• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.151-167
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• 2006

The open approach to teaching school mathematics in the United States is an outcome of the collaboration of Japanese and U. S. researchers. We examine the approach by illustrating its three aspects: 1) Open process (there is more than one way to arrive at the solution to a problem; 2) Open-ended problems (a problem can have several of many correct answers), and 3) What the Japanese call 'from problem to problem' or problem formulation (students draw on their own thinking to formulate new problems). Using our understanding of the Japanese open approach to teaching mathematics, we adapt selected methods to teach mathematics more effectively in the United States. Much of this approach is new to U. S. mathematics teachers, in that it has teachers working together in groups on lesson plans, and through a series of discussions and revisions, results in a greatly improved, effective plan. It also has teachers actively observing individual students or groups of students as they work on a problem, and then later comparing and discussing the students' work.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.10a
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• pp.45-62
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• 2006

The open approach to teaching school mathematics in the United States is an outcome of the collaboration of Japanese and U.S. researchers. We examine the approach by illustrating its three aspects: open process (there is more than one way to arrive at the solution to a problem; 2) open-ended problems (a problem can have several of many correct answers), and 3) what the Japanese call 'from problem to problem' or problem formulation (students draw on their own thinking to formulate new problems). Using our understanding of the Japanese open approach to teaching mathematics, we adapt selected methods to teach mathematics more effectively in the United States. Much of this approach is new to U.S. mathematics teachers, in that it has teachers working together in groups on lesson plans, and through a series of discussions and revisions, results in a greatly improved, effective plan. It also has teachers actively observing individual students or groups of students as they work on a problem, and then later comparing and discussing the students' work.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.421-434
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• 2004

Cognitively Guided Instruction (CGI) is one of the most successful professional development programs for elementary mathematics teachers in US. This article introduces its theoretical background, research-based framework of addition and subtraction work, and how the program has been disseminated. Carpenter and Fennema started CGI aiming to develop a professional development program that focused on research knowledge of children"s thinking. Their goal was. to bring a significant change in teaching by helping teachers understand how children think mathematically. This 3-year NSF funded project grew to be 11-year long, and a number of publications have reported consistent successful learning and teaching by CGI students and teachers compared to counterparts throughout US. CGI′s success by focusing on improving teachers′ knowledge of children′s thinking offers possible opportunities for teacher educators to re-conceptualize teacher education in Korea.

• East Asian mathematical journal
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• v.40 no.2
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• pp.209-229
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• 2024

In this study, we design a teaching unit that constructs Pascal graphs and extended Pascal triangles to explore number patterns inherent in them. This teaching unit is designed to consider the diachronic process of teaching-learning by combining Dörfler's theoretical generalization model with Wittmann's design science ideas, which are applied to the didactical practice of mathematization. In the teaching unit, considering the teaching-learning level of prospective teachers who studied discrete mathematics, we generalize the well-known Pascal triangle and its number patterns to extended Pascal triangles which have directed graphs(called Pascal graphs) as geometric models. In this process, the use of symbols and the introduction of variables are exhibited as important means of generalization. It provides practical experiences of mathematization to prospective teachers by going through various steps of the generalization process targeting symbols. This study reflects Wittmann's intention in that well-understood mathematics and the context of the first type of empirical research as structure-genetic didactical analysis are considered in the design of the learning environment.

• The Mathematical Education
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• v.52 no.3
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• pp.319-334
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• 2013

This study is a literature research on critical mathematics education. In this study, we analyzed the literature about critical theory and critical education, especially focused on Freire's educational works. And also, we reviewed studies and lesson examples about critical mathematics education. The purpose of this research is to improve understanding about critical mathematics education. We found the connection between the goals, teaching methods and contents of critical mathematics education and Freire's theory of critical pedagogy. Critical mathematics lessons stimulated student's sense of social agency and induced student's inquiry. Critical mathematics education has a merit on aspect of mathematical connection and communication by adopting social issues and student's discussion in mathematics lessons. Although there are many obstacles to overcome, critical mathematics education is one of the educational direction to seek.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.419-444
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• 2005

As a theoretical background for this research, the literatures which focus on teaching and loaming of connecting with mathematics and science were investigated. And the rationale of integrated curriculum on the basis of the 7th mathematics curriculum and the goal of mathematics education and the forms of integrated curriculum and the integrated curriculum in foreign school were investigated. Depending on this review, the implement method of the integrated curriculum of mathematics and science in Korea school is suggested as the following: It requires designing inter-disciplinary into-grated problem or various teaching and learning materials which are based upon concept, skill, and principle by commonality found across the subject matter. Based on the analyses upon described above, three inter-disciplinary integrated teaching and learning materials were developed. And then, based on the case stud)', the research questions were analyzed in depth. Students could understand the developing process of linear function, develop the formula and grape representing the relationship between time and velocity, time and distance, and interpret realistic meaning of the slope.

• Journal of Elementary Mathematics Education in Korea
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• v.10 no.1
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• pp.1-19
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• 2006

It is generally accepted that fostering creative thinking is a core in mathematics education and accumulating research products on that topic is really needed. In this study, I hoped to investigate and verify that in mathematics education it was possible to cultivate creative thinking through various and divergent activities, For this purpose, I delat with some illustrations, in which students learned mathematics through the operational activities using teaching tools, problem solving and problem posing activities, and finally they seemed to foster creative mathematical thinking. In conclusion of this paper, I have suggested that in math education those activities should be used to cultivate students' creative thinking in kindergarten or early elementary school. Also I asserted that it is urgently need to store up research products about various materials and methods for those mathematics teaching and learning.

• Journal of the Korean School Mathematics Society
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• v.4 no.2
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• pp.103-113
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• 2001

The teaching-learning method utilizing Web makes it possible for the students take the initiative in any field and offers the teaching strategy, methodology and teaching-learning materials suitable for students' ability and standard. The purpose of this study is to investigate the characteristics of WBI in mathematics class for the effective teaching and learning focusing on the unit 'Function' in the 1st grade of middle school and verify its effectiveness by developing the WBI programs which can progress learning achievement and applying them to math class. Two hypotheses were established for this study. Hypothesis 1 : There will be meaningful difference between the group that studies under WBI and the one that doesn't, Hypothesis 2 : There will be meaningful difference in the attitude and interest toward learning between the group that studies under WBI and the one that doesn't. In order to find out the result, I have made a comparative analysis through t-verification on the object of two classes of the 1st grade in P middle school that I have been working for. The result shows that the class utilizing WBI is more effective than the traditional lecture-oriented class since there is a meaningful difference between the control group and experimental one and also that the class based on WEB has a great influence on students' interest and positive attitude toward math class.

• Journal of the Korean School Mathematics Society
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• v.8 no.2
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• pp.167-181
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• 2005

Statistics is based on a data, therefore a practical use of suitable data is important in teaching statistics. But, most teachers feel always that there is seldom data that students can understand easily. In this study, we presented a teaching method of statistics education that can elevate student's participation and interest in their statistics class using a web-based data collection program and MS Excel software. Also, the presented teaching method may apply extending to various part of statistics education.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.641-654
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• 2011

In order to grow students' rational and creative problem-solving ability which is one of the primary goals in mathematics education. students' proper understanding of mathematical concepts, principles, and rules must be backed up as its foundational basis. For the relevant teaching strategies. National Mathematics Curriculum advises that students should be allowed to discover and justify the concepts, principles, and rules by themselves not only through the concrete hands-on activities but also through inquiry-based activities based on the learning topics experienced from the diverse phenomena in their surroundings. Hereby, this paper, firstly, looks into both the meaning and the inductive reasoning process of mathematical principles and rules, secondly, suggest "learning through discovery teaching method" for the proper teaching of the mathematical principles and rules recommended by the National Curriculum, and, thirdly, examines the possible discovery-led teaching strategies using inductive methods with the related matters to be attended to.