• 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.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.683-700
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• 2016

The traditional teaching-learning in mathematics, which pursue only one correct answer, should be reexamined to cope with an age of uncertainty. In this research, Perry's epistemological development scheme was noticed as a theoretical approach to diagnose problems of dualistic mathematics lessons and to search solutions of the problems. And Design-Based Research method was adopted, We developed the epistemological development scheme through considering Perry's theory and related studies, scaffoldings and teaching-learning to enhance students' epistemological positions in mathematics. Based on these discussions we designed teaching experiment about operations with negative numbers, and analyzed its didactic implications.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.109-128
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• 2009

This study aimed to investigate students' learning process by examining their perception process of problem structure and mathematization, and further to suggest an effective teaching and learning of mathematics to improve students' problem-solving ability. Using the qualitative research method, the researcher observed the collaborative learning of two middle school students by providing problem-posing activities of five lessons and interviewed the students during their performance. The results indicated the student with a high achievement tended to make a similar problem and a new problem where a problem structure should be found first, had a flexible approach in changing its variability of the problem because he had advanced algebraic thinking of quantitative reasoning and reversibility in dealing with making a formula, which related to developing creativity. In conclusion, it was observed that the process of problem posing required accurate understanding of problem structures, providing students an opportunity to understand elements and principles of the problem to find the relation of the problem. Teachers may use a strategy of simplifying external structure of the problem and analyzing algebraical thinking necessary to internal structure according to students' level so that students are able to recognize the problem.

• Education of Primary School Mathematics
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• v.13 no.1
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• pp.1-11
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• 2010

Assessment provides valuable information for both teachers and students regarding how well each is doing. Assessment also defines what students must know and be able to do to succeed in a teacher's class. The purpose of this study is to analysis the mathematics assessment items based on strands of mathematical proficiency of National Research Council. According to the study results, the rate of right answers was high in adaptive reasoning and conceptual understanding(over 80%). On the other hand, the rate of right answers was lower in strategic competence(62%) than other strands.

• Journal of the Korea Convergence Society
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• v.13 no.4
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• pp.39-44
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• 2022

Mathematics franchise education companies are developing various online learning systems to provide on-off integrated education to learners. Most online learning systems deliver one-way lecture content to learners and perform quantitative problem-solving learning for learning results. However, each learner has different academic achievement competencies, and it is impossible to determine exactly where the level of understanding fell when solving a math method. and based on this, establish an online learning system to discover the weak points of learners and propose an effective learner management method. Through the developed learning method and system, it is expected to cultivate balanced problem-solving ability for learners and provide differentiated brand image and counseling service to franchise companies.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.277-293
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• 2011

The purpose of mathematics education is to develop the ability of transforming various problems in general situations into mathematics problems and then solving the problem mathematically. Various teaching-learning methods for improving the ability of the mathematics problem-solving can be tried. However, it is necessary to choose an appropriate teaching-learning method after figuring out students' level of understanding the mathematics learning or their problem-solving strategies. The error analysis is helpful for mathematics learning by providing teachers more efficient teaching strategies and by letting students know the cause of failure and then find a correct way. The following subjects were set up and analyzed. First, the error classification pattern was set up. Second, the errors in the solving process of the function problems were analyzed according to the error classification pattern. For this study, the survey was conducted to 90 first grade students of ${\bigcirc}{\bigcirc}$high school in Chung-nam. They were asked to solve 8 problems in the function part. The following error classification patterns were set up by referring to the preceding studies about the error and the error patterns shown in the survey. (1)Misused Data, (2)Misinterpreted Language, (3)Logically Invalid Inference, (4)Distorted Theorem or Definition, (5)Unverified Solution, (6)Technical Errors, (7)Discontinuance of solving process The results of the analysis of errors due to the above error classification pattern were given below First, students don't understand the concept of the function completely. Even if they do, they lack in the application ability. Second, students make many mistakes when they interpret the mathematics problem into different types of languages such as equations, signals, graphs, and figures. Third, students misuse or ignore the data given in the problem. Fourth, students often give up or never try the solving process. The research on the error analysis should be done further because it provides the useful information for the teaching-learning process.

• Korean Journal of Cognitive Science
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• v.21 no.2
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• pp.283-307
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• 2010

In this study, a new open-ended format math testing system for elementary school students has been proposed. This system is an application of the recently proposed Constructive Multiple-choice Testing (CMT) system on math testing. The CMT system is a testing system in which the examinee has to respond to an item twice, first in an open ended format, and then in the multiple choice format. The advantages of this system is that process information can easily be obtained and that the examinee can receive feedback immediately after the test, based on his/her multiple choice responses. This open-ended format math testing system includes the manager mode, which allows the generation of the test items and student account management, and the testing mode, which allows the students to input their solution process using the menu bar and the keyboard. When two groups, one tested using the CMT system and the other tested using the paper and pencil test, were compared, there was no significant difference in average scores between the two groups although the testing time was longer for the group tested using the CMT system. This result suggests that the open-ended format math testing system proposed in this study can be used effectively in the actual classroom setting.

• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.289-302
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• 2007

I took a look at the note written by the students in math class. But, it was sort of a 'scratch paper' because they focused only on the problems or do not know the writing a notebook. Thus, I prepared organizational writing activity through learning-notebooks and analyzed the results from the writing activity through learning-notebooks in order to recognize the effects how the activity influences students' mathematics academic achievements and attitude. As a result, I could find that writing activity through learning-notebooks contributes to the enhancement of mathematics academic achievement and attitude.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.467-482
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• 2023

In this paper, we present our new teaching and learning materials on gradient descent method, which is widely used in artificial intelligence, available for college mathematics. These materials provide a good explanation of gradient descent method at the level of college calculus, and the presented SageMath code can help students to solve minimization problems easily. And we introduce how to solve least squares problem using gradient descent method. This study can be helpful to instructors who teach various college-level mathematics subjects such as calculus, engineering mathematics, numerical analysis, and applied mathematics.

• The Mathematical Education
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• v.60 no.4
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• pp.509-527
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• 2021

We investigated whether and how pre-service teachers took the realistic contexts seriously in the course of solving word problems; additionally, we investigated how pre-service teachers evaluated students' realistic and non-realistic answers to word problems. Many pre-service teachers, similar to students, solved some of the realistic problems unrealistically without taking the realistic contexts seriously. Besides, they evaluated students' non-realistic answers higher than the realistic answers. Whether the pre-service teachers could solve problems realistically or not, they did not appreciate students' realistic considerations for the reasons that those were not fitted to the intentions of the word problems, or those were evidence of the flaws of the problem. Furthermore, the analysis of premises implied in the pre-service teachers' evaluation comments showed the implicit didactic contracts about realistic word problem solving that they accepted and also anticipated students to follow. Our analysis of the pre-service teachers' conceptions of realistic word problems can help teacher educators design the teacher program to challenge and revise pre-service teachers' folk pedagogy.