• Communications of Mathematical Education
• /
• v.33 no.2
• /
• pp.105-122
• /
• 2019

In Korean textbooks, by T(x,y) = (x+a, y+b) where a and b are horizontal and vertical changes respectively, an arbitrary point on the original figure f(x, y) = 0 has been expressed as a point (x, y) and a point on a translated figure f(x-a, y-b) = 0 has been expressed as a point (x', y'). If an arbitrary point on a figure f(x, y) = 0 is expressed as a point (x, y), then a point (x, y) and a figure f(x, y) = 0 are different targets but the same characters are used. In this following study, there were found that the expressions in these textbooks were stuck for more than 50 years, so students' thoughts were stiff. And therefore these are a need to be improved so that those things are studied as follows. First, inducing a formula, what are the students' responses like when were expressed differently from textbooks? Second, based on the results reviewed, how will the expressions of the textbook be revised? Third, how do the students respond to the modified expressions? As the result, a point on the original figure were expressed differently from textbooks and a point on a translated figure was put as a point (x, y), and about it, all of the students surveyed said that this improved expressions made in the study were easier.

• The Mathematical Education
• /
• v.61 no.4
• /
• pp.559-579
• /
• 2022

Research on lexicon and language provides insights into the interests, values and practices of a community where individuals use the language. The International Classroom Lexicon Project, in which ten countries participated, identified own country's mathematics teaching and learning lexicons by investigating mathematics classroom instruction from teachers' perspectives in a speaking-oriented community. This study, as an extension of the International Classroom Lexicon Project research, investigated pedagogical lexicons used in 「Mathematics and Education」 journals specialized for Korean professional mathematics teachers published by the Korean Society of Teachers of Mathematics. Using the text mining approach, we also traced how these pedegogical lexicons have changed quantitatively over the past 10 years with a diachronic perspective. As a results, several novel terms were found in the writing-oriented community, which were not identified in the speaking-oriented community. In addition, we could discover some pedagogical lexicons have increased statistically significantly and some lexicons appeared(increased) rapidly across years. This implies the teacher community's values and zeitgeist by reflecting these changes in the sociocultural, incidental and social changing (i.e., periodical change) contexts. This study has value as a first step in understanding zeitgeist for mathematics education in Korean mathematics teacher community according to changes of times over the past 10 years. Also, this study contributes to the methodological insights: the text mining technique provides a methodological contribution to researching changes in interests, values and zeitgeist according to these changes in the times.

• Communications of Mathematical Education
• /
• v.35 no.2
• /
• pp.153-172
• /
• 2021

Various competencies such as critical thinking, systems thinking, problem solving competence, communication skill, and data literacy are likely to be required in the 4th industrial revolution. The competency regarding data literacy is one of those competencies. To nurture citizens who will live in the future, it is timely to consider research on teacher education for supporting teachers' development of statistical thinking as well as statistical knowledge. Therefore, in this study we developed and implemented a data analysis project for pre-service teachers to understand their changes in statistical knowledge in addition to their experiences of data-driven decision making process that required them utilizing their statistical thinking. We used a mixed method (i.e., sequential explanatory design) research to analyze the quantitative and qualitative data collected. The findings indicated that pre-service teachers have low knowledge level of their understanding on the relationship between population means and sample means, and estimation of the population mean and its interpretation. When it comes to the data-driven decision making process, we found that the pre-service teachers' experiences varied even when they worked as a small group for the project. We end this paper by presenting implications of the study for the fields of teacher education and statistics education.

• Education of Primary School Mathematics
• /
• v.25 no.1
• /
• pp.57-79
• /
• 2022

Current mathematics It is necessary to ensure that ratio and proportion concept is not distorted or broken while being treated as if they were easy to teach and learn in school. Therefore, the purpose of this study is to analyze the activities presented in the textbook. Based on prior work, this study reinterpreted the proportional reasoning task from the proportional perspective of Beckmann and Izsak(2015) to the multiplicative structure of Vergnaud(1996) in four ways. This compared how they interpreted the multiplicative structure and relationships between two measurement spaces of ratio and rate units and proportional expression and proportional distribution units presented in the revised textbooks of 2007, 2009, and 2015 curriculum. First, the study found that the proportional reasoning task presented in the ratio and rate section varied by increasing both the ratio structure type and the proportional reasoning activity during the 2009 curriculum, but simplified the content by decreasing both the percentage structure type and the proportional reasoning activity. In addition, during the 2015 curriculum, the content was simplified by decreasing both the type of multiplicative structure of ratio and rate and the type of proportional reasoning, but both the type of multiplicative structure of percentage and the content varied. Second, the study found that, the proportional reasoning task presented in the proportional expression and proportional distribute sections was similar to the previous one, as both the type of multiplicative structure and the type of proportional reasoning strategy increased during the 2009 curriculum. In addition, during the 2015 curriculum, both the type of multiplicative structure and the activity of proportional reasoning increased, but the proportional distribution were similar to the previous one as there was no significant change in the type of multiplicative structure and proportional reasoning. Therefore, teachers need to make efforts to analyze the multiplicative structure and proportional reasoning strategies of the activities presented in the textbook and reconstruct them according to the concepts to teach them so that students can experience proportional reasoning in various situations.

• Communications of Mathematical Education
• /
• v.35 no.4
• /
• pp.445-473
• /
• 2021

The purpose of this study is to derive implications for the design of the next curriculum by analyzing the textbooks designed as a new subject in the 2015 revised curriculum. In the mathematics curriculum documents of , 'related learning elements' are presented instead of 'learning elements'. 'Related learning elements' are defined as mathematical concepts or principles that can be used in the context of artificial intelligence, but there are no specific restrictions on the amount and scope of dealing with 'related learning elements'. Accordingly, the aspects of 'related learning elements' reflected in the textbooks were analyzed focusing on the textbook format, the amount and scope of contents, and the ways of using technological tools. There were differences in the format of describing 'related learning elements' in the textbook by textbook and the amount and scope of handling mathematics concepts. Although similar technological tools were dealt with in each textbook so that 'related learning elements' could be used in the context of artificial intelligence, the focus was on computations and interpretation of results. In order to fully reflect the intention of the curriculum in textbooks, a systematic discussion on 'related learning elements' will be necessary. Additionally, in order for students to experience the use of mathematics in artificial intelligence, substantialized activities that can set and solve problems using technological tools should be included in textbooks.

• The Mathematical Education
• /
• v.60 no.4
• /
• pp.555-580
• /
• 2021

The purpose of this study is to explore the factors of situational interest in math learning, and based on the results, to reveal the factors of situational interest included in teaching and learning methods, teaching and learning activities in mathematics class, and extracurricular activities outside of class. As a result of conducting a questionnaire to high school students, the factors of situational interest in learning mathematics were divided into 10 detail-domain(Enjoy, Curiosity, Competence / Real life, Other subjects, Career / Prior knowledge, Accumulation knowledge / Transformation, Analysis), 4 general-domain(Emotion, Attitude / Knowledge, Understanding), 2 higher-domain(Affective / Cognitive) were extracted. In addition, it was revealed that various factors of situational interest were included teaching and learning methods, teaching and learning activities and extracurricular activities. When examining the meaning of 10 situational interest factors, it can be expected that the factors for developing individual interest are included, so it can be expected to serve as a basis for expanding the study on the development of individual interest in mathematics learning. In addition, in order to maintain individual interest continuously, it is necessary to maintain situational interest by seeking continuous changes in teaching and learning methods in the school field. Therefore, it can be seen that the process of exploring the contextual interest factors included in teacher-centered teaching and learning methods and student-centered teaching and learning activities and extracurricular activities is meaningful.

• Communications of Mathematical Education
• /
• v.36 no.1
• /
• pp.139-170
• /
• 2022

In relation to differentiated mathematics education, Russia has a longer experience in research and practice than Korea. The mathematics curriculum for 10-11 grades currently in use in Russia is a level-specific curriculum and consists of a basic level and an advanced level. And in Russia mathematics textbooks for 10-11 grades are also textbooks for each level. In this study, we analyzed basic level textbook and advanced level textbook written by the same author group among the textbooks 'Algebra and Introduction of Mathematical Analysis' of the 10th grade in Russia. To analyze the main learning contents and textbook descriptions that were added in advanced level the 'real numbers' and 'complex numbers' sections were studied. The main contents of basic and advanced level textbooks for 'functions', 'trigonometric functions', 'trigonometric equations', 'conversions of trigonometric expressions', and 'derivatives', which are included in both basic and advanced textbooks were compared and analyzed, and the descriptive characteristics of the definitions and theorems presented in the two levels of textbooks were also compared and analyzed. From the results of this study, it is expected that various information on the contents of various level textbooks of mathematics, the differences between textbooks for each level, and strategies for the composition of textbooks for various level can be accumulated.

• Communications of Mathematical Education
• /
• v.37 no.1
• /
• pp.1-19
• /
• 2023

Mathematics Listening Ability(MLA) refers to the ability to listen to and grasp the meaning of speech language containing mathematical concepts and principles, distinguishing it from daily life and listening in other subject classes. According to literature, MLA might be divided into six types. Among them, interpretation, discovering, evaluating, and evaluation may indicate an attitude that correctly listens to the meaning of the language used in mathematics classes. On the other hand, selective, pretend, and ignore are types of listening attitudes that are not appropriate. Based on the statistical analysis of 834 3rd to 6th graders and a total of 44 homeroom teachers I developed a MLA survey items for elementary school students. In this study, principal component analysis was conducted to verify reliability in the development of survey items, and expert review and correlation analysis of survey results were conducted to verify validity. In addition, the validity was verified by statistically analyzing the survey results of students and their homeroom teachers. Based on literature and statistical analysis, I developed a MLA Survey items(for students) consisting of 25 questions and a mathematical resolution measurement tool(for teachers) consisting of 26 questions.

• The Mathematical Education
• /
• v.63 no.2
• /
• pp.165-186
• /
• 2024

Despite the growing attention on artificial intelligence-based automated scoring technology as a support method for the introduction of descriptive items in school environments and large-scale assessments, there is a noticeable lack of foundational research in mathematics compared to other subjects. This study developed an automated scoring model for two descriptive items in first-year middle school mathematics using the Random Forest algorithm, evaluated its performance, and explored ways to enhance this performance. The accuracy of the final models for the two items was found to be between 0.95 to 1.00 and 0.73 to 0.89, respectively, which is relatively high compared to automated scoring models in other subjects. We discovered that the strategic selection of the number of evaluation categories, taking into account the amount of data, is crucial for the effective development and performance of automated scoring models. Additionally, text preprocessing by mathematics education experts proved effective in improving both the performance and interpretability of the automated scoring model. Selecting a vectorization method that matches the characteristics of the items and data was identified as one way to enhance model performance. Furthermore, we confirmed that oversampling is a useful method to supplement performance in situations where practical limitations hinder balanced data collection. To enhance educational utility, further research is needed on how to utilize feature importance derived from the Random Forest-based automated scoring model to generate useful information for teaching and learning, such as feedback. This study is significant as foundational research in the field of mathematics descriptive automatic scoring, and there is a need for various subsequent studies through close collaboration between AI experts and math education experts.

• Communications of Mathematical Education
• /
• v.38 no.1
• /
• pp.1-26
• /
• 2024

As the limitations of professional development programs and individual attempts to improve teaching expertise have been reported, mathematics teachers have operated various types of teacher learning communities as alternative teacher professional programs. A teacher learning community can be considered a Community of Practice(CoP) in that it satisfies three factors of Cop, which are common purpose, mutual participation, and shared repertoire, so the 'learning' of a teacher community can be interpreted based on the theory of CoP. The purpose of this study is to investigate the process of identity development of five mathematics teachers who have been continuously involved in teacher communities. For this, the researcher collected data on the entire process of community activities through participant observation and conducted individual follow-up interviews to explore mathematics teachers' narratives and personal experiences. Results indicated that mathematics teachers experienced the development of practical knowledge related to mathematics teaching and learning, improvement of teaching practice through continuous reflection and introspection, and recognization the shared value of togethering through community immersion. Based on these experiences, implications for the effective operation of learning communities such as national support of teacher learning communities and horizontal and cooperative teacher norms were discussed, and follow-up research was proposed.