• Journal of Elementary Mathematics Education in Korea
• /
• v.20 no.2
• /
• pp.311-331
• /
• 2016

The purpose of this study was to analyze mathematical errors and the effects of reflective problem posing activities on students' mathematical problem solving abilities and attitudes toward mathematics. We chose two 5th grade groups (experimental and control groups) to conduct this research. From the results of this study, we obtained the following conclusions. First, reflective problem posing activities are effective in improving students' problem solving abilities. Students could use extended capability of selecting a condition to address the problem to others in the activities. Second, reflective problem posing activities can improve students' mathematical willpower and promotes reflective thinking. Reflective problem posing activities were conducted before and after the six areas of mathematics. Also, we examined students' mathematical attitudes of both the experimental group and the control group about self-confidence, flexibility, willpower, curiosity, mathematical reflection, and mathematical value. In the reflective problem posing group, students showed self check on their problems solving activities and participated in mathematical discussions to communicate with others while participating mathematical problem posing activities. We suggested that reflective problem posing activities should be included in the development of mathematics curriculum and textbooks.

• Journal for History of Mathematics
• /
• v.6 no.1
• /
• pp.32-45
• /
• 1990

• Journal of Educational Research in Mathematics
• /
• v.27 no.1
• /
• pp.51-67
• /
• 2017

Analogical reasoning is a mathematically useful way of thinking. By analogy reasoning, students can improve problem solving, inductive reasoning, heuristic methods and creativity. The purpose of this study is to analyze the analogical reasoning of preservice mathematics teachers while constructing quadratic curves defined by eccentricity. To do this, we produced tasks and 28 preservice mathematics teachers solved. The result findings are as follows. First, students could not solve a target problem because of the absence of the mathematical knowledge of the base problem. Second, although student could solve a base problem, students could not solve a target problem because of the absence of the mathematical knowledge of the target problem which corresponded the mathematical knowledge of the base problem. Third, the various solutions of the base problem helped the students solve the target problem. Fourth, students used an algebraic method to construct a quadratic curve. Fifth, the analysis method and potential similarity helped the students solve the target problem.

• Journal of Educational Research in Mathematics
• /
• v.21 no.3
• /
• pp.295-311
• /
• 2011

The importance of problem solving in mathematics education has been emphasized and many studies related to this issue have been conducted. But, studies of problem solving in the aspect of affect domain are lacked. This study found the changing pattern of emotions that occur in process of a problem solving. The results are listed below. First, students experienced a lot of change of emotions and had a positive emotion as well as negative emotion during solving problems. Second, students who solved same problems through same methods experienced different change patterns of emotions. The reason is that students have different mathematical beliefs and think differently about a difficulty level of problem. Third, whether students solved problems with positive emotion or negative emotion depends on their attitude of mathematics. Fourth, students who thought that a difficulty level of problem was relatively high experienced more negative affect than students who think a difficulty level of problem is low experienced.

• Communications of Mathematical Education
• /
• v.22 no.3
• /
• pp.275-288
• /
• 2008

The study aims to figure phenomena and changes that underachievers in mathematics show in the process of learning a function. It is necessary to remind basic concepts once again in advance at a time of teaching underachievers in mathematics to check what they have difficulties in learning for further teaching later on. Five participating students said that teachers' detailed explanation was more helpful, and they found it difficult to learn tables, graphs and formulas at first, but as time progressed, they naturally accepted them. In this regard, it is necessary to use various expressions and means to teach underachievers in mathematics.

• Communications of Mathematical Education
• /
• v.12
• /
• pp.265-280
• /
• 2001

고등학교 수학 I 의 확률 및 통계영역의 교육내용을 정리한 후, 고등학생들에게 확률 및 통계영역에 관한 흥미를 돋구기 위하여 2002년 월드컵을 소재로 한 문제들을 활용하여 비주얼 베이직으로 프로그램한 ‘확률상자’ 라는 확률모형을 개발하였다. 확률상자에는 확률의 역사, 경우의 수, 순열, 같은 것이 있는 순열, 원순열, 조합, 이항계수, 통계적 확률, 조건부 확률, 배반사건 등 모두 10가지 모듈을 포함한다. 확률상자의 초기화면에서 메뉴를 선택하면 선택된 내용에 관한 간단한 정의와 함께 문제가 제시되어 정답을 적도록 하였고, 오답일 때는 힌트를 누르면 정답을 이해할 수 있도록 풀이과정을 제시하였다. 특히, 메뉴가운데서 경우의 수, 순열, 같은 것이 있는 순열, 원순열, 조합, 통계적 확률의 경우에는 풀이과정 중에 애니메이션 또는 시뮬레이션이 실행되도록 하여 이해를 돕도록 하였다.

• Communications of Mathematical Education
• /
• v.12
• /
• pp.397-409
• /
• 2001

‘수학을 한다는 것은 수학자가 하는 것처럼 하는 것이다.’ 이 말은 여러 번의 시도와 실패를 반복해 가면서 ‘왜 이렇게 될까?’ 라는 의문을 가지고 여러 가지 창의적인 수학적 사고를 먼저 해보고 문제를 대하는 것을 뜻한다. 생활 속의 수학 문제는 바로 이 점에서 시사하는 바가 크다. 이런 수학 문제를 풀 때 학생들은 수동적이 아닌 능동적인 논리적 사고를 한다. 본 연구에서는 대학 입시제도로 인해 지금까지의 수학을 암기위주로 수동적으로만 학습하였던 수학 부진학생들에게 생활과 연관된 수학문제들을 제시함으로써 수학 우수 학생과 비슷한 능동적 구성활동을 유발할 수 있었으며 수학 부진 학생들과 우수 학생들의 지금까지 배운 수학 학습의 전이에 어떤 요인이 영향을 주었는지를 조사하였다.

• Education of Primary School Mathematics
• /
• v.27 no.3
• /
• pp.303-320
• /
• 2024

This study presents the development and performance evaluation of a custom GPT-based chatbot tailored to provide solutions following Polya's problem-solving stages. A beta version of the chatbot was initially deployed to assess its mathematical capabilities, followed by iterative error identification and correction, leading to the final version. The completed chatbot demonstrated an accuracy rate of approximately 89.0%, correctly solving an average of 57.8 out of 65 image-based problems from a 6th-grade elementary mathematics textbook, reflecting a 4 percentage point improvement over the beta version. For a subset of 50 problems, where images were not critical for problem resolution, the chatbot achieved an accuracy rate of approximately 91.0%, solving an average of 45.5 problems correctly. Predominant errors included problem recognition issues, particularly with complex or poorly recognizable images, along with concept confusion and comprehension errors. The custom chatbot exhibited superior mathematical performance compared to the general-purpose ChatGPT. Additionally, its solution process can be adapted to various grade levels, facilitating personalized student instruction. The ease of chatbot creation and customization underscores its potential for diverse applications in mathematics education, such as individualized teacher support and personalized student guidance.

• KIPS Transactions on Software and Data Engineering
• /
• v.11 no.8
• /
• pp.315-324
• /
• 2022

In this paper, we propose KoEPT, a Transformer-based generative model for automatic math word problems solving. A math word problem written in human language which describes everyday situations in a mathematical form. Math word problem solving requires an artificial intelligence model to understand the implied logic within the problem. Therefore, it is being studied variously across the world to improve the language understanding ability of artificial intelligence. In the case of the Korean language, studies so far have mainly attempted to solve problems by classifying them into templates, but there is a limitation in that these techniques are difficult to apply to datasets with high classification difficulty. To solve this problem, this paper used the KoEPT model which uses 'expression' tokens and pointer networks. To measure the performance of this model, the classification difficulty scores of IL, CC, and ALG514, which are existing Korean mathematical sentence problem datasets, were measured, and then the performance of KoEPT was evaluated using 5-fold cross-validation. For the Korean datasets used for evaluation, KoEPT obtained the state-of-the-art(SOTA) performance with 99.1% in CC, which is comparable to the existing SOTA performance, and 89.3% and 80.5% in IL and ALG514, respectively. In addition, as a result of evaluation, KoEPT showed a relatively improved performance for datasets with high classification difficulty. Through an ablation study, we uncovered that the use of the 'expression' tokens and pointer networks contributed to KoEPT's state of being less affected by classification difficulty while obtaining good performance.

• Journal of Elementary Mathematics Education in Korea
• /
• v.14 no.3
• /
• pp.885-905
• /
• 2010

This study questions that mathematical evaluations strive to memorize fragmentary knowledge and have an objective test. To solve these problems on mathematical education We did descriptive test. Through the descriptive test, students think and express their ideas freely using mathematical terms. We want to know if that procedure is correct or not, and, if they understand what was being presented. We studied this because We want to analyze where and what kinds of faults they committed, and be able to correct an error so as to establish a correct mathematical concept. The result from this study can be summarized as the following; First, the mistakes students make when solving the descriptive tests can be divided into six things: error of question understanding, error of concept principle, error of data using, error of solving procedure, error of recording procedure, and solving procedure omissions. Second, students had difficulty with the part of the descriptive test that used logical thinking defined by mathematical terms. Third, errors pattern varied as did students' ability level. For high level students, there were a lot of cases of the solving procedure being correct, but simple calculations were not correct. There were also some mistakes due to some students' lack of concept understanding. For middle level students, they couldn't understand questions well, and they analyzed questions arbitrarily. They also have a tendency to solve questions using a wrong strategy with data that only they can understand. Low level students generally had difficulty understanding questions. Even when they understood questions, they couldn't derive the answers because they have a shortage of related knowledge as well as low enthusiasm on the subject.