Proliferation of mathematical knowledge prohibits individual reduplication of all results and causes mathematicians to accept much on faith. To convey the spirit of the mathematical community, and provide maximum content coverage, instruction should allow students to accept some theorems without proof. Students would then find mathematics less…

THIS REPORT PRESENTS A PROGRAM FOR THE UNDERGRADUATE MATHEMATICAL PREPARATION OF ENGINEERS AND PHYSICISTS. THE FOLLOWING STATEMENTS SERVE AS UNDERLYING ASSUMPTIONS FOR ANYONE EXPECTING TO MAKE USE OF THE RECOMMENDATIONS--(1) THE PROGRAM IS ONE FOR THE PRESENT AND THE PROPOSALS ARE SUCH THAT THEY CAN BE CONTINUALLY MODIFIED TO KEEP UP WITH FUTURE…

This is Part III of the first volume of the proceedings of the Committee on the Undergraduate Program in Mathematics (CUPM) Geometry Conference, held at Santa Barbara in June, 1967. The purpose of the conference was to consider the status of geometry in colleges at the undergraduate level. The conference, attended by undergraduate mathematics…

Reported are the results of a study which investigated the relative efficacy of four instructional strategies for promoting three levels of awareness of mathematical concepts. It was determined that there are basically two kinds of moves used in teaching concepts: characterization (C), and exemplification (E). The four patterns studied were C, CE,…

This study reports on the position of programed learning in the teaching of college mathematics. A historical survey is given describing the following programing styles: Skinner, Crowder, eclectic, hybrid, Pressey, and problem. Conclusions based on research are given to claims about the benefits of programing including those of: providing for…

This experiment attempted to teach abstract mathematics fo college freshmen with A.C.T. scores less than 15 in a three semester terminal course sequence. The course content included a formal mathematical language, set theory, Boolean Algebra, relations and functions, operations, cardinals and ordinals, the rational numbers, and college algebra.…

The Statistical Concepts Package (STAT-CONCEPT) is a coordinated collection of interactive computer programs and printed materials designed to enrich graduate instruction in educational statistics. Probability, descriptive statistics, sampling distributions, and power are four of the thirteen topics included. By doing the computational labor and…

The purpose of this study was to determine the effect of using externally paced testing upon cognitive achievement and attitudes of college freshmen who were administered externally paced programed instruction material in mathematics. Three groups, each containing equal numbers of students representing three characteristics work rates, were…

This handbook on effective college mathematics teaching offers suggestions on course planning; lecturing; using the blackboard, textbooks, and visual aids; making assignments; scheduling, composing, and grading tests; and giving grades. It also discusses feedback and instructor evaluation and includes a sample questionnaire that might be given to…

Qualifications for teaching the courses described in "A Transfer Curriculum in Mathematics for Two Year Colleges" is discussed. Important components of the teacher's education are seen to include apprenticeship in teaching and specific mathematics courses, identified by reference to other Committee on the Undergraduate Program in Mathematics…

Twenty-six students who were tutored in freshman mathematics were matched with twenty-six students who did not visit the tutor during the semester. Findings showed that students who received tutorial assistance got significantly higher (p < .05) final grades than the students not receiving help. (DT)

Graphic displays of elliptic, parabolic, and hyperbolic surfaces can be generated by computers. (SD)

When students were given calculus instruction based on the nonstandard defintion of limit, achievement was comparable to that of a control group using regular text materials. Attitudes of teachers regarding the use of the nonstandard approach are reported. (SD)

Repeatedly taking the square root with a calculator yields numbers with logarithmic-type properties, which can be used to define the logarithm functions. (MP)

A major source of challenging problems for students is the use of higher mathematics to derive elementary problems. Several examples are given. (MP)