김성찬 Sung Chan Kim , 김성연 Sung Yeun Kim , 한기순 Ki Soon Han

DOI: JANT Vol.26(No.3) 251-271, 2012

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The purpose of this study is: 1) to determine error sources and the effects of each error source, 2) to investigate optimal measuring conditions from holistic and analytic scoring methods, and 3) to compare the value of reliability between Cronbach`s alpha and the generalizability coefficient in self-introduction letter and teacher`s recommendation letter based on the generalizability theory in identification of mathematical gifted students by observations and nominations. Data of this study were collected from the science education institute for the gifted attached to the university located within in a capital city for the 2011 academic year. Scores from two raters using holistic and analytic scoring methods in both assessment types were used. The results of this study were as follows. First, as to both assessment types, error sources for people were relatively large regardless of scoring methods. However, error sources for raters in holistic scoring methods had a more significant impact than those of analytic scoring methods. Second, to set optimal measuring conditions in the self-introduction letter and teacher`s recommendation letter, if we fixed the number of raters into 2 based on holistic scoring methods, at least 5 and 10 content domains were needed, respectively. In addition, the number of items in teacher`s recommendation letter should be more than 3 when we fixed the number of content domains into 4, and the number of items in self-introduction letter should be more than 8 when we fixed the number of content domains into 6 using analytic scoring methods. Third, Cronbach`s alpha having only a single source of errors was higher than the generalizability coefficient regardless of assessment types and scoring methods. Hence we recommend that generalizability coefficient based on various error sources such as raters, content domains, and items should be considered to keep a satisfactory level of reliability in both assessment types.

김래영 Rae Young Kim , 김구연 Goo Yeon Kim , 노선숙 Sun Sook Noh , 김민경 Min Kyeong Kim , 전지훈 Ji Hoon Jeon , 김기영 Ki Young Kim , 이민희 Min Hee Lee

DOI: JANT Vol.26(No.3) 273-299, 2012

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The purpose of this study is to investigate how constructed-response assessments are currently defined and used to find an alternative way of developing well-defined constructed-response questions and an assessment system. Based on our review of the literature, we analyze constructed-response assessments developed and used in Gyeonggi-do, South Korea and Ohio, U.S.A in terms of their definitions, types of questions, information and guidelines given by the government agencies in each place, and scoring rubrics and their use. The results provide meaningful implications for the development of constructed-response assessments in the future.

강영란 Young Ran Kang , 조정수 Cheong Soo Cho , 김진환 Jin Hwan Kim

DOI: JANT Vol.26(No.3) 301-316, 2012

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Ball, Thames & Phelps(2008) introduced the idea of Mathematical Knowledge for Teaching(MKT) teacher. Specialized Content Knowledge(SCK) is one of six categories in MKT. SCK is a knowledge base, useful especially for math teachers to analyze errors, evaluate alternative ideas, give mathematical explanations and use mathematical representation. The purpose of this study is to analyze the elementary teacher`s SCK. 29 six graders made word problems with respect to division fraction 9/10÷2/5. These word problems were classified four sentence types based on Sinicrope. Mick & Kolb(2002) and then representative four sentence types were given to 10 teachers who have taught six graders. Data analysis was conducted through the teachers` evaluation of the answers(word problems) and revision of students` mathematical errors. This study showed how to know meanings of fraction division for effective teaching. Moreover, it suggested several implications to develop SCK for teaching and learning.

방정숙 Jeong Suk Pang , 권미선 Mi Sun Kwon

DOI: JANT Vol.26(No.3) 317-338, 2012

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This paper compared and contrasted the views of effective mathematics instruction by 223 elementary school teachers and 151 middle school mathematics teachers using a questionnaire with 4 main domains (i.e., curriculum and content, teaching and learning, classroom environment and atmosphere, and assessment) and a total of 48 sub-elements. The analysis of results showed that elementary school teachers put their priority on the curriculum and content domain, while middle school counterparts did on the teaching and learning domain. The teachers commonly agreed with instruction which fosters students` self-directed learning ability, reconstructs the curriculum tailored to students` diverse levels, and establishes appropriate interaction between the teacher and students. However, elementary school teachers agreed more than middle school teachers with regard to the 23 elements related to effective mathematics instruction. In contrast, middle school teachers agreed more than their counterparts as for only 2 elements (instruction fostering mathematical representation and instruction eliciting students` learning motivation). This paper includes suggestions and implications related to Korean teachers` perception of effective mathematics instruction.