• School Mathematics
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• v.15 no.1
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• pp.37-59
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• 2013

The purpose of this study was to examine and analyze the mathematical tasks in the high school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks in the textbooks. We adopted the framework for mathematical task analysis suggested by Smith & Stein (1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at low level and the rest at high level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures.

• School Mathematics
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• v.14 no.2
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• pp.213-232
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• 2012

The purpose of this study was to examine and analyze the cognitive demand of the mathematical tasks suggested in the middle school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks on function in the textbooks. We adopted the framework for mathematical task analysis suggested by Stein & Smith (1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at low level and the rest at high level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures. In particular, the high level tasks were presented at the end of each chapter or unit for wrap up rather than as key resources.

• School Mathematics
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• v.14 no.3
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• pp.395-408
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• 2012

This study aims to examine the trends in research design and methods used in research on K-12 mathematics curriculum. By analyzing 124 peer-reviewed research articles published between 2000 and 2010, we concluded that more rigorous and various research design and methods should be conducted to improve educational research on curriculum. Although increasing scholarly attention has recently been given to systematic empirical studies about this topic, a large proportion of the studies examined in this study appeared to lack either a coherent conceptual framework or a systematic analytic tool or method. More effort needs to be made on improving the rigor of research in terms of research design and methods.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.297-314
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• 2018

This article aims at providing implication for teacher preparation program through interpreting pre-service teachers' knowledge by using Shulman-Fischbein framework. Shulman-Fischbein framework combines two dimensions (SMK and PCK) from Shulman with three components of mathematical knowledge (algorithmic, formal, and intuitive) from Fischbein, which results in six cells about teachers' knowledge (mathematical algorithmic-, formal-, intuitive- SMK and mathematical algorithmic-, formal-, intuitive- PCK). To accomplish the purpose, five pre-service teachers participated in this research and they performed a series of tasks that were designed to investigate their SMK and PCK with regard to students' misconception in the area of geometry. The analysis revealed that pre-service teachers had fairly strong SMK in that they could solve the problems of tasks and suggest prerequisite knowledge to solve the problems. They tended to emphasize formal aspect of mathematics, especially logic, mathematical rigor, rather than algorithmic and intuitive knowledge. When they analyzed students' misconception, pre-service teachers did not deeply consider the levels of students' thinking in that they asked 4-6 grade students to show abstract and formal thinking. When they suggested instructional strategies to correct students' misconception, pre-service teachers provided superficial answers. In order to enhance their knowledge of students, these findings imply that pre-service teachers need to be provided with opportunity to investigate students' conception and misconception.

• Journal of the Korean School Mathematics Society
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• v.20 no.3
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• pp.277-302
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• 2017

Educational objectives for mathematics in the curriculum revised in 2009 and the curriculum revised in 2015 put great emphasis on practical use of math, but perception of that lacks at schools. Accordingly, this research is recognizing the need for paying attention to curriculum focusing on mathematical connectivity and is inspecting CMP curriculum which has been developed over the years to reinforce problem solving competence and improve communication skills. This study analyzes CMP textbooks published as third edition in 2014 after several revisions, focusing on equations, inequalities and functions. First, this thesis analyzes mathematical connectivity using a new analysis framework which applied the modes of representation(situations, verbal description/ tables/ graphs/ formulae) made by Janvier(1987). Second, this research analyzes connectivities between different units, various sections, other subjects and practical contents related to the real life. The results: CMP textbooks use various practical materials for specific situations. They represent twelve processes of connectivity according to the modes of representation of Janvier. The books also show relationship between equations and functions, between inequalities and functions. And CMP textbooks include other subjects and practical contents.

• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.499-514
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• 2016

As people get to aware that the traditional teacher-centered education can not develop individual students' diversity and creativity and cope with the rapidly changing future society, Korean government has emphasized the learner-centered education since the 7th curriculum. Under this background, we have analyzed the problems of mathematics education that teachers recognized and the features of mathematics textbooks that they developed within the framework of leaner-centered education on the basis of the resources developed from 'Student-centered mathematics textbook improvement teacher research group in 2015.' As a result of using the framework of 'Learner-centered psychological principles (APA, 1997)' for analysis, teachers pointed out the problems related to the principles of Motivational and emotional influences on learning, Individual differences in learning, Developmental influences on learning, Nature of the learning process, and Construction of knowledge, in order. The features of textbook teachers developed reflected the principles of Nature of the learning process, Construction of knowledge, and Motivational and emotional influences on learning, in order. Finally, as we have compared teachers' recognition of the problems with the features of the textbooks developed, most of the problems teachers recognized are reflected in the textbooks; however, the Cognitive and metacognitive factor takes higher possession on the textbooks compared with the problems being recognized, and the Motivational and affective factor takes lower possession on the textbooks compared with the problems being recognized. Accordingly, we have been able to search for the solution to realize the learner-centered education through math textbooks.

• School Mathematics
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• v.13 no.1
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• pp.65-88
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• 2011

Epistemological development process of the Fundamental Theorem of Calculus is considered in a history of mathematical notions and the genetic process of the Fundamental Theorem is arranged by the order of geometric, algebraic and formalization steps. Based on this, we studied students' episte- mological obstacles and error and analyzed the content of textbooks related the Fundamental Theorem of Calculus. Then, We developed the "Folding Back Model" of the fundamental theorem of calculus for students to lead meaningful faithfully. The Folding Back Model consists of "the Framework of thou- ght"(figure V-1) and "the Model of genetic understanding of concept"(figure V-2). The framework of thought in the Folding Back Model is included steps of pedagogical intervention which is used "the Monitoring working questions"(table V-3) by the mathematics teacher. The Folding Back Model is applied the Pirie-Kieren Theory(1991), history of mathematical notions and students' epistemological obstacles to practical use of instructional design. The Folding Back Model will contribute the professional development of mathematics teachers and improvement of thinking skills of students when they learn the Fundamental Theorem of Calculus.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.565-584
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• 2009

This study is aimed at providing the theoretical framework of characteristics of mathematical thinking processes and structuring the thinking process patterns of the mathematical gifted students through the analysis of their cognitive thinking processes. For this purpose, this study is trying to analyze characteristics of mathematical thinking processes of the mathematical gifted students in an objective and a systematic way, by using think-aloud method. For comparative study, the analysis framework with the use of the thinking characteristic code as a content-oriented method and the problem-solving processes code as a process-oriented method was developed, and the differences of thinking characteristics between the two groups chosen by the coding system which represented the subjects' thinking processes in the form of the language protocol through thinking-aloud method were compared and analyzed.

• School Mathematics
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• v.17 no.2
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• pp.257-272
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• 2015

This study is related to reinforcement of the continuity between Nuri curriculum and elementary mathematics curriculum emphasized by 2015 revised national curriculum. Considering that teachers tend to rely much more on textbooks than on curriculum, we analyzed the continuity between math-related activities of Nuri manuals for teachers and the elementary mathematics textbooks and aimed to suggest several ways for securing the continuity based on the result of analyses. To do this, we compared and analyzed Nuri manuals (for ages three to five) for teachers and the first and second grade mathematics textbooks in three aspects: mathematical contents, mathematical terms and symbols, and mathematical processes. We adopted the same analysis framework including continuity, discontinuity and reverse continuity as the study on the continuity between Nuri curriculum and elementary mathematics curriculum. As a result, the results of analyses were revealed in three aspects, respectively. We also discussed the results and suggested some implications for securing the continuity of Nuri manuals for teachers and the elementary mathematics textbooks and for revising curriculum and its materials such as textbooks, workbooks or manuals for teachers.