Due in 4 hoursDiscussion 1:Educational psychology serves as the bridge between theory and practice in our classrooms. Best practices in the classroom stem from the research and developed theories about how we learn and behave which is the driving force that guides how we teach, motivate, and assess our students. The research of educational psychology is what supports our continually improvement in what constitutes effective teaching and learning.In Chapter 1 of the text, Table 1.1 displays core INTASC principles that reflect the characteristics of a competent teacher. Be sure to use the text to support your response.Select two of the ten principles and discuss how you currently exhibit these principles. Why might the two selected principles be considered essential elements of teaching?Select two of the ten principles and discuss why they reflect areas of needed growth as you work towards becoming an educator. What will you do to improve these areas?Discussion 2: Cognitive Development Learning TheoriesHave you ever wondered how students learn? Well, there are many learning theorists that have proposed the process in which one acquires new knowledge and each one significantly contributes to the process of cognitive development. Read Chapter 2 of our text to gain a greater understanding of cognitive development that provides teachers with the knowledge of creating developmentally appropriate practices in the classroom. In analyzing the implications of cognitive development on student learning, choose one of the following questions:Describe Piaget’s answers for the primary biological questions he asked: How do children adapt? How can development be classified? Next, share whether or not you agree with Piaget. Then, describe the value for teachers in understanding Piaget’s Theory of Cognitive Development. Apply this to your own role as a future educator.Give an example of what is meant by Vygotsky’s zone of proximal development (ZPD). Explain how your example fully illustrates your understanding of ZPD. Also, describe at least two educational implications of this concept. Use the concept of scaffolding in your answer.Required ResourcesRequired TextLeFrançois, G. R. (2018).Psychology for teaching(2nd ed.). Retrieved from https://content.ashford.eduChapter 1: Psychology for TeachingChapter 2: Socioemotional and Cognitive DevelopmentArticlesCouncil of Chief State School Officers. (2011, April).Intasc model core teaching standards: A resource for state dialogue.Retrieved from http://www.ccsso.org/documents/2011/intasc_model_core_teaching_standards_2011.pdfRecommended ResourcesTextWoolfolk, A. (2013). Educational psychology (12th ed.). Boston, MA: Pearson
Obtain the general solution of the following DEs: i. y′′′ + y′′ − 4y′ + 2y = 0 ii. y(4) + 4y(2) = 0 iii. x(x − 2)y′′ + 2(x − 1)y′ − 2y = 0; use y1 = (1 − x) iv. y′′ − 4y = sin2(x) v. y′′ − 4y′ + 3y = x ; use y1 = e3x vi. y′′ + 5y′ + 6y = e2xcos(x) vii. y′′ + y = sec(x) tan(x)
Obtain the general solution of the following DEs: i. y′′′ + y′′ − 4y′ + 2y = 0 ii. y(4) + 4y(2) = 0 iii. x(x − 2)y′′ + 2(x − 1)y′ − 2y = 0; use y1 = (1 − x) iv. y′′ − 4y = sin2(x) v. y′′