• Research in Mathematical Education
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• v.12 no.4
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• pp.271-281
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• 2008

Quarter a century ago, I founded the Colorado Mathematical Olympiad. The Colorado Mathematical Olympiad is the largest essay-type in-person mathematical competition in the United States, with 600 to 1,000 participants competing annually for prizes. In this article, I explain what it is, how it works, give examples of problems and solutions, and share with the reader careers of some of the Olympiad's winners.

• The Mathematical Education
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• v.60 no.3
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• pp.341-362
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• 2021

The purpose of this study is to explore the qualitative characteristics of pre-service teachers' motivation while they are participating in group activities for developing mathematical essay assessment problem and revising it. For this purpose, we analyzed individual factors about group learning activities as well as contextual factors about practical competency (in developing and revising mathematical essay assessment problem through collecting data of student responses to the problem). As results of data analyses, autonomy, among individual factors regarding group learning activities, was one of the main characteristics in attainment value, utility value, and intrinsic value, whereas task, authority, and grouping, among contextual factors regarding practical competency, appeared to have a positive impact on task value. These results suggest how to think of specific ideas and articulate them in designing a curriculum to develop student-evaluation expertise for pre-service teachers.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1015-1022
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• 2009

Generally, it is considered that analytical skills could not be easily taught and it requires quite a long training period. In this short essay, it was attempted to give four basic analytical skills useful for problem solving in mathematics.

• Journal for History of Mathematics
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• v.24 no.2
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• pp.47-59
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• 2011

Various mathematical models have been widely studied recently in both fields of mathematics and ecology since they help us understand the dynamical process of population changes in biological species living in a certain habitat and give useful predictions. The world population model proposed by Malthus, a British economist, in his work 'An Essay on the Principle of Population' published in the period of 1789~1826 is one of the early mathematical models on population changes. Malthus' models and the carrying capacity models of Verhulst in 1845 were based on exponential type functions. The independent research field of mathematical ecology has been started from Lotka's works in 1920's. Since then various different mathematical models has been proposed and examined. This article mainly deals with single species population change models expressed in terms of ordinary differential equations.

• The Mathematical Education
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• v.38 no.2
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• pp.165-172
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• 1999

$\sub$e/$\^$2/, that were results from those three sources of such imperfection. Especially to eliminate the differences in severity among many raters the randomization procedure of raters sample was very effective in enhancing the reliability of ratings with comparatively small groups of examinees and raters. And we also introduced the new rating methods, i.e. the 2-step diagnostic procedures to check the sizes of the reliability stability of raters and the sore adjustment method to enumerate the optimal mean values in rating the examinees.

• The Mathematical Education
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• v.47 no.1
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• pp.27-47
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• 2008

In this paper, we study the effect of writing activity as mathematical communication on the students's mathematics achievement, learning attitude, and mathematical tendency. For this purpose, we construct a experimental class and then analyze the students' change in those aspects after applying three-divided-note writing activity and colleague feedback on their works those students are in the experimental class. As a result of the experiment, we find that three-divided-note writing activity and colleague feedback made some significant changes on the students achievement in mathematics, learning attitude, but does not affect on mathematical tendency. We also offer some suggestions for further research. Firstly, the mathematical communication ability must be stressed in mathematics education. For this purpose, we need to develop the teaching and the evaluation method to use not only writing but also reading, speaking, and listening skills so that many teachers can apply this method easily to their classes. Second, we need to fix some realistic problems such as fair evaluation , the numbers of students per class, the numbers of lesson, and too much extra-work, and so on. Thirdly, we suggest to explore some methods for extending three- divided-note writing activity to evaluate mathematical essay and to study educational effects of colleague feedback on mathematics performance assessment.

• School Mathematics
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• v.10 no.2
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• pp.181-197
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• 2008

Bertrand's Paradox is known as a paradox because it produces different solutions when we apply different method. This essay analyzed diverse problem solving methods which result from no clear presenting of 'random chord'. The essay also tried to discover the difference between the mathematical calculation of three problem solvings and physical experiment in the real world. In the process for this, whether geometric statistic teaching related to measurement and integral calculus which is the basic concept of integral geometry is appropriate factor in current education curriculum based on Laplace's classical perspective was prudently discussed with its status.

• Korean Journal of Cognitive Science
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• v.23 no.3
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• pp.367-388
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• 2012

The centennial of Alan Mathison Turing(23 June 1912 - 7 June 1954) is an appropriate occasion on which to assess his profound influence on the development of cognitive science. His contributions to and attitudes toward that field are discussed from the metamathematical perspective. This essay addresses (i)Turing's mathematical analysis of cognition, (ii)universal Turing machines, (iii)the limitations of universal Turing machines, (iv)oracle Turing machine beyond universal Turing machine, and (v)Turing test for cognitive science. Turing was a ground-breaker, eager to move on to new fields. He actually opened wider the scientific windows to the mind. The results show that first, by means of mathematical logic Turing discovered a new bridge between the mind and the physical world. Second, Turing gave a new formal analysis of operations of the mind. Third, Turing investigated oracle Turing machines and connectionist network machines as new models of minds beyond the limitations of his own universal machines. This paper explores why the cognitive scientist would be ever expecting a new Turing Test on the shoulder of Alan Turing.

• Journal of the Korean Chemical Society
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• v.45 no.4
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• pp.370-376
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• 2001

In this study, high school students' problem-solving strategy-performing ability was measured by an essay-type test. The relationship between students' logical thinking ability and strategy-performing ability was also investigated. Four classes (N=187) were selected from two high schools in Seoul, and the strategy performance ability test and the Group Assessment of Logical Thinking (GALT) were administered. Evaluation scheme for strategy-performing ability consists of 7 subcategories - understanding given of problems, recalling related law, setting up subgoals, deriving physical quantities, logical progress, mathematical execution, and reviewing. The intercoder agreement for scaling was .92, which indicated substantial strength of agreement. The results revealed that students' ability of understanding given of problems and mathematical execution was relatively high. However, their ability of setting up subgoals and reviewing was very low. The total scores of the strategy performance ability test and all of the scores of each subcategory were significantly correlated with the GALT scores.

• Communications of Mathematical Education
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• v.28 no.2
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• pp.255-279
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• 2014

This study is to investigate the change of intelligent and affective domains through the student self-evaluation to identify causes of wrong answers. Through this evaluation, students could have opportunities to solve the given mathematical problems basically and to reflect their problem-solving process, and further to recognize which mathematical content(concepts or expressions, symbols, etc.) led them to solve the problems incorrectly or wrong. Through this process, they would correct their wrong process and answers and to reinforce the prerequisite knowledges relevant to the problems, and furthermore, to enhance problem-solving abilities. To accomplish this, this study was executed as a case study on the subject of four tenth graders. The subject consisted of two boys and two girls. In this study, three essay types of mathematical problems in tenth grade level were chosen from several domestic tests in Korea. Based on the original three essay type of problems, three types of similar problems, namely equivalent problem, similar problem, and isomorphic problems were reconstructed, respectively by the researchers. The subjects were guided to solve the original three problems, and they corrected their wrong parts of the first problem of the three problems. They solved an equivalent problem of the first problem and executed self evaluation and also corrected wrong parts. Next, they dealt with a similar problem of the first problem and executed self evaluation and also corrected wrong parts. Next, while dealing with an isomorphic problem of the first problem, the subjects did the same things. Thus, for the second and third original problems, the study was implemented in the same way. To explore their intelligent and affective domains through student self-evaluation in-depth, the subjects were interviewed formally before and after conducting the experiment and interviewed informally two times, and the recordings were audio-typed.