• Title/Summary/Keyword: 수학적 연결성

Search Result 206, Processing Time 0.028 seconds

Mathematics teachers' Key Developmental Understandings for teaching equation writing (수학교사의 대수식 쓰기 지도를 위한 발달에 핵심적인 이해)

  • Choi, Yunhyeong;Lee, Soo Jin
    • The Mathematical Education
    • /
    • v.60 no.3
    • /
    • pp.297-319
    • /
    • 2021
  • The present study explored a relationship between mathematical understandings of teachers and ways in which their knowledge transferred in designing lessons for hypothetical students from Gess-Newsome (1999)'s transformative perspective of pedagogical content knowledge. To this end, we conducted clinical interviews with four secondary mathematics teachers of their solving and teaching of equation writing. After analyzing the teacher participants' attention to Key Developmental Understandings (Simon, 2007) in solving equation writing, we sought to understand the relationship between their mathematical knowledge of the problems and mathematical knowledge in teaching the problems to hypothetical students. Two of the four teachers who attended the key developmental understandings solved the problems more successfully than those who did not. The other two teachers had trouble representing and explaining the problems, which involved reasoning with improper fractions or reciprocal relationships between quantities. The key developmental understandings of all four teachers were reflected in their pedagogical actions for teaching the equation writing problems. The findings contribute to teacher education by providing empirical data on the relationship between teachers' mathematical knowledge and their knowledge for teaching particular mathematics.

An Analysis of Gaze Differences between Pre-service Teachers and Experienced Teachers on Mathematics Lesson Plan (예비교사와 경력교사의 수학 수업지도안에 대한 시선 차이 분석)

  • Son, Taekwon;Lee, Kwang-Ho
    • Education of Primary School Mathematics
    • /
    • v.23 no.1
    • /
    • pp.1-26
    • /
    • 2020
  • The purpose of this study was to analyze the process of reading and understanding mathematics lesson plan through eye-tracking to suggest implications of pre-service teacher education. As a result of the analysis, the pre-service teachers felt that the mathematics lesson plans were more difficult than the experienced teacher, they read and understood the mathematics lesson plan in sequential order. Experienced teachers, on the other hand, used a hypertext reading strategy to find key topics and make connections in order to grasp the flow of instruction in mathematics lesson plan. Based on these results, several suggestions were drawn for pre-service teachers when teaching their ability to read and understand mathematics lesson plan.

A Comparative Study of the Mathematics Textbooks' Tasks of Korea and the USA : Focused on Conditions for Parallelograms (우리나라와 미국 수학 교과서의 과제 비교 : 평행사변형 조건을 중심으로)

  • Jung, Hye Yun;Lee, Kyeong Hwa
    • School Mathematics
    • /
    • v.18 no.4
    • /
    • pp.749-771
    • /
    • 2016
  • The purpose of this study is to analyze mathematical tasks of Korea and the USA textbooks focused on conditions for parallelograms. In this study, structures of task, types of proof and reasoning, and levels of cognitive demand are investigated. The conclusion is as follows: First, with respect to structures of task, structures presented in the USA textbooks are more diverse. Second, with respect to types of proof and reasoning, Korea and the USA prefer IC task and DA task. And task types presented in the USA textbooks are more diverse. Third, with respect to levels of cognitive demand, in both Korea and the USA textbooks, PNC task and PWC task account most. And compared to the USA, Korea prefer algorithms. In addition, we find out implications for reconstruction of Korea textbook. It is as follows: First, with respect to structures of task and types of proof and reasoning, the diversity of composition needs to be raised. Second, with respect to levels of cognitive demand, the concentration in PNC task needs to be declined. And levels of cognitive demand on types of tasks need to be reconsidered. Third, with respect to tasks' topic and material, internal and external connectivities of mathematics need to be strengthened.

The Effects of Tasks Setting for Mathematical Modelling in the Complex Real Situation (실세계 상황에서 수학적 모델링 과제설정 효과)

  • Shin, Hyun-Sung;Lee, Myeong-Hwa
    • Journal of the Korean School Mathematics Society
    • /
    • v.14 no.4
    • /
    • pp.423-442
    • /
    • 2011
  • The purpose of this study was to examine the effects of tasks setting for mathematical modelling in the complex real situations. The tasks setting(MMa, MeA) in mathematical modelling was so important that we can't ignore its effects to develop meaning and integrate mathematical ideas. The experimental setting were two groups ($N_1=103$, $N_2=103$) at public high school and non-experimental setting was one group($N_3=103$). In mathematical achievement, we found meaningful improvement for MeA group on modelling tasks, but no meaningful effect on information processing tasks. The statistical method used was ACONOVA analysis. Beside their achievement, we were much concerned about their modelling approach that TSG21 had suggested in Category "Educational & cognitive Midelling". Subjects who involved in experimental works showed very interesting approach as Exploration, analysis in some situation ${\Rightarrow}$ Math. questions ${\Rightarrow}$ Setting models ${\Rightarrow}$ Problem solution ${\Rightarrow}$ Extension, generalization, but MeA group spent a lot of time on step: Exploration, analysis and MMa group on step, Setting models. Both groups integrated actively many heuristics that schoenfeld defined. Specially, Drawing and Modified Simple Strategy were the most powerful on approach step 1,2,3. It was very encouraging that those experimental setting was improved positively more than the non-experimental setting on mathematical belief and interest. In our school system, teaching math. modelling could be a answer about what kind of educational action or environment we should provide for them. That is, mathematical learning.

  • PDF

Clustering Approach for Topology Control in Multi-Radio Wireless Mesh Networks (Multi-Radio 무선 메쉬 네트워크에서의 토폴로지 제어를 위한 클러스터링 기법)

  • Que, Ma. Victoria;Hwang, Won-Joo
    • Journal of the Korea Institute of Information and Communication Engineering
    • /
    • v.11 no.9
    • /
    • pp.1679-1686
    • /
    • 2007
  • Clustering is a topology control approach often used in wireless ad hoc networks to improve scalability and prolong network lifetime. Furthermore, it is also employed to provide semi-management functionalities and capacity enhancement. The usage of clustering topology control technique can also be applied to multi-radio wireless mesh network. This would utilize the advantages of the multi-radio implementation in the network. The aggregation would result to a more stable, connected, scalable and energy-efficient network. On this paper, we design a clustering algorithm for multi-radio wireless mesh network that would use these advantages and would take into consideration both mobility and heterogeneity of the network entities. We also show that the algorithm terminates at a definite time t and the message control overhead complexity is of constant order of O(1) per node.

The Generalization of the Area of Internal Triangles for the GSP Use of Mathematically Gifted Students (중등 영재학생들의 GSP를 활용한 내분삼각형 넓이의 일반화)

  • Lee, Heon-Soo;Lee, Kwang-Ho
    • Journal of the Korean School Mathematics Society
    • /
    • v.15 no.3
    • /
    • pp.565-584
    • /
    • 2012
  • This study investigates how the GSP helps gifted and talented students understand geometric principles and concepts during the inquiry process in the generalization of the internal triangle, and how the students logically proceeded to visualize the content during the process of generalization. Four mathematically gifted students were chosen for the study. They investigated the pattern between the area of the original triangle and the area of the internal triangle with the ratio of each sides on m:n respectively. Digital audio, video and written data were collected and analyzed. From the analysis the researcher found four results. First, the visualization used the GSP helps the students to understand the geometric principles and concepts intuitively. Second, the GSP helps the students to develop their inductive reasoning skills by proving the various cases. Third, the lessons used GSP increases interest in apathetic students and improves their mathematical communication and self-efficiency.

  • PDF

Analysis on the Korean Highway in 2011 and 2017 Using Algorithms of Accessibility indices (접근성 지표의 알고리즘을 이용한 2011년과 2017년의 우리나라 고속도로 분석)

  • Lee, Gwangyeon;Park, Kisoeb
    • Journal of the Korea Society for Simulation
    • /
    • v.27 no.4
    • /
    • pp.9-18
    • /
    • 2018
  • This paper proposes new algorithms of accessibility indices to analyze the connectivity of the Korean highway network. First of all, we find a transportation network that presents Korea's highway network in graphs in 2011 and 2017. And we analyze and compare the nation's highway network in 2011 and 2017 using concepts such as associated number, the relative distance, the accessibility, the degree of connectivity, the index of dispersion, the diameter of graph theory. To do this, an algorithm is presented which can easily obtain various accessibility indices from a given transportation network. Using the simulation results of this study, we can find city that is the center of traffic in the highway transportation network. In addition, cities that are included in the network but are relatively underdeveloped can be found and used as basic data for enhancing the connectivity of the nationwide traffic in the future. Moreover, the proposed algorithms of accessibility indices, which are modeled on highway transport networks, can help identify the accessibility space structure of each city and provide criteria for efficient and reasonable selection of alternatives in various regional planning processes, including transportation.

A study on compositions of listed terms in 2011 elementary mathematics curriculum in Korea (우리나라 2011 초등수학 교육과정 등재용어의 조성에 관한 연구)

  • Park, Kyo-Sik;Kwon, Seo-Kil
    • Journal of Educational Research in Mathematics
    • /
    • v.22 no.3
    • /
    • pp.429-444
    • /
    • 2012
  • As one of the trials for a systematic approach to mathematics terms which occupies an important place in teaching and learning mathematics, compositions of listed terms in 2011 elementary mathematics curriculum in Korea are discussed in this study. To this end, listed terms are classified in view of three points and looked for their characteristics, from which implications are found out for elementary mathematics teaching and learning First of all classifications into grade-group and domain-specific terms, then into newly coined terms and terms from everyday life, and then into korean terms and chinese character terms and english terms are attempted. Next, terms with a kernel and terms without a kernel are distinguished, and in this process, term-sets are presented. Finally, object terms, operation terms, relationship terms, measure terms, conditions terms, graphics terms, name terms are classified. Based on these results, the following implications for elementary mathematics teaching and learning are suggested. First, it should be considered that many of the listed terms in 2011 curriculum are newly coined and chinese character terms. Second, the interconnections between terms should be considered. Third, a variety of roles and functions of the terms should be considered.

  • PDF

Quotitive Division and Invert and Multiply Algorithm for Fraction Division (분수 포함제와 제수의 역수 곱하기 알고리즘의 연결성)

  • Yim, Jaehoon
    • Journal of Elementary Mathematics Education in Korea
    • /
    • v.20 no.4
    • /
    • pp.521-539
    • /
    • 2016
  • The structures of partitive and quotitive division of fractions are dealt with differently, and this led to using partitive division context for helping develop invert-multiply algorithm and quotitive division for common denominator algorithm. This approach is unlikely to provide children with an opportunity to develop an understanding of common structure involved in solving different types of division. In this study, I propose two approaches, measurement approach and isomorphism approach, to develop a unifying understanding of fraction division. From each of two approaches of solving quotitive division based on proportional reasoning, I discuss an idea of constructing a measure space, unit of which is a quantity of divisor, and another idea of constructing an isomorphic relationship between the measure spaces of dividend and divisor. These ideas support invert-multiply algorithm for quotitive as well as partitive division and bring proportional reasoning into the context of fraction division. I also discuss some curriculum issues regarding fraction division and proportion in order to promote the proposed unifying understanding of partitive and quotitive division of fractions.

Analysis of Learning Opportunities Provided in Elapsed Time Instruction: Focusing on Quantitative Objectification (경과시간 수업에서 제공되는 학습기회 분석: 양적 대상화를 중심으로)

  • Han, Chaereen
    • Education of Primary School Mathematics
    • /
    • v.24 no.4
    • /
    • pp.203-216
    • /
    • 2021
  • Seeing the elapsed time as a quantity that can be measured is quite challenging for students while making students see it is also challenging for teachers. Tuning on these challenges, this article reports on what learning opportunities elementary teachers provide when they teach elapsed time focusing on quantitative objectification. I observed three mathematics classrooms where the elapsed time was taught by three elementary teachers and did a narrative analysis on the instructions. All three teachers utilized certain tools to support students access to the elapsed time as a quantity. They appropriated various quantitative attributes of the tool. In the case of the analog clock, one teacher tried to quantification the elapsed time with the number of minute hand's turning, while the other teacher indicated the distance of minute hand's moving. One teacher represented the elapsed time with the longitudinal attribute of the time band. Standing on the findings, the didactical implications of various attempts for quantitative objectification of the elapsed time implemented were discussed.