Describe in your own words the main arguments that Piaget made regarding the nature of cognitive development [not just the “stage” idea], including a brief overview of the stages and the processes involved in knowledge acquisition and in moving from one stage to the next. (*Note: you don’t need to go through and describe the characteristics of all of the stages of development in detail here.) Then, briefly explain, specifically, how instruction (defined loosely, in any type of learning situation) would differ depending on the stage of cognitive development of the learner, with a specific example of learners in one of the specific stages. After evaluating the research evidence and criticisms that have been raised regarding various claims of Piaget, which of his claims do you think is the most “controversial” or detrimental to his theory in terms of not being supported? Cite specific research findings (from the textbook, or another source if you wish) to back up your argument. *One full page response*Textbook:Driscoll, M. P. (2005).Psychology of learning for instruction. Needham Heights, MA: Allyn and Bacon 3rd edition.
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′′