• Title/Summary/Keyword: Guided Reinvention

Search Result 8, Processing Time 0.017 seconds

A study on the teaching of proofs based on Freudenthal's guided reinvention principle (Freudenthal의 안내된 재발명 원리를 적용한 증명 지도 방안에 대한 연구)

  • Han, Hye-Sook;Moon, Su-Jin
    • Communications of Mathematical Education
    • /
    • v.23 no.1
    • /
    • pp.85-108
    • /
    • 2009
  • The purposes of the study were to develop instructional materials based on Freudenthal's guided reinvention principle for teaching proofs and to investigate how the teaching method based on guided reinvention principle affects on 8th grade students' ability to write proofs and learning attitude toward proofs. Teaching based on guided reinvention principle placed emphasis on providing students opportunities to make a mathematical statement and prove the statement by themselves throughout various activities such as exploring, conjecturing, and testing the conjectures. The study found that students who studied proving with instructional materials developed by guided reinvention principle showed statistically higher mean scores on the posttest than students who studied by a traditional teaching method depending onteacher's explanation. Especially, on the posttest item which requested to prove a whole statement without presenting a picture corresponding to the statement, a big difference among students' responses was found. Many more students in the traditional group did not provide any response on the item. According to the results of the questionnaire regarding students' learning attitudes, the group who studied proving by guided reinvention principle indicated relatively more positive attitudes toward learning proofs than the counterparts.

  • PDF

A case study of the impact of inquiry-oriented instruction with guided reinvention on students' mathematical activities (안내된 재발명을 포함한 탐구-중심 수업이 학생들의 수학적 활동에 미치는 영향에 관한 사례연구)

  • Kim, Ik-Pyo
    • The Mathematical Education
    • /
    • v.49 no.2
    • /
    • pp.223-246
    • /
    • 2010
  • Goos(2004) introduced educational researchers' demand for change on the way that mathematics is taught in schools and the series of curriculum documents produced by the National council of Teachers of Mathematics. The documents have placed emphasis on the processes of problem solving, reasoning, and communication. In Korea, the national curriculum documents have also placed increased emphasis on mathematical activities such as reasoning and communication(1997, 2007).The purpose of this study is to analyze the impact of inquiry-oriented instruction with guided reinvention on students' mathematical activities containing communication and reasoning for science high school students. In this paper, we introduce an inquiry-oriented instruction containing Polya's plausible reasoning, Freudenthal's guided reinvention, Forman's sociocultural approach of learning, and Vygotsky's zone of proximal development. We analyze the impact of mathematical findings from inquiry-oriented instruction on students' mathematical activities containing communication and reasoning.

Guided Reinvention of Euler Algorithm: -An Analysis of Progressive Mathematization in RME-Based Differential Equations Course- (오일러 알고리즘의 안내된 재 발명 -RME 기반 미분 방정식 수업에서 점진적 수학화 과정 분석-)

  • 권오남;주미경;김영신
    • The Mathematical Education
    • /
    • v.42 no.3
    • /
    • pp.387-402
    • /
    • 2003
  • Realistic Mathematics Education (RME) focuses on guided reinvention through which students explore experientially realistic context problems to develop informal problem solving strategies and solutions. This research applied this philosophy of RME to design a differential equation course at a university level. In particular, the course encouraged the students of the course to use numerical methods to solve differential equations. In this context, the purpose of this research was to describe the developmental process in which the students constructed and reinvented Euler algorithm in the class. For the purpose, this paper will present the didactical principle of RME and describe the process of developmental research to investigate the inferential process of students in solving the first order differential equation numerically. Finally, the qualitative analysis of the students' reasoning and use of symbols reveals how the students reinvent Euler algorithm under the didactical principle of guided reinvention. In this research, it has been found that the students developed deep understanding of Euler algorithm in the class. Moreover, it has been shown that the experience of doing mathematics in the course had a positive impact on students' mathematical belief and attitude. These findings imply that the didactical principle of RME can be applied to design university mathematical courses and in general, provide a perspective on how to reform mathematics curriculum at a university level.

  • PDF

Development and Application of Teaching and Learning Materials for Gifted Students in Elementary School (초등수학영재를 위한 교수학습 자료 개발 및 적용)

  • Kim, Sung Joon
    • East Asian mathematical journal
    • /
    • v.37 no.4
    • /
    • pp.443-460
    • /
    • 2021
  • This study analyzes the characteristics of elementary math gifted classes through the development and application of teaching and learning materials. We used the guided reinvention methods including quasi-experiential perspectives. To this end, the applicability of Lakatos' quasi-empirical mathematical philosophy in elementary mathematics was examined, and the criteria for the development of teaching and learning materials for gifted students were presented, and then this study was conducted in this theoretical background. The subjects of the study were 21 elementary students at P University's Institute of Science and Gifted Education, and non-face-to-face real-time classes were conducted. Classes were divided into introduction, deployment1, deployment2, organization stages, and in each stage, small group cooperative learning was conducted based on group activities, and in this process, the characteristics of elementary mathematics gifted were analyzed. As a result of the study, elementary mathematics gifted students did not clearly present the essence of justification in the addition algorithm of fractions, but presented various interpretations of 'wrong' mathematics. They also showed their ingenuity in the process of spontaneously developing 'wrong' mathematics. On the other hand, by taking interest in new mathematics starting from 'wrong' mathematics, negative perceptions about it could be improved positively. It is expected that the development of teaching and learning materials dealing with various and original topics for the gifted students in elementary school will proceed through follow-up research.

How can we teach the 'definition' of definitions? (정의의 '정의'를 어떻게 가르칠 것인가?)

  • Lee, Jihyun
    • Journal of the Korean School Mathematics Society
    • /
    • v.16 no.4
    • /
    • pp.821-840
    • /
    • 2013
  • Definition of geometric figure in middle school geometry seems to mere meaning of the term which could be perceived visually through its shape. However, Much research reported the low achievements of definitions of basic geometric figures. It suggested the limitation of instrumental understanding. In this research, I guided gifted middle school students to reinvent definitions of basic geometric figure by the deductive organization of its properties as Freudenthal pointed. These students understood relationally about why some geometric figure can be defined this way and how it could be defined equally via other properties. This analysis of reinventing of definitions will be a stepping stone to reflect on the pedagogical problems in teaching geometry and to search the new alternatives.

  • PDF

Imagining the Reinvention of Definitions : an Analysis of Lesson Plays ('정의'의 재발명을 상상하다 : Lesson Play의 분석)

  • Lee, Ji Hyun
    • School Mathematics
    • /
    • v.15 no.4
    • /
    • pp.667-682
    • /
    • 2013
  • Though teachers' lesson plays, this article analysed teachers' knowledge for mathematical teaching about mathematical definitions and their pedagogical difficulties in teaching defining. Although the participant teachers didn't transmit definitions to students and suggested possible definitions of the given geometric figure in their imaginary lessons, they didn't teach defining as deductive organization of properties of the geometric figure. They considered mathematical definition as a mere linguistic convention of a word, so they couldn't appreciate the necessity of deductive organization in teaching definitions, and the arbitrary nature of mathematical definitions. Therefore, for learning to teach definitions differently, it is necessary for teachers to reflect the gap between the everyday and mathematical definitions in teachers'education.

  • PDF

A Case Study on Guiding the Mathematically Gifted Students to Investigating on the 4-Dimensional Figures (수학 영재들을 4차원 도형에 대한 탐구로 안내하는 사례 연구)

  • Song, Sang-Hun
    • Journal of Gifted/Talented Education
    • /
    • v.15 no.1
    • /
    • pp.85-102
    • /
    • 2005
  • Some properties on the mathematical hyper-dimensional figures by 'the principle of the permanence of equivalent forms' was investigated. It was supposed that there are 2 conjectures on the making n-dimensional figures : simplex (a pyramid type) and a hypercube(prism type). The figures which were made by the 2 conjectures all satisfied the sufficient condition to show the general Euler's Theorem(the Euler's Characteristics). Especially, the patterns on the numbers of the components of the simplex and hypercube are fitted to Binomial Theorem and Pascal's Triangle. It was also found that the prism type is a good shape to expand the Hasse's Diagram. 5 mathematically gifted high school students were mentored on the investigation of the hyper-dimensional figure by 'the principle of the permanence of equivalent forms'. Research products and ideas students have produced are shown and the 'guided re-invention method' used for mentoring are explained.

A Study of Realistic Mathematics Education - Focusing on the learning of algorithms in primary school - (현실적 수학교육에 대한 고찰 - 초등학교의 알고리듬 학습을 중심으로 -)

  • 정영옥
    • Journal of Educational Research in Mathematics
    • /
    • v.9 no.1
    • /
    • pp.81-109
    • /
    • 1999
  • This study aims to reflect the basic principles and teaching-teaming principles of Realistic Mathematics Education in order to suppose an way in which mathematics as an activity is carried out in primary school. The development of what is known as RME started almost thirty years ago. It is founded by Freudenthal and his colleagues at the former IOWO. Freudenthal stressed the idea of matheamatics as a human activity. According to him, the key principles of RME are as follows: guided reinvention and progressive mathematisation, level theory, and didactical phenomenology. This means that children have guided opportunities to reinvent mathematics by doing it and so the focal point should not be on mathematics as a closed system but on the process of mathematisation. There are different levels in learning process. One should let children make the transition from one level to the next level in the progress of mathematisation in realistic contexts. Here, contexts means that domain of reality, which in some particular learning process is disclosed to the learner in order to be mathematised. And the word of 'realistic' is related not just with the real world, but is related to the emphasis that RME puts on offering the students problem situations which they can imagine. Under the background of these principles, RME supposes the following five instruction principles: phenomenological exploration, bridging by vertical instruments, pupils' own constructions and productions, interactivity, and interwining of learning strands. In order to reflect how to realize these principles in practice, the teaming process of algorithms is illustrated. In this process, children follow a learning route that takes its inspiration from the history of mathematics or from their own informal knowledge and strategies. Considering long division, the first levee is associated with real-life activities such as sharing sweets among children. Here, children use their own strategies to solve context problems. The second level is entered when the same sweet problems is presented and a model of the situation is created. Then it is focused on finding shortcomings. Finally, the schema of division becomes a subject of investigation. Comparing realistic mathematics education with constructivistic mathematics education, there interaction, reflective thinking, conflict situation are many similarities but there are alsodifferences. They share the characteristics such as mathematics as a human activity, active learner, etc. But in RME, it is focused on the delicate balance between the spontaneity of children and the authority of teachers, and the development of long-term loaming process which is structured but flexible. In this respect two forms of mathematics education are different. Here, we learn how to develop mathematics curriculum that respects the theory of children on reality and at the same time the theory of mathematics experts. In order to connect the informal mathematics of children and formal mathematics, we need more teachers as researchers and more researchers as observers who try to find the mathematical informal notions of children and anticipate routes of children's learning through thought-experiment continuously.

  • PDF