• Research in Mathematical Education
• /
• v.1 no.1
• /
• pp.1-5
• /
• 1997

We discuss some aspects of mathematics for teachers such as algebra for teachers, geometry for teachers, statistics for teachers, etc., which can be taught in teacher preparation courses. Mathematics for teachers should consider the followings: (a) Various solutions for a problem, (b) The dynamics of a problem introduced by change of condition, (c) Relationship of mathematics to real life, (d) Mathematics history and historical issues, (e) The difference between pure mathematics and pedagogical mathematics, (f) Understanding of the theoretical backgrounds, and (g) Understanding advanced mathematics.

• Research in Mathematical Education
• /
• v.24 no.3
• /
• pp.255-278
• /
• 2021

Proof serves a critical role in mathematical practices as well as in fostering student's mathematical understanding. However, the research literature accumulates results that there are not many opportunities available for students to engage with proving-related activities and that students' understanding about proof is not promising. This unpromising state of instruction of proof calls for a novel approach to address the aforementioned issues. This study investigated an instruction of proof to explore a pedagogy to teach how to prove. The teacher utilized the way of problem posing to make proving a routine part of everyday lesson and changed the classroom culture to support student proving. The study identified the teacher's support for student proving, the key pedagogical changes that embraced proving as part of everyday lesson, and what changes the teacher made to cultivate the classroom culture to be better suited for establishing a supportive community for student proving. The results indicate that problem posing has a potential to embrace proof into everyday lesson.

• The Mathematical Education
• /
• v.57 no.4
• /
• pp.453-475
• /
• 2018

This study examines how elementary students understand fractions with operations conceptually and how they perform procedures in the division of fractions. We attempted to look into students' understanding about fractions with divisions in regard to mathematical proficiency suggested by National Research Council (2001). Mathematical proficiency is identified as an intertwined and interconnected composition of 5 strands- conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. We developed an instrument to identify students' understanding of fractions with multiplication and division and conducted the survey in which 149 6th-graders participated. The findings from the data analysis suggested that overall, the 6th-graders seemed not to understand fractions conceptually; in particular, their understanding is limited to a particular model of part-whole fraction. The students showed a tendency to use memorized procedure-invert and multiply in a given problem without connecting the procedure to the concept of the division of fractions. The findings also proposed that on a given problem-solving task that suggested a pathway in order for the students to apply or follow the procedures in a new situation, they performed the computation very fluently when dividing two fractions by multiplying by a reciprocal. In doing so, however, they appeared to unable to connect the procedures with the concepts of fractions with division.

• Education of Primary School Mathematics
• /
• v.6 no.1
• /
• pp.29-40
• /
• 2002

Fairy-tales give students opportunities to build connections between a problem-solving situation and mathematics as well as to communicate solutions through writing, symbols, and diagrams. Therefore, the purpose of this paper is to introduce how to use fairy-tales in elementary mathematics classroom in order to develope student's mathematical concepts and process in terms of the following areas: ⑴ reconstructing literature ⑵ understanding concepts ⑶ problem posing activity. To be useful, mathematics should be taught in contexts that are meaningful and relevant to learners. Therefore using fairy-tales as a vehicle to teach mathematics gives students a chance to develope mathematics understanding in a natural, meaningful way, and to enhance problem posing and problem solving ability. Further, future study will continue to foster how fairy-tales literatures will enhance children's mathematics knowledge and influence on their mathematics performance.

• Journal of the Korean School Mathematics Society
• /
• v.21 no.1
• /
• pp.63-89
• /
• 2018

In this study, the researcher developed a course integrated mathematical problem posing activities in order to enhance pre-service mathematics teachers' ability to carry out problem posing activities in mathematics classroom, and examined the changes of pre-service mathematics teachers' perceptions about problem posing through the course. The problem posing course developed in this study consisted of three stages: education on the theories regarding problem posing; activities with problem posing; development and implementation of problem posing tasks. According to the results of the questionnaires, interviews, and class journals data analysis, the problem posing experiences provided in this study were very effective in improving pre-service mathematics teachers' understanding of the problem posing strategies and the benefit of problem posing activities to student learning. Particularly, the experience in various problem posing activities and the implementation experience of problem posing provided in the course played a key role in the improvement of pre-service mathematics teachers' understanding of problem posing and PCK.

• Journal of Educational Research in Mathematics
• /
• v.8 no.1
• /
• pp.59-71
• /
• 1998

Recently, most classrooms in Korea are fully equipped with multimedia environments such as a powerful pentium pc, a 43″large sized TV, and so on through the third renovation of classroom environments. However, there is not much software teachers can use directly in their teaching. Even with existing software such as GSP, and Mathematica, it turns out that it doesn####t fit well in a large number of students in classrooms and with all written in English. The study is to analyze the characteristics of problem-solving process and to develop a computer program which integrates the instruction of problem solving into a regular math program in areas of quadratic functions and ellipses. Problem Solving in this study included two sessions: 1) Learning of basic facts, concepts, and principles; 2) problem solving with problem contexts. In the former, the program was constructed based on the definitions of concepts so that students can explore, conjecture, and discover such mathematical ideas as basic facts, concepts, and principles. In the latter, the Polya#s 4 phases of problem-solving process contributed to designing of the program. In understanding of a problem, the program enhanced students#### understanding with multiple, dynamic representations of the problem using visualization. The strategies used in making a plan were collecting data, using pictures, inductive, and deductive reasoning, and creative reasoning to develop abstract thinking. In carrying out the plan, students can solve the problem according to their strategies they planned in the previous phase. In looking back, the program is very useful to provide students an opportunity to reflect problem-solving process, generalize their solution and create a new in-depth problem. This program was well matched with the dynamic and oscillation Polya#s problem-solving process. Moreover, students can facilitate their motivation to solve a problem with dynamic, multiple representations of the problem and become a powerful problem solve with confidence within an interactive computer environment. As a follow-up study, it is recommended to research the effect of the program in classrooms.

• International Journal of Advanced Culture Technology
• /
• v.9 no.3
• /
• pp.100-105
• /
• 2021

This study examines the effectiveness of the study through a case of PBL(problem-based-learning) class conducted in a balanced culture course called at 00- University in the second semester of 2020. The effects of learning are as follows: First, PBL(problem-based-learning) has sufficient active interaction between the teacher and the learner. In the face of prolonged non-face-to-face learning, the PBL teaching method has sufficient interaction between the professors-learner and the learner. Second, PBL learning can actively utilize various problems that fit the characteristics of the subject and actively utilize the process of role sharing and collaboration. By presenting various problem situations suitable for the subject, students will be able to share roles individually or as a team, and fully experience the process of collaboration and discussion in the process of investigating the data. Third, critical perceptions of problem situations can be extended. In modern times, a variety of problem situations arise and critical perceptions of them must be fully learned. In a mass production and mass consumption society, students should develop the ability to blindly recognize and distinguish between real and fake information in a flood of information. The limitations identified in this class case are, first, the nature of the subject, "Understanding Culture and Philosophy," which makes it possible to discuss the global cultural phenomenon, but it should be discussed in terms of philosophy. Second, it is not easy to work as a team on non-face-to-face online. Nevertheless, PBL is a very effective method of learning in which active interactions and learning activities take place between professors and students, whether face-to-face or face-to-face online learning.

• Journal of Fashion Business
• /
• v.27 no.5
• /
• pp.121-134
• /
• 2023

With the development of information and communication technology, interest in new educational approaches that can enhance the learning performance of learners with improved information literacy skills is increasing, and universities are actively promoting educational innovation to foster the talents required by society. In the field of fashion studies education, which is closely related to the fashion industry, there is a strong need to develop field-linked educational programs that reflect the trends in the industry and changes in the educational system. The purpose of this study was to introduce industry-coupled problem-based learning (IC-PBL) to the course "Understanding Fashion Consumption Trends" for non-fashion majors to reflect the current needs and strengthen the educational effectiveness of the learners through a survey. A seven-step curriculum (introduction to the class, practitioner's problem, learner's problem analysis, organizing concepts related to variables, information collection and scenario writing, presentation and scenario proposal, and evaluation) not only enhanced learners' understanding of fashion consumption trends and the fashion industry but also greatly amplified learners' satisfaction with the class. The results of the survey showed that the seven-step curriculum was effective in increasing learners' self-directed learning ability, problem-solving ability, and confidence in learning. Self-directed learning ability was stronger than other factors, consistent with the core principle of problem-based learning to empower learners to take the initiative and promote self-directed learning. Each factor analyzed was positively correlated.

• Journal of The Korean Association For Science Education
• /
• v.21 no.5
• /
• pp.906-923
• /
• 2001

This study investigated university students' (majoring physics education) understanding of some aspects of idealization frequently used in teaching and learning of physics, especially of mechanics. A total of 143 students were given a Questionnaire of six questions requiring written responses. Out of the six questions, the first three were concerned with basic idealized concepts, the next two with the making of the assumptions of ideal conditions for given problem settings, and the last with the identification of the idealization used in the given solution of a problem. Students' written responses were grouped into patterns and the relative frequencies of the patterns were counted. It was found that the students had limited understanding of the idealization and their ideas were diverse and frequently incorrect. The implications of the findings are discussed in relation to the roles of idealization in physics education.

• The Mathematical Education
• /
• v.59 no.2
• /
• pp.101-112
• /
• 2020

The purpose of this study is to analyze the structures of teacher's discourse according to the pattern of interaction between teachers and students in the understanding mathematical word problem. The structures of teacher's discourse could be conceptualized as a process in which the teacher starts, develops and organizes the discourse based on prior research. For this purpose, the fourth class(example, a problem of the same type as the example, formative assessment, and final assessment) was extracted from one semester of experienced teachers who have been practicing teaching methods to facilitate student participation for many years. A methodology used to develop a theory based on data collected through classroom observations. Because the purpose of the study is to identify the structures of teacher's discourse to help the problem understanding, observe the teacher's discourse and collect data based on student engagement. Results show that the structure of teacher's discourse, which consults on important aspects of interaction between teachers-students and creates mathematical meanings, helped students understand the mathematics word problem by promoting their engagement in class. Based on the structures of teacher's discourse to understand problems based on the interaction patterns between teachers and students, it can be said that teachers provided specific methodologies on how to communicate with students in order to understand problems in the future.