• Communications of Mathematical Education
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• v.28 no.4
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• pp.553-571
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• 2014

Mathematical process is an issue in current mathematics education. In this paper discuss how to assess the mathematical process using essay type questions. For this we first suggest the concept of Mathematical Process Oriented Question which is an essay type question and possible to assess mathematical processes, that is, the mathematical communication, reasoning, and problem solving as well as mathematics knowledge. And we develop a framework for developing the mathematical process oriented question and rubric, examples of assessment standards and those questions containing rubric for assessing mathematical processes. The results of this paper can serve as basic data and examples for follow up research about mathematical process assessment.

• Journal of Gifted/Talented Education
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• v.25 no.4
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• pp.581-605
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• 2015

The purpose of this study is to build an instruction method focused on the mathematical process and apply it to 12, 5-year-olds from Kindergarten located in Seoul with a view to explore the changes in their mathematical thinking. In addition, surveys with parents and teachers, as well as those conducted in the field of early childhood education, were conducted to analyze the current situation. The effects focused on the five mathematical processes, namely problem solving, reasoning and proof, connecting, representing and communication was found to help the interactions between teacher-child and child-child stimulate the mathematical thinking of the children and induce changes. The mathematical process-focused instruction aimed to advance mathematical thinking internalized mathematical knowledge, presented an integrated problematic situation, and empathized the mathematical process, which enabled the children to solve the problem by working together with peers. As such, the mathematical thinking of the children was integrated and developed within the process of a positive change in the mathematical attitude in which mathematical knowledge is internalized through mathematical process.

• The Mathematical Education
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• v.48 no.2
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• pp.183-190
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• 2009

This is a following study of the preceding study, Flexibility of mind and divergent thinking in problem solving process that was performed by Choi & Do in 2005. In this paper, we discuss the relationship between ability to shift a viewpoint and insight into invariance, another major consideration in mathematical creativity, in the process of mathematical problem solving.

• Research in Mathematical Education
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• v.26 no.3
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• pp.253-270
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• 2023

This study aims to investigate the extent to which Korean high school textbooks incorporate opportunities for students to engage in the mathematical modeling process through tasks related to exponential and logarithmic functions. The tasks in three textbooks were analyzed based on the actions required for each stage in the mathematical modeling process, which includes identifying essential variables, formulating models, performing operations, interpreting results, and validating the outcomes. The study identified 324 units across the three textbooks, and the reliability coefficient was 0.869, indicating a high level of agreement in the coding process. The analysis revealed that the distribution of tasks requiring engagement in each of the five stages was similar in all three textbooks, reflecting the 2015 revised curriculum and national curriculum system. Among the 324 analyzed tasks, the highest proportion of the units required performing operations found in the mathematical modeling process. The findings suggest a need to include high-quality tasks that allow students to experience the entire process of mathematical modeling and to acknowledge the limitations of textbooks in providing appropriate opportunities for mathematical modeling with a heavy emphasis on performing operations. These results provide implications for the development of mathematical modeling activities and the reconstruction of textbook tasks in school mathematics, emphasizing the need to enhance opportunities for students to engage in mathematical modeling tasks and for teachers to provide support for students in the tasks.

• 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.46 no.3
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• pp.293-302
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• 2007

In this paper, we review definition and concept of mathematical creativity. A couple of criteria have established for perspectives in mathematical creativity, The first is specific domain(mathematics) vs general domain(creativity) and the second is process(thinking process) vs outcome(divergent production). By these criteria, four perspectives have constructed : mathematics-thinking process approach(McTd), mathematics-divergent production approach(MctD), creativity-thinking process approach(mCTd), creativity-divergent production approach(mCtD). When mathematical creativity is researched by the specific reason and particular focus, an appropriate approach can be chosen in four perspectives.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.557-580
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• 2012

Common Core State Standards for Mathematics(CCSSM) is a blueprint for school mathematics in 2010s of the United States. CCSSM can be divided into two major parts, the standards for mathematical content and the standards for mathematical practice. This study focused on the latter. Mathematical practice comes from the mathematical process in 'Principles and standards for school mathematics(NCTM, 2000)' as well as the mathematical proficiency in 'Adding it up(NRC, 2001)'. It is composed of eight standards which mathematically proficient students are expected to do. From Korean perspective, it can also be comparable with the mathematical process which contains mathematical problem solving, mathematical reasoning, and mathematical communication and was provided by the 2009 revised national curriculum for mathematics in Korea. However, few focused the standards for mathematical practice among the studies related to CCSSM in Korea. Moreover, there is a study that even ignores the existence of the standards for mathematical practice itself. This study aims to understand the standards for mathematical practice through analysing the document of CCSSM and its successive materials for implementing the CCSSM. This understanding will help effective implementation of the mathematical process in Korea.

• School Mathematics
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• v.4 no.2
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• pp.147-160
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• 2002

The purpose of this study is to examine the The correlation between information processing types and mathematical communication abilities / word problem solving abilities. The results obtained are as follows: 1 Simultaneous/continuous information process types showed statistically high correlation with mathematical communication abilities. However, the correlation between simultaneous information process and mathematical communication abilities is a little higher than the correlation between continuous information process and mathematical communication abilities. 2. There is a high correlation between mathematical communication abilities and word problem solving abilities. Especially, speaking ability is much more correlated with four factors of word problem solving than reading, writing and listening, Through this study, we can conclude that information process types should be consider ed in order to improve mathematical communication abilities and mathematical communication abilities is essential in word problem solving.

• Journal of the Korean School Mathematics Society
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• v.16 no.2
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• pp.319-335
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• 2013

Chinese mathematical curriculum is divided 4 areas(number and algebra, space and figure, statistics and probability, practice and synthetic application). The purpose of this paper is to analyze the contents of the practice and synthetic application in yanbian elementary textbook. For this, 12-textbook which was published in yeonbeon a publishing company is analyze by topic, mathematical process, area of content and mathematical activity. mathematical process The following results have been drawn from this study. First, contextual backgrounds of practice are restricted in classroom. The contents of synthetic application are limited in connection of mathematical areas. Mathematical problem solving is a main in mathematical process, whereas reasoning activity is a few. Mathematical experience activity is a main in mathematical process, whereas synthetic activity is a few. We can use the suggestions of this paper for development of textbook and the contents of mathematical process.

• The Mathematical Education
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• v.55 no.1
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• pp.41-71
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• 2016

The purpose of this study is to investigate elementary students' communication in process of applying mathematical modeling. For this study, 22 fifth graders in an elementary school were observed by applying mathematical modeling process (presentation of problem ${\rightarrow}$ model inducement activity ${\rightarrow}$ model exploration activity ${\rightarrow}$ model application activity). And the level of their communication with their activity sheets and outputs, observation records and interviews were also analyzed. Additionally, by analyzing the activity cases of and , this study researched that what is a positive influence on students' communication skills. Whereas showed significant advance in the level of communication, who communicated actively on speaking area but not on every areas showed insensible changes. To improve communication abilities, cognitive tension and debate situation are needed. This means, mathematical education should continuously provide students with mathematical communication learning, and a class which contains mathematical communication experiences (such as mathematical modeling) will be needed.