• Journal of the Korean School Mathematics Society
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• v.10 no.1
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• pp.129-148
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• 2007

Recent reform movement in mathematics education has focused not only on the curriculum development but also on teachers' learning or professional development. Whereas various theoretical paradigms call for different programs of professional development for teachers, one of the common emphases is on the pedagogical content knowledge [PCK] which encompasses contents and methods to teach. Against this background, this study developed comprehensive instructional materials for the purpose of fostering PCK in mathematics for elementary school teachers with 17 essential learning themes such as fraction, plane geometry, and area. Each loaming theme was first summarized on the basis of literature reviews and surveys in terms of knowledge in mathematics contents, knowledge in teaching methods, and knowledge in students' mathematical understanding and learning. Each theme was then analyzed in detail on how it was represented in the national curriculum and its concomitant textbooks along with workbooks. Finally, this report included a reconstruction of one unit in textbooks per each learning theme, followed by teaching notes and suggestions from classroom implementation. This was intended for teachers to apply what they might loam from this material to their actual mathematics instruction. Given the page limit, this paper dealt only with the learning theme of ratio.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.1-15
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• 2016

In this paper, the following three issues are discussed in connection with intensive quantities. (1) Is there any relationship among intensive quantity, per unit quantity, and ratio? (2) Which intensive quantities obtained by two same extensive quantities are handled? And How are they handled? (3) Which intensive quantities obtained by two different extensive quantities are handled? And How are they handled? Based on the results of this discussions, three implications are suggested as conclusions to explore the direction for the development of handling intensive quantities in elementary math textbooks and workbooks. Firstly, it is necessary to systematize the systemize a series of processes to handle intensive quantities. There is a need to rethink to use terms like speed and velocity before handling the ratio. Secondly, there is a need to rethink the definition of intensive quantities which have the particular names. For example, it is necessary to rethink using average distance in the definition of speed and the average population in the definition of density of population. Thirdly, it is necessary to consider the limiting the kinds of intensive quantities obtained by two same extensive quantities handled in the elementary math. There is a need to set limit to them which are used in daily life, and there is a need to rethink to use them which are used in the specialized area. There is a need to rethink the using hitting ratio in the form of %.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.501-525
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• 2015

This study analyzes arithmetic word problem of multiplication and division in the mathematics textbooks and workbooks of 3rd grade in elementary school according to 2009 revised curriculum. And we analyzes type of the problem solving ability which 4th graders prefer in the course of arithmetic word problem solving and the problem solving ability as per the type in order to seek efficient teaching methods on arithmetic word problem solving of students. First, in the mathematics textbook and workbook of 3rd grade, arithmetic word problem of multiplication and division suggested various things such as thought opening, activities, finish, and let's check. As per the semantic element, multiplication was classified into 5 types of cumulated addition of same number, rate, comparison, arrayal and combination while division was classified into 2 types of division into equal parts and division by equal part. According to result of analysis, the type of cumulated addition of same number was the most one for multiplication while 2 types of division into equal parts and division by equal part were evenly spread in division. Second, according to 1st test result of arithmetic word problem solving ability in the element of arithmetic operation meaning, 4th grade showed type of cumulated addition of same number as the highest correct answer ratio for multiplication. As for division, 4th grade showed 90% correct answer ratio in 4 questionnaires out of 5 questionnaires. And 2nd test showed arithmetic word problem solving ability in the element of arithmetic operation construction, as for multiplication and division, correct answer ratio was higher in the case that 4th grade students did not know the result than the case they did not know changed amount or initial amount. This was because the case of asking the result was suggested in the mathematics textbook and workbook and therefore, it was difficult for students to understand such questions as changed amount or initial amount which they did not see frequently. Therefore, it is required for students to experience more varied types of problems so that they can more easily recognize problems seen from a textbook and then, improve their understanding of problems and problem solving ability.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.1-17
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• 2013

In this paper, firstly, 'value', 'vertices', 'height' are discussed, which are used in the multiple contexts. Then 'sketch', 'mental math', 'zero point oneth place/zero point zero oneth place/zero point zereo zero oneth place', 'number of place', 'natural number part/decimal part' are discussed, which are not used consistently. Finally, middle school mathematics terms 'distance', 'number line', 'the value of the expression' are discussed which are used in elementary school mathematics textbooks/workbooks. From these discussions, the following four suggestions are proposed as conclusions. First, as a mathematical term 'value' and 'distance' should be emphasized. As 'distance' is a middle school term, there is a need to consider the 'height' as 'the length of the line segment' instead of 'distance'. Second, 'number of place' which can be replaced with other suitable term, 'the value of the expression' including 'value of $20{\times}4$', 'natural number part/decimal part', 'vertex of pyramid/vertex of cone', 'mental math' should not be used. Third, there is a need to consider the use of 'mixed decimal' and 'proper decimal'. In addition, there is a need to expand the use of 'sketch'. Fourth, there is a need to consider the confirmation of 'number line' as an elementary school mathematics term. In addition, there is a need to consider to specify that 'decimal first place', 'decimal second place', 'decimal third place' can be used equivalently with 'zero point oneth place', 'zero point zero oneth place', 'zero point zereo zero oneth place' respectively.

• The Mathematical Education
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• v.62 no.4
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• pp.551-567
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• 2023

Even and odd numbers are taught in elementary school mathematics, but the introductory activities, definitions, and properties of sum on even and odd numbers vary depending on which grade they are presented. The purpose of this study was to compare and analyze the activities related to even and odd numbers presented in Korean mathematics textbooks developed under the different curriculum revisions, and to further analyze the related activities in foreign textbooks to draw implications for the teaching of even and odd numbers. In Korean textbooks, from the time of the fourth mathematics curriculum until the 2007 revision, even and odd numbers were covered in the multiples and divisors unit of the fifth grade textbook, while since the 2009 revision, the first grade textbook has covered the topic along with teaching numbers up to 50 or 100. In addition, the definitions of even and odd numbers varied depending on the grade level and the nature of the unit being taught, and activities addressing the properties of sum were only presented in the mathematics textbook under the third curriculum along with a few mathematics workbooks. In foreign textbooks, even and odd numbers were introduced in Grades 1, 2, or 5, and their related activities varied accordingly. Based on these findings, this study discusses the implications for the teaching of even and odd numbers.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.185-205
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• 2013

In this study, to begin with, it was discussed to gather vocabularies which are expected to be vocabularies related to four fundamental rules of arithmetic and classify them according to kinds and groups, to demarcate vocabularies related to four fundamental rules of arithmetic for using in elementary school mathematics which are associated with addition, subtraction, multiplication, and division directly. Next, the basic vocabularies related to four fundamental rules of arithmetic were discussed. At this time, regarding vocabularies related addition, subtraction, multiplication, and division as coming from the verb add, subtract, multiply, divide respectively, vocabularies that contains the stem of each verb were considered as the basic vocabularies related to four fundamental rules of arithmetics. Following it, vocabularies which assist the operation and indicate the result of the operation were included, then, vocabularies related to four fundamental rules of arithmetic for using in elementary school mathematics were demarcated and presented according to the following criteria. First, a newly coined verb or derivative using the noun form of a certain verb as a root should not be used. Second, such vocabularies of which examples do not exist or rarely exist in textbooks/workbooks should not be used, even though they are registered in mathematics glossary book published by ministry of education or Korean dictionary published by the national institute of Korean language. Third, vocabularies which are not replaceable and vocabularies which have some didactical reasons for using them should be used.