Mathematics Education at the University: An Item Difficult to Enter on. The difficulties are: high deficiency of mathematical knowledge that new students bring from high school and absence of motivation and lack of training of the students for problem solving. To solve these problems a research group on mathematics education at the School of Biochemistry designed a distance education course. This course is written with an historical view and based in the heuristic methodology. Since motivation is very important, they looked for problems intimately connected with the discipline chosen. The visual impact plays important roles in motivation because sensitive experiences are the background upon which deeper knowledge is built. Finally, the problem solving is the methodology with which we are working. The resolution of mathematical problems supplies students with techniques, which can be used in different areas, even to everyday problems. Mathematical thinking is logical and strict, intuitive and creative, dynamic and changing.
The Preparation Needs of New Graduate Teaching Assistants. In the USA, Graduate Teaching Assistants (GTAs, both domestic and international) are critical in the effective mathematics education of undergraduates because they teach a large percentage of lower division courses. A variety of efforts have been implemented to prepare these instructors to teach in a variety of ways with a diversity of students and an evolving curriculum, a context which is often different from the one in which GTAs learned mathematics. The joint Committee on Teaching Assistants and Part-Time Instructors of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA) has held sessions at national conferences in order to explore this issue. I will present: (1) an analysis of themes and emerging ideas from the AMS/MAA sessions and (2) results from an in-depth study of 25 new GTAs at the University of Oklahoma. This latter project will examine the perspective of new GTAs, using journal entries, statements of teaching philosophy, and videotapes of classroom teaching as data.
Four Clues to Teaching Mathematics: Good or Right and Complexity or Abstraction. In studying mathematics two types of attitude are required; one acceptance or agreement and the other argument. Definitions and notations are important in mathematics and they are something that is adopted. They are essentially matters of good or bad. On the other hand another important part of mathematics is logical argument. Logical argument is essentially a matter of right or wrong, not good or bad. Many students tend to have interchanged attitudes in this aspect. I believe that their wrong attitudes make their study of mathematics harder. If we take these attitudes as warp, there are two types of difficulties of mathematics as woof: one the difficulty due to complexity, the other due to abstraction. Abstraction is harder to conceive and rather unfamiliar to everyone, and thus requires extra work for it. I believe that if instructors indicate the nature of the difficulty according to these four clues it would increase the effectiveness of teaching mathematics.
The Genetic Principle in Teaching University Mathematics. The genetic approach in mathematics teaching has been known from the times of Diesterweg, but it was almost never used in teaching higher mathematics: it was assumed that for undergraduate students, mathematics should be taught in strict logical and deductive way. For example, the teaching of mathematical disciplines in universities began with detailed account of logical and set-theoretic foundations, the linear algebra courses began with the general theory of vector spaces etc. However, modern experience has shown that the strict logical and deductive teaching of mathematics is inappropriate for undergraduate mathematics teaching, too. This presentation discusses the genetic approach to teaching higher mathematics. This approach consists in presenting subject matter as developing out of the principles that have determined its presented form. Such approach requires, for example, that elements of number theory should be taught before abstract algebra.
Statistical Literacy: A Pre-Stats Bridging Course. The traditional applied statistics course is not accomplishing its mission. It has too many topics and does not do enough in helping students evaluate non-statistical arguments involving statistics. This paper argues that there are two causes. First, an over-emphasis on statistical inference -- on chance, sampling distributions, confidence intervals and hypothesis tests. Second, an under-emphasis on statistical literacy: the distinction between association and causation, between experiments and observational studies, between a biased measurement and a spurious association, between a frequentist p-value and a Bayesian strength of belief. Since both statistical inference and statistical literacy are extremely important, this paper proposes a new course: a "Statistical Literacy" bridging course. This is not a "baby stats" course; it is not just a vocational remediation course that reviews arithmetic and algebra. Instead, this is a critical thinking course that focuses on descriptive statistics and modeling with a strong emphasis on conditional thinking and on written communication using proper English.