• Title/Summary/Keyword: mathematical knowledge

Search Result 865, Processing Time 0.027 seconds

A Short Discussion about Connection of Informal and Formal Mathematical Knowledge (비형식적 수학적 지식과 형식적 수학적 지식의 결합에 관한 소고)

  • 김진호
    • School Mathematics
    • /
    • v.4 no.4
    • /
    • pp.555-563
    • /
    • 2002
  • The purpose of this paper is to try formulating a working definition of connection of informal and formal mathematical knowledge. Many researchers have suggested that informal mathematical knowledge should be connected with school mathematics in the process of learning and teaching it. It is because informal mathematical knowledge might play a important role as a cognitive anchor for understanding school mathematics. To implement the connection of them we need to know what the connection means. In this paper, the connection between informal and formal mathematical knowledge refers to the making of relationship between common attributions involved with the two knowledge. To make it clear, it is discussed that informal knowledge consists of two properties of procedures and conceptions as well as formal mathematical knowledge does. Then, it is possible to make a connection of them. Now it is time to make contribution of our efforts to develop appropriate models to connect informal and formal mathematical knowledge.

  • PDF

Relationship of mathematical knowledge for teaching and mathematical quality in instruction: Focus on high schools (수업을 위한 수학적 지식과 수업의 수학적 질 사이의 관계: 고등학교를 중심으로)

  • Kim, Yeon
    • The Mathematical Education
    • /
    • v.59 no.3
    • /
    • pp.237-254
    • /
    • 2020
  • The current study investigated the relationships between mathematical knowledge for teaching and the mathematical quality in instruction in order to gain insight about teacher education for secondary teachers in South Korea. We collected and analyzed twelve high school teachers' scores of the multiple-choice assessment for mathematical knowledge for teaching developed by the Measures of Effective Teaching project. Their instruction was video recorded and analyzed with the mathematical quality in instruction developed by the Learning Mathematics for Teaching project. We also interviewed the teachers about how they planned and assessed their instruction by themselves in order to gain information about their intention and interpretation about instruction. There was a statistically significant and positive association between the levels of mathematical knowledge for teaching and the mathematical quality in instruction. Among three dimensions of the mathematical quality in instruction, mathematical richness seemed most relevant to mathematical knowledge for teaching because subject matter knowledge plays an important role in mathematical knowledge for teaching. Furthermore, working with students and mathematics as well as students participation were critical to decide the quality of instruction. Based on these findings, the current study discussed offering opportunities to learn mathematical knowledge for teaching and philosophy about how teachers need to consider students in high schools particularly in terms of constructivism.

A Study on Teachers' Conceptions of Mathematics (교사의 수학적 관념에 대한 연구)

  • 김용대
    • The Mathematical Education
    • /
    • v.41 no.1
    • /
    • pp.35-44
    • /
    • 2002
  • The purpose of this study is to estimate teachers'conceptions of mathematics through the conception on compositions of mathematical knowledge, the conception on structure of mathematical knowledge, the conception on status of mathematical knowledge, the conception on mathematical activity, and the conception of mathematics learning. This study reached the following conclusions: Most of teachers has more internal viewpoint than external viewpoint on the compositions, structures and status of mathematical knowledge, mathematical activity and mathematics learning.

  • PDF

Analysis of Mathematics Preservice Teachers' Mathematical Content Knowledge based on PISA 2012 Items (PISA 2012 공개 문항을 활용한 예비수학교사의 수학내용지식 분석 사례연구)

  • Rim, Haemee;Lee, Min Hee
    • The Mathematical Education
    • /
    • v.54 no.3
    • /
    • pp.207-222
    • /
    • 2015
  • Mathematics preservice teachers' Mathematical Content Knowledge ("MCK") includes not only knowledge for mathematics, but also academic knowledge for school mathematics and mathematical process knowledge. We can consider the items in PISA 2012 as suitable tools to assess process knowledge as well as mathematical content knowledge because these items are developed by competent international educational experts. Therefore, the responses to items with the low percentage of correct answers in conjunction with the mathematical contents were analyzed with focus on FMC. The results showed the reasoning competency in responses using the conditions of the problem and of understanding the conditions after reading the complex problems within the context (i.e. the reasoning and argumentation competency, and communication competency) requires improvements. Furthermore the results indicated the errors due to a lack of ability of devising strategies for problem solving. Based on the foregoing results, the implications towards the directions of the education for the preservice mathematics teachers have been derived.

Effects of Constructivism-Based Teacher Education Program for Supporting Infant's Mathematical Inquiry Activity on Variables Related to Infant Teacher's Mathematics Teaching (영아 수학적 탐색활동 지원을 위한 구성주의 교사교육프로그램이 영아교사의 수학지도 관련 변인에 미치는 효과)

  • Ko, Eunji;Kim, Jihyun
    • Human Ecology Research
    • /
    • v.58 no.1
    • /
    • pp.105-120
    • /
    • 2020
  • This study helps infant teachers practice a constructivism-based teacher education program that supports infant mathematical inquiry activities and examines improvements in mathematical teaching knowledge, mathematical teaching initiatives, mathematical interaction, constructivism belief and mathematical teaching efficacy. Twenty two experiment group infant teachers and twenty two comparison group infant teachers were chosen at two workforce educare centers. The experiment group infant teachers participated in 18 sessions of a constructivism teacher training program for 8 weeks, but the comparison group infant teachers did not take part in the program. Pretest and post-tests were implemented for the mathematical teaching knowledge, mathematical teaching initiatives, mathematical interactions, constructivism belief and mathematical teaching efficacy in the experiment group. Independent sample t-test and ANCOVA were tested using Windows SPSS statistics 21.0. The homogeneity test for the experiment and comparison group revealed significant differences. ANCOVA was carried out after the pretest score was controlled as a co-variance. Significant differences were indicated in mathematical teaching knowledge, mathematical teaching initiative, mathematical interaction, constructivism belief and mathematical teaching efficacy. The results indicated that a constructivism-based teacher education program to support infant mathematical inquiry activities influenced improvements in mathematical teaching knowledge, mathematical teaching initiative, mathematical interaction, constructivism belief and mathematical teaching efficacy. This study proved the effects of the program based on constructivism theory content for the knowledge, skills and attitude about infant teaching of mathematical initiatives and practiced a program of exploration, investigation, application and assessment for infant teachers. The results can help infant teachers teach mathematical exploration activities and help activate infant mathematical exploration activities.

Theoretical Discussion on Mathematical Knowledge for Teaching from Constructivists' Perspective

  • LEE, Soo Jin;SHIN, Jaehong
    • Research in Mathematical Education
    • /
    • v.19 no.2
    • /
    • pp.101-115
    • /
    • 2015
  • In the present paper, we argue any research concerning human knowledge construction, components, or types needs to clarify its epistemological stance regarding 'knowledge' in that such viewpoint might have much influence on the nature of knowledge the researcher sees and the way in which evidence for knowledge development is gathered. Thus, we suggest two alternative research groups who conducted their studies on mathematical knowledge for teaching with an explicit epistemological standpoint. We finalize our discussion by reviewing concrete examples in the previous literature on teacher knowledge of fraction conducted by the two groups.

Pre-service Teachers' Conceptualization of Arithmetic Mean (산술 평균에 대한 예비교사들의 개념화 분석)

  • Joo, Hong-Yun;Kim, Kyung-Mi;Whang, Woo-Hyung
    • The Mathematical Education
    • /
    • v.49 no.2
    • /
    • pp.199-221
    • /
    • 2010
  • The purpose of the study were to investigate how secondary pre-service teachers conceptualize arithmetic mean and how their conceptualization was formed for solving the problems involving arithmetic mean. As a result, pre-service teachers' conceptualization of arithmetic mean was categorized into conceptualization by "mathematical knowledge(mathematical procedural knowledge, mathematical conceptual knowledge)", "analog knowledge(fair-share, center-of-balance)", and "statistical knowledge". Most pre-service teachers conceptualized the arithmetic mean using mathematical procedural knowledge which involves the rules, algorithm, and procedures of calculating the mean. There were a few pre-service teachers who used analog or statistical knowledge to conceptualize the arithmetic mean, respectively. Finally, we identified the relationship between problem types and conceptualization of arithmetic mean.

A Study on the Relationship between Mathematics Teachers' Knowledge and Teaching Practice (수학교사의 지식과 수업 실제와의 관계)

  • 신현용;이종욱
    • The Mathematical Education
    • /
    • v.43 no.3
    • /
    • pp.257-273
    • /
    • 2004
  • In this paper, we analyze what the components of mathematics teacher` knowledge are, and find that mathematics teacher need knowledge of three areas: subject matter knowledge, pedagogical knowledge, and pedagogical content knowledge. Studies of practicing teachers suggest that When teachers lack understanding in their respective disciplines, it inhibits them from providing students the best learning opportunities, but that a teacher possessing pedagogical content knowledge provides learners with multiple approaches into learning. Some teachers having sound knowledge of mathematics and students were able to respond appropriately to students' questions, design appropriate learning activities involving a variety of mathematical representations, and orchestrate mathematical discourse in the classroom. Thus, it appears that mathematics teachers' knowledge positively affect teaching and student learning..

  • PDF

An Analysis on the Elementary Students' Mathematical Thinking in the Mathematical Problem Solving Processes (수학 문제해결 과정에서 나타나는 초등학생들의 수학적 사고 분석)

  • Cho, Doo-Kyoung;Park, Man-Goo
    • The Mathematical Education
    • /
    • v.47 no.2
    • /
    • pp.169-180
    • /
    • 2008
  • The purpose of this study was to analyze the elementary students' mathematical thinking, which is found during mathematical problem solving processes based on mathematical knowledge, heuristics, control, and mathematical disposition. The participants were 8 fifth grade elementary students in Seoul. A qualitative case study was used for investigating the students' mathematical thinking. The data were coded according to the four components of the students' mathematical thinking. The results of the analyses concerning mathematical thinking of the elementary students were as follows: First, in terms of mathematical knowledge, the elementary students frequently used conceptual knowledge, procedural knowledge and informal knowledge during problem solving processes. Second, students tended not to find new heuristics or apply new one, but they only used the heuristics acquired from the experiences of the class and prior experiences. Third, control was found while students were solving problems. Last, mathematical disposition influenced on the mathematical problem solving processes. Teachers need to in-depth observations on the problem solving processes of students, which leads to teachers'effective assistance on facilitating students' problem solving skills.

  • PDF

A Study on Reconstruction of Trigonometry Based on Ascent from the Abstract to the Concrete (추상에서 구체로의 상승을 통한 삼각함수의 재구성)

  • Kang, Mee Kwang;Han, Inki
    • The Mathematical Education
    • /
    • v.56 no.1
    • /
    • pp.101-118
    • /
    • 2017
  • In this article we study a reconstruction of mathematical knowledge on trigonometry by the method of ascent from the abstract to the concrete from the pedagogical viewpoint of dialectic. The direction of education is shifting in a way that emphasizes the active constitution of knowledge by the learning subjects from the perspective that knowledge is transferred from the teacher to the student. In mathematics education, active discussions on the construction of mathematical knowledge by learners have been going on since the late 1990s. In Korea, concepts and aspects of constructivism such as operational constructivism, radical constructivism, and social constructivism were introduced. However, examples of practical construction according to the direction of construction of mathematical knowledge are very hard to find. In this study, we discuss the direction of the actual construction of mathematical knowledge and suggest a concrete example of the actual construction of trigonometry knowledge from a constructivist point of view. In particular, we discuss the process of the construction of theoretical knowledge, the ascent from the abstract to the concrete, based on the literature study from the pedagogical viewpoint of dialectic, and show how to construct the mathematical knowledge on trigonometry by the method of ascent from the abstract to the concrete. Through this study, it is expected to introduce the new direction and new method of knowledge construction as 'the ascent from the abstract to the concrete', and to present the possibility of applying dialectic concepts to mathematics education.