• The Mathematical Education
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• v.51 no.1
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• pp.47-61
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• 2012

Students can infer mathematical principles in a very natural way by connecting mutual relations between mathematical fields. These process can be revealed by taking tasks that can derive mathematical connections. The task of this study is to make expression and design it and derive mathematical principles from the design. This study classifies the mathematical field of expression for design and analyzes mathematical thinking process by connecting mathematical fields. To complete this study, 40 gifted students from 5 to 8 grade were divided into two classes and given 4 hours of instruction. This study analyzes their personal worksheets and e-mail interview. The students make expressions using a functional formula, remainder and figure. While investing mathematical principles, they generalized design by mathematical guesses, generalized principles by inference and accurized concept and design rules. This study proposes the class that can give the chance to infer mathematical principles by connecting mathematical fields by designing.

• School Mathematics
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• v.15 no.1
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• pp.201-219
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• 2013

The purpose of this study was to analyse the belief about mathematics teaching of elementary preservice teachers and mathematics teachers. This study involved 100 respondents from the preservice teachers and 114 respondents from the mathematics teachers. The instruments used in this study consist 15 items of mathematical knowledges and 19 items of mathematical activities. The finding showed that preservice teachers emphasized the conceptual knowledge, whereas mathematics teachers emphasized the procedural knowledge in the mathematical knowledges. And preservice teachers emphasized the knowledge representation, knowledge generation, knowledge deliberation, knowledge communication, whereas mathematics teachers emphasized the use of knowledge(syntax) in the mathematical activities. Finally, even though two groups showed the significant difference in some items, preservice teachers and mathematics teachers emphasized the various mathematical knowledges and mathematical activities.

• Communications of Mathematical Education
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• v.38 no.1
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• pp.69-92
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• 2024

This study analyzed students' mathematical noticing in high school sequence classes based on students' two perceptions of sequence. Specifically, mathematical noticing was analyzed in four aspects: center of focus, focusing interaction, task features, and nature of mathematics activities, and the following results were obtained. First of all, the change pattern of central of focus could not be uniquely described by any one component among 'focusing interaction', 'task features', and 'the nature of mathematical activities'. Next, the interactions between the components of mathematical noticing were identified, and the teacher's individual feedback during small group activities influenced the formation of the center of focus. Finally, students showed two different modes of reasoning even within the same classroom, that is, focusing interaction, task features, and nature of mathematics activities that resulted in the same focus. It is hoped that this study will serve as a catalyst for more active research on students' understanding of sequence.

• East Asian mathematical journal
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• v.31 no.4
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• pp.569-585
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• 2015

Many mathematics teachers in characterization high schools have been troubled to teach students because most of the students have weak interests in mathematics and they are also lack of preliminary mathematical knowledges. Currently many of mathematics teachers in such schools teach students using worksheets owing to the situation that proper textbooks for the students are not available. In this study, we referred to Chevallard's didactic transposition theory based on Brousseau's theory of didactical situations for mathematical teaching and learning. Our lessons utilizing worksheets necessarily entail encouragement of students' self-directed activities, active interactions, and checking the degree of accomplishment of the goal for each class. Through this study, we recognized that the elaborate worksheets considering students' level, follow-up auxiliary materials that help students learn new mathematical notions through simple repetition if necessary, continuous interactions in class, and students' mathematical activities in realistic situations were all very important factors for effective mathematical teaching and learning.

• 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.15 no.1
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• pp.57-75
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• 2011

This research aimed to explore the effects of collaborative writing activities in a mathematical context, specifically pertaining to areas such as numbers and operation, geometrical figure, and measurement in Mathematics: Level 5-b, on their mathematical achievement gain and disposition among Grade 5 students. To do this, out of a total of 62 students selected from two Grade 5 classes of J Elementary School in Dalseo-gu, Daegu City, who were found to be homogenic from the tests of math performance and dispositions, an experimental group(n=31) was designed and compared to a control group (n=31). Over a six week period from October to November in 2009, the experimental group was given collaborative writing lessons in math classes while the control group was given teacher-oriented regular lessons. The results were as follows. First, there was more or less considerable, though not significant, difference in overall mathematical achievement in the students experiencing collaborative writing activities when compared with the students in the control group. However, in terms of numbers and operation, a sub-category of mathematics, there was significant difference between the two groups. Second, the students experiencing collaborative writing activities were more positively affected in all sub-categories of mathematical disposition: confidence, flexibility, determination, curiosity, reflection, and value, than those in the control group. In summing up, the exposure of collaborative writing activities to mathematics learning was found to help students not only to have a concrete and proper grasp of the relevant problem solving process, which was observed from their mathematical achievement gain especially in the sphere of numbers and operation, but also to have their mathematical disposition set towards more positive direction, which was seen in all sub-categories of mathematical disposition measurement.

• Korean Journal of Childcare and Education
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• v.15 no.3
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• pp.83-113
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• 2019

Objective: This study aimed to develop and apply the home connection program for promoting the mathematical interaction of parents of 3-year-olds. Methods: We surveyed questionnaires for 36 parents and interviewed 3 parents of 3-year-olds for the development of the program. Twenty-one 3-year-olds were selected as participants in the program. Quantitative data from a checklist for parent's mathematical interaction were analyzed using repeated measures ANOVA. Qualitative data from self-evaluation of teachers and parents were categorized and analyzed in terms of meaning. Results: Based on the home connection program, the session were provided in the following order [educare center activities ${\rightarrow}$ home-linked activities ${\rightarrow}$ home+educare integrated activities] and in each session, the three-step course [sharing of thinking ${\rightarrow}$ gathering of thinking ${\rightarrow}$ broadening of thinking] was applied. Implementation of this program led to promoting parental mathematical interaction. Conclusion/Implications: This study will lead to follow-up studies that reveal positive effects of our program.

• The Mathematical Education
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• v.58 no.4
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• pp.545-566
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• 2019

The purpose of this study is to show that research community activities can contribute to the professional development in respect of average concepts and mathematical creativity. In the community, activities were undertaken to transform the existing task into the task that contributes to the manifestation of creativity. In this process, researchers tried to connect the theory with the practice of the class, and the teacher acted as an active learner. The findings show that the teacher who had difficulty in teaching average could overcome difficulties, and also derived the way of task modification and strategies necessary for teaching average. The modified task induced improvements in students' achievement levels, which led to change in teachers' perspective on the relationship between mathematical creativity and learning. Research community activities have been shown to have contributed to improvements with regard to both teaching the average and promoting mathematical creativity.

• The Mathematical Education
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• v.50 no.2
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• pp.165-184
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• 2011

The purpose of this study is to detect the possibility of the development of conception of a graph and the formula with the absolute value through context questions, and also to investigate the effectiveness of the each step of the mathematical modeling activities in helping students to have the conception. The research was conducted to analyze the process of development of the mathematical conception by applying the mathematical modeling activities two times to subjects of two academic high school students in the first grade. The results of the study are as follows: Firstly, the subjects were able to comprehend the geometric conception of the absolute value and to make the graph and the formula with the sign of the absolute value by utilizing the condition of the question. Secondly, the researcher set five steps of the intentional mathematical model in order to arouse the effective mathematical notion and each step performed a role in guiding the subjects through the mathematical thinking process in consecutive order; consequently, it was efficacious in developing the conception.

• Research in Mathematical Education
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• v.17 no.1
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• pp.1-14
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• 2013

Stochastic phenomena induce us to construct a probability model and structure our thinking; corresponding models help us to understand and interpret the reality. They in turn equip us with tools to recognize, reconstruct and solve problems. Therefore, various implications in terms of methodology as well as epistemology naturally flow from different adoptions of models for probability. Right from the basic scenarios of different perspectives to explore reality, students are occasionally exposed to misunderstanding and misinterpretations. With realistic examples a multi-faceted image of probability and different interpretation will be considered in mathematical modelling activities. As an exploratory investigation, mathematical modelling activity for probability learning was elaborated through semiotic analysis. Especially, the coherence structure in mathematical modelling discourse was reviewed form a semiotic perspective. The discourses sampled from group activities were analyzed on the basis of semiotic perspectives taxonomical coherence relations.