• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.137-144
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• 1998

A common geoboard puzzel serves as the point of departure for an investigation that lends itself to whole-group discussion with a class of prospective secondary school teachers. Students are provided with opportunities to devise and carry out problem-solving strategies (called 'heuristics' by Polya); exploit inerrelationships among geometry, arithmetic and algebra; formulate generalizations and conjectures; plan and execute an computational project; construct mathematical arguments to establish theorems; and find counter-examples to dispose of a false conjecture. In recent tears, Eugene F. Krause wrote two papers having the same title except for the numeral In that papers he arrives at an theorem about the sizes of squares with lattice point vertices in the coordinate plane, In this paper we follow a different path genearlization to coordinate 3-space

• Communications of Mathematical Education
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• v.30 no.2
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• pp.121-138
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• 2016

Most of elementary and secondary school mathematical terms in Korean are Sino-Korean words. We check Chinese characters relating to such Sino-Korean words by using Chinese dictionaries, and critically judge how much we can understand Sino-Korean words by Chinese characters. Through this search, we classify Sino-Korean words into three categories; words which can be understood by Chinese characters, words which can not be understood by Chinese characters, words which are misunderstood by Chinese characters.

• Research in Mathematical Education
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• v.6 no.1
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• pp.53-63
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• 2002

This study investigates the impact of Calculator-Based Ranger (CBR) activities in the performance of middle school students' graphing abilities of physical phenomena. Two issues about CBR activities on graphing abilities were addressed in this study; (1) the effect of CBR activities on graphing abilities, and (2) the influence of instructional styles on students' graphing abilities. Following the use of CBR activities, students' graphing abilities were significantly more developed in three components-interpreting, modeling, and transforming. Significant differences were found in students' achievement depending on instructional styles related to differentiation, which is closely connected to transforming distance-time graphs to velocity-time graphs. The findings of this study indicate that CBR activities may enhance students in constructing appropriate webs of related concepts and ability to qualitatively interpret graphs. Using collaborative CBR activities to introduce and explore graphing of physical phenomena is, therefore, recommended for inclusion in the secondary mathematics curriculum.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.441-448
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• 2012

Let R be a prime ring with center Z and characteristic different from two, U a nonzero Lie ideal of R such that $u^2{\in}U$ for all $u{\in}U$ and $d$ be a nonzero (${\sigma}$, ${\tau}$)-derivation of R. We prove the following results: (i) If $[d(u),u]_{{\sigma},{\tau}}$ = 0 or $[d(u),u]_{{\sigma},{\tau}}{\in}C_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$. (ii) If $a{\in}R$ and $[d(u),a]_{{\sigma},{\tau}}$ = 0 for all $u{\in}U$, then $U{\subseteq}Z$ or $a{\in}Z$. (iii) If $d([u,v])={\pm}[u,v]_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$.

• The Mathematical Education
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• v.52 no.1
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• pp.83-95
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• 2013

The purpose of this paper is to explain and reinterprets Apollonius' Symptoms on conic sections based on the current secondary curriculum of mathematics, present the historical background of Apollonius' Symptoms to teachers and students and introduce visualization proof of Apollonius' symptoms on a parabola, a hyperbola and an ellipse by a new method using dynamic geometry software(GSP) respectively.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.421-442
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• 2016

This study analyzed characteristics which emerged while 38 secondary school teachers observed a video clip about a centroid of triangles instruction. The aim of this study based on the analysis was to deduce implications in terms of the various means which would enhance teachers' knowledge in teaching mathematics and assist in designing mathematics education programs for teachers and professional development initiatives. To achieve this goal, this research firstly reviewed previous studies relevant to the 'Knowledge Quartet' as a framework of analyzing teachers' knowledge in mathematics instructions. Secondly, this study probed the observation results from the teachers in the light of the KQ. Therefore, some issues in the teacher education program for teaching mathematics were thirdly identified in the categories of 'Foundation', 'Transformation', 'Connection', and 'Contingency' based on the analysis. This research inspires the elaboration of what features have with regard to effective teachers' knowledge in teaching mathematics through the analyzing process and additionally the elucidation of essential matters related to mathematics education on the basis of the analyzed results.

• The Mathematical Education
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• v.27 no.1
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• pp.15-23
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• 1988

We are at the onset of a major revolution in education, a revolution unparalleled since the invention of the printing press. The computer will be the instrument of this revolution. Computers and computer application are everywhere these days. Everyone can't avoid the influence of the computer in today's world. The computer is no longer a magical, unfamiliar tool that is used only by researchers or scholars or scientists. The computer helps us do our jobs and even routine tasks more effectively and efficiently. More importantly, it gives us power never before available to solve complex problems. Mathematics instruction in secondary schools is frequently perceived to be more a amendable to the use of computers than are other areas of the school curriculum. This is based on the perception of mathematics as a subject with clearly defined objectives and outcomes that can be reliably measured by devices readily at hand or easily constructed by teachers or researchers. Because of this reason, the first large-scale computerized curriculum projects were in mathematics, and the first educational computer games were mathematics games. And now, the entire mathematics curriculum appears to be the first of the traditional school curriculum areas to be undergoing substantial trasformation because of computers. Recently, many research-Institutes of our country are going to study on computers in orders to use it in mathematics education, but the study is still start ing-step. In order to keep abreast of this trend necessity, and to enhance mathematics teaching/learning which is instructed lecture-based teaching/learning at the present time, this study aims to develop/present practical method of computer-using. This is devided into three methods. 1. Programming teaching/learning method This part is presented the following five types which can teach/learn the mathematical concepts and principle through concise program. (Type 1) Complete a program. (Type 2) Know the given program's content and predict the output. (Type 3) Write a program of the given flow-chart and solve the problem. (Type 4) Make an inference from an error message, find errors and correct them. (Type 5) Investigate complex mathematical fact through program and annotate a program. 2. Problem-solving teaching/learning method solving This part is illustrated how a computer can be used as a tool to help students solve realistic mathematical problems while simultaneously reinforcing their understanding of problem-solving processes. Here, four different problems are presented. For each problem, a four-stage problem-solving model of polya is given: Problem statement, Problem analysis, Computer program, and Looking back/Looking ahead. 3. CAI program teaching/learning method This part is developed/presented courseware of sine theorem section (Mathematics I for high school) in order to avail individualized learning or interactive learning with teacher. (Appendix I, II)

• School Mathematics
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• v.11 no.3
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• pp.369-387
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• 2009

Recently there has been a high request for support for teachers' professional development and quality control to meet the demand of educational policy to introduce teacher evaluation, master teacher status, incentives for teacher competency, etc. It has been suggested that reeducation and support for professional development would be more effective to beginning teachers with a high developmental potential than to experienced teachers with routinized instruction. Since 2005, KICE-TLC has conducted research on the development of teacher supporting programs such as teaching consultation and pedagogical content knowledge(PCK) in school subjects. In line with the current education policy and previous research by KICE, this research has been conducted to meet the need for novice teacher induction by developing consulting program focused on PCK. The goal of this research was to (1) explore the in-depth meaning of PCK in light of teaching consultation, (2) conduct a preliminary study on how to develop teaching consulting programs for secondary beginning teachers, (3) develop teaching consulting programs focused on pedagogical content knowledge (PCK), and (4) suggest implications for educational policy regarding pre-service and in-service teachers' continuing professional development and support.

• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.341-351
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• 2007

The primary purpose of this treatise is to suggest the solutions as follows for the errors concerning the triangle determination and congruence in every Korean mathematics textbook for 7th graders: showing that SsA, along with SSS, SAS, ASA, should also be included as the condition for triangle determination, congruence and similarity; proving that contrary to what has been believed, minimality applies only to congruence and similarity but not to determination; examining related Euclidean propositions; discussing the confusion about the characteristics of determination and congruence; and considering the negative effects of giving definite figures in construction education. The secondary purpose is to analyze the significance of triangle determinant that is not dealt with in either Euclid's Elements or the text books in the U.S. or Japan, and suggest a way to effectively deal with triangle determination and congruence in education.

• School Mathematics
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• v.18 no.2
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• pp.349-373
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• 2016

Comparison of curriculum between various countries is a major research method for studying a course and content quoted on Korea's national curriculum. Therefore this research focuses on comparing and analyzing a new curriculum which Australia has announced on 2012 and conducting since 2015. From this research result, we found that Australia's curriculum achievement shows some unique characteristics. Such examples can be dealing a concept with real life context and proposing a mathematical content specifically. Also they introduce the definite integral by defining to the sum of series. There are other characteristics such as modelling motion, and numerical integration which Korea's highschool curriculum achievement doesn't deal with, and the content of vector calculus is handled more deeply. As a result of analyzing Australia's textbook, it fully deals with the supplementary notion to help understand mathematical definition. Hence further research will be needed later on to relieve the aspect of cognitive burden on Korean learners.