Recently, it seems that people like to know the solution soon, but in the classroom
it is rather important to understand how to reach the solution. In this respect, school
teachers of mathematics should have their own attitude to mathematics as a meaningful
part of science, and it is also worthy for students of teacher's college to follow the theories
established by excellent mathematicians in the far past. In this paper we pay attention to the
great achievements due to Archimedes and Fourier. The former established a thought method,
which is a basis of modern sciences, in the time of the Greek, and the latter contributed
greatly in the 18th century to the development of the modern mathematics. In this paper we
recommend for teachers and students of mathematics to learn a lot of things from Archimedes
and Fourier, since they were standard bearers of scientific ideas in the respective periods.
In our college, some subjects teach it by the theme of enviornment at the same time,
which we say "Interdisciplinary Colaborative Education". In the class of mathematics, we analyzed
the change in the number of individuals of the Japanese crane by the difference equation, and we confirmed
that the change applied to the logistic curve. Moreover, we illustrated that the logistic curve
appeared in the various scenes, and we developed it into chaos phenomena. A lot of students were
surprised that mathematics was effective for such a natural world, in the following questionnaires.
In this paper, we shall consider the mathematics knowledge needed in this teaching material, and
the meaning of taking up such real data in the class.
The purpose of this paper is to present generalized models of compact folding/wrapping
method of flat circular membranes around a central hub using modified Archimedean spiral
configurations. By using the formulated simple angle relations between fold-lines, various kinds of
wrapping models are shown to be easily designed. The present models are expected not only to
design a fundamental modeling of sail wrapping of solar-sail spacecraft but also to be used for
instructional materials with edutainment.
In the present-day, it is generally important to teach the probability. However, it is said
that both quantity and quantity are not enough for teaching the probability in Japan.
Especially, the probability is hardly taught in elementary schools. So the purpose of this
study is to make the curriculum of teaching the probability in elementary schools.
In this paper, we researched cognition about the probability to 1st, 2nd and 3rd
graders who have not been taught the probability. From the result of the research, the
possibility of teaching the probability from the first grade in elementary schools was
There arc two methods to extend the set of rational numbers to the one of real numbers.
One of them is due to Dedekind and another due to Cantor. Their ideas are respectively based on
the concept of "cut" and on the one of "fundamental sequence". Both are complete theories on the
real numbers which give theoretical definitions of fundamental properties of real numbers, such as
the continuity (or completeness). But, unfortunately it seems not easy for students of high schools
to understand their theories without studing the general set theory (and the mathematical logic).
Nevertheless it would be expected at least for all students belonging to any courses of sciences to
study this subject as a part of liberal arts. For this purpose we need to compose a continuous
program on the study of "numbers" without theoretical gaps throughout junior high school, high
school and universitiy. In this paper, we try to evolve the theory on the extension of numbers,
especially the extension from the set of rational numbers to the one of real numbers based on
interminate deeimals and report a lesson practiced in a high school.
We introduce our lecture on mathematical education in universities. First, we
describe the purpose of our class, our attention while teaching, the contents and the outline of
our class. Next, we explain our lecture on the natural numbers and the Fibonacci sequence,
precisely. Since it is troublesome to start with Peano's axioms, we pick up 11 formulas from the
natural numbers and consider them as the new axioms. While we are making the new axioms,
we come across the question why one plus one is equal to two and have some answer to it. As for
the Fibonacci sequence, we discuss about how to solve pan+2+qan+1+ran = 0 and describe our
study on the arrangement of leaves. We define the condition of the ideal arrangement of leaves
and show that 137.5 degrees, which is the angle derived by the Fibonacci sequence, satisfies the