This introductory book contains a rich collection of exercises and worked examples in Metric Spaces. Other than questions in the traditional setting, plenty of True-or-False type questions and open-ended questions are included. With detailed solutions, these are highly effective in helping students gain a bird's eye view and master the subject and pitfalls better. The presentation is clear in nurturing the mathematical insights and mathematical maturity of the readers.In this book, the pictorialization or visualization of abstract situations into simple pictures is very often crucially conducive to the understanding of the materials. This serves to give an insightful view of the intricate problems, as well as a clue or a direction to formulate rigorous arguments.The learning outcomes include:

The increasingly prevalent use of online- or blended-learning in schools universities has resulted in asynchronous online discussion forum becoming an increasingly common means to facilitate dialogue between instructors and students, as well as students and students beyond the boundaries of their physical classrooms. This proposed academic book contributes to the literature on asynchronous online discussions in the following three main ways: First, it reviews previous research studies in order to identify the factors leading to limited student contribution. Limited student contribution is defined as students making few or no postings, students exhibiting surface-level thinking or students demonstrating low-level knowledge construction in online discussions.It then identifies the various empirically-based guidelines to address the factors. Second, three potential guideline dilemmas that educators may encounter: (a) use of grades, (b) use of number of posting guideline, and (c) instructor-facilitation are introduced. These are guidelines where previous empirical research shows mixed results when they are implemented. Acknowledging the dilemmas is essential for educators and researchers to make informed decisions about the discussion guidelines they are considering implementing. Third, nine exploratory case studies related to student-facilitation and audio-based discussionare reported on and examined. Using students as facilitators may be an alternative solution to educators who wish to avoid the instructor-facilitation guideline dilemma. Using audio discussion would be useful for participants with poor typing skills or those who prefer talking to typing. The proposed book is distinctive in comparison to current competitor titles because all the findings and guidelines are empirically-based. Furthermore, the nine expanded case studies provided specifically address the issue of student/peer facilitation and audio-based discussion. Student/peer facilitation and audio discussion are two areas that hitherto received comparatively lesser attention compared to instructor facilitation and text-based discussion. "

This book discusses evidence-based practices related to the use of blended learning in both K-12 and higher education settings. Specifically, this book features evidence-based practices in relation to the following five learning goals: (a) Fostering students' attitude change toward country, (b) Helping students' solve ill-structured design task problems, (c) Improving students' critical thinking in assessing sources of information, (d) Improving students' narrative and argumentative writing abilities and (e) Enhancing students' knowledge retention and understanding. To achieve this aim, the authors draw upon their own research studies as well as some other relevant studies to reveal the pedagogical approaches, the specific instructional/learning activities, the technologies utilized and the overall framework for developing blended learning experiences.

The increasingly prevalent use of online- or blended-learning in schools universities has resulted in asynchronous online discussion forum becoming an increasingly common means to facilitate dialogue between instructors and students, as well as students and students beyond the boundaries of their physical classrooms. This proposed academic book contributes to the literature on asynchronous online discussions in the following three main ways: First, it reviews previous research studies in order to identify the factors leading to limited student contribution. Limited student contribution is defined as students making few or no postings, students exhibiting surface-level thinking or students demonstrating low-level knowledge construction in online discussions. It then identifies the various empirically-based guidelines to address the factors. Second, three potential guideline dilemmas that educators may encounter: (a) use of grades, (b) use of number of posting guideline, and (c) instructor-facilitation are introduced. These are guidelines where previous empirical research shows mixed results when they are implemented. Acknowledging the dilemmas is essential for educators and researchers to make informed decisions about the discussion guidelines they are considering implementing. Third, nine exploratory case studies related to student-facilitation and audio-based discussion are reported on and examined. Using students as facilitators may be an alternative solution to educators who wish to avoid the instructor-facilitation guideline dilemma. Using audio discussion would be useful for participants with poor typing skills or those who prefer talking to typing. The proposed book is distinctive in comparison to current competitor titles because all the findings and guidelines are empirically-based. Furthermore, the nine expanded case studies provided specifically address the issue of student/peer facilitation and audio-based discussion. Student/peer facilitation and audio discussion are two areas that hitherto received comparatively lesser attention compared to instructor facilitation and text-based discussion.