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Flipped classroom teaching at Clintondale High School in Michigan, United States. A flipped classroom is an instructional strategy and a type of blended learning.It aims to increase student engagement and learning by having pupils complete readings at home, and work on live problem-solving during class time. [1]
The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]
The Saxon Math 1 to Algebra 1/2 (the equivalent of a Pre-Algebra book) curriculum [3] is designed so that students complete assorted mental math problems, learn a new mathematical concept, practice problems relating to that lesson, and solve a variety of problems. Daily practice problems include relevant questions from the current day's lesson ...
A typical sequence of secondary-school (grades 6 to 12) courses in mathematics reads: Pre-Algebra (7th or 8th grade), Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs [3] while many complete high school without passing Calculus or Statistics.
Since the TIMSS publication of Singapore's high ranking in mathematics, professional mathematicians in the U.S. took a closer look at Singapore mathematics textbooks such as Primary Mathematics. [11] The term Singapore math was originally coined in the U.S. to describe the teaching approach based on these textbooks. [4]
Topics introduced in the New Math include set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra. [2] All of the New Math projects emphasized some form of discovery learning. [3] Students worked in groups to invent theories about problems posed in the textbooks.
Mathematics education reform built up momentum in the early 1980s, as educators reacted to the "new math" of the 1960s and 1970s.The work of Piaget and other developmental psychologists had shifted the focus of mathematics educators from mathematics content to how children best learn mathematics. [3]
Problem #6 at IMO 1988: Let a and b be positive integers such that ab + 1 divides a 2 + b 2. Prove that a 2 + b 2 / ab + 1 is a perfect square. [8] [9] Fix some value k that is a non-square positive integer. Assume there exist positive integers (a, b) for which k = a 2 + b 2 / ab + 1 .
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