• Communications of Mathematical Education
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• v.22 no.4
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• pp.489-503
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• 2008

It is not an easy matter to develop problems which help students understand mathematical concepts correctly and precisely. The aim of this paper is to review the merits and demerits of three problem types (i.e. one answer problems, multiple choice problems and proof problems) and to suggest some points that should be taken into consideration in problem making. First, we presented the merits and demerits of three types of problems by examining actual examples. Second, we discussed some examples of misleading problems and the ways to make desirable ones. Finally, on the basis of our examination and discussion, we suggested some points that should be kept in mind in problem making. The major suggestions are as follows; i) In making one answer problems, we should consider the possibility of sitting a solution by wrong precesses, ii) In formulating multiple choice tests which are layered for their easiness of grading, we should take into account the importance of checking whether the students are fully understanding the concepts, iii) We may depend on the previous research result that multiple choice tests for proof problems can be helpful for the students who have insufficient math background. Besides those suggestions, we made an overall proposal that we should endeavor to find ways to implement the demerits of each problem type and to develop instructive problems that can help students understanding of math.

• Journal of The Korean Association For Science Education
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• v.34 no.1
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• pp.1-9
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• 2014

This study aimed to explore the over-efficacy in problem solving and overconfidence of knowledge of students performing assessments in two different test formats: multiple-choice and supply-type. Two hundred and four female middle school students participated in this study. Multiple-choice and supply-type formats of tests on photosynthesis were used, and each item contained scales indicating one's self-efficacy on problem-solving and confidence of knowledge. The results showed that the correlation coefficients of performance between the two different assessment formats were less than 0.5 and the correlation coefficients between efficacy/confidence and actual performance were less than 0.45. Moreover, students tended to exhibit more over-efficacy and overconfidence in multiple-choice formats. The percentage of over-efficacy and overconfidence was higher in the group that completed the multiple-choice test first followed by the supply-type assessment than in the group that started with the supply-type followed by the multiple-choice assessment. From this study, it can be suggested that more use of supply-type assessment is required in science education. If test administrators require the combination of both multiple-choice and supply-type in an assessment, the supply-type assessment format should come first so that students can maintain the appropriate level of efficacy and confidence. In addition, science educators need to develop new learning programs to enhance students' self-monitoring skills of their problem-solving ability and knowledge.

• Korean Journal of Cognitive Science
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• v.21 no.2
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• pp.283-307
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• 2010

In this study, a new open-ended format math testing system for elementary school students has been proposed. This system is an application of the recently proposed Constructive Multiple-choice Testing (CMT) system on math testing. The CMT system is a testing system in which the examinee has to respond to an item twice, first in an open ended format, and then in the multiple choice format. The advantages of this system is that process information can easily be obtained and that the examinee can receive feedback immediately after the test, based on his/her multiple choice responses. This open-ended format math testing system includes the manager mode, which allows the generation of the test items and student account management, and the testing mode, which allows the students to input their solution process using the menu bar and the keyboard. When two groups, one tested using the CMT system and the other tested using the paper and pencil test, were compared, there was no significant difference in average scores between the two groups although the testing time was longer for the group tested using the CMT system. This result suggests that the open-ended format math testing system proposed in this study can be used effectively in the actual classroom setting.

• Korean Journal of Cognitive Science
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• v.28 no.4
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• pp.315-328
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• 2017

Even though assessment using information and communication technology will most likely lead the future of educational assessment, there is little domestic research on this topic. Computerized assessment will not only cut costs but also measure students' performance in ways not possible before. In this context, this study introduces a tool which can overcome the problems of multiple choice tests, which are most widely used type of assessment in current Korean educational setting. Multiple-choice tests, in which options are presented with the questions, are efficient in that grading can be automated; however, they allow for students who don't know the answer, to find the correct answer from the options. Park(2005) has developed a modified multiple-choice testing system (CMMT) using the interactivity of computers, that presents questions first, and options later for a short time when the student requests for them. The present study was conducted to find out if penalizing wrong answers could lower the possibility of students choosing an answer among the options when they don't know the correct answer. 116 students were tested with the directions that they will be penalized for wrong answers, but not for no response. There were 4 experimental conditions: 2 conditions of high or low percentage of penalizing, each in traditional multiple-choice or CMMT format. The results were analyzed using a two-way ANOVA for the number of no response, the test score and self-report score. Analysis showed that the number of no response was significantly higher for the CMMT format and that test scores were significantly lower when the penalizing percentage was high. The possibility of applying CMMT format tests while penalizing wrong answers in actual testing settings was addressed. In addition, the need for further research in the cognitive sciences to develop computerized assessment tools, was discussed.

• Journal of The Korean Association For Science Education
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• v.26 no.1
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• pp.1-8
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• 2006

This study investigated the causal relationships between high school student multiple-choice algorithmic chemistry problem solving and 1) the motivational variables of achievement goal (task goal/performance goal/performance-avoidance) and perceived ability, and 2) the cognitive variables of learning strategy (deep learning/surface learning) and self-regulation. Path analysis supported a causal model in which perceived ability and task goal were found to positively influence algorithmic chemistry problem-solving ability via self-regulation. In particular it was found that perceived ability directly influenced algorithmic chemistry problem-solving ability. Moreover, deep learning was found to have been influenced by perceived ability and task goal, while surface learning was influenced by performance-avoidance goal. Lastly, there did not appear to be any causal relationship between learning strategy and algorithmic chemistry problem-solving ability.

• Korean Journal of Cognitive Science
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• v.21 no.4
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• pp.627-653
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• 2010

The present study proposes and examines a new type of multiple-choice math test. In this format, the options are the intermediate derivatives of the math problem solution process rather than the final answers. This idea originates from the studies on the effect of worked-out examples. In these studies, it has been shown that students learn better when they were presented with worked-out examples than when presented with final answers by themselves. In line with these findings, we introduced the intermediate derivatives of the solution process as the options of multiple-choice items so that the test-taker will have a chance to examine the solution process. The test was implemented as a computerized test in which students can solve problems in a short answer format, and then pick a multiple-choice option which appears when requested. The experimental group had multiple-choice options which were intermediate derivatives of the solution process, and the control group had the final answers as the options as in most multiple-choice tests. The participants were 6th graders in elementary school. The posttest results revealed that the average score of the experimental group was higher than that of the control group. The results suggest that tests that use intermediate derivatives of the problem solution process as options can be used as learning tools in the classrooms. Finally, directions for further studies were discussed.

• Communications of Mathematical Education
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• v.15
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• pp.129-134
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• 2003

수학과의 평가는 수학의 학습 내용에 대한 학생들의 성취도를 다양한 유형의 평가기법을 이용하여 파악하고, 이를 통해 수학교육의 질을 관리하는데 그 목적이 있다. 그러나 지금까지의 대부분의 평가는 수학교육의 본질이라 할 수 있는 학습자의 수학적 사고력을 제대로 측정하지 못하고 단편적인 수학적 지식을 결과 위주로 평가하는 데 만족해 왔다. 한편으로는 지극히 교과서적이고 인위적인, 단지 문제를 위한 수학 문제는 수학 무용론을 부추기기도 하였다(박경미, 1998). 이와 같은 수학과의 위기를 탈출하기 위해서는 결과만을 고려하는 선다형의 문제가 아닌 과정을 중시하는 서술형 주관식 문제, 기능 위주의 고립된 수학적 지식을 측정한 학업성취 결과보다는 수학 학습에 대한 태도나 노력, 관심, 탐구적 활동 그리고 성향 등 정의적 영역의 평가가 절실히 요구된다. 따라서 기존의 지필 검사를 뛰어넘는 다양한 평가의 틀이 요구된다 하겠다. 이런 점에서 1999학년도부터 시행되고 있는 고등학교에서의 수행평가는 변화하는 교육기조의 교수 ${\cdot}$ 학습에 대한 적절한 평가의 한 방법이라 생각된다. 이에 본 연구는 다양한 평가의 틀 가운데 수학과 수행평가에 관한 고찰을 통해서 현장에서의 수행평가활용 방법을 찾는데 있다.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.531-543
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• 2009

This study identified what cognitive attributes are required of eighth graders to solve geometrical problems such as 'Recall,' 'Analyze,' 'Justify,' 'Synthesize/Integrate,' and 'Solve Non-routine Problems' by using the cognitive diagnostic theory. The five attributes are proved as the skills for solving the geometric problems. Many students have not fully mastered the attributes of 'Justify' and 'Synthesize/Integrate'. There was high correlation between these attributes. 'Analyze' best predicted the changes in the geometric achievement. And while students with high levels of geometrical achievement have mastered all the five attributes, those in the mid- and low-level range of performance have mastered fewer attributes.

• The Mathematical Education
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• v.57 no.3
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• pp.197-213
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• 2018

Descriptive problems can be used to grow student's ability of thinking logically and creatively, because it shows if the students had a reasonable way of thinking. Rate of descriptive problems is increasing in middle and high school exams. However, students in middle and high schools are generally used to answering multiple-choice or short-answer questions rather than describing the solving process. The purpose of this paper is to gain a theoretic ground to increase the rate of descriptive problems. In this study, students were to solve some multiple-choice problems, and after a few weeks, to solve the problems of same contents in the form of descriptive problems which requires the students to write the solving process. The difference of the scores were measured for each problems to each students, and students were asked what they think the reason for rise or fall of the score is. The result is as follows: First, average scores of 7 of 8 problems used in this study had fallen when it was in descriptive form, and for 5 of them in the rate of 11.2%~16.8%. Second, the main reason of falling is that the students have actual troubles of describing the solving process. Third, in the case of rising, the main reason was that partial scores were given in the descriptive problems. Last, there seems a possibility gender difference in the reason of falling. From these results, followings are suggested to advance the learning, teaching and evaluation in mathematics education: First, it has to be emphasized enough to describe the solving process when solving a problem. Second, increasing the rate of descriptive problems can be supported as a way to advance the evaluation. Third, descriptive problems have to be easier to solve than multiple-choice ones and it is convenient for the students to describe the solving process. Last, multiple-choice problems have to be carefully reviewed that the possibility of students' choosing incorrect answer with a small mistake is minimal.

• Proceedings of the Korea Information Processing Society Conference
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• 2003.05b
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• pp.903-906
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• 2003

인터넷 문화의 급속한 보급과 더불어 일반 학생들이 스스로 지식을 획득하고 구조화하여 자기 주도적 문제 해결 능력을 기를 수 있는 다양한 학습 코스웨어들이 개발 보급되어 왔다. 대부분의 코스웨어들은 학업 성취도를 평가하기 위해 사지선다형이나 단답형 방식을 채택하였다 그러나. 정보처리기능사 자격증 취득을 위한 실기 평가와 같이 기존 방식과는 다른 평가 체계의 개발이 요구되고 있다. 이에 본 연구에는 웹을 통해 정보처리기능사 자격 취득을 위해 실기 시험의 전 과정을 자기 주도적으로 학습하고, 상호작용을 통해 학습 결과와 학습 진행 정도를 확인하고 피드백이 가능하도록 하는 코스웨어를 개발한다.