• Journal for History of Mathematics
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• v.25 no.1
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• pp.15-27
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• 2012

Thomas Harriot(1560-1621) introduced a simplified notation for algebra. His fundamental research on the theory of equations was far ahead of that time. He invented certain symbols which are used today. Harriot treated all answers to solve equations equally whether positive or negative, real or imaginary. He did outstanding work on the solution of equations, recognizing negative roots and complex roots in a way that makes his solutions look like a present day solution. Since he published no mathematical work in his lifetime, his achievements were not recognized in mathematical history and mathematics education. In this paper, by comparing his works with Viete and Descartes those are mathematicians in the same age, I show his achievements in mathematics.

• School Mathematics
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• v.15 no.4
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• pp.941-955
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• 2013

In this study, we conducted mathematics teacher training courses for an applying of 'Socratic method' in school mathematics. Teacher training courses were conducted with a total of 3 hours for 68 secondary mathematics teachers. In these courses, we overviewed the characteristics of Socratic method. Moreover we examined the mathematics lessons by Socratic method. And we dealt with the educational examples of Socratic method identified in previous studies. In addition, the survey was conducted before and after the teacher training courses. Through the survey, teachers have an opportunity to check their knowledge on Socratic method and reflect on their mathematics class. Based on the survey response data, we analyzed mathematics teachers' knowledge on Socratic method and the changes in teachers' thinking on their mathematics class. Based on the findings of this study, we proposed three directions of teacher education.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.139-152
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• 2017

In this paper, we examine how secondary school mathematics textbooks on calculus introduce the history of calculus. In order to identify the problem, we consider the Babylonian integration by trapezoidal rule, which was made to calculate the location of Jupiter in 350-50 B.C., and the integration by the method of the rotating plate of ibn al-Haytham in Egypt, about 1000 years. In conclusion, our secondary school mathematics textbooks describe Newton and Leibniz as inventing calculus and place their roots in ancient Greece. The origin of the calculus is in Babylonia and the Faṭimah Dynasty (909-1171) (Egypt) and it is desirable that the calculus is developed in Europe after the development of the power series in India, and that the value of Asia Africa is introduced in the textbooks.

• School Mathematics
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• v.9 no.2
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• pp.197-222
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• 2007

The study aims to reflect the elementary school geometry education based on the Realistic Mathematics Education in the Netherlands in the light of the results from recent researches in geometry education and the direction of geometry standards for school mathematics of the National Council of Teachers of Mathematics in order to induce implications for improving korean geometry curriculum and textbook series. In order to attain these purposes, the present paper reflects the history of elementary school geometry education in the Netherlands, sketches the elementary school geometry education based on the Realistic Mathematics Education in the Netherlands by reflecting general goals of the mathematics education, the core goals for geometry strand of the Netherlands, and geometry and spatial orientation strand of Dutch Pluspunt textbook series for the elementary school more concretely. Under these reflections on the documents, it is analyzed what is the characteristics of geometry strand in the Netherlands as follows: emphasis on realistic spatial phenomenon, intuitive and informal approach, progressive approach from intuitive activity to spatial reasoning, intertwinement of mathematics strands and other disciplines, emphasis on interaction of the students, cyclical repetition of experiencing phase, explaining phases, and connecting phase. Finally, discussing points for improving our elementary school geometry curriculum and textbook series development are described as follows: introducing spatial orientation and emphasizing spatial visualization and spatial reasoning with respect to the instruction contents, considering balancing between approach stressing on grasping space and approach stressing on logical structure of geometry, intuitive approach, and integrating mathematics strands and other disciplines with respect to the instruction method.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.43-56
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• 2006

This paper aims to introduce a construction method for the 'Wooden Die for Drinking Game' and to find some geometrical structures and mathematics educational viewpoints. As the results, we get two methods which are eventually same with Figure 5 and Figure 6-3. We proved the ground that classical probability of this Die's each side showing up is one out of fourteen and introduced few other empirical probabilities with Table 1 to Table 3. Also, some Chinese characters were corrected and re-interpreted. In fact, 象人打鼻 changed to 衆人打鼻, and 醜物 is interpreted as 'ugly animal' such as frog, toad, earthworm or pine caterpillar.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.113-122
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• 2006

We investigate the mathematical background, statistical methodology, and the teaching of computer-software field using smoothing methodology in this paper. Also we investigate conception and methodology of histogram, kernel density estimator, adaptive kernel estimator, bandwidth selection based on mathematics and statistics.

• Journal for History of Mathematics
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• v.27 no.5
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• pp.347-364
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• 2014

This study aims at what is required knowledge and ability to pre-service math teachers in teacher certificate examination. First, the items are analyzed and among questions of discipline of mathematics education in the last five years are analyzed and classified. Second, an analytical framework suitable for item analysis is examined and the items are analysed by the analytical framework. Finally, helpful implications for discipline of mathematics education assessment can be drawn from this study. It is found that the discipline of mathematics education assessment has the following characteristics: 1) It assesses specific content of the assessment component; 2) It assesses a teacher's theoretical knowledge, practical knowledge and creative knowledge in terms of teaching ability; 3) There are six cognitive assessments; 4) There is an item for difficulty adjustment.

• Journal for History of Mathematics
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• v.27 no.5
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• pp.365-384
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• 2014

The purpose of this study is to assess the changes that occur to pre-service mathematics teachers by using survey on the self-reflection during their education practices. For four weeks of the education practice period, the changes to pre-service teachers are analyzed from teaching and learning perspectives. The teaching perspective is sub-categorized into lesson contents, teaching methods, and evaluation on teaching, and the learning perspective is sub-categorized into monitoring on learning, support for learning and evaluation on learning. The analysis shows that significant changes occur in teaching contents from the teaching perspective and in all the sub-categories from the learning perspective. Based on the analysis, preservice teachers are suggested to utilize self-reflection programs during their education practices to promote their professionalism in teaching.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.69-80
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• 2009

The computer programming is a useful tool to cultivate the logical thinking and encourage the problem solving competence. With the purpose of specifying the computer programming, this study mainly concerns with what the computer programming is in the Math/Stat education, and the role of the computer programming when it regards the problem solving procedure. This provides the possibility of Math/Stat major to be specified with the connection of IT related courses, and eventually the specified Math/Stat major enables more qualified graduates to be educated.

• Journal for History of Mathematics
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• v.30 no.2
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• pp.101-119
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• 2017

This paper is a follow up study of [2]. In this paper we analyse the contents of middle school mathematics textbooks published in the 1st National Curriculum Period centered on the concept 'straight line' and discuss how they are different from contemporary mathematics textbooks in view of connectedness of contents, mathematical terms, textbook as a learning material vs. teaching material, relationship between contents of national curriculum and textbooks, and some topics related to direct proportion, function, method of equivalence as a method for solving simultaneous linear equations and so on. The results of our analysis and discussion suggest implications for reforming mathematics curriculum and developing mathematics textbooks.