• The Mathematical Education
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• v.39 no.2
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• pp.101-125
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• 2000

Since the 1980\`s metacognition has been one of the core subjects in the studies on mathematical education, the purpose of this study is to examine and analyze the mathematical creativity, problem-solving ability, and beliefs of math of middle school using the metacognition learning method. The results of this study is as follows; the first, we found that the metacognition learning methods were more effective method than classic method to improve the creativity and the problem-solving ability in math.

• The Mathematical Education
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• v.52 no.2
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• pp.175-190
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• 2013

The purpose of this article is to suggest using portfolio for professional development of secondary pre-service mathematics teachers based on actual application case. To achieve this goal, 28 pre-service mathematics teachers developed their own portfolios in the regular study course for one semester under the pre-planned components of portfolio. Then they participated in the survey of their beliefs in mathematics and mathematics education and in the structured interview for drawing implications of using a pre-service mathematics teacher portfolio. According to the collected data, developing a pre-service mathematics teacher portfolio made a significant difference in beliefs of mathematics teachers' roles and showed the potential to improve the professional development of pre-service mathematics teachers as well as their learning. Continued investigation for more effective components of a pre-service mathematics teacher portfolio would be needed.

• 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.

• Research in Mathematical Education
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• v.15 no.4
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• pp.357-371
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• 2011

In mathematical problem solving, students may make various errors. In order to draw useful lessons from the errors, and then correct them, we surveyed 24 eighth-grade students' performances in geometrical problem solving according to Casey's hierarchy of errors. It was found that: 1. Students' effect can lead to errors at the stage of "comprehension", "strategy selection", and "skills manipulation"; and 2. Students' geometric schemas also influenced their strategy selection".

• Research in Mathematical Education
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• v.4 no.1
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• pp.23-31
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• 2000

This research elaborated five components for pre-service mathematics teacher training: 1) Mathematical content knowledge, 2) Pedagogical content knowledge, 3) Pedagogical reasoning, 4) System of training, and 5) Mathematics teachers' beliefs. For the effect teaching, mathematics teacher program should be reformed. The key to improvement should be concerntrated on developing knowledge about effective teaching and translating it into algorithms those teachses can learn and incorporate in their planning prior to teaching. A theory of instruction should specify the most effective sequences in which to present the materials to be learned.

• Research in Mathematical Education
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• v.3 no.1
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• pp.35-56
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• 1999

The evolution of the function concept was delineated in terms of the 17th and 18th Centuries' dependent nature of function, and the 19th and 20th Centuries' arbitrary and univalent nature of function. According to mathematics educators' beliefs about the value of the function concept in school mathematics, certain definitions of the concept tend to be emphasized. This study discusses three types - genetical (dependence), logical (settheoretical), analogical (machine/equations) - of definition of function and their values.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.381-393
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• 2007

The study focuses on what to consider and do for the improvement of math education of Korean Universities by comparing freshmen and seniors of department of math education in their beliefs in mathematics and math. education. The major comparing topics in the beliefs are composed of perception of mathematics as a science, learning methods of mathematics, teaching methods of mathematics, and roles and qualifications of math. teachers. The results of the study show that junior students tend to be more positive in their beliefs, especially in math education area than that of mathematics, compared to the freshmen. It implies that how important the role of topics covered in math education during college years is for changing the future teachers' beliefs in math and math education more positively. The supposed influencing contents of the curriculum of math. education are composed of learning reflection method based on problem-based learning, understanding mathematics as originated from the real world, mathematical pedagogy, text analysis, practice in classroom, and understanding various concepts in math. education area.

• Research in Mathematical Education
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• v.12 no.3
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• pp.215-233
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• 2008

Deep comprehension of basic mathematical notions and concepts is a basic condition of a successful teaching. Some elements of algebraic thinking belong to the elementary school mathematics. The question "What stays the same and what changes?" link arithmetic problems with algebraic conception of variable. We have studied beliefs and comprehensions of future elementary school mathematics teachers on early algebra. Pre-service teachers from three academic pedagogical colleges deal with mathematical problems from the pre-algebra point of view, with the emphasis on changes and invariants. The idea is that the intensive use of non-formal algebra may help learners to construct a better understanding of fundamental ideas of arithmetic on the strong basis of algebraic thinking. In this article the study concerning arithmetic series is described. Considerable number of pre-service teachers moved from formulas to deep comprehension of the subject. Additionally, there are indications of ability to apply the conception of change and invariance in other mathematical and didactical contexts.

• The Journal of Fisheries Business Administration
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• v.47 no.3
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• pp.71-92
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• 2016

This study examines the effects of consumer beliefs for food certifications on the behavioral intentions and the behavioral intention biases to purchase the certified seafoods by a subjective probability model which is on the basis of the mathematical probability model and the covariance model. The food certifications used on this study are 'Organic foods', 'Traceability system of food products' and. 'HACCP'. The representative foods of fishery products on this study is seasoned laver. The current study showed the following results. First, consumers have more than two different beliefs each for all certifications which are the subjects of this study. The beliefs of the certifications have an impact on the consumers when they consider to buy the certified seafood products. Second, consumers try to persuade by themselves to ensure that their particular belief about the certification could lead to a purchase the seafood products. Consumer beliefs of the "environmentally friendly production" on the organic foods certification is an important factor as much as the "guarantee of food safety" belief making a positive purchasing behavior intentions(PBI) bias for the organic seafood products. Consumers also have a positive PBI bias for certified seafood products in all certifications as long as a certification is considered to "guarantee the transparency of the food distribution process" as its belief. 'Traceability system' was the only one which didn't generate a positive PBI bias from the belief of "guarantee of food safety" out of three certifications.

• Journal for History of Mathematics
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• v.13 no.1
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• pp.49-62
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• 2000

In this paper we analyzed the histo-genetic principle and constructivism on the mathematics education. This study is tried to suggest teacher's a role in mathematics learning and to find out the teacher's mathematical beliefs on the mathematics education be based on the histo-genetic principle and constructivism.