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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Rote learning is widely used in the mastery of foundational knowledge.Examples of school topics where rote learning is frequently used include phonics in reading, the periodic table in chemistry, multiplication tables in mathematics, anatomy in medicine, cases or statutes in law, basic formulae in any science, etc.
An artificially produced word problem is a genre of exercise intended to keep mathematics relevant. Stephen Leacock described this type: [1] The student of arithmetic who has mastered the first four rules of his art and successfully striven with sums and fractions finds himself confronted by an unbroken expanse of questions known as problems ...
The NCF 2005 serves as a guideline for syllabus, [1] textbooks, and teaching practices for the schools in India. The NCF 2005 [ 2 ] has based its policies on previous government reports on education, such as Learning Without Burden [ 3 ] and National Policy of Education 1986–1992, [ 4 ] and focus group discussion. [ 5 ]
Just-in-time teaching promotes active learning by using pre-class questions to create common ground among students and teachers before the class period begins. These warmup exercises are generally open ended questions designed to encourage students to prepare for class and to elicit student's thoughts on learning goals.
The effectiveness of traditional instruction and passive learning methods have been under debate for some time. [2] The modern origins of progressive education, with active learning as a component, can be traced back to the 18th century works of John Locke and Jean-Jacques Rousseau, both of whom are known as forerunners of ideas that would be developed by 20th century theorists such as John Dewey.
Socratic questioning (or Socratic maieutics) [1] is an educational method named after Socrates that focuses on discovering answers by asking questions of students. According to Plato, Socrates believed that "the disciplined practice of thoughtful questioning enables the scholar/student to examine ideas and be able to determine the validity of those ideas". [2]
Inquiry-based learning (also spelled as enquiry-based learning in British English) [a] is a form of active learning that starts by posing questions, problems or scenarios. It contrasts with traditional education, which generally relies on the teacher presenting facts and their knowledge about the subject.