• Journal of Elementary Mathematics Education in Korea
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• v.21 no.4
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• pp.547-574
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• 2017

The purpose of analysis of foreign curriculums and textbooks is to aimed to get the implications for the revision of curriculum, publishment of textbooks and teaching mathematics. In this study, Common Core State Standards and its textbooks was analyzed. The U. S. doesn't have the national mathematics curriculum. So, it can be happen some problems: students' lower mathematical achievement, assessment policy, decision of teaching contents, etc. In 2010, Common Core State Standards was developed by states. Furthermore, The California Department of Education reshaped standards: CA-CCSSM. This study analyzed the contents of fraction in CA-CCSSM and its textbooks. Fraction has many concepts and methods and models in teaching process. This study analyzed the equal parts, introducing fraction concept, the types of fraction, equivalent fractions, comparison of fractions. The conclusions are as follows; The equal parts are the important concept of fraction and introduced in geometry area before teaching of fraction. CA-CCSSM aims to understand a fraction as a number on the number line and represent fractions on a number line diagram. There are some similarity and difference in mixed number, fractions as a division and ratio, equivalent fractions and comparison of fractions between Korean curriculum and textbooks and CA-CCSSM.

• 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.

• 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.

• Education of Primary School Mathematics
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• v.22 no.2
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• pp.129-147
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• 2019

Because of the various concepts and meanings of fractions and the difficulty of learning, studies to improve the teaching methods of fraction have been carried out. Particularly, because there are various methods of teaching depending on the type of fractions or the models or methods used for problem solving in fraction operations, many researches have been implemented. In this study, I analyzed the fractional operations of CCSSM-CA and its U.S. textbooks. It was CCSSM-CA revised and presented in California and the textbooks of Houghton Mifflin Harcourt Publishing Co., which reflect the content and direction of CCSSM-CA. As a result of the analysis, although the grades presented in CCSSM-CA and Korean textbooks were consistent in the addition and subtraction of fractions, there are the features of expressing fractions by the sum of fractions with the same denominator or unit fraction and the evaluation of the appropriateness of the answer. In the multiplication and division of fractions, there is a difference in the presentation according to the grades. There are the features of the comparison the results of products based on the number of factor, presenting the division including the unit fractions at first, and suggesting the solving of division problems using various ways.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.437-464
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• 2014

Curriculum for mathematic sis the system that selects and organizes the contents which have to be taught in school. Ultimately it can be the whole plan of school mathematical education. The study about curriculum for mathematics is the basic study field of the mathematical education, so curriculum-related studies have been continuously promoted in terms of character, organization and implement of the curriculum, learning contents contained by the curriculum, the connection between school levels, and comparison and analysis of domestic and foreign curricula. Thus, this paper investigated the 2009 Revised Curriculum for Mathematics, which is the curriculum of Korea and the CCSSM which is the curriculum of the U.S. Both have been adopted in schools recently. The purpose of this study is to understand the curricula for mathematics in elementary school of Korea and the U.S. in depth and obtain the implication for the further curriculum revision, by comparing and analyzing the curricula of two countries.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.2
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• pp.239-257
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• 2016

The Common Core States Standards was developed by building on the best state standards in the U.S.; examining the expectations of other highperforming countries around world; and carefully studying the research and literature available on what students need to know. The Common Core States Standards for Mathematics are reshaping the teaching and learning of mathematics in California classroom using the California Common Core States Standards for Mathematics(CA CCSSM). The aim of this study is to observe CA CCSSM. The CA CCSSM were established to address the problem of having a curriculum that is 'a mile wide and an inch deep'. And it have two types of standards. One is standards for mathematical practice which are the same at each grade level, the other is standards for mathematical content which are different at each grade level. This study focused on standards for mathematical content, in particular, on Geometry domain in elementary level, using Mathematics Framework for California Public Schools.

• School Mathematics
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• v.17 no.1
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• pp.1-18
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• 2015

The mathematical processes are strongly emphasized in 2009 revised national curriculum for mathematics and are expected to be complemented and extended in 2015 revised one. This study aims to investigate how much the processes are being implemented in mathematics classroom and select some elements which need complementation. To do this, we selected the mathematical practices of CCSSM as a reference, because it plays the corresponding role in the United States to the mathematical processes in Korea. We recognized common elements and different elements between the two and analyzed. Considering those, we searched the possibility of newer mathematical process and analyzed the 4th grade mathematics textbooks in relation to questions for mathematical practices. We provided the results of analyses and several suggestions for revising mathematics curriculum and textbooks.

• Research in Mathematical Education
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• v.22 no.1
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• pp.47-82
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• 2019

Pennsylvania is one of the states that adopted the Common Core State Standards for Mathematics (CCSSM) and crafted its own standards (The PA Core State Standards). Pennsylvania teachers are required to have a clear understanding of the PA Core Standards. It is timely and appropriate to study Pennsylvania teachers' beliefs, as the standards have been adopted and implemented for several years since the revision of the PA Core Standards (2014). This study examined how eight western Pennsylvania elementary school teachers' beliefs about teaching and learning mathematics related to the SMP. To this end, I conducted an in-depth interview with each participating teacher. The in-depth interviews featured the teachers' overarching mathematical instructional goals and their productive beliefs. Furthermore, I linked these beliefs with the CCSSM Standards for Mathematical Practice (SMP).

• Research in Mathematical Education
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• v.23 no.3
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• pp.149-164
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• 2020

This study aimed to establish an observation protocol for mathematical modeling as an alternative way to examine instructional alignment to the Common Core State Standards for Mathematics. The instructional alignment observation protocol (IAOP) for mathematical modeling was established through careful reviews on the fidelity of implementation (FOI) framework and prior studies on mathematical modeling. I shared the initial version of the IAOP including 15 items across the structural and instructional critical components as the FOI framework suggested. Thus, the IAOP covers what teachers should do and know for practices of mathematical modeling in classrooms and what teachers and students are expected to do. Based on the findings in this study, validity and reliability of the IAOP should be evaluated in follow-up studies.

• Research in Mathematical Education
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• v.23 no.1
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• pp.47-62
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• 2020

Learning through "recreational mathematics" has become a meaningful outlet to children of all ages. The Edumatrix set is a didactic tool for the development of logical and abstract reasoning among students. In this paper, we provide several illustrative exercises involving Edumatrix that teachers can utilize in their classrooms. We formulate students' expected learning outcomes by aligning each exercise to the CCSSM content standards as well as examining which Standards for Mathematical Practices (SMP) our proposed exercises promote.