Abstract: Teaching - learning Mathematics in school assume mastering and the use of mathematical language. It is made up of the natural language of the spoken language (of teachers and students) plus a series of mathematical signs and symbols, but also a series of specific propositions. In this paper we will present two fundamental concepts of mathematical language; namely, the theorem and the definition respectively. Thus, we will present here, all types of mathematical propositions (direct, reciprocal, contrary and reciprocal of the contrary or contrary of the reciprocal), which if true become theorems (direct, reciprocal, contrary and reciprocal of the contrary or contrary of the reciprocal). Regarding the concept of definition, we will refer to its two component parts (the proximate genus and the specific difference) and to the two types of definitions (natural and / or artificial). Finally, we will analyze and exemplify the concept of theorem of characterization. We will exemplify all this with propositions / theorems from Algebra, Mathematical Analysis and Geometry.

Abstract: This study examined the nature and difference of STEM career choice among international college students in the U.S., by using Baccalaureate and Beyond Longitudinal Study (B&B: 08/12). STEM and Non-STEM differences among gender, race/ethnicity, SAT scores, STEM credits, STEM GPA, annualized salary in 2009 and 2012, and hours worked per week were examined. Results indicated a significant difference in STEM credit earned among international college students. Recommendations for future research on STEM career choice among international students were discussed.

Abstract: Service-learning programs often involve multiple stake holders and generate intended main effects as well as unanticipated spillover impacts. While evaluations aiming at a single aspect of impact and focusing on a single stage of a service-learning program can be informative and valuable in answering isolated questions, they often fail to provide a complete picture to fully capture the multifaceted effects that a service learning program can generate in the process and at the end. This proposal describes an effective 360° evaluation of a service-learning tutoring program in teacher education at a research university by following Stuff lebeam’s context, input, process, product (CIPP) model. The process and advantages of the 360° evaluation during the context, input, process, product evaluation is described and discussed. The 360° evaluation using the CIPP model is systematic and can help researchers strive toward a more holistic appraisal of service-learning programs.

Abstract: Leadership is a fundamental factor required to enhance the instructional quality of teachers. Teacher leaders possess excellent class management skills and are more capable of driving students toward academic success. In the current body of work, limited studies have focused on the impact of teacher leaders on student learning, while having leadership responsibilities inside the classroom. The purpose of this study is to explore in depth the entire concept of teacher leadership in the classroom and its relationship to student performance and achievement. The study involves a synthesis of evidence in education literature that describes the concept of teacher leadership and student performance. The findings reveal that teacher leaders, whether outside or within the classroom, are driven by the desire to improve student learning. Students taught by teacher leaders have a high probability of succeeding academically compared to those under non-leader educators.

Abstract: African American females have been cited as viable options to fulfill positions in the STEM workforce. Given the need for prepared individuals in STEM and the projected increase of minorities representing a large portion of the U.S. population by 2050, African Americans remain a strong talent. Even with this information, the literature is limited regarding female African American community college transfer students' STEM experiences in the HBCU environment. With HBCUs educating many Americans in STEM and a large population of African American women in the community college environment, this population's voices are essential to the community college and HBCU environments. Utilizing Triple Quandary Theory and Jackson-Smith’s Model of STEM Education, Preparation and Career Exploration, this study explores community colleges' role in preparing African American female community college transfer students in STEM from the community college to the HBCU environment. Implications are provided based on the overall results of this study.

Abstract: The COVID-19 pandemic fast-tracked digital education implementation plans for many higher educational institutions and academic staff around the world. In Europe, academics (n=43) from 5 countries, participated in a training programme designed to teach them how to effectively design, deliver and evaluate online study-units. This paper presents a mixed methods evaluation of this programme. Upon analysis of the formative and summative surveys’ Cronbach’s alpha were respectively 0.942 and 0.987 u with statistical significance set at p<0.05. Qualitative data from surveys and semi-structured interviews corroborated these positive results. The necessity of accelerating the online instructional paradigm points to the requirements for administrative backing and durable educational technology. This infrastructure supports intentional development of education and training for academic staff that in turn ensures the quality of students’ online educational experiences. In presenting an evaluation of a course for online teaching, this paper is relevant to educators seeking to develop or enhance indicated support and training for academic staff.

Abstract: In recent years, Tanzania has been experiencing increasing in number of SMEs business in rural areas particularly in areas where Rural Electrification Programs (REA) have been well implemented. These programs are always associated with low connecting costs which attract many households to use the energy. This study examined the effects of rural electrification programs to the SMEs’ performances measured in revenues collected by these SMEs. The study was done in Mvomerodistrict, Morogoro. The Ordered Logistic Regression (OLR) model was employed in the data analysis. Tests suchas Oparallel and Brant were used to assess the assumptions of parallel lines. Findings on the determinants of electrical adoption reveals that 59.385 percent of SMEs’ owners who have higher revenues adopt electricity while education influence on the electrical adoption among SMEs’ owner is only 8.29 percent. Moreover, findings on the effects of rural electrification programs on SMEs’ performances shows that distance to the nearby transformer, willingness to pay for REA, affordability of the REA programs and adoption of the REA energy among SMEs increase SMEs performances significantly. Consequently, the government is advised to ensure that, through policies and other regulatory roles that rural SMEs get growing up. This can be done if these rural SMEs are enabled to solicit credits from financial facilities to expanding their businesses and making beneficial utilization of REA services. The economic outcome, through multiplier effects in employment creation and subjective economic welfare, might be tremendous.