• Communications of Mathematical Education
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• v.22 no.2
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• pp.229-252
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• 2008

The purpose of this research was to make fair assessment methods which took into account characteristics of mathematically underachievers. The researchers devised an descriptive tests and interviews and applied them to the mathematics underachievers who could not reveal their achievements in the traditional assessment and then analyzed their cognitive and affective characteristics in the alternative assessments. After selecting three students by the normal assessment made of simple subjective and multiple choice questions, the cognitive and affective characteristics found in the general assessment were reflected to the descriptive tests and interviews. The descriptive tests and interviews are comprised of descriptive narrations and informal interview questions. After the assessment, the teacher and students gave feedbacks one another. All the assessment activities were recorded by a camcorder to analyze cognitive and affective characteristics of the children. Throughout the research, the following conclusions were made. The mathematics underachievers showed the characteristics which didn't appeared in the normal assessment. They showed normal abilities of problem solving and communication In the cognitive area. Also they brought in positive result in most parts in the affective area. However, the student B displayed considerable ability of mathematical thinking that is over the average level of mathematical underachievers. This implies that we can definite the mathematical underachievers differently when we use the detailed and relief assessment method instead of the traditional assessment. On the other hand, one student tended to depend on the teacher and another student overheard what the others talk during the study. This defect should be complemented by the further studies about assessment method for the mathematical underachievers. Also appropriate assessment methods should be made for applying to the various mathematical underachievers. Many studies have been concentrated on the learning for mathematical underachievers but there is little concern about the assessment for the mathematical underachievers. However it is the fundamental way to reduce the number of mathematics underachievers that we construct consistent learning methods and assessments for the mathematical underachievers.

• East Asian mathematical journal
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• v.29 no.2
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• pp.207-239
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• 2013

This research is a study on student's understanding fundamental concepts of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's concepts about that domain and get the mathematical teaching methods. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometric figures. And we analyze the student's understanding extent through investigating questions of descriptive assessment. In this research, we concluded that most of students are having difficulty with defining the fundamental concepts of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. And they can't distinguish between concept definition and concept image. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometric concepts.

• Education of Primary School Mathematics
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• v.12 no.2
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• pp.63-80
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• 2009

In this study, we analyzed teachers' recognitions of the necessity of mathematical descriptive tests and their practices in the elementary schools. We then suggested several examples of improved formats of the mathematical descriptive evaluation. For analyzing teachers' recognitions and practices of mathematical descriptive assessment, we surveyed 104 elementary school teachers in Seoul. We collected the test items from the schools and analyzed them to find how they are practiced in the schools. The results were as follows. First, most elementary school teachers are basically recognizing the direction and the purpose of mathematical descriptive assessment. Second, the ratio of the descriptive test items was very low compared with the teachers' recognition of necessity of including descriptive items in the tests. Third, the teachers usually made the descriptive items with their colleagues using textbooks, test manuals for teachers, and the references that the office of education provided. Fourth, to enhance teachers' understanding of descriptive assessment, systematic training programs for teachers about the descriptive assessment should be continued. Finally, the office of education and research institutes should provide various types of test items and more teacher training programs on descriptive assessments.

• The Mathematical Education
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• v.47 no.4
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• pp.487-503
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• 2008

In this paper, descriptive assessment method for middle school mathematics was evaluated by developing a framework for designing and grading problems for descriptive assessment and analyzing the effectiveness of the problems. The new descriptive assessment problems were developed by reviewing the current 7th National Mathematics Curriculum of Korea and aligned mathematics textbooks to define a set of problem design principles and evaluation framework for the assessment strategy. The developed problems were first pilot tested and then revised based on the feedback from the test. The final version was field tested by 100 students in 7th grade middle school. After the field test, the problems were graded by two middle school math teachers and one math education researcher to determine the overall correlation between graders and also to analyze effectiveness of the evaluation framework of the test. This result of this study is expected to assist in the further development of descriptive problems and grading framework by providing a reference work for teachers to better understand the process and the limitations of executing the new assessment strategy.

• East Asian mathematical journal
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• v.37 no.2
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• pp.169-196
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• 2021

The purpose of this study was to improve academic achievement and mathematics learning attitudes in the formative assessment using descriptive problems as an effective teaching method. In this paper we set the following research questions. First, how would you improve students' academic achievement utilizing descriptive evaluation? Second, how would improve students' mathematics learning attitudes utilizing descriptive evaluation? Third, what was the reaction utilizing the descriptive method to evaluate? The result of this study could be seen as follows. The experimental group than the control group on academic achievement shows a significant improvement. Second, the experimental group compared to the control group in mathematics learning attitude changes could be helpful and appreciated. Third, experimental group than in the control group indicates significance could be seen in the reaction.

• East Asian mathematical journal
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• v.30 no.4
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• pp.527-544
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• 2014

The purpose of this thesis is to analyze mathematical errors in descriptive problems of the Mathematics Level Assessment(MLA) which is conducted in P University. We classified mathematical errors, which are easily made in solving the descriptive problems of the MLA, into nine types as misused data, misinterpreted language, logically invalid inference, misunderstood theorem or definition, unmatched solution, technical errors, omission of solving process, ambiguous errors, and unattempted errors. With classifying the errors in nine types, we analyzed the errors of students, who are in intermediate and low level grades, by descriptive problems. On the basis of these analysis results, we suggest plans for improving the implementation of the MLA and the teaching-learning methods about College General Mathematics.

• Journal of the Korean School Mathematics Society
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• v.11 no.4
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• pp.543-567
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• 2008

The current 2007 Mathematics Curriculum in Korea emphasizes mathematical problem solving, advanced mathematical thinking and effective mathematical communicating. Therefore, in order to assess and evaluate these important thinking attributes, performance evaluation using descriptive and essay type of assessments are emphasized. In this paper, analysis of the elementary mathematics curriculum is used to develop descriptive assessment problems and grading rubrics that could be used objectively and consistently by teachers of the grade 6 school mathematics. The assessment problems were developed, pilot tested, revised, implemented and analyzed in detail to understand the overall effectiveness of the descriptive evaluation method in school mathematics.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.207-226
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• 2007

The purpose of this study was to design and develop the processes of tasks and assessment rubrics of open-ended tasks, and those for the 5th graders of elementary school mathematics. 7 tasks were finally developed, and 'problem understanding', 'problem solving process', 'communication' were selected as the criteria for assessment rubrics. The result was that the ability of mathematical power covering problem understanding ability, problem solving ability and mathematical communication ability was low. Specifically, problem understanding ability was the highest, problem solving ability was middle, and mathematical communication ability was the lowest.

• Journal of Science Education
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• v.46 no.1
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• pp.121-149
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• 2022

Descriptive assessment is a meaningful assessment method in relation to problem solving ability, reasoning ability, and communication ability as emphasized in mathematics curriculum. In Korea, as performance assessment has been emphasized since the 7th mathematics curriculum, descriptive assessment is being conducted as a method of performance assessment in schools. However, descriptive assessment has not been introduced in the university scholastic ability test for various reasons. Considering that descriptive assessment is emphasized in the mathematics classroom and has sufficient educational value, a serious discussion on the implementation of descriptive assessment in the university scholastic ability test will be necessary. In this study, we analyzed the descriptive assessment of Russia's unified state examination (USE) in the mathematics, which corresponds to Korea's university scholastic ability test. Through a literature review, we investigated how mathematics examination problems were structured in the USE and which mathematical abilities were required for the examination. In particular, the outer structure of the problems was analyzed focusing on the mathematics problems of the USE 2021, and the scoring method of the descriptive problems was also analyzed. The results of this study are expected to provide a variety of information on the possibility of introducing descriptive assessment in the Korean university scholastic ability tests.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.719-745
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• 2012

This research is a study on student's understanding fundamental conception of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's wrong conception about that domain and get the mathematical teaching method. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometry. And we figured out the student's understanding extent through analysing questions of descriptive assessment in geometry. In this research, we concluded that most of students are having difficulty with defining the fundamental conception of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometry.