• Journal of Elementary Mathematics Education in Korea
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• v.1 no.1
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• pp.99-108
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• 1997

A great amount of research and reform has teen done in education, but not much about education has been improved. Much of the research and debate has stemmed from the attempt at making education a science. But, in most of this research, a very important factor has been left out - the individual, Techniques and procedures that are used by scientists on animals in controlled situations in laboratory setting can not be used effectively on humans. Therefore, we must team from our past, decide what we want from education - from the student and the teacher, match our methods with our goals, and look towards the future, while always keeping in mind-the human factor.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.453-472
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• 2009

This article describes the interview data with two preservice teachers where they dealt with five water-filling problems for the investigation of their covariational thinking. The study's results revealed that two students developed their covariation levels from Direction level to Instantaneous Rate with an aid of the pre-constructed GSP simulations for the problem situations. However, this study also points out that there is a missing important feature for a function notion, 'causality' in the covariation framework and suggests that future research should combine students' conception of causality with their covariational thinking for the investigation of their development of a function concept.

• School Mathematics
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• v.9 no.4
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• pp.467-486
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• 2007

In mathematical modeling activity modeling process is usually an iterative process. When model can not be solved, the model needs to be simplified by treating some variables as constants, or by ignoring some variables. On the other hand, when the results from the model are not precise enough, the model needs to be refined by considering additional conditions. In this study we investigate the role of spreadsheet model in model refinement and modeling process. In detail, we observed that by using spreadsheet model students can solve model which can not be solved in paper-pencil environment. And so they need not go back to model simplification process but continue model refinement. By transforming mathematical model to spreadsheet model, the students can predict or explain the real word situations directly without passing the mathematical conclusions step in modeling process.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.657-677
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• 2014

The present qualitative case study explored the ways in which three middle school students constructed and refined their mathematical models and modeling processes, and factors that had influenced such refinement. The results suggest that students' modeling processes are non-sequential in that the participant students reformulated their initial problem from the real-world problem situation and revised the model when they could not get a satisfactory solution or the acquired solution did not make sense. Moreover, the students' model refinement processes were affected by the following four elements: the types of real-word problem situations, students' metacognitive thinking, communications between teachers and peers, and the role of teachers.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.927-941
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• 2013

In this paper, we investigate and analysis high school students' generalization of cosine rule using analogy, and we study teaching and learning methods improving students' analogical thinking ability to improve mathematical thinking process. When students can reproduce what they have learned through inductive reasoning process or analogical thinking process and when they can justify their own mathematical knowledge through logical inference or deductive reasoning process, they can truly internalize what they learn and have an ability to use it in various situations.

• The Mathematical Education
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• v.47 no.2
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• pp.113-133
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• 2008

This study is to develop the methods of specifying teaching that can consider individual differences in middle school geometry education. The purpose of this study is to decide the variations causing individual differences and to find the proper learning methods considering the variations. Through literature review, this study made it clear that the matter of individual difference is just the matter of talent and examined what factors make up mathematical talents. On the basis of the result, five important variations and fourteen subordinate factors were determined. I researched into the learning methods that consider the determined subordinate factors using the 'congruence' unit of middle school textbooks and developed specific learning methods for each of the subordinate factors through specific congruence problem solving situations. This study can be summarized as follows : I researched the studies of mathematical ability conducted by several educators and psychologists. This research is divided into the early study and the developed study of mathematical ability. Through this study five specific variations were determined. And fourteen subordinate factors have been made from the determined variations. The specific learning methods based on individual differences was developed according to the fourteen subordinate factors on the basis of middle school textbooks of Korea, Gusev's textbook, problem books of Russia, and etc.

• School Mathematics
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• v.11 no.3
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• pp.351-368
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• 2009

This study presents data from a year-long teaching experiment which illustrate how two seventh graders modified their multiplicative thinking and interacted with their representing symbols in the context of combinatorial problem situations. Damon was at the process of construction of recursively multiplicative thinking by modifying his multiplicative reasoning, but Carol appeared to remain at the stage of a binary multiplicative scheme. The two students' struggles with their representing symbols or represented symbols by the teacher show that even well-organized symbolic systems from teachers' perspective do not necessarily help students advance their mathematical capacity.

• Journal for History of Mathematics
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• v.30 no.6
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• pp.341-351
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• 2017

In the 21st century, the era of artificial intelligence, it is demanded to make a change of the paradigm of education by the recent impact of the 4th industrial revolution. The education up to now has emphasized knowledge, meanwhile the human resources for the future are required to be armed with four C's: critical thinking, creativity, communication and collaboration capability, rather than being equipped with just knowledge. That is because the future society demands such abilities, especially the creativity of each individual. At this point, we are asked to consider the aim of education and teaching methods. In school education, students are to be respected and considered able to develop their potentials by themselves. They shouldn't be estimated by tests in the process of learning as they are now. We reconsider the aim of education here by taking a look at Whitehead's opinions and the present educational situations.

• School Mathematics
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• v.5 no.3
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• pp.343-360
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• 2003

In this paper, we deal with the teaching of algebra based on patterns and generalization. The past algebra curriculum starts with letters(variables), algebraic expressions, and equations, but these formal approaching method has many difficulties in the school algebra. Therefore we insist the new algebraic approaches should be needed. In order to develop these instructions, we firstly investigate the relationship of patterns and algebra, the relationship of generalization and algebra, the steps of generalization from patterns and levels of difficulties. Next we look into the algebra instructions based arithmetic patterns, visual patterns and functional situations. We expect that these approaches help students learn algebra when they begin school algebra.

• The Mathematical Education
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• v.52 no.1
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• pp.43-63
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• 2013

The purpose of this study is to find meaningful implications for developing curriculum and textbooks by comparison between Korean middle school mathematics textbooks and U.S.A.'s CMP textbooks. After comparing and analysing how the contents are composed focusing on the equations and functions and how the contents are presented according to 'Project 2061' mathematical textbook analytical framework, and how the contents ere different in terms of the mathematical connectivity, the research reached the following conclusions. First, compared to Korean textbooks, the CMP textbooks clearly present learners' behavior goals in a detailed way, and emphasize communication and connectivity. Second, Korean textbooks focus on explaining concepts and solving problems related to their concepts and discussion questions are briefly introduced. But all the textbooks contain a lot of problems required to be solved with algorithms. On the other hand, CMP textbooks provide students with opportunities to find the necessary concepts on their own, through problem solving processes, after presenting various real-life problem situations.