• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.329-349
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• 2003

Mathematics education is accomplished by systems such as mathematical curriculum and tools such as a textbook which reflects such systems. Human beings make such systems and tools. Therefore, a viewpoint of mathematics of those who make them is an important factor. The view point of mathematics is formed during doing and learning mathematics, but the already formed viewpoint of mathematics affects doing and teaching mathematics. Hence, it will be a factor which affects basically that those who employ themselves on mathematics education have a certain viewpoint of mathematics. This article presents dialectical materialistic viewpoint as the viewpoint of mathematics which affects fundamentally on mathematical teaching-learning practice. The dialectical materialism is carried through the process and result of mathematics development. This shows that mathematical knowledge is objective. Mathematical knowledge has developed according to three basic rules of dialectical materialism i.e. the transformation of quantity into quality, the unification of antagonistic objects, and the negation of negation. This viewpoint of mathematics should offer the viewpoint of mathematics education which is different from the view point of absolutism, relativism or formal logic. In this article I considered mathematics separating standpoint of mathematics into materialistic viewpoint and dialectical viewpoint. 1 did so for the convenience of analysis, but you will be able to look at the unified viewpoint of dialectical materialism. 1 will make mention of teaching-learning method on another occasion.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.19-30
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• 2016

This study examined pre-service teachers' pedagogical content knowledge of fraction division in a context where they were asked to write a story problem for a symbolic expression illustrating a whole number divided by a proper fraction. Problem-posing is an important instructional strategy with the potential to create meaningful contexts for learning mathematical concepts, especially when real-world applications are intended. In this study, story problems written by 135 elementary pre-service teachers were analyzed with respect to mathematical correctness. error types, and division models. Patterns and tendencies in elementary pre-service teachers' knowledge of fraction division were identified. Implicaitons for teaching and teacher education are discussed.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.843-863
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• 2010

The basic purpose of 2007 revision curriculum is content of activity oriented, management of differentiated instruction, communication, introduction of story mathematics, mathematical exploration and problem solving ability and so on. In this paper, we investigate some characteristics of number teaching in the primary school of New Zealand. Especially, focused on materials and methods and so on. So we've got the following results. First, there are no fundamental differences in materials and methods in teaching number between Korea and New Zealand but in New Zealand there are no national textbook like us so there is a possibility not to teach number systematically like our Korea. On the contrary, they divide number region from one to six level and are offering achievement objects, suggestive learning experiences, sample assessment activities for each level and also they do not guide activities itself in detail like us and so have learners themselves think about the given problems. Second, there is a strategy stage in getting knowledge about number in New Zealand and so children can take advantage of this steps according to the type of problems. Third, it must be developed some materials and idea to reach the learning purpose rousing interest of children.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.183-197
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• 2012

Geometry having long history of mathematics have important role for thinking power and creativity progress in middle school. The regular polygon included in plane geometry was mainly taught convex regular polygon in elementary school and middle school. In this study, we investigated the denotation's extension of regular polygon by mathematical basic knowledge included in school curriculum. For this research, first, school mathematical knowledge about regular polygon was analyzed. And then, basic direction of research was established for inquiry. Second, based on this analysis inductive inquiry activity was performed with research using geometry software(Cabri Geometry II). Through this study the development of enriched learning material and showing the direction of geometry research is expected.

• Research in Mathematical Education
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• v.22 no.4
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• pp.261-282
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• 2019

The research related to testing pupils' achievement in the field of Measurement and Measure in initial teaching of geometry points to an insufficient adoption of the basic components of the length measurement concept among pupils. In order to discover the cause, we looked at the basic components on which the procedure of measuring length using a ruler is based, highlighted the possibilities of introducing the procedure in measuring length, and determined pupils' achievement during the procedure of measuring length using a ruler. The research sample consisted of 145 pupils, out of which 72 were the 2^nd grade pupils and 73 were the 4^th grade pupils. A descriptive method was applied in the research. The technique we used was testing, and for the statistical data processing we used a χ² test. The results of the research show that, when drawing a straight line of a given length using a ruler, there is no statistical difference in achievement between the 2^nd and 4^th grade pupils, nor in the pupils' knowledge regarding drawing a ruler independently, while drawing a straight line of a given length using a "broken" ruler 4^th grade pupils are statistically better. The results of the research indicate that pupils' achievement is better in doing standard tasks than in non-standard ones, given that the latter require conceptual knowledge. The components of the concept of length measurement using ruler have not been sufficiently developed yet, and these include: zero-point, partitioning a measured object in a series of consecutive measurement units and their iteration. We shed more light on the critical stage in the procedure of length measurement - the transition from non-standard to standard units and the formation of the length measurement scale. For further research, we propose to look at the formation of the concept of length measurement using the ruler through all its components and their inclusion in the mathematics curriculum, as well as examining the correlation of pupils' achievement in the procedure of measuring length with their achievement in measuring area (and volume).

• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.223-237
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• 2008

In this paper, We focus on grasping De Morgan's perspectives on mathematics education systematically. His perspectives can be summarized as followings. First, historico-genesis of mathematics must be considered in the teaching and learning of mathematics. Second, mathematical conception of students must be formulated progressively. Third, it is important to use errors which come out continually in the process of passing from inductive stage to deductive stage. Fourth, personal knowledge of students is important in the teaching and learning of mathematics. These De Morgan's four perspectives are the way of approach for experiencing moral certainty first of all to get to mathematical certainty. Moral certainty which he presented is a combination of rationality and humanity to fill up gaps between Platonism and general public education.

• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.

• The Mathematical Education
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• v.60 no.3
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• pp.265-279
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• 2021

In this study, by analyzing of types and functions of questions presented in Data and Chance area of the mathematics textbooks for grades 1-6 of the 2015 revised curriculum, the characteristics of the questions presented in the textbook were identified, and implications for teaching and learning related to the questions in this textbook were obtained. Types and functions of the presented questions showed different proportions of appearance according to the grade clusters, and this seems to be related to the learning contents for each grade clusters and the characteristics of grade clusters. In addition, it can be seen that the functions of questions are related to the types of questions. Teachers should have pedagogical content knowledge about Data and Chance area as well as developmental characteristics for each grade clusters. In addition, the teacher should present an suitable question for the level of grade clusters and the nature of the content to be taught so that effective learning can be achieved based on the understanding of the characteristics and functional characteristics of each type of questions. The results of this study can contribute to statistical teaching in a progressive direction by providing a foundation for textbook writing and teaching/learning.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.107-134
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• 2012

The purpose of this study is to investigate the effectiveness of two teaching methods of word problems, one based on mathematical modeling learning(ML) and the other on traditional learning(TL). Additionally, the influence of mathematical modeling learning in word problem solving behavior, application ability of real world experiences in word problem solving and the beliefs of word problem solving will be examined. The results of this study were as follows: First, as to word problem solving behavior, there was a significant difference between the two groups. This mean that the ML was effective for word problem solving behavior. Second, all of the students in the ML group and the TL group had a strong tendency to exclude real world knowledge and sense-making when solving word problems during the pre-test. but A significant difference appeared between the two groups during post-test. classroom culture improvement efforts. Third, mathematical modeling learning(ML) was effective for improvement of traditional beliefs about word problems. Fourth, mathematical modeling learning(ML) exerted more influence on mathematically strong and average students and a positive effect to mathematically weak students. High and average-level students tended to benefit from mathematical modeling learning(ML) more than their low-level peers. This difference was caused by less involvement from low-level students in group assignments and whole-class discussions. While using the mathematical modeling learning method, elementary students were able to build various models about problem situations, justify, and elaborate models by discussions and comparisons from each other. This proves that elementary students could participate in mathematical modeling activities via word problems, it results form the use of more authentic tasks, small group activities and whole-class discussions, exclusion of teacher's direct intervention, and classroom culture improvement efforts. The conclusions drawn from the results obtained in this study are as follows: First, mathematical modeling learning(ML) can become an effective method, guiding word problem solving behavior from the direct translation approach(DTA) based on numbers and key words without understanding about problem situations to the meaningful based approach(MBA) building rich models for problem situations. Second, mathematical modeling learning(ML) will contribute attitudes considering real world situations in solving word problems. Mathematical modeling activities for word problems can help elementary students to understand relations between word problems and the real world. It will be also help them to develop the ability to look at the real world mathematically. Third, mathematical modeling learning(ML) will contribute to the development of positive beliefs for mathematics and word problem solving. Word problem teaching focused on just mathematical operations can't develop proper beliefs for mathematics and word problem solving. Mathematical modeling learning(ML) for word problems provide elementary students the opportunity to understand the real world mathematically, and it increases students' modeling abilities. Futhermore, it is a very useful method of reforming the current problems of word problem teaching and learning. Therefore, word problems in school mathematics should be replaced by more authentic ones and modeling activities should be introduced early in elementary school eduction, which would help change the perceptions about word problem teaching.

• School Mathematics
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• v.16 no.1
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• pp.111-133
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• 2014

This study aims to explore mathematical belief system and core belief factors to be found. The mathematical belief system becomes an auto regulation device for students' using mathematical knowledge in mathematical situations and provides them with the context to perceive and understand mathematics. They have individual mathematical beliefs for each of mathematics subject, mathematical problem solving, mathematical teaching and learning and self-concept, and these beliefs of students construct mathematical belief system according to mutual relationships among the mathematical beliefs. Using correlation analysis and multiple regression, mathematical belief system was structuralized and core belief factors were found. Mathematical belief system is structuralized and, as a result the core belief factors that are psychological centrality of high school students' mathematical belief system are found to be persistence, challenge, confidence and enjoyment. These core belief factors are formed on the basis of personal experiences and they are personal primitive beliefs that cannot be changed with ease and cannot be shared with other people but they are related with many other beliefs influencing them.