• Journal of the Korean School Mathematics Society
• /
• v.23 no.1
• /
• pp.129-158
• /
• 2020

In this study, we presented two geometric tasks to three 11th grade students to identify the characteristics of the images that the students had at the beginning of problem-solving in the problem situations and investigated how their images changed during problem-solving and effected their problem-solving behaviors. In the first task, student A had a static image (type 1) at the beginning of his problem-solving process, but later developed into a dynamic image of type 3 and recognized the invariant relationship between the quantities in the problem situation. Student B and student C were observed as type 3 students throughout their problem-solving process. No differences were found in student B's and student C's images of the problem context in the first task, but apparent differences appeared in the second task. In the second task, both student B and student C demonstrated a dynamic image of the problem context. However, student B did not recognize the invariant relationship between the related quantities. In contrast, student C constructed a robust quantitative structure, which seemed to support him to perceive the invariant relationship. The results of this study also show that the success of solving the task 1 was determined by whether the students had reached the level of theoretical generalization with a dynamic image of the related quantities in the problem situation. In the case of task 2, the level of covariational reasoning with the two varying quantities in the problem situation was brought forth differences between the two students.

• Human Ecology Research
• /
• v.51 no.6
• /
• pp.591-602
• /
• 2013

This paper aims to explore the role of the home economics subject in helping high school students preparing for an independent aged life and to develop problem based teaching plans toward this goal. Contents related to the elderly in the high school home economics and technology 2007 and 2009 revised curricula were analyzed, and elderly-related contents in other subject areas (the 2009 revised curricula of ethics, public health, and social studies) were also comparatively analyzed to determine the identity of the home economics subject in relation to preparation for independent aging. Based on these analysis, five subjects and teaching plans were presented: the aging society and population changes, the characteristics of the elderly, individual preparation for aging, care of the elderly, and welfare services for the elderly. The ultimate objectives of the lessons were, through critical reasoning, to inquire into the causes of current problems the elderly face so that teenagers can understand aging societies and the elderly and to seek reasonable alternatives for teenagers as they prepare for successful and independent aging, increasing their problem-solving abilities in choosing the best course of action by considering the ripple effect of consequences of each of those alternatives. Suggestions on what direction elderly-related education should take in the future, and what roles teachers should take are also provided.

• Education of Primary School Mathematics
• /
• v.24 no.4
• /
• pp.189-202
• /
• 2021

The teacher's questions presented in the problem-solving situation stimulate students' mathematical thinking and lead them to find a solution to the given problem situation. In this research, the types and functions of questions presented in chapters of Pattern area of the 2015 revised elementary school mathematics textbooks were compared and analyzed by grade cluster. Through this, it was attempted to obtain implications for teaching and learning in identifying the characteristics of questions and effectively using the questions when teaching Pattern area. As a result of this research, as grade clsuter increased, the number of questions per lesson presented in Pattern area increased. Frequency of the types of questions in textbooks was found to be high in the order of reasoning questions, factual questions, and open questions in common by grade cluster. In chapters of Pattern area, relatively many questions were presented that serve as functions to help guess, invent, and solve problems or to help mathematical reasoning in the process of finding rules. It can be inferred that these types of questions and their functions are related to the learning content by grade cluster and characteristics of grade cluster. Therefore, the results of this research can contribute to providing a reference material for devising questions when teaching Pattern area and further to the development of teaching and learning in Pattern area.

• Journal of The Korean Association For Science Education
• /
• v.26 no.2
• /
• pp.212-221
• /
• 2006

The purposes of this study were to examine the characteristics of teacher help in small group Thinking Science(TS) activities and analyze the way students respond to teacher help. For this study, twenty-four 5th grade and twenty-four 7th grade students were selected, to undertake TS activities. Out of the 8 activities students participated in, the verbal interactions in activity 4 and 6, by students in four small groups, which incorporated relatively active argumentation was analyzed. Students' cognitive level was identified through a science reasoning task and the students were grouped heterogeneously according to their cognitive level. This study showed that teachers predominately used simple confirmation questions in preference to metacognitive question. Also, teacher help varied according to one's personal traits, work experience and degree of activity recognition. It was discovered that when the teacher provided student appropriate metacognitive questions and sufficient feedback, students actively engaged in argumentation. On the other hand, when the teacher asked simple confirmation questions and interfered in the activity, students did not participate in argumentation actively.

• The Mathematical Education
• /
• v.62 no.2
• /
• pp.269-287
• /
• 2023

Matrix theory is widely used not only in mathematics, natural sciences, and engineering, but also in social sciences and artificial intelligence. In the 2009 revised mathematics curriculum, matrices were removed from high school math education to reduce the burden on students, but in anticipation of the age of artificial intelligence, they will be reintegrated into the 2022 revised education curriculum. Therefore, there is a need to analyze the matrix content covered in other countries to suggest a meaningful direction for matrix education and to derive implications for textbook composition. In this study, we analyzed the German mathematics curriculum and standard education curriculum, as well as the matrix units in the German Hesse state mathematics curriculum and textbook, and identified the characteristics of their content elements and development methods. As a result of our analysis, it was found that the German textbooks cover matrices in three categories: matrices for solving linear equations, matrices for explaining linear transformations, and matrices for explaining transition processes. It was also found that the emphasis was on mathematical reasoning and modeling when learning matrices. Based on these findings, we suggest that if matrices are to be reintegrated into school mathematics, the curriculum should focus on deep conceptual understanding, mathematical reasoning, and mathematical modeling in textbook composition.

• Education of Primary School Mathematics
• /
• v.14 no.3
• /
• pp.237-259
• /
• 2011

Mathematics learning disabilities is a specific learning disorder affecting the normal acquisition of arithmetic and spatial skills. Reported prevalence rates range from 5 to 10 percent and show high rates of comorbid disabilities, such as dyslexia and ADHD. In this study, the characteristics and the causes of this disorder has been examined. The core cause of mathematics learning disabilities is not clear yet: it can come from general cognitive problems, or disorder of innate intuitive number module could be the cause. Recently, researchers try to subdivide mathematics learning disabilities as (1) semantic/memory type, (2) procedural/skill type, (3) visuospatial type, and (4) reasoning type. Each subtype is related to specific brain areas subserving mathematical cognition. Based on these findings, the author has performed a basic research to develop grade specific diagnostic tests: number processing test and math word problems for lower grades and comprehensive math knowledge tests for the upper grades. The results should help teachers to find out prior knowledge, specific weaknesses of students, and plan personalized intervention program. The author suggest diagnostic tests are organized into 6 components. They are number sense, conceptual knowledge, arithmetic facts retrieval, procedural skills, mathematical reasoning/word problem solving, and visuospatial perception tests. This grouping will also help the examiner to figure out the processing time for each component.

• Journal of The Korean Association For Science Education
• /
• v.38 no.2
• /
• pp.135-145
• /
• 2018

In this study, we investigated the argumentations of group and classroom discussions in socioscientific issues (SSI) discussion classes. Twenty-seven high school students participated in the SSI discussion classes on nuclear power generation. We observed and recorded the classes and also conducted semi-structured interviews. For the analyses, we revised a previous framework that was developed to analyze dialogic argumentations in the context of SSI. The analyses of the results indicated that there were more discourse schemes in the classroom discussions than the group discussions which are related to awareness and openness to multiple perspectives, evidence based reasoning, and on-going inquiry and skepticism. And there were few discourse schemes related to moral and ethical sensitivity in the group and classroom discussions. Various grounds, data, and information were presented in the classroom discussions. Students concentrated on carrying their claims and were not able to sympathize with and accept other opinions. Therefore, there were few discourse schemes to reach consensus. In addition, they perceived classroom discussions as competitive and actively rebutted other claims or grounds. The levels of argumentation were also high in the classroom discussions. The group discussions were held in relaxed atmosphere, and they asked the opponents more for clarification or additional information and evidences. However, classroom discussions were held in serious atmosphere, and they actively queried the validity of the claims or grounds. Based on the results, some suggestions to implement SSI discussion classes were discussed.