• Research in Mathematical Education
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• v.24 no.1
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• pp.1-27
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• 2021

For elementary school children, learning the standard multiplication algorithm with accuracy, clarity, consistency, and efficiency is a daunting task. Nonetheless, what should be our expectation in procedural fluency, for example, in finding the product of 25 and 37 among fifth grade students? Collectively, has the mathematics education community emphasized the value of conceptual understanding to the detriment of procedural fluency? In addition to examining these questions, we survey multiplication algorithms throughout history and in textbooks and reconceptualize the standard multiplication algorithm by using a new tool called the Multiplication Aid Template.

• Research in Mathematical Education
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• v.25 no.3
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• pp.175-188
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• 2022

Measurement has been an important part of mathematics content students must learn through their schooling. Many studies suggest students' weak measurement learning, particularly related to length measurement, on the part of lower grade students. This difficulty has been attributed to mathematics curriculum as well as instruction. Building on a view of teaching as an interactive activity, this paper explores how a first grade teacher interacted with her students in small groups in a length measurement lesson to promote conceptual understanding as well as procedural fluency. I found that even though the teacher supported students to explain and justify what they understood, the ways the teacher interacted with students were not effective to promote students' understanding. Even though this finding is based on an analysis of a single mathematics lesson, it provides an example of challenges in promoting students' understanding through interaction with students in the context of teaching length measurement.

• English Language & Literature Teaching
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• v.8 no.1
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• pp.165-198
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• 2002

The purpose of this research is to improve the writing ability of students by an ideal test model of English writing based on strategies of procedural learning stages enhancing the level of students' writing ability. Assessment of writing in the field of English education has been limited so far to very restricted areas with no appropriate scientific scrutiny. Assessment is really meaningful only when it exactly estimates the ability of students. Since English writing competence has become indispensable in this era of global village, writing instruction should be most emphasized. The most forceful method of busting writing instruction is to utilize the so-called washback effect of testing. So, to develop a good test model of writing, the first thing that is required is to inspect writing strategy in steps and, then, testing itself. First of all, analyzed with a special reference to the 6th high school English curriculum were the goals and contents of the syllabus reflected in one kind of junior high textbook and eight different kinds of senior high textbooks. Then questionnaires on the whole area of writing and tendencies of English writing classes were given to 100 English teachers, 300 students. The results of questionnaires were statistically analyzed. Then, some suggestions and opinions about the questioning method were made: the procedural strategy in steps, English writing instruction and test model of assessment were applied to the syllabus referring to teaching plans. On the bases of the results of the questionnaires, three pretests and a final test of English writing were administered to verify the effect of enhanced English writing competence which had been gradually promoted and, through the promotion, produced the test criteria of English writing. In conclusion, guidance and evaluation of English writing through in steps are really indispensable to increase student's practical ability and, accordingly, we are in need of the development of a testing method of useful writing practiced in school class above anything else. So, it is necessary to further the study on methods to assess writing ability on the bases of participation and fluency of students with their keen interest in English. Also, to intensify the effect of the test model, more accommodating reorganization of syllabus is required in our education. For instance, we need a flexible operation in organizing time units from the current 50 minutes to 100-130 minutes.

• The Mathematical Education
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• v.57 no.4
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• pp.453-475
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• 2018

This study examines how elementary students understand fractions with operations conceptually and how they perform procedures in the division of fractions. We attempted to look into students' understanding about fractions with divisions in regard to mathematical proficiency suggested by National Research Council (2001). Mathematical proficiency is identified as an intertwined and interconnected composition of 5 strands- conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. We developed an instrument to identify students' understanding of fractions with multiplication and division and conducted the survey in which 149 6th-graders participated. The findings from the data analysis suggested that overall, the 6th-graders seemed not to understand fractions conceptually; in particular, their understanding is limited to a particular model of part-whole fraction. The students showed a tendency to use memorized procedure-invert and multiply in a given problem without connecting the procedure to the concept of the division of fractions. The findings also proposed that on a given problem-solving task that suggested a pathway in order for the students to apply or follow the procedures in a new situation, they performed the computation very fluently when dividing two fractions by multiplying by a reciprocal. In doing so, however, they appeared to unable to connect the procedures with the concepts of fractions with division.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.279-295
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• 2014

The Korean national curriculum will be revised in 2015. Before revisions are to be made, we must discuss the direction the curriculum changes will take. In this study, we compare the contents of the current 2011 elementary school mathematics curriculum in Korea with the Common Core State Standards for Mathematics (CCSSM) in the United States. The results from this comparative analysis may be helpful in the revision of the Korean mathematical curriculum. We find that the CCSSM introduces certain mathematical concepts earlier and in greater detail than the Korean curriculum does. The CCSSM also covers a broader range of mathematical concepts. These results indicate that the Korean curriculum needs to emphasize conceptual understanding, as well as procedural skill and fluency, in the early grades. Moreover, the 'grade band' is unnecessary in the mathematics curriculum. The Korean curriculum revision process must be debated more intensely, must be made public, and must take into consideration the key points of CCSSM.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.309-327
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• 2018

This study is a case study of an elementary school teacher's reflection and practice in the process of planning, executing and criticizing his lesson on division with decimals. The purpose of this study was to clarify what kinds of problems an elementary school teacher was thinking about and how his focus was changing in the process of planning and executing a lesson and criticizing his lesson with his peers. The teacher was set in three periods: a teacher planning a lesson, a teacher executing a lesson, and a teacher criticizing his or her own lesson. Each period was analyzed in eight aspects: Establishing the goals for mathematics, implementing tasks, connecting mathematical representations, facilitating mathematical discourse, posing questions, building procedural fluency from conceptual understanding, supporting productive struggles, and using evidences of students' thinking.

• Korean Journal of Cognitive Science
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• v.13 no.4
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• pp.80-80
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• 2002

The main thesis of this article is that the decisive point of creativity education is the cultivation of critical thinking capability. Although the narrow conception of creativity as divergent thinking is not subsumed under that of critical thinking, the role of divergent thinking is not so crucial in the science context of creative problem-solving. On the contrary, the broad conception of creativity as focusing on the reference to utility and the third conception of creativity as a process based on the variation and combination of existing pieces of information are crucial in creative problem-solving context, which are yet subsumed under that of critical thinking. The emphasis on critical thinking education is connected with the characteristics of contemporary knowledge-based society. This rapidly changing society requires situation-adaptive or situation-sensitive cognitive ability, whose core is critical thinking capability. Hence, the education of critical thinking is to be centered on the learning of blowing-how and procedural knowledge but not of knowing-that and declarative knowledge. Accordingly, the learning of critical thinking is to be headed towards the cultivation of competence but not just of performance. In conclusion, when a rational problem-solving through critical and logical thinking turns out consequently to be novel, we call it creative thinking. So, creativity is an emergent property based on critical and logical thinking.

• Korean Journal of Cognitive Science
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• v.13 no.4
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• pp.81-90
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• 2002

The main thesis of this article is that the decisive point of creativity education is the cultivation of critical thinking capability. Although the narrow conception of creativity as divergent thinking is not subsumed under that of critical thinking, the role of divergent thinking is not so crucial in the science context of creative problem-solving. On the contrary, the broad conception of creativity as focusing on the reference to utility and the third conception of creativity as a process based on the variation and combination of existing pieces of information are crucial in creative problem-solving context, which are yet subsumed under that of critical thinking. The emphasis on critical thinking education is connected with the characteristics of contemporary knowledge-based society. This rapidly changing society requires situation-adaptive or situation-sensitive cognitive ability, whose core is critical thinking capability. Hence, the education of critical thinking is to be centered on the learning of blowing-how and procedural knowledge but not of knowing-that and declarative knowledge. Accordingly, the learning of critical thinking is to be headed towards the cultivation of competence but not just of performance. In conclusion, when a rational problem-solving through critical and logical thinking turns out consequently to be novel, we call it creative thinking. So, creativity is an emergent property based on critical and logical thinking.