• Communications of Mathematical Education
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• v.29 no.3
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• pp.533-551
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• 2015

Problem posing in school mathematics is generally regarded to make a new problem from contexts, information, and experiences relevant to realistic or mathematical situations. Also, it is to reconstruct a similar or more complicated new problem based on an original problem. The former is called as problem generation and the latter is as problem reformulation. The purpose of this study was to explore the co-relation between problem generation and problem reformulation, and the educational effectiveness of each problem posing. For this purpose, on the subject of 33 pre-service secondary school teachers, this study developed two types of problem posing activities. The one was executed as the procedures of [problem generation${\rightarrow}$solving a self-generated problem${\rightarrow}$reformulation of the problem], and the other was done as the procedures of [problem generation${\rightarrow}$solving the most often generated problem${\rightarrow}$reformulation of the problem]. The intent of the former activity was to lead students' maintaining the ability to deal with the problem generation and reformulation for themselves. Furthermore, through the latter one, they were led to have peers' thinking patterns and typical tendency on problem generation and reformulation according to the instructor(the researcher)'s guidance. After these activities, the subject(33 pre-service teachers) was responded in the survey. The information on the survey is consisted of mathematical difficulties and interests, cognitive and affective domains, merits and demerits, and application to the instruction and assessment situations in math class. According to the results of this study, problem generation would be geared to understand mathematical concepts and also problem reformulation would enhance problem solving ability. And it is shown that accomplishing the second activity of problem posing be more efficient than doing the first activity in math class.

• Communications of Mathematical Education
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• v.21 no.2 s.30
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• pp.271-282
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• 2007

Producing tools for actively meeting social needs in a radical changing society due to the development of modern technology has been shifted from physical ability to intelligent ability. The prominence of educating creativity is perceived as a good preparation in order to deal with them. Considered that assessment which is systematic activity to collect, analyze, diagnose, and judge information of a series of instruction practices is means to impart evidence and feedback of teaching learning practices, education and assessment is placed on reciprocal relationship. Nevertheless, there has been some tendency of neglect of assessment, comparing education for upbringing creativity. In this paper model of pencil and paper problem is discussed focusing on the sub-components of creativity and problem solving as one of the variety of means to extend mathematical creativity.

• Research in Mathematical Education
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• v.14 no.1
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• pp.33-50
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• 2010

The mathematical thinking which transforms important mathematical content and developed into mathematical structure is a vital process in building up mathematical ability as mathematical knowledge based on structure. Such process based on students' recognition of mathematical concept. Developing mathematical thinking into mathematical structure happens when different cognitive units are connected and compressed to form schema of solution, which could happen through some guided problems. The effort of arithmetic approach in problem solving did not necessarily provide students the structure schema of solution. The using of equation to solve the problem is based on the schema of building equation, and is not necessary recognizing the structure of the solution, as the recognition of structure may be lost in the process of simplification of algebraic expressions, leaving only the final numeric answer of the problem.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.113-124
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• 2005

In this study, we have analysed and compared the cognitive, affective, and emotional aspects of the mathematically gifted, the scientifically gifted, and common middle school students in cognitive, affective, and emotional aspects. The mathematically gifted students are proved to have better continuous/simultaneous information processing, more positive mathematical disposition, more preference to difficult tasks, and higher EQ than the common students do. On another hand, no difference is found between the mathematically gifted and the scientifically gifted students in creative problem solving ability however, the mathematically gifted have more self-confidence, more curiosity for mathematics, stronger will, and more disposition to monitor and reflect, and more efficient self-control than the scientifically gifted do. In short, the mathematically gifted are superior to common students in mostly all aspects, and better than the scientifically gifted in the affective part.

• Education of Primary School Mathematics
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• v.6 no.1
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• pp.29-40
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• 2002

Fairy-tales give students opportunities to build connections between a problem-solving situation and mathematics as well as to communicate solutions through writing, symbols, and diagrams. Therefore, the purpose of this paper is to introduce how to use fairy-tales in elementary mathematics classroom in order to develope student's mathematical concepts and process in terms of the following areas: ⑴ reconstructing literature ⑵ understanding concepts ⑶ problem posing activity. To be useful, mathematics should be taught in contexts that are meaningful and relevant to learners. Therefore using fairy-tales as a vehicle to teach mathematics gives students a chance to develope mathematics understanding in a natural, meaningful way, and to enhance problem posing and problem solving ability. Further, future study will continue to foster how fairy-tales literatures will enhance children's mathematics knowledge and influence on their mathematics performance.

• School Mathematics
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• v.16 no.4
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• pp.691-708
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• 2014

In general, the intuitive knowledge that can use in mathematics problem solving is one of the important knowledge to teachers as well as students. So, this study is aimed to analyze the elementary preservice teachers' intuitive knowledge in relation to intuitive and counter-intuitive problem solving. For this, I performed survey to use questionnaire consisting of problems that can solve in intuitive methods and cause the errors by counter-intuitive methods. 161 preservice teachers participated in this study. I got the conclusion as follows. preservice teachers' intuitive problem solving ability is very low. I special, many preservice teachers preferred algorithmic problem solving to intuitive problem solving. So, it's needed to try to improve preservice teachers' problem solving ability via ensuring both the quality and quantity of problem solving education during preservice training courses. Many preservice teachers showed errors with incomplete knowledges or intuitive judges in counter-intuitive problem solving process. For improving preservice teachers' intuitive problem solving ability, we have to develop the teacher education curriculum and materials for preservice teachers to go through intuitive mathematical problem solving. Add to this, we will strive to improve preservice teachers' interest about mathematics itself and value of mathematics.

• Education of Primary School Mathematics
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• v.15 no.3
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• pp.219-233
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• 2012

Practicality and value of mathematics can be verified when different problems that we face in life are resolved through mathematical knowledge. This study intends to identify whether the fraction teaching is being taught and learned at current elementary schools for students to recognize practicality and value of mathematical knowledge and to have the ability to apply the concept when solving problems in the real world. Accordingly, contextual problems and noncontextual problems are proposed around fractional arithmetic area, and compared and analyze the achievement level and problem solving processes of them. Analysis showed that there was significant difference in achievement level and solving process between contextual problems and noncontextual problems. To instruct more meaningful learning for student, contextual problems including historical context or practical situation should be presented for students to experience mathematics of creating mathematical knowledge on their own.

• Journal of Educational Research in Mathematics
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• v.12 no.1
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• pp.109-124
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• 2002

This study investigated various effects of WBD(web-based discussion) on mathematical communication, interaction and problem solving in the classroom. We developed a web site including BBS and chat room in order to encourage students' mathematical curiosities and self-studies. The web site had been operated for 6 months. Five classes of 1st grade students were selected from an middle school in Daejon. Moreover, we analyzed several cases for interactional behavior and effect. WBD promote dialogue between a teacher and students. Analysis of feed-back from BBS revealed that student's negative attitudes could be changed to positive ones by step-by-step discussions. Moreover, collaborative learning is enhanced by on-line discussion. But the effects of WBD are affected by the character and ability of a student.

• The Mathematical Education
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• v.42 no.3
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• pp.353-368
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• 2003

Analogy, based on a similarity, is to infer the properties of the similar object from properties of an object. It can be a very useful thinking tool for learning mathematical patterns and laws, noticing on relational properties among various situations. The purpose of this study, when manipulating hint condition, figure and table conditions and the amount of original learning by using algebra word problems, is to verify the effects of analogical transfer in solving equivalent, isomorphic and similar problems according to the similarity of source problems and target ones. Five study questions were set up for the above purpose. It was 354 first grade students of S and G middle schools in Seoul that were experimented for this study. The data was processed by MANOVA analysis of statistical program, SPSS 10.0. The results of this studies would indicate that most of the students would be poor at solving isomorphic and similar problems in the performance of analogical transfer according to the similarity of source and target problems. Hints, figure and table conditions did not facilitate the analogical transfer. Merely, on the condition that amount of teaming was increased, analogical transfer of the students was facilitated. Therefore, it is necessary to have students do much more analogical problem-solving experience to improve their analogical reasoning ability through the instruction program development in the educational fields.

• Journal of The Korean Association of Information Education
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• v.14 no.3
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• pp.319-328
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• 2010

Computer programming education gives students a chance to use computers independently and actively. This plays a very positive role in acquiring higher cognitive skills such as mathematical skills and creative logical thinking. Thus the purpose of this study is to measure the degrees of students' problem-solving abilities using MCU programming kits based on the ICT Education Guide. The experiment confirms that programming classes using MCU kits have a more positive effect on the students problem-solving abilities than do those using the existing computer textbooks. The sub-constituents of problem-solving abilities - problem recognition, information gathering, analysis, diffuse thinking, decision-making, planning, execution, evaluation and feedback - also show significant statistical differences. Therefore, we can conclude that programming classes using MCU kits are very effective in advancing problem-solving abilities.