The science of mathematics education

The science of mathematics education involves inquiry in and study within the domains of curriculum, pedagogy, and evaluation. Skillful and accomplished mathematics teachers are knowledgeable of theoretical education philosophies and are able to put theory into practice by designing, delivering, and assessing learning experiences for all students.
Using the above preface of “theory-into-practice” as the focus and theme of your essays, please respond to any two of the following prompts:
1. Discuss the importance of teacher competence in the subject of mathematics and the understanding of facilitating active learning.
2. Discuss the importance of teacher responsibilities for managing a community of mathematics learners and monitoring effective strategies that engage learners.
3. Discuss the importance of reflective practices that provide opportunities for mathematics teachers to systematically assess the effects of their practice and experiences.
4. Discuss the importance of collaboration and collegiality of mathematics teachers as members of learning communities and as agents of social change.
Be sure to cite relevant literature, court cases, and expert opinion in your response as needed.