• Education of Primary School Mathematics
• /
• v.16 no.3
• /
• pp.267-283
• /
• 2013

Mathematical justification is the process through which one's claim is validated to be true based on proper and trustworthy data. But it serves as a catalyst to facilitate mathematical discussions and communicative interactions among students in mathematics classrooms. This study is designed to investigate the effects of mathematical justification on students' problem-solving and communicative processes occurred in a mathematics classroom. In order to fulfill the purpose of this study, mathematical problem-solving classes were conducted. Mathematical justification processes and communicative interactions recorded in problem understanding activity, individual student inquiry, small and whole group discussions are analyzed. Based on the analysis outcomes, the students who participated in mathematical justification activities are more likely to find out various problem-solving strategies, to develop efficient communicative skills, and to use effective representations. In addition, mathematical justification can be used as an evaluation method to test a student's mathematical understanding as well as a teaching method to help develop constructive social interactions and positive classroom atmosphere among students. The results of this study would contribute to strengthening a body of research studying the importance of teaching students mathematical justification in mathematics classrooms.

• Journal of Digital Contents Society
• /
• v.8 no.2
• /
• pp.235-243
• /
• 2007

Students develop mathematical concepts through concrete operations in the area of mathematics. However, most of the learning contents provided on the web are not interactive and limit interactions with learners. To overcome the limitations, there have been needs to develop learning contents to support active interactions with students according to their cognitive levels. In this study, the curriculum of numbers and number operations in elementary mathematics was analyzed. Based on the object-oriented design principle, "Number Classes" on numbers and number operations were designed and implemented. A class-based learning applet was developed with theses "Number Classes". It was developed in small unit programs based on learning themes of mathematics in elementary schools. With this learning applet, the active explorations through easy operations will help students to learn concepts and principles of numbers and number operations. It will strengthen active interactions of students with computer.

• School Mathematics
• /
• v.19 no.2
• /
• pp.405-421
• /
• 2017

This study provides a concrete example of the development of the task in collaboration with the in-service teacher and the pre-service teacher. In the process, the roles of pre-service teachers and in-service teachers were analyzed and the possibility of cooperation was grasped. As a result, pre-service teachers and field teachers considered the level and interest of the students and considered mathematical contents in the process of developing the tasks. Each subject did not directly consider the interaction of the students and contents, but they could confirm the improvement of the tasks as their roles affected each other.

• School Mathematics
• /
• v.15 no.2
• /
• pp.243-262
• /
• 2013

This study attempts to create an analytical framework of the transformation and transmission of knowledge by teachers to students. I focuses on the assertion that the cognitive thinking of a teacher is reflected in his use of mathematical language. Mathematical language is one of the critical elements of communicating mathematical knowledge to students. I examined the cognitive teaching style of different teachers as expressed in their use of mathematical language. An analytical framework of Mathematics Teaching styles was created integrating thinking factors of each visual and analytic style into 5 categories. After that, I regarding the teaching style of mathmatics teachers places its significance not on which teaching style is right or wrong but on identifying the strong and weak points of the teaching styles through actual analysis. With the help of this analytical framework, I conducted an analysis on the videotaped classes and found that the teachers were not biased to one side but in fact there were teachers who demonstrated visual, analytic or mixed teaching style. Therefore, I concludes that math teachers can analyze their teaching styles and improve them through the analytical framework provided in these findings.

• 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.

• Journal of Educational Research in Mathematics
• /
• v.12 no.1
• /
• pp.109-124
• /
• 2002

This study investigated various effects of WBD(web-based discussion) on mathematical communication, interaction and problem solving in the classroom. We developed a web site including BBS and chat room in order to encourage students' mathematical curiosities and self-studies. The web site had been operated for 6 months. Five classes of 1st grade students were selected from an middle school in Daejon. Moreover, we analyzed several cases for interactional behavior and effect. WBD promote dialogue between a teacher and students. Analysis of feed-back from BBS revealed that student's negative attitudes could be changed to positive ones by step-by-step discussions. Moreover, collaborative learning is enhanced by on-line discussion. But the effects of WBD are affected by the character and ability of a student.

• Communications of Mathematical Education
• /
• v.19 no.1 s.21
• /
• pp.151-165
• /
• 2005

효과적인 교육을 위한 다양한 연구들이 진행되어 왔지만, 이러한 결과를 실제 수업현장에 적용하기에는 많은 시간과 노력 등이 필요하여 잘 활용되지 못하고 있는 것이 현실이다. 따라서 교실 수업, 특히 지필 위주의 수업에서는 여전히 따분해하며 집중하지 못하는 학생들을 흔하게 볼 수 있다. 본 연구에서는 학생들의 적극적 참여를 통한 효과적인 교육을 구현하기 위한 방안으로 구성주의적 교수학습 방안과 정보 기술을 기반으로 교수자와 개별 학생들 사이의 실시간 상호작용을 극대화시키는 교수방안을 제안하고자 한다. 구현 사례로 통계적 추정의 표본추출 단원에 적용할 수 있는 교수학습 모형과 시스템을 제시한다.

• Communications of Mathematical Education
• /
• v.11
• /
• pp.47-69
• /
• 2001

본 논문은 고등학교 교육과정상에서 학습자들이 오류를 범하기 쉽고, 어려워 하는 극한에 대해 보다 효과적인 지도방법을 제시한다. 현실적으로 교수활동은 교실이라는 공간에서 일정한 수업시간동안에 교사와 학습자와의 관계속에서 이루어진다. 그 속에서 학습자들은 주변의 세계를 관찰함으로써, 혹은 추측과 반박을 통해 시행착오적으로 사고함으로써 혹은 모순, 어려움, 불균형을 일으키는 주위환경에 동화 ${\cdot}$ 조절을 함으로써 자신을 적응시켜 가면서 학습하게 된다. 따라서 교수학적 의도가 미비한 환경은 학습자에게 획득하기를 기대하는 학습을 할 수 없게 한다. Brousseas의 교수학적 상황론에 근거하여 교육의 현장인 교실에서의 교사와 학생간의 상호작용에 따른 교수-학습의 중요성에 초점을 둔 본 논문은 Freudenthal의 역사발생적 원리에 의한 극한의 정의와 학습자의 오류수정을 위한 교수학습 전략으로 Lakatos의 발견술을 제안하였다. 또한 극한 개념에 대해 실생활에서 학습자에게 쉽게 동화 ${\cdot}$ 조절이 일어날 수 있는 학습 방법을 제안하였다.

• School Mathematics
• /
• v.5 no.1
• /
• pp.77-95
• /
• 2003

We have web-based online discussion to implement active interaction and a variety of communicative activities. I have gathered the following research questions to study about the meaning of web-based online discussion as a mathematical communication teaching method. First, what changes are there in students mathematical communication ability in web-based online discussion\ulcorner Second, how do students evaluate the web-based online discussion experience\ulcorner In this web-based online discussion, groups of middle school first grade 34 students and each group had chatting at 8 times for 10 weeks. I analyzed what they had discussed by the prints that they had sent me by e-mail. I also surveyed what they had experienced and analyzed them. In this research, the online web based discussion has given positive influence on students' competence of speaking, writing, reading and listening which are crucial to mathematical communication. Students' mathematic thinking power improved and attitudes to mathematics have become more positive.

• School Mathematics
• /
• v.5 no.1
• /
• pp.115-133
• /
• 2003

Investigation of the students' mathematical misconceptions is very important for improvement in the school mathematics teach]ng and basis of curriculum. In this study, we categorize second-grade middle school students' misconceptions on the learning of linear function and make a comparative study of the error-remedial effect of students' collaborative learning vs explanatory leaching. We also investigate how to change and advance students' self-diagnosis and treatment of the milton ceptions through the collaborative learning about linear function. The result of the study shows that there are three main kinds of students' misconceptions in algebraic setting like this: (1) linear function misconception in relation with number concept, (2) misconception of the variables, (3) tenacity of specific perspective. Types of misconception in graphical setting are classified into misconception of graph Interpretation and prediction and that of variables as the objects of function. Two different remedies have a distinctive effect on treatment of the students' misconception under the each category. We also find that a misconception can develop into a correct conception as a result of interaction with other students.