• Journal of the Korean School Mathematics Society
• /
• v.22 no.3
• /
• pp.241-256
• /
• 2019

In this paper, we analyzed the types of tasks presented in the 'Probability and Statistics' textbooks and how the cognitive competences required to perform the tasks provide students with opportunity-to-learn. To this end, the analysis of the 9 books of the 'Probability and Statistics' test textbooks according to the 2015 revised mathematics curriculum showed that the context-based tasks(CF type, RE type) ranged from 67.5% to 78.0% of the total number of tasks in each textbook, but the ratio of relevant and essential tasks related to real life is from 0.4% to 2.0%, it was found that most of the context-based tasks presented in the textbooks were disguised as real life materials. The cognitive competences of context-based tasks ranged from 29.6% to 50.0% in reproduction category, from 33.8% to 54.3% in connection category, and from 8.8% to 20.0% in reflection category. As a result, there was not enough opportunity-to-learn for students to experience reflective cognitive processes.

• The Mathematical Education
• /
• v.62 no.2
• /
• pp.289-302
• /
• 2023

In today's digital information society, student knowledge and skills to analyze big data and make informed decisions have become an important goal of school mathematics. Integrating big data statistical projects with digital technologies in high school <Artificial Intelligence> mathematics courses has the potential to provide students with a learning experience of high impact that can develop these essential skills. This paper proposes a set of guidelines for designing effective big data statistical project-based tasks and evaluates the tasks in the artificial intelligence mathematics textbook against these criteria. The proposed guidelines recommend that projects should: (1) align knowledge and skills with the national school mathematics curriculum; (2) use preprocessed massive datasets; (3) employ data scientists' problem-solving methods; (4) encourage decision-making; (5) leverage technological tools; and (6) promote collaborative learning. The findings indicate that few textbooks fully align with these guidelines, with most failing to incorporate elements corresponding to Guideline 2 in their project tasks. In addition, most tasks in the textbooks overlook or omit data preprocessing, either by using smaller datasets or by using big data without any form of preprocessing. This can potentially result in misconceptions among students regarding the nature of big data. Furthermore, this paper discusses the relevant mathematical knowledge and skills necessary for artificial intelligence, as well as the potential benefits and pedagogical considerations associated with integrating technology into big data tasks. This research sheds light on teaching mathematical concepts with machine learning algorithms and the effective use of technology tools in big data education.

• Communications of Mathematical Education
• /
• v.28 no.3
• /
• pp.353-366
• /
• 2014

Recently, the widespread usage of 3D-Printing has grown rapidly in popularity and development of a high level technology for 3D-Printing has become more necessary. Given these circumstances, effectively using mathematical knowledge is required. So, we have developed free web tools for 3D-Printing with Sage, for mathematical 3D modeling and have utilized them in college education, and everybody may access and utilize online anywhere at any time. In this paper, we introduce the development of our innovative 3D-Printing environment based on Calculus, Linear Algebra, which form the basis for mathematical modeling, and various 3D objects representing mathematical concept. By this process, our tools show the potential of solving real world problems using what students learn in university mathematics courses.

• 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 Science Education
• /
• v.45 no.2
• /
• pp.257-273
• /
• 2021

This study explores classes for pre-service mathematics teachers. The purpose of this study is to examine the differences between 'non-face-to-face' classes & 'face-to-face' classes, as well as the differences in learning outcomes between these two methods. A Professors' Learning Group was formed to effectively carry out this study. Through this learning group, we shared how to plan and operate the lecture. The subjects of this study are 'non-face-to-face calculus courses & face-to-face calculus courses' and 'non-face mathematics education theory courses & face-to-face mathematics education theory courses." Specifically, in these two pairs of courses, we analyze the differences in course management and the differences in the outcomes of students' assessments. Non-face-to-face classes were planned, developed, implemented and evaluated based on the 'non-face class design model.' The results of this study are as follows: First, we explored the differences between 'non-face-to-face classes/mixed classes' and 'face-to-face classes.' Second, the achievement results in calculus courses were higher in face-to-face classes than in non-face classes. Third, the results of achievements in mathematics education theory courses were higher in mixed classes than in face-to-face classes. Through the results of this study, we hope that the non-face-to-face class capabilities can be improved in pre-service mathematics teacher training.

• Journal of the Korean School Mathematics Society
• /
• v.20 no.4
• /
• pp.387-404
• /
• 2017

In this paper, in the last 4 years(2014~2017 school year), we classified the probability and statistical items based on the evaluation scope of the mathematics subject content knowledge which were presented by the Korea Institute for Curriculum and Evaluation, and the classified items were analyzed. As a result, First, in order to induce normalization of the probability and statistical curriculum, four assessment field should be evenly distributed. Second, integrated thinking and comprehensive analytical thinking assessment is required. Third, item an epilogue should be used to measure mathematical thinking and logical competence. Fourth, the ratio of the number of items in probability and statistics to the number of that was 7.7%~10.0%, and the ratio according to the item weighting was 5.0%~7.5%. Fifth, it maintains the policy of stabilizing a good the level of difficulty of the items. Finally, probability and statistical assessment should focus on measuring problem solving ability from an inductive point of view.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.6
• /
• pp.1539-1545
• /
• 2017

In this paper, we analyze and discuss the trend of the probability and statistics problems that have been made in the public secondary school teacher employment exam for mathematics teachers. In order to properly teach the national mathematics curriculum in 2015 in terms of content and function, we investigate the probability and statistics contents that a mathematics teachers should know. We also analyze the contents and trends of the items that have been submitted for 15 years in public secondary school teacher employment exam, and discuss the contents, scope, level and direction of the future contents. In conclusion, considering the significance of the Big Data in the 4th industrial revolution, the problems of statistical thinking of data and probability, exploratory data analysis, sample survey, and statistical inference are needed more.

• Communications of Mathematical Education
• /
• v.37 no.3
• /
• pp.497-516
• /
• 2023

The purpose of this study is to explore the possibility of enhancing teachers' pedagogical design capacity using ChatGPT. For this purpose, a survey was conducted to investigate preservice teachers' perceptions of ChatGPT, and lesson plans created using ChatGPT were analyzed from the perspectives of design elements, conversations with ChatGPT, and information transforming. The results showed that pre-service teachers have a rather passive attitude toward the use of ChatGPT, and that teacher moderation and ChatGPT characteristics affect pre-service teachers' perceptions of the use of ChatGPT. In addition, pre-service teachers mainly used ChatGPT for motivational activities and play activities, and there were significant differences in the level of utilization of ChatGPT among individuals, i.e., how they interacted with ChatGPT and how they transformed information. Based on these findings, we explored the possibility of using ChatGPT for teacher professional development and teacher education.

• Communications of Mathematical Education
• /
• v.31 no.1
• /
• pp.17-48
• /
• 2017

This case study examined mathematics anxiety of a public high school sophomore who was unable to perform well in mathematics but later overcame his fear of mathematics. In this study, he showed high levels of mathematics anxiety in the assessment tools that evaluate mathematical anxiety factors. Cognitive and behavior treatments were carried out to alleviate his anxiety. First, cognitive treatments that were implemented include: understanding his own problems, writing down his thoughts on a record sheet, and changing intermediate and core beliefs. This paper explored cognitive and affective changes and reactions during the treatment process. Second, behavioral treatments that were conducted include: the divided-page method and peer tutoring. The divided-page technique involves the test subject to write down and solve his problems on a note to see what kind of cognitive and affective changes occur during the process. This paper also explored how Su-chul, an overly competitive student, changed and reacted cognitively and affectively through peer tutoring. The results revealed that Su-chul's exam anxiety, as well as other factors, has decreased. Moreover, he regained his self-confidence by solving math problems that he had felt difficult. His competitive attitude also has turned into a cooperative and thoughtful one.

• Communications of Mathematical Education
• /
• v.30 no.3
• /
• pp.375-392
• /
• 2016

The purpose of this study is to provide a philosophical reflection on mathematical process consistently emphasized in our curriculum and to stress the importance of sharing creativity and its applicability to the mathematical process with the value of sharing and participation. For this purpose, we describe five stages of changing process in a peer mentoring teaching method conducted by a teacher who taught this method for 17 years with the goal of sharing creativity and examine components of mathematical process and their impact on it in each stage based on learning environment, learning process, and assessment. Results suggest that six principles should be underlined and considered for students to be actively involved in mathematical process. After analyzing changes in the five stages of the peer mentoring teaching method, the five principles scrutinized in mathematical process are the principles of continuous interactivity, contextual dependence, bidirectional development, teacher capability, and student participation. On the basis of these five principles, the principle of cooperative creativity is extracted from effective changes of mathematical process as a guiding force.