• Research in Mathematical Education
• /
• v.11 no.1
• /
• pp.33-51
• /
• 2007

The present study explores mathematics teachers' understanding of division by zero and their approaches to explaining the impossibility of division by zero. This study analyzes Chinese and Korean middle school mathematics teachers' responses to the teaching task of explaining the impossibility of dividing 7 by zero, and examples of teachers' reasoned explanations for their answers are presented. The findings from this study suggest that most Korean teachers offer multiple types of mathematical explanations for justifying the impossibility of division by zero, while Chinese teachers' explanations were more uniform and based less on mathematical ideas than those of their Korean counterparts. Another finding from this study is that teachers' particular conceptions of zero were strongly associated with their justifications for the impossibility of division by zero, and the influence of the teachers' conceptions of zero was revealed as a barrier in composing a well-reasoned explanation for the impossibility of division by zero. One of the practical implications of this study is those teachers' basic attitudes toward always attempting to give explanations for mathematical facts or mathematical concepts do not seem to be derived solely from their sufficient knowledge of the facts or concepts of mathematics.

• Journal of Elementary Mathematics Education in Korea
• /
• v.23 no.1
• /
• pp.43-57
• /
• 2019

The meaning of zero as a number signifying nothing is introduced as a number 1 less than 1 in the first grade mathematics textbook. In addition, the first appearance of the properties of zero are described by exemplary situations of adding zero, subtracting zero, and multiplying by zero in the first and second grade mathematics textbooks. The meaning and the properties of 0, however, are not explicitly dealt with any longer in the follow-up learning. In this study, we discuss the way of introducing zero and the applications of the properties of zero for solving number sentences so that they could help elementary school students understand the meaning and the properties of zero. Based on these results, we suggest some educational implications on teaching and learning mathematics of zero.

• School Mathematics
• /
• v.8 no.4
• /
• pp.397-415
• /
• 2006

This paper is to find out the reason why students often make mistakes with 0 during computation and to get some instructional implication. For this, history of 0 is reviewed and mathematics textbook and workbook are analyzed. History of 0 tells us that the ancients had almost the same problem with 0 as we have. So we can guess children's problems with 0 have a kind of epistemological obstacles. And textbook analysis tells us that there are some instructional problems with 0 in textbooks: method and time of introducing 0, method of introducing computational algorithms, implicit teaching of the number facts with 0, ignoring the problems which can give rise to errors with 0. Finally, As a reult of analysis of Japanese and German textbooks, three instructional implications are induced:(i) emphasis of role of 0 as a place holder in decimal numeration system (ii) explicit and systematic teaching of the process and product of calculation with 0 (iii) giving practice of problems which can give rise to errors with 0 for prevention of systematical errors with 0.

• The Mathematical Education
• /
• v.48 no.1
• /
• pp.81-91
• /
• 2009

This paper focuses on two problems in the 10th grade mathematics, the rational zero theorem and the content(the integer divisor) of a polynomial Among 138 students participated in the problem solving, 58 of them (42 %) has used the rational zero theorem for the factorization of polynomials. However, 30 of 58 students (52 %) consider the rational zero theorem is a mathematical fake(false statement) and they only use it to get a correct answer. There are three different types in the textbooks in dealing with the content of a polynomial with integer coefficients. Computing the greatest common divisor of polynomials, some textbooks consider the content of polynomials, some do not and others suggest both methods. This also makes students confused. We suggests that a separate section of the rational zero theorem must be included in the text. As for the content of a polynomial, we consider the polynomials are contained in the polynomial ring over the rational numbers. So computing the gcd of polynomials, guide the students to give a monic(or primitive) polynomial as ail answer.

• Korean Institute of Interior Design Journal
• /
• v.26 no.6
• /
• pp.24-32
• /
• 2017

STEAM education is an effective teaching method to develop self-problem-solving skills through creative thinking. In order to revitalize STEAM education, various program models are being developed recently. The purpose of this study is to develop a STEAM education program based on the project-based learing method that includes the process of solving global environmental problems. The STEAM element was extracted by linking the zero energy house design with the middle school curriculum, and the STEAM education program was developed considering career activities. It was analyzed whether the developed program can improve STEAM core competence and job preparation ability. The education program was conducted for middle school students and the program was evaluated through questionnaires. In order to strengthen the STEAM competency, project-based learning method was applied and it was able to enhance the active problem solving ability of learners. In addition, opportunities for career experience could be provided through career exploration programs and various activities. Through this STEAM education program, it is expected to contribute to cultivating human resources with convergence knowledge and core competency.

• English Language & Literature Teaching
• /
• v.13 no.4
• /
• pp.109-126
• /
• 2007

English article has been considered as one of the most difficult areas to learn among ESL/EFL students. The current paper reviews English learners' article error patterns as well as pedagogy in order to teach English articles and to minimize learning difficulties on English articles. Different pedagogy for English articles on the basis of learners' proficiency levels are suggested as each proficiency level student shows a different error tendency; beginning level language learners used the zero article with the most facility while intermediate level language learners used the definite article the most accurately. However, studies about high advanced level learners' error patterns present that these high accuracy rates among beginning level students might be a result of students' plain guessing. Considering these error patterns, pedagogy for advanced level is also suggested.

• Hip & pelvis
• /
• v.35 no.4
• /
• pp.228-232
• /
• 2023

Purpose: Prosthetic joint infection (PJI) has an enormous physiological and psychological burden on patients. Surgeons rightly wish to minimise this risk. It has been shown that a standardised, evidence-based approach to perioperative care leads to better patient outcomes. A review of current practice was conducted using a cross-sectional survey among surgeons at multiple centers nationwide. Materials and Methods: An 11-question electronic survey was circulated to hip and knee arthroplasty consultants nationally via the BOA (British Orthopaedic Association) e-newsletter. Results: The respondents included 56 consultants working across 19 different trusts. Thirty-four (60.7%) screen patients for asymptomatic bacteriuria (ASB) preoperatively, with 19 (55.9%) would treating with antibiotics. Fifty-six (100%) screen for methicillin-resistant Staphylococcus aureus and treat if positive. Only 15 (26.8%) screen for methicillin-sensitive S. aureus (MSSA) or empirically eradicate. Zero (0%) routinely catheterize patients perioperatively. Forty-one (73.2%) would give intramuscular or intravenous gentamicin for a perioperative catheterisation. All surgeons use laminar flow theatres. Twenty-six (46.4%) use only an impervious gown, 6 (10.7%) exhaust pipes, and 24 (42.3%) surgical helmet system. Five different antimicrobial prophylaxis regimens are used 9 (16.1%) cefuroxime, 2 (3.6%) flucloxacillin, 19 (33.9%) flucloxacillin and gentamicin, 10 (17.9%) teicoplanin, 16 (28.6%) teicoplanin and gentamicin. Twenty-two (39.3%) routinely give further doses. Conclusion: ASB screening, treatment and intramuscular gentamicin for perioperative catheterisation is routinely practiced despite no supporting evidence base. MSSA screening and treatment is underutilised. Multiple antibiotic regimens exist despite little variation in organisms in PJI. Practice varies between surgeons and centers, we should all be practicing evidence-based medicine.

• Journal of the Korea Society of Computer and Information
• /
• v.28 no.8
• /
• pp.195-204
• /
• 2023

In this study, prompt engineering that improves prompts was explored to improve the performance of teaching and learning materials recommendations using generative artificial intelligence such as GPT and Stable Diffusion. Picture materials were used as the types of teaching and learning materials. To explore the impact of the prompt composition, a Zero-Shot prompt, a prompt containing learning target grade information, a prompt containing learning goals, and a prompt containing both learning target grades and learning goals were designed to collect responses. The collected responses were embedded using Sentence Transformers, dimensionalized to t-SNE, and visualized, and then the relationship between prompts and responses was explored. In addition, each response was clustered using the k-means clustering algorithm, then the adjacent value of the widest cluster was selected as a representative value, imaged using Stable Diffusion, and evaluated by 30 elementary school teachers according to the criteria for evaluating teaching and learning materials. Thirty teachers judged that three of the four picture materials recommended were of educational value, and two of them could be used for actual classes. The prompt that recommended the most valuable picture material appeared as a prompt containing both the target grade and the learning goal.

• Journal of Elementary Mathematics Education in Korea
• /
• v.18 no.2
• /
• pp.257-278
• /
• 2014

The concept of zero(0) and calculations involving 0 are a few of the most difficult topics that students experience in learning mathematics. Therefore, it implies that proper guidance to help students understand the desirable concept of 0 and acquire calculating process involving 0 should be provided when we teach numbers and operations. This study aims to investigate instructional situations in relation to the errors of 0 and to search for efficient ways to teach them based on the previous research. To do this, we analysed elementary mathematics textbooks and workbooks. The result showed that $0{\div}$(a number) and the division of which quotient includes 0 as a middle digit lacked in current textbooks and workbooks. We devised the learning activities of the two topics for 3rd grades and 4th grades, respectively. We expect that the activities will be helpful to devise learning activities of textbook and suggest some implications for teaching the calculations involving 0.

• Journal of Elementary Mathematics Education in Korea
• /
• v.22 no.2
• /
• pp.183-198
• /
• 2018

In this paper, I theoretically considered joining and separating activities and revisited the textbooks from 7 countries and Korean mathematics textbooks from 5th revised curriculum to 2015 revised curriculum to find implication for the treatment of 0 in the joining and separating activities. The 'joining' has definition and properties similar to addition, but the 'separating'is difficult to define and is not considered to have properties similar to subtraction. In the sense of computation, joining and separating can be seen as' part-part-to-whole' situations, but are just part of the addition and subtraction situations. The analysis of textbooks from 7 counties showed that Singapore and Malaysia textbooks already studied zero and then included it in joining and separating activities, but other countries did not include it as joining and separating activities. The textbooks of South Korea have consistently suggested not to include zero, but teacher's guide has shown that there is a little consistency in the treatment of zero. As a conclusion, I suggested that it was necessary to propose a proper context of the situation in order to introduce joining and separating without including 0 in terms of student level and to propose that a more consistent presentation of zero handling in the teaching in the teacher's guide.