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How reform curricula in the USA and Korea present multiplication and division of fractions

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Abstract

In order to give insights into cross-national differences in schooling, this study analyzed the development of multiplication and division of fractions in two curricula: Everyday Mathematics (EM) from the USA and the 7th Korean mathematics curriculum (KM). Analyses of both the content and problems in the textbooks indicate that multiplication of fractions is developed in KM one semester earlier than in EM. However, the number of lessons devoted to the topic is similar in the two curricula. In contrast, division of fractions is developed at about the same time in both curricula, but due to different beliefs about the importance of the topic, KM contains five times as many lessons and about eight times as many problems about division of fractions as EM. Both curricula provide opportunities to develop conceptual understanding and procedural fluency. However, in EM, conceptual understanding is developed first followed by procedural fluency, whereas in KM, they are developed simultaneously. The majority of fraction multiplication and division problems in both curricula requires only procedural knowledge. However, multistep computational problems are more common in KM than in EM, and the response types are also more varied in KM.

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Notes

  1. Because the USA has no commonly accepted national mathematics curriculum, national data about textbook usage are not routinely collected. Data on textbook use collected in 2004–2005 found that EM was one of the three most widely used mathematics textbook series in grades K-5. In grades 3–5, EM and another series written in response to the NCTM Standards accounted for 18% of texts in use (Dossey, Halvorsen & McCrone, 2008).

  2. EM provides ideas for individualizing content in each lesson by including activities for re-teaching, extra skill practice, or enrichment. KM provides ideas for individualizing content only after formative assessment at the end of each unit.

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Authors and Affiliations

  1. University of Tennessee at Knoxville, Knoxville, TN, USA

    Ji-Won Son

  2. Michigan State University, East Lansing, MI, USA

    Sharon L. Senk

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  1. Ji-Won Son
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Correspondence to Ji-Won Son.

Appendices

Appendix 1

Resources analyzed

Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., and Saecker, P. (2002a). Everyday Mathematics Fifth Grade Math Journal Volume 2 (2nd ed.): The University of Chicago School Mathematics Project. Chicago: Everyday Learning Corporation.

Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., and Saecker, P. (2002b). Everyday Mathematics Fifth Grade Student Reference Book (2nd ed.): The University of Chicago School Mathematics Project. Chicago: SRA/McGraw-Hill.

Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., and Saecker, P. (2002c). Everyday Mathematics Fifth Grade Teacher’s Lesson Guide Volume 2 (2nd ed.): The University of Chicago School Mathematics Project. Chicago: Everyday Learning Corporation.

Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., and Saecker, P. (2002d). Everyday Mathematics Sixth Grade Math Journal Volume 1 (2nd ed.): The University of Chicago School Mathematics Project. Chicago: Everyday Learning Corporation.

Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., and Saecker, P. (2002e). Everyday Mathematics Sixth Grade Math Journal Volume 2 (2nd ed.): The University of Chicago School Mathematics Project. Chicago: Everyday Learning Corporation.

Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., and Saecker, P. (2002f). Everyday Mathematics Sixth Grade Student Reference Book (2nd ed.): The University of Chicago School Mathematics Project. Chicago: Everyday Learning Corporation.

Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., and Saecker, P. (2002g). Everyday Mathematics Sixth Grade Teacher’s Lesson Guide Volume 1 (2nd ed.): The University of Chicago School Mathematics Project. Chicago: Everyday Learning Corporation.

Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., and Saecker, P. (2002h). Everyday Mathematics Sixth Grade Teacher’s Lesson Guide Volume 2 (2nd ed.): The University of Chicago School Mathematics Project. Chicago: Everyday Learning Corporation.

Korean Ministry of Education and Human Resources Development (2002a). Mathematics Fifth Grade-Ga. Seoul: DaeHan Printing and Publishing Co., Ltd.

Korean Ministry of Education and Human Resources Development (2002b). Mathematics Workbook Fifth Grade-Ga. Seoul: DaeHan Printing and Publishing Co., Ltd.

Korean Ministry of Education and Human Resources Development (2002c). Mathematics Fifth Grade-Ga Teacher’s Manual. Seoul: DaeHan Printing and Publishing Co., Ltd.

Korean Ministry of Education and Human Resources Development (2002d). Mathematics Fifth Grade-Na. Seoul: DaeHan Printing and Publishing Co., Ltd.

Korean Ministry of Education and Human Resources Development (2002e). Mathematics Workbook Fifth Grade-Na. Seoul: DaeHan Printing and Publishing Co., Ltd.

Korean Ministry of Education and Human Resources Development (2002f). Mathematics Fifth Grade-Na Teacher’s Manual. Seoul: DaeHan Printing and Publishing Co., Ltd.

Korean Ministry of Education and Human Resources Development (2002g). Mathematics Sixth Grade-Na. Seoul: DaeHan Printing and Publishing Co., Ltd.

Korean Ministry of Education and Human Resources Development (2002h). Mathematics Workbook Sixth Grade-Na. Seoul: DaeHan Printing and Publishing Co., Ltd.

Korean Ministry of Education and Human Resources Development (2002i). Mathematics Sixth Grade-Na Teacher’s Manual. Seoul: DaeHan Printing and Publishing Co., Ltd.

Appendix 2

Table 10 Titles of the lessons on multiplication and division of fractions in EM and in KM
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Appendix 3

Table 11 Topics and objectives for multiplication of fractions in EM and in KM
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Appendix 4

Table 12 Topics and objectives for division of fractions in EM and in KM
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Son, JW., Senk, S.L. How reform curricula in the USA and Korea present multiplication and division of fractions. Educ Stud Math 74, 117–142 (2010). https://doi.org/10.1007/s10649-010-9229-6

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