• Education of Primary School Mathematics
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• v.26 no.4
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• pp.219-236
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• 2023

This study examined the relationship between preservice teachers' mathematical understanding and problem posing in fractions multiplication and division. To this purpose, 41 preservice teachers performed visual representation and problem posing tasks for fraction multiplication and division, measured their mathematical understanding and problem posing ability, and examined the relationship between mathematical understanding and problem posing ability using cross-tabulation analysis. As a result, most of the preservice teachers showed conceptual understanding of fraction multiplication and division, and five types of difficulties appeared. In problem posing, most of the preservice teachers failed to pose a math problem that could be solved, and four types of difficulties appeared. As a result of cross-tabulation analysis, the degree of mathematical understanding was related to the ability to pose problems. Based on these results, implications for preservice teachers' mathematical understanding and problem posing were suggested.

• East Asian mathematical journal
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• v.27 no.4
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• pp.381-389
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• 2011

The flexible mathematical thinking - the ability to generate and connect various representations of concepts - is useful in understanding mathematical structure and variation in problem solving. In particular, the flexible mathematical thinking with the inventive mathematical thinking, the original mathematical problem solving ability and the mathematical invention is a core concept, which must be emphasized in all branches of mathematical education. In this paper, the author considered a case of flexible mathematical thinking with an inventive problem solving ability shown by his student via real analysis courses. The case is on the proofs of the equivalences of three different definitions on the concept of limit superior shown in three different real analysis books. Proving the equivalences of the three definitions, the student tried to keep the flexible mathematical thinking steadily.

• The Mathematical Education
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• v.50 no.4
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• pp.467-487
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• 2011

The purpose of this study is to analyze of gifted students' improvement on mathematical attitude and problem-solving ability through project-based materials in science high school. For this study, research questions are established as follows. 1. Does the project-based materials-used instruction have a positive effect on improving problem-solving ability? 2. Does the project-based materials-used instruction have a positive effect on improving mathematical attitude? To solve these research questions, this study employed a survey and interview type investigation for gifted students' mathematical attitude and problem-solving ability. A subject of classes were randomly selected among the 11th grader in D science high school and designated one class as the experimental group and the other class as the control group. Twelve hours of the project-based materials-used instruction and the traditional textbook-oriented instruction had been carried out in each class. Findings on this study are as follows: First, the project-based material-used instruction is shown to be more effective in enhancing problem-solving ability than the traditional textbook-oriented instruction. Second, the project-based material-used instruction is shown to be more effective in improving mathematical attitude than the traditional textbook-oriented instruction.

• Research in Mathematical Education
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• v.16 no.1
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• pp.15-29
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• 2012

One of the important aims in mathematics education is to enhance mathematical thinking for students. And students posing questions is a vital process in mathematical thinking as it is part of the reasoning and communication of their learning. This paper investigates how students develop their mathematical thinking through working on tasks in fractions and posing their own questions after successfully solved the problems. The teaching was conducted in primary five classes and the results showed that students' reasoning is related to their analogy with what previously learned. Also, posing their problems after solving the problem not only helps students to understand the structure of the problem, it also helps students to explore on different routes in solving the problem and extend their learning content.

• IE interfaces
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• v.13 no.3
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• pp.539-547
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• 2000

An architecture of a Web-based Decision Support system for mathematical analysis is presented. Front-end modules provide web-client GUI environment for mathematical analysis. The networking architecture is built upon client/server system by Java socket and accesses database by JDBC in WWW. Back-end modules provide decision supporting service and data management for mathematical programming analysis. In the back-end any analysis tools, such as mathematical optimizer, simulation package, or statistics package can be used. As an application example for this implementation, optimal facility replacement decision problem is selected. In the implementation the optimal facility replacement decision problem is formulated as a shortest path problem. It uses Oracle DB and CPLEX package as the mathematical optimizer. While ORAWeb is designed and implemented on the optimal facility replacement problem, it can easily be extended to any decision supporting problems that would require mathematical optimization process.

• Research in Mathematical Education
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• v.17 no.3
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• pp.199-220
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• 2013

The main objective of this study is to explore the relationship between psychological factors (i.e. math anxiety, attention, attitude, Working Memory Capacity (WMC), and Field dependency) and students' mathematics problem solving based on Revised Bloom Taxonomy. A sample of 169 K11 school girls were tested on (1) The Witkin's cognitive style (Group Embedded Figure Test). (2) Digit Span Backwards Test. (3) Mathematics Anxiety Rating Scale (MARS). (4) Modified Fennema-Sherman Attitude Scales. (5) Mathematics Attention Test (MAT), and (6) Mathematics questions based on Revised Bloom Taxonomy (RBT). Results obtained indicate that the effect of these items on students mathematical problem solving is different in each cognitive process and level of knowledge dimension.

• Education of Primary School Mathematics
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• v.4 no.1
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• pp.51-61
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• 2000

Mathematical Problem solving has been the focus of a considerable amount of research over past 30 years. But nowadays problem solving is being beginning to be of less interest to mathematics education researchers. Moreover, mathematics teachers have an urgent need to be provided with well-documented informations about "teaching of(expecially, via) problem solving" though following research issues ：ⅰ) the role of the teacher in a problem-centered classroom, ⅱ) what actually takes place in problem-centered classrooms, and iii) groups and whole classes' problem solving rather than individuals. This paper intends to give some informations about practice of teaching mathematical problem solving in elementary school.ry school.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.107-134
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• 2012

The purpose of this study is to investigate the effectiveness of two teaching methods of word problems, one based on mathematical modeling learning(ML) and the other on traditional learning(TL). Additionally, the influence of mathematical modeling learning in word problem solving behavior, application ability of real world experiences in word problem solving and the beliefs of word problem solving will be examined. The results of this study were as follows: First, as to word problem solving behavior, there was a significant difference between the two groups. This mean that the ML was effective for word problem solving behavior. Second, all of the students in the ML group and the TL group had a strong tendency to exclude real world knowledge and sense-making when solving word problems during the pre-test. but A significant difference appeared between the two groups during post-test. classroom culture improvement efforts. Third, mathematical modeling learning(ML) was effective for improvement of traditional beliefs about word problems. Fourth, mathematical modeling learning(ML) exerted more influence on mathematically strong and average students and a positive effect to mathematically weak students. High and average-level students tended to benefit from mathematical modeling learning(ML) more than their low-level peers. This difference was caused by less involvement from low-level students in group assignments and whole-class discussions. While using the mathematical modeling learning method, elementary students were able to build various models about problem situations, justify, and elaborate models by discussions and comparisons from each other. This proves that elementary students could participate in mathematical modeling activities via word problems, it results form the use of more authentic tasks, small group activities and whole-class discussions, exclusion of teacher's direct intervention, and classroom culture improvement efforts. The conclusions drawn from the results obtained in this study are as follows: First, mathematical modeling learning(ML) can become an effective method, guiding word problem solving behavior from the direct translation approach(DTA) based on numbers and key words without understanding about problem situations to the meaningful based approach(MBA) building rich models for problem situations. Second, mathematical modeling learning(ML) will contribute attitudes considering real world situations in solving word problems. Mathematical modeling activities for word problems can help elementary students to understand relations between word problems and the real world. It will be also help them to develop the ability to look at the real world mathematically. Third, mathematical modeling learning(ML) will contribute to the development of positive beliefs for mathematics and word problem solving. Word problem teaching focused on just mathematical operations can't develop proper beliefs for mathematics and word problem solving. Mathematical modeling learning(ML) for word problems provide elementary students the opportunity to understand the real world mathematically, and it increases students' modeling abilities. Futhermore, it is a very useful method of reforming the current problems of word problem teaching and learning. Therefore, word problems in school mathematics should be replaced by more authentic ones and modeling activities should be introduced early in elementary school eduction, which would help change the perceptions about word problem teaching.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.623-647
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• 2020

The greatest integer that does not belong to a numerical semigroup S is called the Frobenius number of S. The Frobenius problem, which is also called the coin problem or the money changing problem, is a mathematical problem of finding the Frobenius number. In this paper, we introduce the Frobenius problem for two kinds of numerical semigroups generated by the Thabit numbers of the first kind, and the second kind base b, and by the Cunningham numbers. We provide detailed proofs for the Thabit numbers of the second kind base b and omit the proofs for the Thabit numbers of the first kind base b and Cunningham numbers.

• The Mathematical Education
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• v.41 no.2
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• pp.189-202
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• 2002

Problem-centered learning reflects learning strategy based on constructivism. In this learning, students should find the solution in a small group discussion, and share their solutions with classmates in whole class discussion. So students participate in mathematics instruction actively and interact with other students about the strategies. We expect students would change their attitudes on mathematics and mathematical learning in these processes. In this study, we analyzed students' attitudes on mathematics and mathematical learning when they participated the problem-centered learning program. We found the change of students' attitudes to mathematics via problem-centered learning.