• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.67-88
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• 2020

This study analyzed the characteristics of prospective teachers' Horizon Content Knowledge(HCK) related to understandings of an inverse function symbol. This study aimed to deduce implications of developing HCK in terms of the means which would enhance mathematics teachers' professional development. In order to achieve the aim, this study identified features of HCK by examining the previous literature on HCK, which has conformed Ball & Bass(2009) and exploring the research in AMT, including Zazkis & Leikin(2010) which has emphasized cultivating AMT through university mathematics education. In addition, a questionnaire was developed regarding the features of HCK and taken by 57 prospective teachers. By analyzing the data obtained from the written responses the participants presented, this study delineated the specific characteristics of the teachers' HCK with regard to an inverse function symbol. Additionally, several issues in the teacher education for improving HCK were discussed, and the results of this research could inspire designing and implementing a teacher education program relevant to HCK.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.69-82
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• 2012

The objective of this paper is to study De Morgan's perspective on teaching and learning complex numbers. De Morgan's didactical approaches reflect the process of development of his thoughts about algebra from universal arithmetic, symbolic algebra to meaning algebra. De Morgan develop his perspective on algebra by justifying and explaining complex numbers. This implies that teaching and learning complex numbers is a catalyst for mathematical development of De Morgan.

• 한국게임학회지
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• v.8 no.1
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• pp.32-38
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• 2011

The help or guide sentences of educational math games which use mathematical statements need to represent graphical forms for the learners of the game generation whose cognitive style is graphic first. In this paper, we proposed an object-based visual representation method for mathematical statements. It has object-based description rules to use graphical symbols and mathematical symbols with text words. It is easy to describe or to understand accurately mathematical meaning and is also fast for learners to read for understanding. The proposed method is good for learners of the game generation to get the help as scaffolding for learning math by educational games.

• School Mathematics
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• v.9 no.2
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• pp.313-326
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• 2007

Recently in algebra curriculum, to recognizes and explains general nile expressing patterns is presented as the one alternative and is emphasized. In the seventh School Mathematic Curriculum regarding 'regularity and function' area, in elementary school curriculum, is guiding pattern activity of various form. But difficulty and problem of students are pointing in study for learning through pattern activity. In this article, emphasizes generalization process through research activity of pictorial/geometric pattern that is introduced much on elementary school mathematic curriculum and investigates various approach and strategy of student's thinking, state of symbolization in generalization process of pictorial/geometric pattern. And discusses generalization of pictorial/geometric pattern, difficulty of symbolization and suggested several proposals for research activity of pictorial/geometric pattern.

• School Mathematics
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• v.9 no.1
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• pp.161-180
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• 2007

The purpose of this study is to analyse how a mathematically gifted student constructs a nested signification model of three signs, while he abstracts the solution of a given NIM game. The findings of a qualitative case study have led to conclusions as follows. In general, we know that most of mathematically gifted students(within top 0.01%) in the elementary school might be excellent in constructing representamen and interpretant But it depends on the cases. While a student, one of best, is making the meaning of object in general level of abstraction, he also has a difficulty in rising from general level to formal level. When he made the interpretant in general level with researcher's advice, he was able to rise formal level and constructed a nested signification model of three signs. We suggested 3 considerations to teach the mathematically gifted students in elementary school level.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.173-192
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• 2013

It may be replacement proofs with understanding and explaining geometrical properties that was a remarkable change in school geometry of 2009 revised national curriculum for mathematics. That comes from the difficulties which students have experienced in learning proofs. This study focuses on one of those difficulties which are caused by the forms of proofs: using letters for designating some sides or angles in writing proofs and understanding some long sentences of proofs. To overcome it, this study aims to investigate the applicability of Byrne's method which uses coloured diagrams instead of letters. For this purpose, the proofs of three geometrical properties were taught to middle school students by Byrne's visual method using the original source, dynamic representations, and the teacher's manual drawing, respectively. Consequently, the applicability of Byrne's method was discussed based on its strengths and its weaknesses by analysing the results of students' worksheets and interviews and their teacher's interview. This analysis shows that Byrne's method may be helpful for students' understanding of given geometrical proofs rather than writing proofs.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.627-641
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• 2012

We found a few students had an error in the function and equation units, because most of mathematicians omitted the multiplication signs. In the mathematical history, the multiplication and parentheses signs had various changes. Based on the Histogenetic Principle, high level students know that the letter in the functions and equations represents a number and the related principles, so they have no big problems. But since the low level students stay in the early days in the mathematical history, they have some problems in the modern function and equation. Therefore, while we study the function and equation units with the low level students, we present that we have to be cautious when we omit the multiplication and parentheses signs.

• The Journal of Natural Sciences
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• v.11 no.1
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• pp.195-199
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• 1999

There are many symbols in mathematics and physics to simplify complex operations of caculations. But there're no symbols in certain part in spite of routine caculations which are often have to be done, and some proper new symbols are proposed in this paper.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.309-327
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• 2003

In this paper, we deal with the teaching of algebra in the elementary school mathematics, and call this algebra teaching method as ‘early algebra’. Early algebra is appeared in the 1980's with the discussion of ‘algebraic thinking’. And many studies about early algebra is in progress since 1990's. These studies aims at reducing difficulties in the teaching of algebra and the development of algebra curriculum. We investigate the background of early algebra, and justify teaching of early algebra. Also we examine the projects and studies in progress around the world. Finally through these discussions, we compare our elementary textbooks with early algebra, and verify the characters of early algebra from our arithmetic curriculum.

• School Mathematics
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• v.18 no.3
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• pp.527-539
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• 2016

A word 'is' in "A parallelogram is trapezoid." is ambiguous and very rich when it comes to its meaning. In this paper, 'is' as in everyday language will be identified as semantic primes that can be interpreted in different ways depending on context and situation, and meanings of 'is' in mathematics will be discussed separately. Focusing on 'identity', 'is' will be reinterpreted in the view of equivalence relation and van Hieles' work. 'Is', as a mathematical sign, is thought to have a significant importance in producing mathematical ideas meaningfully.