• The Mathematical Education
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• v.62 no.1
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• pp.57-78
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• 2023

Students' engagement in lessons not only determines the direction and result of the lessons, but also affects academic achievement and continuity of follow-up learning. In order to provide implications related to teaching strategies for encouraging students' engagement in elementary mathematics lessons, this study implemented lessons for middle-low achieving fifth graders using open-ended tasks and analyzed characteristics of students' engagement in the light of the framework descripors developed based on previous research. As a result of the analysis, the students showed behavioral engagement in voluntarily answering teacher's questions or enduring difficulties and performing tasks until the end, emotional engagement in actively expressing their pleasure by clapping, standing up and the feelings with regard to the topics of lessons and the tasks, cognitive engagement in using real-life examples or their prior knowledge to solve the tasks, and social engagement in helping friends, telling their ideas to others and asking for friends' opinions to create collaborative ideas. This result suggested that lessons using open-ended tasks could encourage elementary students' engagement. In addition, this research presented the potential significance of teacher's support and positive feedback to students' responses, teaching methods of group activities and discussions, strategies of presenting tasks such as the board game while implementing the lessons using open-ended tasks.

• Communications of Mathematical Education
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• v.38 no.1
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• pp.1-26
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• 2024

As the limitations of professional development programs and individual attempts to improve teaching expertise have been reported, mathematics teachers have operated various types of teacher learning communities as alternative teacher professional programs. A teacher learning community can be considered a Community of Practice(CoP) in that it satisfies three factors of Cop, which are common purpose, mutual participation, and shared repertoire, so the 'learning' of a teacher community can be interpreted based on the theory of CoP. The purpose of this study is to investigate the process of identity development of five mathematics teachers who have been continuously involved in teacher communities. For this, the researcher collected data on the entire process of community activities through participant observation and conducted individual follow-up interviews to explore mathematics teachers' narratives and personal experiences. Results indicated that mathematics teachers experienced the development of practical knowledge related to mathematics teaching and learning, improvement of teaching practice through continuous reflection and introspection, and recognization the shared value of togethering through community immersion. Based on these experiences, implications for the effective operation of learning communities such as national support of teacher learning communities and horizontal and cooperative teacher norms were discussed, and follow-up research was proposed.

• School Mathematics
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• v.15 no.4
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• pp.819-832
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• 2013

This study was performed to investigate the pedagogical knowledge of pre-service teachers and to explore the possibility of using Lesson Play in pre-service teacher education. Lesson Play refers to a lesson written in script form, featuring imagined interactions between a teacher and his/her students. The participants of this study were 20 pre-service teachers enrolled in mathematics education at a University in Seoul and they conducted a dialogue between a teacher and students who said that 91 is a prime number and 462 is a multiple number of 4. Conclusions were drawn based on the virtual scripts of pre-service teachers. First, it was found that the teaching strategies of pre-service teachers were not diverse. Second, pre-service teachers mainly explained the mathematical principles and concepts. Third, pre-service teachers could not understand the current state of students. Therefore, Lesson Play is helpful to analyse the pedagogical knowledge of pre-service teachers and is a applicable teaching method that can improve the practical knowledge of pre-service teachers.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.495-515
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• 2012

This study is to diversely analyze teachers' Pedagogical Content Knowledge (PCK) regarding to the area of plane figures and discuss the consideration for the materialization of the effective class in learning the area of plane figures by identifying the improvements based on problems indicated in PCK. The subjects of inquiry are what the problems with teachers' PCK regarding to the area of plane figures are and how they can be improved. In which is the first domain of PCK, teachers need to fully understand the concept of the area and the properties and classification of the area and length, recognized the sequence structure as a subject of guidance and improve the direction which naturally connects the flow of measurement by using random units in guidance of the area. In which is the second domain of PCK, teachers need to establish understanding of the concept for the area and understanding of a formula as a subject matter object and improve the activity, discovery and research oriented class for students as a guidance method by escaping from teacher oriented expository class and calculation oriented repetitive learning. They also need to avoid the biased evaluation of using a formula and evenly evaluate whether students understand the concept of the area as a performance evaluation method. In which is the third domain of PCK, teachers need to fully understand the concept of the area rather than explanation oriented correction and fundamentally teach students about errors by suggesting the activity to explore the properties of the area and length. They also need to plan a method to reflect student's affective aspects besides a compliment and encouragement and apply this method to the class. In which is the fourth domain of PCK, teachers need to increase the use of random units by having an independent consciousness about textbooks and supplementing the activity of textbooks and restructure textbooks by suggesting problematic situations in a real life and teaching the sequence structure. Also, class groups will need to be divided into an entire group, individual group, partner group and normal group.

• Education of Primary School Mathematics
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• v.11 no.2
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• pp.141-159
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• 2008

The purpose of this study id to delve into how elementary mathematics textbook deal with the quadrilaterals from a view of Didactic Transposition Theory. Concerning the instruction period and order, we have concluded the following: First, the instruction period and order of quadrilaterals were systemized when the system of Euclidian geometry was introduced, and have been modified a little bit since then, considering the psychological condition of students. Concerning the definition and presentation methods of quadrangles, we have concluded the following: First, starting from a mere introduction of shape, the definition have gradually formed academic system, as the requirements and systemicity were taken into consideration. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Concerning the contents and methods of instruction, we have concluded the following: First, the subject of learning has changed from textbook and teachers to students. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Third, when instructing the characteristics and inclusive relation, students could build up their knowledge by themselves, by questions and concrete operational activities. Fourth, constructions were aimed at understanding of the definition and characteristics of the figures, rather than at itself.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.157-177
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• 2006

The concepts of ratio and proportion do not develop in isolation. Rather, they are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. The current study attempted to clarify the beginning of this development process. One fourth student, Kyungsu, was encourage to schematize his trial-and-error-based method, which was effective in solving so-called missing-value tasks. This study describes several advancements Kyungsu made during the teaching experiment and analyzes the challenges Kyungsu faced in attempting to schematize his method. Finally, the mathematical knowledge Kyungsu needed to further develop his ratio and proportion concepts is identified. The findings provide additional support for the view that the development of ratio and proportion concepts is embedded within the development of the multiplicative conceptual field.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.63-81
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• 2014

Korean students have shown high achievements on the cognitive domain of mathematics in a range of international assessment tests. On the affective domain, however, significantly low achievements have been reported. Among the factors in the affective domain, this article discusses on the value of mathematics in the perspective of Michael Polanyi's philosophy, which centers personal knowledge and tacit knowing. Polanyi emphasizes abstractness and generalization in mathematics accompanied by intellectual beauty and passion. In his perspective, therefore, utilitarian aspects and usefulness of mathematics imparted through linguistic representations have limits in motivating students to learn mathematics. Students must be motivated from recognition of the value of mathematics formed through participating authentic mathematical problem solving activity with immersion, tension, confusion, passion, joy and the like.

• Journal of Engineering Education Research
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• v.22 no.5
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• pp.29-36
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• 2019

Here we analyze a case of redesigned course named "Prospect of Nuclear Engineering" as an example of student-entered education which came to the fore of university education innovation. This course was reformed from lecture-based to student-centered class by changing the context as follows: Stimulating students by addressing various problems or episodes behind scientific and mathematical concepts in the history; Offering experimental project to perceive the importance of differential equations; Exploring the research status and issues of nuclear engineering and the ways of attacking them by discipline; Discussing the public acceptance of nuclear power plants. Small group activities using 'small group discussion' and 'peer-learning' have been applied in this course to enhance students' critical and creative ability. In the survey, students rated highly in the fact that they could actively interact with the peers and that they could think for themselves through 'small group discussion' and 'peer-learning' which is not just the way of conveying knowledge.

• Journal of The Korean Association For Science Education
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• v.34 no.3
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• pp.295-301
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• 2014

The purpose of this study is to investigate the difficulties of teachers and students on the unit about 'measuring weight.' In this research, we have acquired data about teachers through survey, interview, and self-reflection journals, at the same time we have collected information on the students through survey, assessment test, and interview. We have extracted the difficulties from analysis with constant comparison method. In addition, we have analysed the curriculum of science and mathematics to know the leaning sequence. The analysis had been checked up by experts in science education. The result of the study is as follows: The difficulties of teachers are from the lack of teachers' descriptive knowledge, disorder of conceptual hierarchy in the curriculum, poor experimental instruments, and low psychomotor skill of students. The difficulties of students are from common misconceptions, opaque concepts, lack of manipulation skill, insufficiency of mathematical ability, difficulty of application of principles to the real situation, and lack of problem-solving ability. In addition, teachers have recognized that students face more difficulties in experiment class, while students think that they face more difficulties in conceptual understanding class.

• School Mathematics
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• v.11 no.4
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• pp.625-642
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• 2009

This paper presents an overview of theories about ethnomathematics to seek for implications for multicultural mathematics education. Initiated by anthropological inquiries into mathematics outside of Europe, research of ethnomathematics has revealed the facets of mathematics as a historicocultural construct of a community. Specifically, it has been shown that mathematics is culturally relative knowledge system situated within a certain communal epistemological norms. This implies that indigenous mathematics, which had traditionally been regarded as primitive and marginal knowledge, is a historicocultural construct whose legitimacy is conferred by the system of the communal epistemological norms. The recognition of the cultural facets in mathematics has faciliated the reconsideration of what is legitimate mathematics. what is mathematical competence, and what teaching and learning mathematics is an about. This paper inquires multicultral discourses of mathematics education that research of ethnomathematics provides and identifies its implications concerning multicultural mathematics education.