• East Asian mathematical journal
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• v.28 no.4
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• pp.353-361
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• 2012

In this paper, we apply mathematising activities to geometry contents of corrent in middle and high school in order to actualize learning and teaching through Freudenthal's, Piaget's, and Van Hieles's mathematising among many theories affecting teaching and learning methods. Learners find out mathematical idea through the activities of mathematising that interprete mathematical problemm. And we derive mathematic through the experience of vertical mathematising that expresses it. Based on it, Freudenthal's progressive mathematising process, etc are used in doing the activities of applicative mathematising.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.323-345
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• 2015

This study is intended to establish and apply a program created with RME for mathematising instruction and learning and identify how it influences on the mathematical thinking process in the field. In order to deal with this study inquiries, related theories have been analyzed establishing a program for mathematising instruction and learning method based on a model of them and RME theory principles and re-organizing education courses for instruction on the fields concerned. Study subjects were limited to two classes consisting of fifth graders in S elementary school located in the city of Daegu and divided them in an experiment group and a control group. An experiment group was given a mathematising learning method applied with RME, while a control group had a class with regular methods of learning and instruction during the period of experiment. As a summary of aforementioned results of the study, mathematising learning method applied with RME had an effect on improving mathematical thinking ability for students and also on promoting mathematising outcome through a repetitive experience in each procedure obtained on a regular basis.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.345-365
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• 2006

This study, to effectively teach the concepts, principles and problem solving ability of the 2nd graders' learning of numbers and operations, offers realistic problem situation and focuses on the learning based on 'mathematization', one of the most important principles of RME (Realistic Mathematics Education) which is the mathematics education trend of Netherlands influenced by Freudenthal's theory. The instruction is applied to forty-one students of the 2nd grader for six weeks in twelve series in an elementary school, located in Seoul. To investigate the effects of the mathematising experience instruction for improving mathematical abilities, the group takes tests before and after the instruction. Also the qualitative analysis on the students' mathematising aspects through students' output at the instruction process is taken into account to evaluate the instruction's effects. The result shows that the mathematising experience instruction for improving mathematical abilities is proved to improve students' understanding of mathematical concepts and principles and their problem solving ability in learning numbers and operations after carrying out this instruction. Also the result indicates that students' mathematising aspects are mostly horizontal and vertical mathematization.

• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.57-75
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• 2003

The goal of this paper is to offer material which make mathematising Fruedenthal(1991) proposed be experienced through the process of teaching and learning mathematics. In this paper, the number of unit squares a diagonal passes through for an m$\times$n lattice rectangle is studied and its generalization is discussed. Through this discussion, the adaptability of this material Is analysed. Especially, beyond inductional conjecture, the number of unit squares is studied by more complete way, and generalization in 3-dimension and 4-dimension are tried. In school mathematics, it is enough to generalize in 3-dimension. This material is basically appropriate for teaching and learning mathematising in math classroom. In studying the number of unit squares and unit cubes, some kinds of mathematising are accompanied. Enough time are allowed for students to study unit squares and unit cubes to make them experience mathematising really. To do so, it is desirable to give students that problem as a task, and make them challenge that problem for enough long time by their own ways. This material can be connected to advanced mathematics naturally in that it is possible to generalize this problem in n-dimension. So, it is appropriate for making in-service mathematics teachers realize them as a real material connecting school mathematics and advanced mathematics.

• School Mathematics
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• v.4 no.2
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• pp.261-282
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• 2002

This study intended to search for the way of NIE use as follows: 1) Setting up theoretical base about the way of NIE use to math loaming in primary school. 2) Analyzing the course mathematising through NIE use in math learning in practice. 3) Searching for the way of NIE use to aim at mathematising. As the result, this presented NIE model for mathematising according to the character of each step of the mathematising course. This paper says two things : The first, the way for using learning materials as reonstructing articles of newspapers to teach math learning 1) is searched for each information, scrapped to materialize. 2)is to extract the contents of NIE teaming available to the field and the unit of math curriculum. 3) searches for and applies the model for math NIE teaming. 4) makes up learning materials for each level using articles and presents the matters of deepening and supplement suitable for students. The second, the way for teaching math NIE with a view to helping students' mathematising during the course of teachers' math teaming. 1) reconstructs materials chosen by students' reality. 2) should offer students' communication and abundant context materials which mathematical model is possible. 3)needs to guide students to have motivation teaming so that they can mathematise their real matters by rediscovery 4) progresses mathematical activity using newspapers so that they can apply to new reality by applying informed Idea.

• School Mathematics
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• v.8 no.2
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• pp.161-176
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• 2006

Some adequate programs for mathematising are necessary to pre-service mathematics teachers, if they can guide their prospective students in secondary school to make a mathematising. They should be used to mathematising. In this paper, mathematising teaching units for the inquiry into number partition models with constant differences are designed for this purpose. They guide a series of process to make nooumenon for organizing phainomenon which is organized already through number partition model. Especially the new nooumenon and the process of obtaining it are discussed. But it is restricted when the numbers for partitioning are natural numbers, and elements and their differences are integers. Through these teaching units, pre-service mathematics teachers can experience and practice secondary mathematising, as they go through the procedures which are similar with those of mathematicians making theorems.

• School Mathematics
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• v.8 no.3
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• pp.327-339
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• 2006

In this study, a teaching units for teaching and learning of secondary preservice teachers' mathematising is designed, focusing on reinvention of Bretschneider's formula. preservice teachers can obtain the following through this teaching units. First, preservice teachers can experience mathematising which invent a noumenon which organize a phenomenon, They can make an experience to invent Bretscheider's formula as if they invent mathematics really. Second, preservice teachers can understand one of the mechanisms of mathematics knowledge invention. As they reinvent Brahmagupta's formula and Bretschneider's formula, they understand a mechanism that new knowledge is invented Iron already known knowledge by analogy. Third, preservice teachers can understand connection between school mathematics and academic mathematics. They can understand how the school mathematics can connect academic mathematics, through the relation between the school mathematics like formulas for calculating areas of rectangle, square, rhombus, parallelogram, trapezoid and Heron's formula, and academic mathematics like Brahmagupta's formula and Bretschneider's formula.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.2
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• pp.99-115
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• 2007

The purpose of this study was to look into whether this mathematising learning utilizing realistic context has an effect on the mathematical thinking. To solve the above problem, two 5th grade classes of D Elementary School in Seoul were selected for performing necessary experiments with one class designated as an experimental group and the other class as a comparative group. Throughout 17 times for six weeks, the comparative group was educated with general mathematics learning by mathematics and "mathematics practices," while the experimental group was taught mainly with mathematising learning using realistic context. As a result, to start with, in case of the experimental group that conducted the mathematising learning utilizing realistic coherence, in the analogical and developmental thoughts which are mathematical thoughts related to the methods of mathematics, in the thinking of expression and the one of basic character which are mathematical thoughts related to the contents of mathematics, and in the thinking of operation, the average points were improved more than the comparative group, also having statistically significant differences. The study suggested that it is necessary to conduct subsequent studies that can verify by expanding to each grade, sex and region, develop teaching methods suitably to the other content domains and purposes of figures, and demonstrate the effects. In addition to those, evaluation tools which can evaluate the mathematical thinking processes of children appropriately and in more diversified methods will have to be developed. Furthermore, in order to maximize mathematising for each group in each mathematising process, it would be necessary to make efforts for further developing realistic problem situations, works and work sheets, which are adequate to the characteristics of the upper and lower groups.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.69-96
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• 2008

The purpose of this paper is to perceive the problems of current geometry education in the middle school mathematics, to develop some learning materials fitted for the mathematising activities based on Freudenthal's learning theories and to analyze the mathematising process followed by teaching-learning activities. For this purpose, we design activity-oriented learning materials for geometry based on Freudenthal's learning theories, and appropriate teaching-learning models are established for the middle school geometry at the 8-NA stage level according to the theory of van Hiele's geometry learning steps. After applied to the practical lessons, the effects of mathematical activities are analyzed.

• Journal of the Korean School Mathematics Society
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• v.9 no.1
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• pp.57-76
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• 2006

In this paper, we generalized number partion problems in elementary situations to number partition models that provide some mathematical problem situations for experiencing mathematising of secondary pre-service teachers. We designed substantial teaching units entitled 'the inquiry intof number partition models' through 4 steps: (1) key problems, (2) integration from the view of partition, (3) defining partition (4) a real practice of inquiry into models. This teaching unit can contribute to secondary pre-service teacher education as follows: first, This teaching unit have pre-service teachers experience mathemtising. second, This teaching unit have pre-service teachers see the connection between school mathematics and academic mathematics. third, This teaching unit have pre-service teachers foster their mathematical creativity.