• The Mathematical Education
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• v.48 no.2
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• pp.149-167
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• 2009

This study was aimed to examine problem-solving ability of fifth graders on two types of mathematical essay problems, and to analyze the process of mathematical justification in solving the essay problems. For this purpose, a total of 14 mathematical essay problems were developed, in which half of the items were single tasks and the other half were data-provided tasks. Sixteen students with higher academic achievements in mathematics and the Korean language were chosen, and were given to solve the mathematical essay problems individually. They then were asked to justify their solution methods in groups of 4 and to reach a consensus through negotiation among group members. Students were good at understanding the given single tasks but they often revealed lack of logical thinking and representation. They also tended to use everyday language rather than mathematical language in explaining their solution processes. Some students experienced difficulty in understanding the meaning of data in the essay problems. With regard to mathematical justification, students employed more internal justification by experience or mathematical logic than external justification by authority. Given this, this paper includes implications for teachers on how they need to teach mathematics in order to foster students' logical thinking and communication.

• School Mathematics
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• v.18 no.3
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• pp.503-526
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• 2016

The study aimed at determining the identity of mathematics essay test in the university entrance examination. For this purpose, a document research was conducted for higher order thinking and mathematics essay ability and it analyzed the goal of assessment and the tendency of problem settings and looked into mathematics essay problems of twenty-five universities. As a result, the study found out that evaluation factors of mathematics essay test requires higher order thinking ability including mathematical knowledge and essay ability such as mathematical knowledge, understanding, problem solving, logical and critical thinking, creative ability, power of expression, argument skills. Also, problems from previous mathematics essay tests were set mainly to assess mathematical knowledge, understanding and problem solving. Based on the findings, the past mathematics essay tests in university entrance examination in Korea that require logical and critical thinking, creative ability, power of expression, argument skills were a rather small percentage of questions.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.541-563
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• 2014

The purpose of this study is to investigate how the curriculum, in which pre-service teachers experience mathematical process and develop assessment items and standards through the process experience in a mathematical essay course, affects the pre-service teachers and suggest its implications for teacher education. Fourty nine pre-service teachers, registered at a mathematical essay course in a K university in Seoul, developed mathematical essay problems and their assessment standards, and their developed processes were analyzed. According to the analysis results, first, mathematical essay problems developed by the fifty students reflect components of mathematical processes. Especially, one characteristic in revising assessment items shows that pre-service teachers considered not only justification process through different levels of difficulty and mathematical reasoning, but also logical descriptions through problem solving, when they worked on group discussions and examined middle school and high school students' responses. Second, while pre-service teachers developed rubrics for their assessment items and revised the rubrics based on students' responses, they established assessment standards which employed mathematical process by focusing on problem solving process rather than results and considering students' unexpected problem solving. The results imply a concrete method in planning and executing a mathematical essay course which makes use of mathematical process in teacher education.

• East Asian mathematical journal
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• v.32 no.4
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• pp.519-543
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• 2016

Today the high school mathematics lesson has an effect on the scholastic achievement internationally, but fails to lead to the interest in the mathematics which stimulates the intellectual curiosity. Due to this, 2015 revised curriculum includes the effort to improve the emotional aspect of mathematics positively. It is needed that the teaching method through discussion and debate must be introduced to accomplish the objective of the mathematics in 2015 revised curriculum focused on the improvement of the ability and attitude to solve the problems creatively by increasing the mathematical communication skill of the students. The purpose of this study is to investigate the effect of mathematical essay-typed lesson focused on discussion and debate on the mathematical disposition and attitude of high school student. The findings from this study provided that the essay-typed lessons focused on discussion and debate improved the subject students' mathematical achievement and disposition and attitude, but it is not significant change.

• 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.

• 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.

• 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.

• 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.

• The Mathematical Education
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• v.25 no.1
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• pp.1-8
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• 1986

It is a common saying that markov-chain is a special case of probability course. That is to say, It means an unchangeable markov-chain process of the transition-probability of discontinuous time. There are two kinds of ways to show transition probability parade matrix theory. The first is the way by arrangement of a rightangled tetragon. The second part is a vertical measurement and direction sing by transition-circle. In this essay, I try to find out existence of procession for transition-probability applied markov-chain. And it is possible for me to know not only, what it is basic on a study of chain but also being applied to abnormal problems following a flow change and statistic facts expecting to use as a model of air expansion in physics.

• Journal of the Korean School Mathematics Society
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• v.11 no.4
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• pp.543-567
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• 2008

The current 2007 Mathematics Curriculum in Korea emphasizes mathematical problem solving, advanced mathematical thinking and effective mathematical communicating. Therefore, in order to assess and evaluate these important thinking attributes, performance evaluation using descriptive and essay type of assessments are emphasized. In this paper, analysis of the elementary mathematics curriculum is used to develop descriptive assessment problems and grading rubrics that could be used objectively and consistently by teachers of the grade 6 school mathematics. The assessment problems were developed, pilot tested, revised, implemented and analyzed in detail to understand the overall effectiveness of the descriptive evaluation method in school mathematics.