• The Mathematical Education
• /
• v.41 no.2
• /
• pp.189-202
• /
• 2002

Problem-centered learning reflects learning strategy based on constructivism. In this learning, students should find the solution in a small group discussion, and share their solutions with classmates in whole class discussion. So students participate in mathematics instruction actively and interact with other students about the strategies. We expect students would change their attitudes on mathematics and mathematical learning in these processes. In this study, we analyzed students' attitudes on mathematics and mathematical learning when they participated the problem-centered learning program. We found the change of students' attitudes to mathematics via problem-centered learning.

• Journal of The Korean Association For Science Education
• /
• v.38 no.1
• /
• pp.11-26
• /
• 2018

The purpose of this study is to investigate teachers' responsive practices in whole class discussion after small group argumentation and the underlying epistemological framing. Three teachers and 84 students participated in this study by engaging in argumentation activities about the sensory system. We recorded both their discussions in the classes and our interviews with the teachers, which were transcribed for analysis. The results of the analysis showed that the teachers' responsive practices and the epistemological framing were categorized into four types. By framing the discussion as 'reaching the correct answer through discussion,' the teacher focused on whether students' ideas corresponded to scientific concepts and transferred scientific ideas to the students. By framing the discussion as 'eliciting appropriate conceptual resources and developing them into a scientific idea through critical evaluation,' the teacher engaged in the students' discussion as another participant, and considered the small groups' arguments as resources that could develop into scientific concepts. By framing the discussion as 'sharing small groups' arguments,' the teacher responded by asking for clarification of each group's argument, considering it as a valid argument in its own way. By framing the discussion as 'reaching a consented argument through critical evaluation,' the teacher negotiated students' critical evaluation and revision of the arguments. We explored the implications and limitations of each type of responsive practice and considered that the results of this study will contribute to developing teachers' responsive teaching strategies in argumentation activities.

• The Mathematical Education
• /
• v.46 no.4
• /
• pp.423-443
• /
• 2007

Based on the framework of Huffered-Ackles, Fuson and Sherin(2004), data were analyzed in terms of 3 components: explaining(E), questioning(Q) and justifying(J) of students' mathematical concepts and problem solving in a math classroom. The students used varied presentations to explain and justify their mathematical concepts and ideas. They corrected their mathematical errors or misconceptions through discourses. In addition, they constructed and clarified their concepts and thinking while they were interacted. We were able to recognize there was a special feature in discourses that encouraged the students to construct and develop their mathematical concepts. As they participated in math class and received feedback on their learning, the whole class worked cooperatively in a positive way. Their discourse was improved from the level of the actual development to the level of the potential development and the pattern of interaction moved from ERE(Elicitaion-Response-Elaboration to PD(Proposition Discussion).

• Journal of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.289-309
• /
• 2019

This paper is intended as a discussion of some generalizations of the notion of a reversible ring, which may be obtained by the restriction of the zero commutative property from the whole ring to some of its subsets. By the INCZ property we will mean the commutativity of idempotent elements of a ring with its nilpotent elements at zero, and by ICZ property we will mean the commutativity of idempotent elements of a ring at zero. We will prove that the INCZ property is equivalent to the abelianity even for nonunital rings. Thus the INCZ property implies the ICZ property. Under the assumption on the existence of unit, also the ICZ property implies the INCZ property. As we will see, in the case of nonunital rings, there are a few classes of rings separating the class of INCZ rings from the class of ICZ rings. We will prove that the classes of rings, that will be discussed in this note, are closed under extending to the rings of polynomials and formal power series.

• Journal of Korean Elementary Science Education
• /
• v.25 no.3
• /
• pp.307-317
• /
• 2006

Those students with ability and interest in science should be supported to develop their potential and to reach high levels of achievement in science and technology. In order to ensure that gifted pupils are able to enhance their creativity as well as research abilities, appropriate learning programs and environments are essential. One of the various teaching and learning models for the gifted in science is the discovery learning model based on inductive science activities. There is a clear line of continuity between knowledge discovery at the forefront of research and student's learning activities. If students receive excellent training in organizing scientific concepts for themselves, they will be able to skillfully apply appropriate scientific concepts and solve problems when facing unfamiliar situations. It is very important to offer an appropriate learning environment to maximize the learning effect whilst, at the same time, understanding individual student's characteristics. In this study, the authors took great pains to research effective learning environments for gifted science students. Firstly, appropriate classroom learning environments thought by the teacher to offer the most potential were investigated. 3 different classes in which a revised teaching and learning environment was applied in sequence were examined. Inquiries were conducted into students' activities and achievement through observation, interviews, and examination of students' worksheets. A Science Education expert and 5 elementary school teachers specializing in gifted education also observed the class to examine the specific character of gifted science students. A number of suggestions in discovery learning classes for elementary students gifted in science are possible; 1) Readiness is essential in attitudes related to the inquiry. 2) The interaction between students should be developed. A permissive atmosphere is needed in small group activities. 3) Students require training in listening to others. In a whole class discussion, a permissive atmosphere needs to be restricted somewhat in order to promote full and inclusive discussion. 4) Students should have a chance to practice induction and abduction methods in solving problems.

• Journal of Korean Physical Therapy Science
• /
• v.9 no.4
• /
• pp.83-94
• /
• 2002

Within physical therapy education, there has been increased attention to curricula and course that emphasize problem solving, clinical reasoning, and synthesis of information across traditional discipline-specific boundaries. This article describes the development implementation, and outcomes of a problem-based learning course in Physical therapy. The course was designed to help students to integrate the various elements of a physical therapy curriculum and to enhance their abilities to respond to an ever-changing health care environment. An evaluation of the course by the first 50 students who completed it revealed both strengths and weaknesses. Students responded that the course enhanced their professional behavior, including interpersonal communication skills, team work, and follow-through with professional responsibilities. The learning package was developed by the authors and implemented to a college students during three weeks of the first semester of 2001. Most studies which conducted PBL module development were short period or temporary PBL package application and evaluation rather than a whole semester's. While, this study carried on partial integrated PBL curriculum development and application with recomposing content of the two subjects to one subject Physical therapy which includes four PBL packages. This package was developed from a simple concept to complex and partial integrated PBL curriculum application systematically variable learning methods such as discussion, practice, lecture, video. There are 2 classes, each class has 25 students, in the college. Each class has 5 small groups consisting 5 students. Two tutors proceeded discussion charging each class also, they used multiple methods and materials like tutorials, self-directed learning, lecture, and video. The package is 5 grades and 5 hours per week and the rate of discussion, lecture is 4, 1 respectively. One of the most change is the increase of interaction between students and tutors. Whenever students need information and suggestion, they can visit tutors who provide reading materials and guide for the direction of self learning. Therefore, this study describes the PBL package development process and application during one semester recomposing contents of two subjects to Physical therapy concepts. Besides, it will contribute to active application of existing each subject to tutors who intend to convert as PBL methods. The study has significant meaning to show potentiality of partially integrated PBL application, using systematic PBL package development from two subjects contents. However, when students' need of yearning is over the extent of Introduction of Physical therapy and Rehabilitation medicine, tutors should set learning extent. So, there is limitation to attain completely integrated PBL education within one subject, therefore, it is high lighted to proceed development of integrated curriculum to maximize learning effects of PBL. It is exected that partial integrated PBL package development and application will distribute to prosper excellent physiotherapist in practice.

• Journal of Educational Research in Mathematics
• /
• v.8 no.1
• /
• pp.137-144
• /
• 1998

A common geoboard puzzel serves as the point of departure for an investigation that lends itself to whole-group discussion with a class of prospective secondary school teachers. Students are provided with opportunities to devise and carry out problem-solving strategies (called 'heuristics' by Polya); exploit inerrelationships among geometry, arithmetic and algebra; formulate generalizations and conjectures; plan and execute an computational project; construct mathematical arguments to establish theorems; and find counter-examples to dispose of a false conjecture. In recent tears, Eugene F. Krause wrote two papers having the same title except for the numeral In that papers he arrives at an theorem about the sizes of squares with lattice point vertices in the coordinate plane, In this paper we follow a different path genearlization to coordinate 3-space

• The Mathematical Education
• /
• v.48 no.3
• /
• pp.303-328
• /
• 2009

In this study, we developed the teaching methods using manipulative materials to teach regular polytopes, and applied these to first-year student of middle school who is attending the extra math class. In that class, we focused on the change of the mathematical representations -especially verval, visual and symbolic representations- and mathematical behavioral. By analyzing characterstics the students' work sheets, we obtained affirmative results as follows. First, manipulative materials played an important role on drawing a development figure of regular polyhtopes describing the verval representation definition of regular polytopes. Second, classes utilizing manipulative materials changed students verbalism level of representations the definition of regular polytopes. For example, in the first class about 60% of students are in the $0{\sim}2$ vervalism level, but in the third class, about 65% of students are in the $6{\sim}7$ level. Third, classes utilizing manipulative materials improved visual representation about development figure. After experiences making several development figures about regular octahedron directly, and discussion, students found out key points to be considered for draws development figure and this helped to draw development figures about other regular polytopes. Fourth, students were unaccustomed to make symbolic representations of regular polytopes. But, they obtained same improvement in symbolic representations, so in fifth the class some students try to make symbol about something in common of whole regular polytopes. Fifth, after the classes, we have significant differences in the students, especially behavioral characteristics in II items such as mind that want to study own fitness, interest, attachment, spirit of inquiry, continuously mathematics posthumously. This means that classes using manipulative materials. Specially, 'mind that want to study mathematics continuously' showed the biggest difference, and it may give positive influence to inculcates mathematics studying volition while suitable practical use of manipulative materials. To conclude, classes using manipulative materials may help students enhance the verbal, visual representation, and gestates symbol representation. Also, the class using manipulative materials may give positive influence in some part of mathematical behavioral characteristic. Therefore, if we use manipulative materials properly in the class, we have more positive effects on the students cognitive perspect and behavioral cteristics.

• Journal of The Korean Association For Science Education
• /
• v.35 no.2
• /
• pp.217-229
• /
• 2015

In this study, we explored the development of scientific model through the social-construction process on "combustion." Students were 8th graders from one middle school class. Each student engaged in small group discussions three times and made a group model on combustion. Discourses between peers and teacher were videotaped, audiotaped, and transcribed. The results show that the small groups constructed an initial concept: 'Conditions of combustion', which they then evaluated and revised the initial concept through combustion experiment. Following the discussions, some small groups evaluated their model and made a revised model. Then, the small groups compared various models and constructed a scientific model through consensus within the small group and as a whole class. Finally, students kept revising their model to 'Burning needs oxygen.' This tells us that the social construction process of scientific model made a meaningful role to build scientific model through diverse discussion between the students and their teacher, although they have had some difficult process to reach the final consensus. The data also showed some group features: the members were open to other's ideas. They analyzed the differences between their own ideas from others and revised their model after the whole class discussion. Lastly, they showed the tendency to make a good use of teacher's guidance. This study implies the importance of having social interaction process for students to understand the scientific model and learn the nature of scientific inquiry in class.

• Journal of Educational Research in Mathematics
• /
• v.11 no.1
• /
• pp.11-35
• /
• 2001

Many teachers report familiarity with and adherence to reform ideas, but their actual teaching practices do not reflect a deep understanding of reform. Given the challenges in implementing reform, this study intended to explore the breakdown that may occur between teachers' adoption of reform objectives and their successful incorporation of reform ideals. To this end, this study compared and contrasted the classroom social norms and sociomathematical norms of two United States second-grade teachers who aspired to implement reform. This study is an exploratory, qualitative, comparative case study. This study uses the grounded theory methodology based on the constant comparative analysis for which the primary data sources were classroom video recordings and transcripts. The two classrooms established similar social norms including an open and permissive learning environment, stressing group cooperation, employing enjoyable activity formats for students, and orchestrating individual or small group session followed by whole group discussion. Despite these similar social participation structures, the two classes were remarkably different in terms of sociomathematical norms. In one class, the students were involved in mathematical processes by which being accurate or automatic was evaluated as a more important contribution to the classroom community than being insightful or creative. In the other class, the students were continually engaged in significant mathematical processes by which they could develop an appreciation of characteristically mathematical ways of thinking, communi-eating, arguing, proving, and valuing. It was apparent from this study that sociomathematical norms are an important construct reflecting the quality of students' mathematical engagement and anticipating their conceptual learning opportunities. A re-theorization of sociomathematical norms was offered so as to highlight the importance of this construct in the analysis of reform-oriented classrooms.