• Journal of Educational Research in Mathematics
• /
• v.25 no.3
• /
• pp.303-321
• /
• 2015

This research purposes to find out the mathematical cognitive characteristics of Korean students and compare it with that of TIMSS 2011 high-achieving countries based on the Cognitive Diagnostic Theory. Based on framework and questions of TIMSS 2011, we select cognitive attributes. Using the data of 8th grade students' mathematical achievement in TIMSS 2011, we compare and analyze the top 15-countries students' cognitive traits. As a result, cognition domain of TIMSS 2011 is reclassified as 9 cognitive attributes. we could distinguish between easy attributes and difficult attributes that students in each country relatively think. Especially, Students of Korea relatively think Recall/Recognize, Compute, Classify/Measure and Represent are easy. On the other hand, relatively they have difficulties in Retrieve, Implement, and Generalize. Based on this research result, It is necessary to establish an educational measures for each attributes which students have difficulties.

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

• School Mathematics
• /
• v.10 no.2
• /
• pp.259-277
• /
• 2008

Conventional assessments only provide a single summary score that indicates the overall performance level or achievement level of a student in a single learning area. For assessments to be more effective, test should provide useful diagnostic information in addition to single overall scores. Cognitive diagnosis modeling provides useful information by estimating individual knowledge states by assessing whether an examinee has mastered specific attributes measured by the test(Embretson, 1990; DiBello, Stout, & Rousses, 1995; Tatsuoka, 1995). Attributes are skills or cognitive processes that are required to perform correctly on a particular item. By the results of this study, students, parents, and teachers would be able to see where a student stands with respect to mastering the attributes. Such information could be used to guide the learner and teacher toward areas requiring more study. By being able to assess where they stand in regard to the attributes that compose an item, students can plan a more effective learning path to be desired proficiency levels. It would be very helpful to the examinee if score reports can provide the scale scores as well as the skill profiles. While the scale scores are believed to provide students' math ability by reporting only one score point, the skill profiles can offer a skill level of strong, weak or mixed for each student for each skill.

• School Mathematics
• /
• v.15 no.2
• /
• pp.289-314
• /
• 2013

Achievement profile by attribute in Korean students' mathematics was analyzed by applying cognitive diagnostic model, which is the newest measurement theory, to 2011 NAEA(National Assessment of Educational Assessment) results. The results are as follows. As the level of school is higher from 6th grade, 9th grade to 11th grade, the percentage of students mastering cognitive attribute 9(expressions using picture, table, graph, formula, symbol, writing, etc) drastically declined from 78%, 35% to 26%. It is necessary to have learning strategies to reinforce their abilities of expressing table, graph, etc. that higher graders in mathematics are more vulnerable to. Next, the property of mastering cognitive attributes according to gender, multi-cultural family was analyzed. In terms of mathematics, the percentage of girls mastering most of the attribute generally is higher than that of boys from 6th grade to 9th grade, however, boys show higher mastery in almost attributes than girls in the 11th grade. Compared to boys, the part where girls have the most trouble is attribute 9 in mathematics(expressions using picture, table, graph, formula, symbol, writing, etc). As international marriage, influx of foreign workers, etc. increase, the number of students from Korea's multi-cultural families is expected to be higher, therefore, identifying the characteristics of their educational achievement is significant in reinforcing Korea's basic achievement. In mathematics, gap of mastery level of attributes between multi-cultural group and ordinary group is more severe in higher grade and the type of multi-cultural group that needs supports for improving achievement most urgently changed in 6th grade, 9th grade and 11th grade respectively. In the 6th and 11th grade, migrant students from North Korea show the lowest level of mastering attributes, however, in the 9th grade, the mastery rate of immigrant students is lowest. Therefore, there is an implication that supporting plans for improving achievement of students from multi-cultural family should establish other strategies based on the characteristics of school level.

• Education of Primary School Mathematics
• /
• v.22 no.4
• /
• pp.223-237
• /
• 2019

There is a close interaction between the linguistic-syntactic representation system and the affective representation system that appear in the mathematical process. On the other hand, since the mathematical conceptual system is fundamentally metaphoric, the analysis of the mathematical concept structure through linguistic representation can help to identify the source of cognitive and affective obstacles that interfere with mathematics learning. In this study, we analyzed the problem-solving protocols of mathematical gifted children from the perspective of cognitive language and meta-affect to identify the relationship between the functional characteristics of the text and metaphor they use and the functional characteristics of meta-affect. As a result, the behavior of the cognitive and affective characteristics of mathematically gifted children differed according to the success of problem solving. In the case of unsuccessful problem-solving, the use of metaphor as an internal representation system was relatively more frequent than in the successful case. In addition, while the cognitive linguistic aspects of metaphors play an important role in problem-solving, meta-affective attributes are closely related to the external representation of metaphors.

• School Mathematics
• /
• v.15 no.1
• /
• pp.61-75
• /
• 2013

This study analyzed Korean students' affective characteristics in mathematical learning according to school and sex by Factor Analysis and Cognitive Diagnosis Theory. In numerical affective achievements by Factor Analysis, there are mean differences between schools, i.e. elementary school and secondary school. And there are sexual differences within schools and boys show more positive achievement than girls. By Cognitive Diagnosis Theory, I investigated 6 affective attributes' proportions that students achieved according to school and sex. Middle school students' proportion is highest in self-control and anxiety and the attribute that students achieved most in all school is cognizing mathematical value. Boys show higher proportion in self directivity, interest and confidence than girls, but girls show higher proportion in anxiety than boys. In personal profiles, the proportion of students who achieved 5 attributes except anxiety is highest.

• Korean Journal of Comparative Education
• /
• v.28 no.5
• /
• pp.1-19
• /
• 2018

The purpose of educational assessments such as the Trends in International Mathematics and Science Study (TIMSS) is to compare groups such as countries. When the unit of measurement is above the student level, group-level diagnostic assessment based on multilevel item response theory (ML-IRT) can be considered just as cognitive diagnosis models are developed from item response theory. This study suggests an ML-IRT-based group-level diagnostic assessment model by modifying an item feature model by Park and bolt (2008). The model is illustrated on the recently released TIMSS 2015 Grade 8 mathematics assessment. The results provide skill profiles for the studied countries and the nine cognitive attributes; that is, the attribute effects can be compared across the countries and also across the attributes. By controlling unexplained variance, the suggested model may provide more reliable and more informative group-level comparisons. The results are interpreted using an example. Limitations and directions for future research are also discussed.

• Journal of Elementary Mathematics Education in Korea
• /
• v.13 no.1
• /
• pp.97-114
• /
• 2009

The purpose of this study was to investigate the effects of digital mathematics textbook on spatial abilities, interest and achievement of 6th graders. For this, research questions were set as follow: A. Is there any difference in cognitive ability in the space perception test between the experimental group and the control group. B. What distinctive attributes exist between the experimental group and the control group in the Spatial abilities? C. Is there any difference in learners' interest and achievement between the experiment group and the control group. To investigate the research questions, two classes of 6th grade children were selected from an elementary school in Daejeon and assigned one as experimental group and the other as control group. The experimental group studied mathematics using Digital Textbooks under an individual PC environment while the control group studied using the existing book-type textbooks. The following results and conclusions were obtained from the research. First, the effect of the Digital Textbooks on children's mathematics achievement was not statistically meaningful even though there was some progress in children's achievement. Furthermore, it was not found that the usage of a Digital Textbooks consistently influenced improvement in the students' interest in mathematics. Second, there were some positive changes in the achievement of Spatial ability of the middle subgroup of pretest score in the experiment group. It can have some educational implication that the Digital Textbooks can affect positively to the middle group in mathematics achievement who dominated more than 50% of the class. Third, the number of correct answers was found to be somewhat higher than that of the control group in spatial reasoning items. This means that the learning environment with Digital Textbooks allow more opportunities for manipulating geometric objects physically and mentally. Therefore, It seems necessary to offer various resources such as digital contents for students' geometric learning. For future research, It is strongly recommended to fix the bugs of the digital textbook programs and to upgrade the operating system of the computer.