In this study, in recognition of a probability concept, while considering this structure,
educational contents and the method for promoting the rise of a level are developed, and it aims at
constituting a curriculum. In this report, I developed the teaching materials for schoolchildren. And,
I report on the result of the experiment that uses it. It was shown that this learning promoted the
rise of a level in conclusion.
Mathematical modeling appeared in the 1980's during the historical trend
when students were encouraged to study mathematics on their initiative. Since
then, educational practice of mathematical modeling has been developed
multifariously, and has made progress in Japan. Today, the diversification of
learners and the need to raise their ability both individually and as a group are
increasing even more than before. On the other hand, confusion has begun over
"Mathematical Activity" (a new junior high school course of study). In this
situation, it can be said that we are at a phase where research and practice of
mathematical modeling must also search for a new direction. Considering the
above mentioned issues, the authors in this paper look back earnestly on the
mathematical modeling research and practice up to now, illustratively show their
current state and limits, and conclude by proposing a new direction in mathematical
modeling research and practice.
In this paper, we showed clearly how the teachers of elementary schools understood
structural relations between the learning elements of a teaching unit in arithmetic. We made 95
teachers draw concept maps of unit "Ratio" of arithmetic grade 5 and unit "Multiplication and
Division of Fraction" of arithmetic grade 6 in six elementary schools and analyzed the concept maps
with a transfer coefficient. As a result, the following matters became clear.
(1) For the analysis of recognition of the teaching materials structure, a method with a transfer
coefficient by using concept map is effective, and the value of transfer coefficient may be effective
to explain a style of the recognition structure.
(2) The recognition of the understanding teaching materials structure of teachers is very low because
96% of teachers seldom understand the structural relations of the teaching contents.
(3) Even if the teaching profession years of experience of teachers increase, the understanding of
structural relations is same and the recognition of teaching materials structure of teachers is not
(4) The recognition of teaching materials structure of teachers tends to become weak as a time
The survey aims to know how analytical thinking is taught at high school classrooms.
Depending on 102 teachers' responses on the survey for all high schools in Ibaraki prefecture, the
results are followings. Firstly, less than half teachers teach the analytical reasoning through the
typical problem on the survey. Secondly, the ratio of teachers who did not write the reasoning for
students' understanding of the problem solution is larger in the case of experienced or higher
achievers' schools teachers. The ratio of the teachers who do not teach analytical reasoning on the
problem was improved through the survey.
In this paper we will descrive the system of teacher education of Finland. It is said
that one of the reasons behind Finnish students' success in the PISA would be a high quality of
school teachers. We Japanese have to know and learn the Finnish teacher education. Then we will
get some suggestions from it. It is expected to have a good reflectoion to the Japanese education
of mathematics and science. We will also descrive the general education system of Finland and
the actual students' teaching practice in the teacher training school of Turku University.
This research aimed to develop the subject matter to teach the idea of fundamental theorem on calculus for
under achieved students. The idea of fundamental theorem is defined by the change of changes (differentiation)
and the summation of changes (integration). The research surveyed the understanding of
under achieved students, developed the teaching with the subject matters and tools,
and evaluated the effect of teaching from their achievements.
We have famous golden ratio in the history of mathematics. But what is the value of golden ratio? We have six kinds of textbook in Japan. The author was astonished by the different two kinds of value of golden ratio. That is to say, one textbook states the golden ratio is (-1+√5)/2, the other five textbooks state (1 +√5)/2. The author asserts that the golden ratio is “(-1 +√5)/2 or (1+√5)/2.”