As the era of solving various and complex problems in the real world using artificial intelligence and big data appears, problem-solving competencies that can solve realistic problems through a mathematical approach are required. In fact, the 2015 revised mathematics curriculum and the 2022 revised mathematics curriculum emphasize mathematical modeling as an activity and competency to solve real-world problems. However, the real-world problems presented in domestic and international textbooks have a high proportion of artificial problems that rarely occur in real-world. Accordingly, domestic and international countries are paying attention to the reality of mathematical modeling tasks and suggesting the need for authentic tasks that reflect students' daily lives. However, not only did previous studies focus on theoretical proposals for reality, but studies analyzing teachers' perceptions of reality and their competency to reflect reality in the task are insufficient. Accordingly, this study aims to analyze in-service mathematics teachers' perception of reality among the characteristics of tasks for mathematical modeling and the in-service mathematics teachers' competency for designing the mathematical modeling tasks. First of all, five criteria for satisfying the reality were established by analyzing literatures. Afterward, teacher training was conducted under the theme of mathematical modeling. Pre- and post-surveys for 41 in-service mathematics teachers who participated in the teacher training was conducted to confirm changes in perception of reality. The pre- and post- surveys provided a task that did not reflect reality, and in-service mathematics teachers determined whether the task given in surveys reflected reality and selected one reason for the judgment among five criteria for reality. Afterwards, frequency analysis was conducted by coding the results of the survey answered by in-service mathematics teachers in the pre- and post- survey, and frequencies were compared to confirm in-service mathematics teachers' perception changes on reality. In addition, the mathematical modeling tasks designed by in-service teachers were evaluated with the criteria for reality to confirm the teachers' competency for designing mathematical modeling tasks reflecting the reality. As a result, it was shown that in-service mathematics teachers changed from insufficient perception that only considers fragmentary criterion for reality to perceptions that consider all the five criteria of reality. In particular, as a result of analyzing the basis for judgment among in-service mathematics teachers whose judgment on reality was reversed in the pre- and post-survey, changes in the perception of in-service mathematics teachers was confirmed, who did not consider certain criteria as a criterion for reality in the pre-survey, but considered them as a criterion for reality in the post-survey. In addition, as a result of evaluating the tasks designed by in-service mathematics teachers for mathematical modeling, in-service mathematics teachers showed the competency to reflect reality in their tasks. However, among the five criteria for reality, the criterion for "situations that can occur in students' daily lives," "need to solve the task," and "require conclusions in a real-world situation" were relatively less reflected. In addition, it was found that the proportion of teachers with low task development competencies was higher in the teacher group who could not make the right judgment than in the teacher group who could make the right judgment on the reality of the task. Based on the results of these studies, this study provides implications for teacher education to enable mathematics teachers to apply mathematical modeling lesson in their classes.
The purpose of this research is to construct research framework for international franchising based on existing literature and to identify research components in the framework. Franchise can be defined as management styles that allow franchisee use various management assets of franchisor in order to make or sell product or service. It can be divided into product distribution franchise that is designed to sell products and business format franchise that is designed for running it as business whatever its form is. International franchising can be defined as a way of internationalization of franchisor to foreign country by providing its business format or package to franchisee of host country. International franchising is growing fast for last four decades but academic research on this is quite limited. Especially in Korea, research about international franchising is carried out on by case study format with single case or empirical study format with survey based on domestic franchise theory. Therefore, this paper tries to review existing literature on international franchising research, providing research framework, and then stimulating new research on this field. International franchising research components include motives and environmental factors for decision of expanding to international franchising, entrance modes and development plan for international franchising, contracts and management strategy of international franchising, and various performance measures from different perspectives. First, motives of international franchising are fee collection from franchisee. Also it provides easier way to expanding to foreign country. The other motives including increase total sales volume, occupying better strategic position, getting quality resources, and improving efficiency. Environmental factors that facilitating international franchising encompasses economic condition, trend, and legal or political factors in host and/or home countries. In addition, control power and risk management capability of franchisor plays critical role in successful franchising contract. Final decision to enter foreign country via franchising is determined by numerous factors like history, size, growth, competitiveness, management system, bonding capability, industry characteristics of franchisor. After deciding to enter into foreign country, franchisor needs to set entrance modes of international franchising. Within contractual mode, there are master franchising and area developing franchising, licensing, direct franchising, and joint venture. Theories about entrance mode selection contain concepts of efficiency, knowledge-based approach, competence-based approach, agent theory, and governance cost. The next step after entrance decision is operation strategy. Operation strategy starts with selecting a target city and a target country for franchising. In order to finding, screening targets, franchisor needs to collect information about candidates. Critical information includes brand patent, commercial laws, regulations, market conditions, country risk, and industry analysis. After selecting a target city in target country, franchisor needs to select franchisee, in other word, partner. The first important criteria for selecting partners are financial credibility and capability, possession of real estate. And cultural similarity and knowledge about franchisor and/or home country are also recognized as critical criteria. The most important element in operating strategy is legal document between franchisor and franchisee with home and host countries. Terms and conditions in legal documents give objective information about characteristics of franchising agreement for academic research. Legal documents have definitions of terminology, territory and exclusivity, agreement of term, initial fee, continuing fees, clearing currency, and rights about sub-franchising. Also, legal documents could have terms about softer elements like training program and operation manual. And harder elements like law competent court and terms of expiration. Next element in operating strategy is about product and service. Especially for business format franchising, product/service deliverable, benefit communicators, system identifiers (architectural features), and format facilitators are listed for product/service strategic elements. Another important decision on product/service is standardization vs. customization. The rationale behind standardization is cost reduction, efficiency, consistency, image congruence, brand awareness, and competitiveness on price. Also standardization enables large scale R&D and innovative change in management style. Another element in operating strategy is control management. The simple way to control franchise contract is relying on legal terms, contractual control system. There are other control systems, administrative control system and ethical control system. Contractual control system is a coercive source of power, but franchisor usually doesn't want to use legal power since it doesn't help to build up positive relationship. Instead, self-regulation is widely used. Administrative control system uses control mechanism from ordinary work relationship. Its main component is supporting activities to franchisee and communication method. For example, franchisor provides advertising, training, manual, and delivery, then franchisee follows franchisor's direction. Another component is building franchisor's brand power. The last research element is performance factor of international franchising. Performance elements can be divided into franchisor's performance and franchisee's performance. The conceptual performance measures of franchisor are simple but not easy to obtain objectively. They are profit, sale, cost, experience, and brand power. The performance measures of franchisee are mostly about benefits of host country. They contain small business development, promotion of employment, introduction of new business model, and level up technology status. There are indirect benefits, like increase of tax, refinement of corporate citizenship, regional economic clustering, and improvement of international balance. In addition to those, host country gets socio-cultural change other than economic effects. It includes demographic change, social trend, customer value change, social communication, and social globalization. Sometimes it is called as westernization or McDonaldization of society. In addition, the paper reviews on theories that have been frequently applied to international franchising research, such as agent theory, resource-based view, transaction cost theory, organizational learning theory, and international expansion theories. Resource based theory is used in strategic decision based on resources, like decision about entrance and cooperation depending on resources of franchisee and franchisor. Transaction cost theory can be applied in determination of mutual trust or satisfaction of franchising players. Agent theory tries to explain strategic decision for reducing problem caused by utilizing agent, for example research on control system in franchising agreements. Organizational Learning theory is relatively new in franchising research. It assumes organization tries to maximize performance and learning of organization. In addition, Internalization theory advocates strategic decision of direct investment for removing inefficiency of market transaction and is applied in research on terms of contract. And oligopolistic competition theory is used to explain various entry modes for international expansion. Competency theory support strategic decision of utilizing key competitive advantage. Furthermore, research methodologies including qualitative and quantitative methodologies are suggested for more rigorous international franchising research. Quantitative research needs more real data other than survey data which is usually respondent's judgment. In order to verify theory more rigorously, research based on real data is essential. However, real quantitative data is quite hard to get. The qualitative research other than single case study is also highly recommended. Since international franchising has limited number of applications, scientific research based on grounded theory and ethnography study can be used. Scientific case study is differentiated with single case study on its data collection method and analysis method. The key concept is triangulation in measurement, logical coding and comparison. Finally, it provides overall research direction for international franchising after summarizing research trend in Korea. International franchising research in Korea has two different types, one is for studying Korean franchisor going overseas and the other is for Korean franchisee of foreign franchisor. Among research on Korean franchisor, two common patterns are observed. First of all, they usually deal with success story of one franchisor. The other common pattern is that they focus on same industry and country. Therefore, international franchise research needs to extend their focus to broader subjects with scientific research methodology as well as development of new theory.