Recently, the importance of discussion on the development of mathematical thinking increases in mathematics education. The recent study due to the author found that the students of teacher training course do not fully understand the core concepts of mathematical thinking. In this paper, we confirm the current situation on how does the students understand the view of mathematical thinking, and we report on the related issues and methods for its overcoming. Then we consider the development of mathematical thinking from the viewpoint of teacher training.
This study aims to develop math educational environment of early childhood that is
based on infants’ cognition and mathematical system. In this paper, we analyzed the
characteristics from preceding studies, and the mathematics environment and cognition
of an infant (34-month-old child). We got some findings such that it is effective to set the
abundant and high quality mathematical environment early.
This study aims to develop math educational environment of early childhood that is based on infants’ cognition and mathematical system. In this paper, we analyzed the mathematics environment and cognition of an infant (36 to 40 months old). As a result, we have found that abundant and high quality math educational environment gives an effective impact on math cognition of an infant.
The purpose of our research is to clarify what type of strategies students of each level or each stage use and how respective strategies develop in relation to the scales for assessing the degrees of students' understanding about “ The Decimal Multiplied by The Decimal, The Decimal Divided by The Decimal ”. 177 students on X defined as a set of 12 multiplicative questions, 185 students on Y defined as a set of 11 divisional questions, and 187students on Z defined as a set of 13 divisonal questions were subjects of analyses. A s a result of analyses, we clarifyed thefollowig. (1)For X , there was the difference between 5th grades and 6th grades on the score , which depends on their strategies, but for Y and Z, there wasn't the difference on the scores. (2)We knew it was easy for students to understand the situations of questions in order of ' X → Z → Y '.
In this paper, the purpose of our research is to develop the scale for assessing
the teacher's capacity for giving lessons in arithmetic education. For that purpose, we
differentiated the teacher's capacity into the plan-capacity, the development-capacity, and
the assessment-capacity. We designed the test which consists of 51 items and carried it out on a
total of 290 teachers in elementary schools. We then conducted exploratory fact analysis on
a result of the test, and 4 factors were selected from 13 items . Cronbach's coefficient of
reliability was positive for 4 factors. The Goodness of Fit Index(GFI), Adjusted Goodness
of Fit Index(AGFI), Comparative of Fit Index(CFI), and Root Mean Square Error of
Approximation(RMSEA) were positive for 13 items in terms of conirmatory factor analysis. As
a result, 13 items of the test were deems to be valid. So we could develop the scale for
assessing the teacher's capacity for giving lessons in arithmetic education.
The present study, showed what kind of contents have been researched and practiced in mathemati
cs education in early childhood by reviewing textbooks and other teaching materials. Based on the evalu
ation of different materials, the present study shows high possibilities to use practical mathematics educa
tion in the early childhood period. Main examination items were the contents of mathematics in early chi
ldhood, to apply practical mathematics education in the early childhood, validity of contents and teachi
ng methodology. Furthermore, how to connect these educational contents to mathematics education of
the elementary school, especially for the first grade. The result showed that mathematics teaching conte
nts are already systematized from each position of mathematics and psychology. However, the present s
tudy revealed that further, comprehensive practical research in needed. It is necessary to research and f
urther practice the contents of older, but presently still available textbooks and materials to cross-examin
e and challenge those in the ever changing teaching environment in our time.
In this paper, the purpose of research is to try the bringing-up of abduction as mathematical
inference, to develop teaching materials for abduction, to give lessons intended for 6th-year students, and to clarify effects of lessons. So we mentioned deduction, induction, analogy, and abduction.
Abduction is defined the following by Peirce, C. S.. : Abduction is the process of forming an
explanatory hypothesis. As a result of consideration of prior researches and lessons which have
incorporated the idea of abduction on the basis of Zollman's research, we have clarified the
following. (1)We could place abduction in arithmetic education. (2)Lessons of abduction intended
for 6th-year students had effects according to t-test.
Since Euler’s polyhedron theorem included in topology was newly added in the current national courses of study for Mathematics A, we selected twelve topics on topology, and lectured college students that aimed to a teacher about these topics in omnibus form. In this study, we have obtained the result that nine of twelve topics interest many students. Moreover, the results of this lecture show that it is highly probable that students will be interested in topics at the contents of figures with models of polyhedrons and balls, and to give mathematical interpretation for a real phenomenon.