• Education of Primary School Mathematics
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• v.25 no.4
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• pp.343-360
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• 2022

In mathematics classes, the verbal explanation may contain diverse mathematical concepts and principles in short sentences. It may also include mathematics symbols and terms that might not be used in everyday life. Therefore, students may need particular listening ability in order to understand and participate in mathematics communication. Unlike general listening, the listening ability for mathematics classes may require student to integrate their mathematical and linguistic knowledge. The aim of this study is to reveal the subdomains of listening ability for mathematics classes in a elementary school. I categorized listening ability for mathematics classes in a elementary school from the literature. The categories of listening ability for mathematics are Interpretive Listening, Evaluative Listening, Hermeneutic Listening, Selective Listening, Pretend Listening, and Ignored Listening. In order to develop a framework for understanding listening ability for mathematics classes, I investigated a hierarchy of 412 South Korean elementary teachers' perception. Through a web-based survey, the teachers were asked to rank order their beliefs about and students' listening ability. Findings show that teachers' perceptions about listening ability for mathematics classes are divergent from current research trends. South Korean elementary teachers perceived Interpretive Listening as the most important listening.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.139-155
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• 2015

This study aimed to investigate teacher learning in the context of a community. For the purpose of this study, two research questions about the kinds of teacher noticing in a community and the role of partnership were addressed. To build a learning community, a professional development project, PRIME, established partnerships with 11 high schools and one of the cluster meetings were investigated in this study. Three mentor teachers, three preservice teachers, and one university supervisor participated in the cluster meeting. For this study, the multiple data such as audio tapes of cluster meetings, observation notes, and interviews were analyzed using the analysis of narratives. The results showed that the participants engaged in different kinds of noticing of their own beliefs about teaching and learning, teacher practices, and teacher identities including noticing of students' understanding in classroom situations. The partnership played the crucial role of reinforcing relationships among teachers, assigning tasks, and creating various communities.

• The Mathematical Education
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• v.63 no.2
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• pp.139-163
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• 2024

The purpose of this study is to examine the capabilities of ChatGPT as a tool for supporting students in generating mathematical arguments that can be considered proofs. To examine this, we engaged students enrolled in a mathematics pathways course in evaluating and revising their original arguments using ChatGPT feedback. Students attempted to find and prove a method for the area of a triangle given its side lengths. Instead of directly asking students to prove a formula, we asked them to explore a method to find the area of a triangle given the lengths of its sides and justify why their methods work. Students completed these ChatGPT-embedded proving activities as class homework. To investigate the capabilities of ChatGPT as a proof tutor, we used these student homework responses as data for this study. We analyzed and compared original and revised arguments students constructed with and without ChatGPT assistance. We also analyzed student-written responses about their perspectives on mathematical proof and proving and their thoughts on using ChatGPT as a proof assistant. Our analysis shows that our participants' approaches to constructing, evaluating, and revising their arguments aligned with their perspectives on proof and proving. They saw ChatGPT's evaluations of their arguments as similar to how they usually evaluate arguments of themselves and others. Mostly, they agreed with ChatGPT's suggestions to make their original arguments more proof-like. They, therefore, revised their original arguments following ChatGPT's suggestions, focusing on improving clarity, providing additional justifications, and showing the generality of their arguments. Further investigation is needed to explore how ChatGPT can be effectively used as a tool in teaching and learning mathematical proof and proof-writing.

• Journal of Educational Research in Mathematics
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• v.21 no.3
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• pp.295-311
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• 2011

The importance of problem solving in mathematics education has been emphasized and many studies related to this issue have been conducted. But, studies of problem solving in the aspect of affect domain are lacked. This study found the changing pattern of emotions that occur in process of a problem solving. The results are listed below. First, students experienced a lot of change of emotions and had a positive emotion as well as negative emotion during solving problems. Second, students who solved same problems through same methods experienced different change patterns of emotions. The reason is that students have different mathematical beliefs and think differently about a difficulty level of problem. Third, whether students solved problems with positive emotion or negative emotion depends on their attitude of mathematics. Fourth, students who thought that a difficulty level of problem was relatively high experienced more negative affect than students who think a difficulty level of problem is low experienced.

• Journal of the Korean earth science society
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• v.25 no.3
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• pp.160-175
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• 2004

This study examined the knowledge and practices of scientific inquiry displayed by three student teachers and two beginning teachers at secondary levels. Observations using the instrument of OTOP designed by the research team of OCEPT (Oregon Collaborative for Excellent in the Preparation of Teachers) generalized similar teaching strategies of scientific inquiry between student and beginning teachers, such as using group work for students' first hand experience, using concrete materials for experimentation or visual tools for demonstration, using questions for factual knowledge mainly without opportunities to understand how scientific knowledge is constructed. Those scientific inquiry activities were very confirmative ones to follow the steps without opportunities of understanding nature of science or nature of scientific inquiry. However, all participants in this study hold knowledge of scientific inquiry envisioned by the National Science Education Standards [NSES] (NRC, 1996), where students identify their hypothesis, use critical and logical thinking, and consider alternative explanations through argumentation as well as experimentation. An inconsistent relationship between participating teachers knowledge and practices about scientific inquiry resulted from their lack of pedagogy skills of implementing it in the classroom. Providing opportunities for these teachers to reflect on their beliefs and practices about scientific inquiry was recommended for the future study. Furthermore, increasing college faculty interest in new teaching approaches for upgrading the content knowledge of student teachers and beginning teachers was recommended as a solution, since those teachers showed evidence of influence by college faculties at universities in their pedagogy skills.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.229-259
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• 2012

The purpose of the present study is to develop instrument of mathematical belief of middle school and high school students and to analysis results of test using the instrument. Based on the results of literature review, mathematical belief is the cumulative effects of self-assessment and self-concept in mathematical learning and achievement experience. Four sub-components of mathematical belief is identified belief of school mathematics, belief of mathematical problem solving, mathematical self-concept, belief of mathematical teaching and learning. The instrument was developed to investigate mathematical belief by reflecting Korean middle school and high school students' psychological characters. To develop the appropriate items for the mathematical belief, after reviewing literature thoroughly, first version of the instrument was developed and exploratory factor analysis and confirmatory factor analysis were conducted. Then, to reduce the effect of the gender difference and achievement level difference, Correlation Analysis and 1-way ANOVA was performed. Also, using multiple group confirmatory factor analysis, this instrument was investigated to see whether this can be used for both middle school and high school. The final items for middle school students is consisted 7 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 10 items of belief of mathematical teaching and learning. Instrument of mathematical belief for high school students is consisted 9 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 11 items of belief of mathematical teaching and learning. This study examined the differences about mathematical belief's sub-factors shown by three groups of mathematics achievement level. Students of higher achievement level showed that the degree of most factors ware the highest excepting stereotype of belief of school mathematics. Also, Male students preferred more positive in mathematics belief than female students.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.225-243
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• 2013

This study was to analyze the effects of basic computational abilities using G-learning contents, which was developed for mathematically slow learners. The participant students were 146 mathematically slow learners in grade 3-6 in Seoul. The researchers analyzed the difference between pre and post test scores to check their effectiveness. Also, teachers and parents as well as students responded survey items to check dispositions and satisfactions towards the program. The research results showed that the application of the G-learning contents on basic computation areas was effective to develop students' basic computational skills. In addition, students also showed that they were satisfied studying basic computations with the G-learning contents. They had increased beliefs about and decreased difficulties in mathematics. Parents and teachers also had satisfactions in using the G-learning programs in spite of some negative effects such as errors in the contents, use of computers, and concentration on the game itself. For the improvement of G-learning contents, we need to keep studying on G-learning contents with wide range of areas and long term studies.

• Journal of The Korean Association For Science Education
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• v.34 no.7
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• pp.693-701
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• 2014

Based on social cognitive theory, self-efficacy in the context of learning has been steadily emphasized as an indicator of students' motivation and performance. The premise for developing such an instrument was that a specific measure of Physics self-efficacy was deemed to be an important predictor of the change processes necessary to improve students' physics understanding. In this study we described the process of developing and validating an instrument to measure students' beliefs in their abilities to perform essential tasks in physics and then investigated high school students' self-efficacy about physics learning and performance. Validity and reliability of PSEI were tested using various statistical techniques including the Cronbach alpha coefficient, exploratory factor analysis. The result of factor analysis supported the contention that the Physics Self-Efficacy Inventory (PSEI) was a multidimensional construct consisting of at least four dimensions: understanding and application of Physics concepts, achievement motivation, confidence for physics laboratory, confidence for Mathematics. The result showed that Kroean high schools students have low Physics self-efficacy for the all four dimensions. Therefore, researchers should focus on development of students' Physics self-efficacy. In addition, the instrument may lead to further understanding of student behavior, which in turn can facilitate the development of strategies that may increase students' aspiration to understand and study Physics. More specifically, by using the PSEI as a pre- and post-test indicator, instructors can gain insight into whether students' confidence levels increase as they engage in learning Physics, and, in addition, what type of teaching strategies are most effective in building deeper understanding of Physics concepts.where they freely exchanged opinions and feedback for constructing better collective ideas.

• Lingua Humanitatis
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• v.6
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• pp.147-166
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• 2004

Whitehead's discussion of language is not to be found in any one book or article. It is interwoven with his discussion of many other questions. He was, however, greatly concerned with the problem of symbolism in general and the uses of language. He regards language, spoken or written, as an instrument devised by men to aid them in their adjustment to the environment in which they live Language is used for many specific purposes in the process of this adjustment. Words are employed not only to refer to data and to express emotions. They may be used also to record experiences, and thoughts about these experiences. Worts also function as instruments in the organization of experiences as they are considered in retrospect. Thus words free us from the bondage of the immediate. And Whitehead's theory of meaning is implicit in his discussion of the functions of language. According to him, the human mind is functioning symbolically when some components of its experience elicit consciousness, beliefs, emotions, and usages, respecting other components of its experiences. The former set of components are the 'symbols', and the latter set constitute the 'meaning' of the symbols. Whitehead points out that one word may have several meanings, i.e. refer to several different data. In order to understand, thus, the meaning to which a word refers, it is sometimes very important to appreciate the system of thought within which a person is operating. Further, Whitehead's discussion of language includes a number of cogent warning the deficiencies of language, and hence the need for great care in the use of words. In fact, language developed gradually. For the most part we have created words designed to deal with practical problems. Attention focuses on the prominent features in a situation, in particular the changing aspects of things. With reference to such data our words are relatively adequate. However, this issues in an unfortunate superficiality. The enduring, the subtle, the complex and the general aspects of the universe do not have adequate verbal representation. for this reason, Whitehead's position concerning the uses of language in speculative philosophy is stated with pungent directness. The uncritical trust in the adequacy of language is one of the main errors to which philosophy is liable. Since ordinary language does not do justice to the generalities, profundities and complexities of life, it is obvious that philosophy requires new words and phrases, or at least the revision of familiar words and phrases. Proceeding to develop the theme Whitehead contends that words and phrases must be stretched towards a generality foreign to their ordinary usage. In the same vein Whitehead refers to the need to realize that language which is the tool of philosophy needs to be redesigned just as in physical science available physical apparatus needs to be redesigned. But even these words and phrases, stretched or redesigned, are never completely adequate in philosophical speculations. They are, in his opinion, merely a great improvement over ordinary language or the language science, mathematics or symbolic logic.

• Asia pacific journal of information systems
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• v.24 no.2
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• pp.233-253
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• 2014

Can the stock market really be predicted? Stock market prediction has attracted much attention from many fields including business, economics, statistics, and mathematics. Early research on stock market prediction was based on random walk theory (RWT) and the efficient market hypothesis (EMH). According to the EMH, stock market are largely driven by new information rather than present and past prices. Since it is unpredictable, stock market will follow a random walk. Even though these theories, Schumaker [2010] asserted that people keep trying to predict the stock market by using artificial intelligence, statistical estimates, and mathematical models. Mathematical approaches include Percolation Methods, Log-Periodic Oscillations and Wavelet Transforms to model future prices. Examples of artificial intelligence approaches that deals with optimization and machine learning are Genetic Algorithms, Support Vector Machines (SVM) and Neural Networks. Statistical approaches typically predicts the future by using past stock market data. Recently, financial engineers have started to predict the stock prices movement pattern by using the SNS data. SNS is the place where peoples opinions and ideas are freely flow and affect others' beliefs on certain things. Through word-of-mouth in SNS, people share product usage experiences, subjective feelings, and commonly accompanying sentiment or mood with others. An increasing number of empirical analyses of sentiment and mood are based on textual collections of public user generated data on the web. The Opinion mining is one domain of the data mining fields extracting public opinions exposed in SNS by utilizing data mining. There have been many studies on the issues of opinion mining from Web sources such as product reviews, forum posts and blogs. In relation to this literatures, we are trying to understand the effects of SNS exposures of firms on stock prices in Korea. Similarly to Bollen et al. [2011], we empirically analyze the impact of SNS exposures on stock return rates. We use Social Metrics by Daum Soft, an SNS big data analysis company in Korea. Social Metrics provides trends and public opinions in Twitter and blogs by using natural language process and analysis tools. It collects the sentences circulated in the Twitter in real time, and breaks down these sentences into the word units and then extracts keywords. In this study, we classify firms' exposures in SNS into two groups: positive and negative. To test the correlation and causation relationship between SNS exposures and stock price returns, we first collect 252 firms' stock prices and KRX100 index in the Korea Stock Exchange (KRX) from May 25, 2012 to September 1, 2012. We also gather the public attitudes (positive, negative) about these firms from Social Metrics over the same period of time. We conduct regression analysis between stock prices and the number of SNS exposures. Having checked the correlation between the two variables, we perform Granger causality test to see the causation direction between the two variables. The research result is that the number of total SNS exposures is positively related with stock market returns. The number of positive mentions of has also positive relationship with stock market returns. Contrarily, the number of negative mentions has negative relationship with stock market returns, but this relationship is statistically not significant. This means that the impact of positive mentions is statistically bigger than the impact of negative mentions. We also investigate whether the impacts are moderated by industry type and firm's size. We find that the SNS exposures impacts are bigger for IT firms than for non-IT firms, and bigger for small sized firms than for large sized firms. The results of Granger causality test shows change of stock price return is caused by SNS exposures, while the causation of the other way round is not significant. Therefore the correlation relationship between SNS exposures and stock prices has uni-direction causality. The more a firm is exposed in SNS, the more is the stock price likely to increase, while stock price changes may not cause more SNS mentions.