• Research in Mathematical Education
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• v.10 no.2 s.26
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• pp.103-113
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• 2006

The mathematics instructional beliefs of a teacher include the exterior mathematics instructional beliefs and the internal mathematics instructional beliefs. These two kinds of beliefs are formed in two kinds of different situations. The situated theory thinks that beliefs are related with the situations; so, the two kinds of beliefs are showed in the different situations. The internal instructional mathematics beliefs effect on the actual mathematics instruction, they ought to be noticeable.

• Journal of Educational Research in Mathematics
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• v.9 no.2
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• pp.473-491
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• 1999

The learning of mathematics happens in some situations. It is natural that students should learn mathematics in more appropriate situations. But, so far It has been hardly studied about concrete situation and milieu where math can be successfully taught. In today's math education, the situation of education as a external circumstance become realized more and more importantly with influence of open education. But they don't embody situation as an internal circumstance where the intrinsic concept of mathematics can be obtained. We started this thesis from this tried to answer it on the basis of Brousseau's question, have theory about the didactical situations. One of the purpose of this study is to understand the theory of didactical situations, which focuses on how we can elaborate situations which really make a mathematical notion function. In this study, It is attempted clarify some concepts of the theory of didactical situations. The other is to discuss about what the theory of didactical situations suggests us in math zeducation. The method of math teaching and learning and the teacher's role were discussed in the viewpoint of Brousseau's theory. Finally, We elaborated and presented some didactical situations which make the notion of the area of rectangle.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.651-662
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• 1998

Mathematics is means for making sense of one's experiential world and products of human activities. A usefulness of mathematics is derived from this features of mathematics. Keeping the meaning of situations during the mathematizing of situations. However, theories about the development of mathematical concepts have turned mainly to an understanding of invariants. The purpose of this study is to show the possibility of computer in representing situation and phenomena. First, we consider situated cognition theory for looking for the relation between various representation and situation in problem. The mathematical concepts or model involves situations, invariants, representations. Thus, we should involve the meaning of situations and translations among various representations in the process of mathematization. Second, we show how the process of computational mathematization can serve as window on relating situations and representations, among various representations. When using computer software such as ALGEBRA ANIMATION in mathematics classrooms, we identified two benifits First, computer software can reduce the cognitive burden for understanding the translation among various mathematical representations. Further, computer softwares is able to connect mathematical representations and concepts to directly situations or phenomena. We propose the case study for the effect of computer software on practical mathematics classrooms.

• School Mathematics
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• v.1 no.2
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• pp.417-431
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• 1999

In this study, I consider Brousseau's theory of didactical situation focused on 'the development process of situations', and analyze some examples of didactical situation related to instruction of 'decimal' concept. To elaborate situations which really make a mathematical notion function, we have to analyze the essence of the notion, and to construct the situation which can be developed to situations of 'action-formulation-validation - institutionalization'. From this view, it can be said that the instruction of decimal concept in our country mainly lies in the situations of 'action' and 'institutionalization'. we have to provide more situations of 'formulation' and 'institutionalization' which can connect 'action' and 'institutionalization'.

• School Mathematics
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• v.11 no.3
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• pp.479-496
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• 2009

Some children can construct a basic concept of addition and subtraction during the preschool years. Children start to experience mathematics via numbers and their of operations and contact with various contexts of addition and subtraction. In special, word problems reflect mathematics which is appliable to real life. In this paper, I analyse the types of word problems in text book and its students' responses. First, I analyse the types of addition word problems which consist of change add-into situations and part-part-whole situations. Second, I analyse the types of subtraction word problems which consist of change take-away situations, compare situations and equalize situations. Third, I analyse the students' responses by the types of word problems in addition and subtraction. And 115 2nd grade elementary school students participated in this survey. The following results have been drawn from this study. First, the proposition of word problems of part-part-whole situations is higher than that of change add-into situations and the proposition of word problems of take-away situations is higher than that of compare situations and equalize situations. According to the analysis about students' responses, It is no difference between change add-into situations and part-part-whole situations. But the proposition of word problems of take-away situations is higher than that of compare situations and equalize situations. This results from word problems which contain unnecessary information in problem. So, we have to present the various word problems to students.

• Journal of the Korean School Mathematics Society
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• v.4 no.2
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• pp.27-32
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• 2001

The paper describes some principles how we design the mathematics curriculum through mathematical Modelling. since the motivation for modelling is that it give us a cheap and rapid method of answering illposed problem concerning the real world situations. The experiment was focussed on the possibility that they can involved in modelling problem sets and carry modelling process. The main principles could be described as follows. principle 1. we as a teacher should introduce the modelling problems which have many constraints at the begining situation, but later eliminate those constraints possibly. principle 2. we should avoid the modelling real situations which contain the huge data collection in the classroom, but those could be involved in the mathematics club and job oriented problem solving. principle 3. Analysis of modelling situations should be much emphasized in those process of mathematics curriculum principle 4. As a matter of decision, the teachers should have their own activities that do mathematics curriculum free. principle 5. New strategies appropriate in solving modelling problem could be developed, so that these could contain those of polya's heusistics

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.883-898
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• 2013

The purpose of this study is to examine that high school students recognize mathematical situation when they are requested for changing identical mathematics situations into different situations. The results of the study are followings. First, percentage of correct answers to the questions of turning equal mathematical situation into function is higher than the one of turning equal mathematical situation into equation and inequality. As a result of individual interview for comprehensibility of the students on these relations, it is found that if degree goes up and there is different expressions of questionaries although mathematical situation is identical, it affects comprehensibility of the subjects. Second, we found that they cannot understand identical mathematics situations because they have trouble in drawing graph or applying to get the answer while many students understand a point of intersection on the graph as a correct answer. Third, As a result of individual interview for comprehensibility of the students on relation between equation, inequality and function, we found that students manage to get correct answer even without perfect comprehensibility on this relation.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.237-249
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• 1998

Calculators can be instructional instruments to be used specially in problem situations which need calculations through calculators. A calculator-calculations is one of the various calculation methods. As there are problem situations for each method, there are problem situations for a calculator-calculation, too. Basically, calculator-calculations can be admitted in any cases which need not paper-and-pencil calculations, estimations, mental calculations, and computer-calculations. In this paper, some basic knowledges on how to use calculators in elementary mathematics education are offered. Students learn concepts easier by doing complex and tedious calculations through calculators than through paper-and-pencil calculations. And, by doing complex and tedious calculations in problem solving, they can focus on understanding problems, planning, and looking back. Calculator can be used directly in phases of understanding and planning. Calculators can be used to practice guess and check strategies. Problems which contain calculations beyond students' paper-and-pencil calculations abilities. So, as a result, students' experiences on problem solving can be extended. Calculators experiences can affect students' persistences, confidences, enthusiasms, self-esteems positively.

• Research in Mathematical Education
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• v.25 no.2
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• pp.159-164
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• 2022

Critical mathematics education has developed in many directions and has a broad range of approaches. There will probably be many different ways of expressing critical mathematics education. The book, An Invitation to Critical Mathematics Education by Ole Skovsmose (2011) has elucidated critical mathematical education by discussing and reinterpreting its concerns and preoccupations. He reinterprets thoughts and arguments that have been taken for granted and premised in mathematics education, and also discusses unquestioned widespread notions by associating them with his projects or specific practices carried out by him and his colleagues. This review intoduced and examined his crucial notions of critical mathematics education, such as "Diversity of situations," "Students' foreground, Landscapes of investigation," "Mathemacy," and "Uncertainty." These notions will make you to meet his theories with his pratices and look back on something overlooked in mathematics education.

• East Asian mathematical journal
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• v.32 no.4
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• pp.443-464
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• 2016

The purpose of ths study is to compare and analyze the sequence of teaching multiplication facts in the elementary school mathematics. Generally, the multiplication in the elementary school mathematics is composed of the followings; concepts of multiplication, situations involving multiplication, didactical models for multiplication, and multiplication strategies for teaching multiplication facts. This study is focusing to multiplication facts, especially to the sequence of teaching and multiplication strategies. The method of this study is a comparative and analytic method. In order to compare textbooks, we select the Korean elementary mathematics textbooks(1st curriculum~2009 revised curriculum) and the 9 foreign elementary mathematics textbooks(Japan, China, Germany, Finland, Hongkong etc.). As results of comparative investigation, the sequence of teaching multiplication facts is reconsidered on a basis of elementary students' mathematical thinking. And the connectivity of multiplication facts is strengthened in comparison with the foreign elementary mathematics textbooks. Finally multiplication strategies for teaching multiplication facts are discussed for more understanding and reasoning the principles of multiplication facts in the elementary school mathematics.