• Journal of the Korean School Mathematics Society
• /
• v.15 no.1
• /
• pp.137-154
• /
• 2012

The purposes of this study are to develop the formative assessment program in geometry area for a 1st-grade class of middle school and to test the effect of this program. This formative assessment program was based on mathematics curriculum for the 1st graders of middle school. In addition, we examined how the 1st graders of middle school understand the geometric concepts by analyzing their response in the pretest and the posttest. This formative assessment program and the results of its analysis would be the useful information for the effective teaching and learning in geometry area for the 1st grades of middle school.

• Communications of Mathematical Education
• /
• v.15
• /
• pp.141-146
• /
• 2003

중학교 기하교육의 목적은 학생들의 수학적인 상황을 보는 기하학적인 직관과 논리적 추론능력의 향상이다. 그러나 이 두 가지 모두 만족스럽지 못한 실정이다. 본 고에서는 중학교 기하교육의 문제를 직관기하와 형식기하의 단절이라는 보고, 직관기하에서 증명의 학습요소를 미리 학습하여 직관기하와 형식기하를 연결하자는 대안을 제시한다. 이를 위해 7-나 교과서의 증명요소를 분석하고자 하였다. 관련문헌을 검토하여 7가지 증명의 학습요소를 선정한 후, 교과서를 분석하였다. 분석 결과, 기호화를 제외한 다른 증명의 학습요소는 매우 빈약한 것으로 나타났다. 직관기하 영역에 대한 교과서 구성이 개선될 필요가 있음을 알 수 있다.

• Proceedings of the Korea Society of Mathematical Education Conference
• /
• 2008.05a
• /
• pp.17-28
• /
• 2008

이 논문은 중학교 기하 영역의 수업에 대한 학생들의 성취도가 낮은 것을 관찰하고, 그에 대한 고민으로 교육과정을 분석하고, 수학교육의 질적 접근을 위한 교수 실험을 통해 실제 중학교 과정에서 운용되는 논증기하 교육의 문제점과 그 대안을 탐색하고자 하였다. 본 연구에서는 교사가 반드시 갖춰야 할 지식으로 Shulman(1986)이 제시한 교과 내용 지식과 교수학적 내용 지식, 그리고 교육과정 관련 지식을 받아들였으며, 중학교 기하 영역에서 이런 지식을 갖추기 위해 교사가 폭넓은 고민을 하여 수업의 개선점을 찾는 과정을 보여주고 있다. 연구를 통해서 학생들에게 명제를 지도할 때 주의할 점과 학습자에게 증명을 하도록 제시하는 방법상의 문제점, 그리고 이등변삼각형의 지도에서의 그 증명이 갖는 의미를 잘 이해하여 학생들에 증명 학습에 진정한 도움이 될 수 있는 방향을 탐색하였다. 그리고 절차만을 학습시키는 현행 작도 수업을 개선하기 위한 여러 시도와 등변사다리꼴의 학습에서와 같이 학생들이 수학 용어를 되돌아보는 수업이 필요성을 탐색하여, 많은 교수 실험을 통한 교육과정의 바람직한 개정을 제안하였다.

• Journal for History of Mathematics
• /
• v.26 no.1
• /
• pp.33-56
• /
• 2013

This is a literature study about the concept of 'Division into Equal Parts' in middle school geometry. First, we notice that the concept of the division into equal parts in middle school geometry is given in four themes, which are those of line segments, angles, arches and areas. Second, we investigate and analyse the historical backgrounds of these four kinds of divisions into equal parts. Third, the possibility of extension in terms of method and concept was researched. Through the result of this study, we suggest that it is desirable to use effective utility of history in mathematical teaching and learning in middle school.

• Journal of Educational Research in Mathematics
• /
• v.16 no.1
• /
• pp.1-23
• /
• 2006

It is regarded as critical to analyse and re-appreciate Euclidean geometry for the sake of improving school geometry This study, a critical analysis of demonstrative plane geometry in current secondary school mathematics with an eye to the viewpoints of 'Elements of Geometry', is conducted with this purpose in mind. Firstly, the 'Elements' is analysed in terms of its educational purpose, concrete contents and approaching method, with a review of the history of its teaching. Secondly, the 'Elemens de Geometrie' by Clairaut and the 'histo-genetic approach' in teaching geometry, mainly the one proposed by Branford, are analysed. Thirdly, the basic assumption, contents and structure of the current textbooks taught in secondary schools are analysed according to the hypothetical construction, ordering and grouping of theorems, presentations of proofs, statements of definitions and exercises. The change of the development of contents over time is also reviewed, with a focus on the proportional relations of geometric figures. Lastly, tile complementary way of integrating the two 'Elements' is explored.

• Communications of Mathematical Education
• /
• v.24 no.3
• /
• pp.691-708
• /
• 2010

The purpose of this study is to analyze 'datum' of 'The Data' in the textbooks of middle school on the basis of 'The Data of Euclid' and develop datum. For this, the followings are conducted. First, the distinctive structure of datum of 'The Data' is considered. Second, some learning materials the contents of geometry in the textbooks of middle school are analyzed and the mathematical meanings are explored. Third, the applicable datum to geometry education of middle school are developed and the way of educational use is studied. The hopefully, the result of this study will make school mathematics education more plentiful and give meaningful implications to revision of mathematics education curriculum and the improvement of teaching and learning.

• Journal of the Korean School Mathematics Society
• /
• v.14 no.3
• /
• pp.325-337
• /
• 2011

There have been several studies regarding strict and formal proof in the field of geometry in middle school curriculum, and the level of proof has been gradually lowered along with the changes in the curriculum. In the 2011 Revised Middle School Math Curriculum, there have been efforts to eliminate the term 'proof' and instead to replace it with the new one, 'justification'. Therefore, this study intends to present specific and practical examples of justification by analyzing the current math textbook especially in the field of geometry. As a result, it identified that strict and practical proof has been sharply increased in the second year of middle school. It also witnessed the possibility of justification from the various examples presented in the first, second, and the third year of the middle school math textbook.

• Communications of Mathematical Education
• /
• v.13 no.2
• /
• pp.515-525
• /
• 2002

중학교 기하영역 중 피타고라스의 정리를 논증적인 증명 대신에 역동적인 방법으로 이해할 수 있도록 GSP(Geometer's Skechpad)를 활용하여 구현했으며, 멀티미디어 환경에 익숙한 중학생들에게 시 ${\cdot}$ 공간을 초월하여 웹 상에서 개별학습, 반복학습을 할 수 있도록 JAVA 언어를 사용하여 웹으로 변환시켰다.

• Journal of Educational Research in Mathematics
• /
• v.19 no.4
• /
• pp.531-543
• /
• 2009

This study identified what cognitive attributes are required of eighth graders to solve geometrical problems such as 'Recall,' 'Analyze,' 'Justify,' 'Synthesize/Integrate,' and 'Solve Non-routine Problems' by using the cognitive diagnostic theory. The five attributes are proved as the skills for solving the geometric problems. Many students have not fully mastered the attributes of 'Justify' and 'Synthesize/Integrate'. There was high correlation between these attributes. 'Analyze' best predicted the changes in the geometric achievement. And while students with high levels of geometrical achievement have mastered all the five attributes, those in the mid- and low-level range of performance have mastered fewer attributes.

• School Mathematics
• /
• v.16 no.2
• /
• pp.201-218
• /
• 2014

The purpose of this study is to research the Actual Introduction of Justification that mentioned in the middle school mathematics of 2009 Revised Curriculum. For this, researcher analyzed the new mathematics textbooks for 8th grade that will be applied 2014. Researcher and cooperators analyzed the 8th grade geometry using the criteria of advanced research. The conclusion of this study is following. Frist, Teacher need to present the various types of Justification to be used students of the different levels. Second, Teacher have to lead the activity of Justification to satisfy the needs of students.