathematics, and physics departments of the college, was dedicated Nov. 16. The chemistry curriculum has been changed to meet the needs of students in a modern liberal arts college, Dr. Robert Walter, head of Haverford's chemistry department, says. Other members of the chemistry department working with Dr. Walter are Dr. John P. Chesick, Dr. Harmon C. Dunathan, and Dr. Colin F. MacKay. One of the features of the program is its flexibility. This is especially im portant for first-year college students, Dr. Walter says, because of their varied high school backgrounds in chemistry. Alternatives. There are several al ternatives available to freshmen chem istry students in the Haverford pro gram. Besides the usual two-semester introductory course for students with usual preparation in chemistry, an ac celerated one-semester course is given for those who come to Haverford un usually well prepared in chemistry. About 75% of those students planning to major in chemistry have had suf ficient background in high school to allow them to take the new course, Dr. Walter says. He expects this percentage to increase as strong high school chemistry courses become more common. After completing the accelerated course, students can begin the se quence of physical chemistry courses in the second semester of the fresh man year. As a third option, those few who have unusual background and ability in science can start or ganic chemistry at the beginning of the first semester, and complete both organic and one semester of physical chemistry as freshmen. Although more college freshmen have better backgrounds in chemistry than ever before, they are not neces sarily brighter, Dr. Walter believes. It is a mistake to assume that students in an introductory course today are able to learn more rapidly than those
in previous years. It is true, he adds, that more advanced topics can be in cluded in a freshman course because of improved science curriculums in many secondary schools. The two-semester normal introduc tory course at Haverford is designed for science majors and also for stu dents who will probably not take any additional science. The first semester includes the usual topics of atomic structure, stoichiometry, thermochem istry, and chemical equilibrium, but it does not include much descriptive chemistry. In the second semester, concepts of structure, isomerism, chemical bonding, and properties of substances related to bond type are emphasized. The chemistry of ele ments in the first transition series and simple stereochemistry are taught. There is no descriptive organic chem istry included. Obligation. In developing a course for all types of students, care must be taken to maintain the substance of the course at a high level, Dr. Walter warns. There are students enrolled in most general chemistry courses who only take one science course to meet the science requirements. The liberal arts college has an obligation to those students because the impressions the course leaves with them are important in determining their attitudes toward science as citizens in later life, Dr. Walter believes. He believes that students who finish the first-year course at Haverford are reasonably well grounded in funda mentals to understand advanced topics in later courses. It is possible, for example, to use detailed arguments based on structure or stereochemistry in introductory organic chemistry. This is particularly useful in teaching modern notions of reaction mecha nisms, Dr. Walter says. Instruments. The new curriculum includes three semesters of physical chemistry. The first semester coveis the first and second laws of thermody namics and the quantitative treatment of chemical equilibrium based on free energy functions. This is the course which can be taken by better-prepared freshmen. The second semester is
devoted to the third law of thermodynamics and chemical kinetics; molecular physical chemistry is the third part. The laboratory work for the first two courses deals with quantitative studies of equilibrium and reaction systems. Here students get training in techniques of classical quantitative analysis without devoting time to analyses as ends in themselves, Dr. Walter says. The molecular physical chemistry course given in the third semester does not include lab work. A separate lab course in advanced physical and instrumental methods is given to provide training in spectroscopic and diffraction methods for the study of molecular structure. No separate courses in analytical chemistry are given at Haverford. The department believes that training in quantitative techniques and an appreciation of the precision of experimental methods should be emphasized in all lab work, beginning in the introductory course. Laboratory. Instrumental methods are used whenever suitable. The saving in time by the elimination of analytical chemistry courses makes it possible to carry training in physical chemistry beyond the level ordinarily possible in two semesters. In the Haverford program, three semesters are required for all chemistry majors. After a student completes the basic courses in general, organic, and physical chemistry, he is offered a choice of advanced work. One-semester courses in inorganic chemistry, organic qualitative analysis, quantum mechanics, and theoretical organic chemistry are available. The new science building (the first major academic building added to the Haverford campus since 1929) enhances the new chemistry curriculum, Dr. Walter says. For example, wellequipped laboratories are now available for seniors to work on research problems. Although a senior project is not required of chemistry majors, all students who intend to go to graduate school are expected to do some research, Dr. Walter says. (Each faculty member also has laboratory space for his own research program.) A distinct advantage of the new program at Haverford is that it frees time for the advanced work by permitting the best students to advance more rapidly through the basic courses, Dr. Walter says.
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