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Meaning and Structure of Understanding in Mathematics Education (수학 교육에서 '이해'의 의미와 구조에 대한 고찰)

  • 정인철
    • The Mathematical Education
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    • v.42 no.1
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    • pp.11-18
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    • 2003
  • One of the terms that are most often used in mathematics classrooms by either teachers or students might be about 'understanding' of mathematical concepts. Although 'understanding' in mathematics teaching and learning has been highly emphasized by many people, there is no exact and undebatable definition of 'understanding' as of yet. This paper tries to contribute to unfolding the meaning and the structure of understanding in mathematics education along with various literature and finally enhance our understanding of 'understanding' in mathematics education.

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Paying Attention to Students and Promoting Students' Mathematics Understanding

  • Li, Miao;Tang, Jian-Lan;Huang, Xiao-Xue
    • Research in Mathematical Education
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    • v.12 no.1
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    • pp.67-83
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    • 2008
  • Promoting students' mathematics understanding is an important research theme in mathematics education. According to general theories of learning, mathematics understanding is close to active learning or significant learning. Thus, if a teacher wants to promote his/her students' mathematics understanding, he/she should pay attention to the students so that the students' thinking is in active situation. In the first part of this paper, some mathematics teachers' ideas about paying attention to their students in Chinese high school are given by questionnaire and interview. In the second part of this paper, we give some teaching episodes about how experienced mathematics teachers promote their students' mathematics understanding based on paying attention on them.

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"Once Mathematics is Understood, Then..." -An Elementary Teacher′s Teaching of Mathematics with Understanding- ("이해만 됐다면 수학은..." -어느 초등 교사의 이해 중심의 수학지도-)

  • 조정수
    • The Mathematical Education
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    • v.41 no.2
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    • pp.173-187
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    • 2002
  • The purpose of this study through ethnographic inquiry is to describe how an elementary teacher teaches mathematics with understanding. The ways that teachers'beliefs affect instructional activities, what means understanding from the view of cognitive psychology, and ethnographic research tradition were reviewed to anchor theoretical background of this study. A third-grade teacher and his 45 students were selected in order to capture vivid and thick descriptions of the teaching and learning activities of mathematics. Three major sources of data, that is, participant-observation with video taping, formal and informal interviews with the teacher and his students, and a variety of official documents were collected. These data were analyzed through two phases: data analysis in the field and after the fieldwork. According to data analysis, ‘teaching mathematics with understanding’ was identified as the teachers central belief of teaching mathematics. In order to implement his belief in teaching practices, the teacher made use of three strategies: ⑴ valuing individual student's own way of understanding, ⑵ bring students' everyday experiences into mathematics classroom, and ⑶ lesson objectivies stated by students. It is suggested for future research that concrete and specific norms of mathematics classroom for the improvement of mathematics understanding are needed to be identified and that experienced and skillful teachers' practical knowledge should be incorporated with theories of teaching mathematics and necessarily paid more attention by mathematics educators.

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Toward Students' Full Understanding of Trigonometric Ratios

  • Yi, Jung-A;Yoo, Jae-Geun;Lee, Kyeong Hwa
    • Research in Mathematical Education
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    • v.17 no.1
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    • pp.63-78
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    • 2013
  • Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

The Analysis on Students' Understanding of Mathematics Terms Being Used in Elementary School Mathematics Textbooks - Centering on the Field of Geometry - (초등 수학 교과서에 사용되고 있는 수학 용어에 대한 학생들의 이해도 분석 - 도형 영역을 중심으로 -)

  • Kwon, Yoo-Mi;Ahn, Byoung-Gon
    • Journal of Elementary Mathematics Education in Korea
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    • v.9 no.2
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    • pp.137-159
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    • 2005
  • As what exactly understands a meaning of mathematics terms, is a starting point of mathematical thinking, it plays a very important role in the mathematics learning. What understood mathematics terms which were defined here, includes not only the terms of comprising its definition, but also all of the understanding in context, situation, intention and purpose, which came to give its definition. Due to this reason, it needs to be examined how much students are correctly understanding about mathematics terms which appear in the texts, and to seek for its cause for the terms which are felt to be difficult. Accordingly, this study investigated into mathematics terms which are used for the field of geometry in the elementary school mathematics textbooks, and tried to analyze students' understanding level about each term.

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Korean Mathematics Adds Value to Teachers' Conceptual Understanding in the United States

  • Janice, Grow-Maienza;Alberts, Scott;Kim, Hyun-Joo
    • Research in Mathematical Education
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    • v.13 no.3
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    • pp.235-250
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    • 2009
  • Researchers at Truman State University in Missouri, located in the heartland of the United States, have been using materials adapted from the English translations of the sixth national primary mathematics curriculum from Korea for professional development and assessment with groups of Missouri teachers for the purpose of enhancing teachers' understanding of the fundamentals of mathematics since 2002 [gecKo Mathematics (2008). Korean Mathematics in American Classrooms. Edited by J. Grow-Maienza. Adapted from Korean Mathematics (2001). Kirksville, MO: Truman State University. http://kmath.truman.edu/]. A professional development initiative for 50 teachers conducted in Missouri this past year is reported here. Significant gains in teacher understanding of fundamental mathematics concepts and pedagogy necessary for student achievement in primary mathematics were found as a result of the initiative.

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A Note on Understanding and Problem Solving in Mathematics (수학에 있어서 이해와 문제 해결에 관한 소고)

  • Kang Shin Po
    • Journal of Elementary Mathematics Education in Korea
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    • v.3 no.1
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    • pp.41-59
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    • 1999
  • We believe that there can be a mutually supportive relationship between emphasizing problem solving and emphasizing understanding in mathematics instruction, when teachers teach via problem solving, as well as about it and for it they provide their student with a powerful and important means of developing their own understanding. As students' understanding of mathematics becomes deeper and richer, their ability to use mathematics to solve problem increases.

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The Study on the Investigation of the Mathematics Teaching Evaluation Standards Focused on Understanding of Learners (교사의 학습자 이해 지식에 초점을 둔 수학 수업평가 요소 탐색)

  • Hwang, Hye-Jeang
    • Journal of the Korean School Mathematics Society
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    • v.13 no.4
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    • pp.569-594
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    • 2010
  • On the standards or elements of teaching evaluation, the Korea Institute of Curriculum and Evaluation(KICE) has carried out several research as follows : 1) establishment of observation elements for selecting examples of good mathematics instruction between 2001 and 2002, 2) development of the standards on teaching evaluation between 2004 and 2006, and 3) investigation on the elements of Pedagogical Content Knowledge including understanding of learners between 2007 and 2008. The purposes of development of mathematics teaching evaluation standards through those studies were to improve not only mathematics teachers' professionalism but also their own teaching methods or strategies. In this study, the standards were revised and modified by analyzing the results of those three studies (namely, evaluation standards) focused on the teacher knowledge of learners' understanding. For this purpose, the meaning of learners' understanding was also investigated in-depth. Finally, the concrete elements on teaching evaluation focused on the teacher knowledge of learners' understanding in math class were new developed, based on the literature reviews on learners' understanding. Then, those evaluation elements were developed according to the five domains of learners' understanding such as evaluation domains such as students' intellectual and achievement level, students' misconception in math, students' motivation on learning, students' attitude on mathematics learning, and students' learning strategies.

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Children's Representations of Numbers

  • Park, Han-Shick
    • Research in Mathematical Education
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    • v.1 no.1
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    • pp.1-5
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    • 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.

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First-year Undergraduate Students' Understanding about Statements (대학 신입생들의 명제에 대한 이해)

  • Kim, Young-Ok
    • School Mathematics
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    • v.11 no.2
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    • pp.261-280
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    • 2009
  • This study was motivated by recognizing the weakness of teaching and learning about the concepts of statements in high school mathematics curriculum. To report the reality of students' understanding about statements, this study investigated the 33 first-year undergraduate students' understanding about the concepts of statements by giving them 22 statement problems. The problems were selected based on the conceptual framework including five types of statement concepts which are considered as the key ideas for understanding mathematical reasoning and proof in college level mathematics. The analysis of the participants' responses to the statement problems found that their understanding about the concepts of prepositions are very limited and extremely based on the instrumental understanding applying an appropriate remembered rule to the solution of a preposition problem without knowing why the rule works. The results from this study will give the information for effective teaching and learning of statements in college level mathematics, and give the direction for the future reforming the unite of statements in high school mathematics curriculum as well.

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