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The zone of proximal development for each student, or cohort of students, sets exercises at a level of difficulty that challenges but does not frustrate them. Some comments in the preface of a calculus textbook [4] show the central place of exercises in the book:
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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]
However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school (grades 9 to 12, for students typically aged 14 to 18), while seventeen states and the District of Columbia require four. [2]
Quiz bowl (quizbowl, [1] scholars' bowl, scholastic bowl, academic bowl, academic team, academic challenge, etc.) is a family of quiz-based competitions that test players on a wide variety of academic subjects.
An example is the function that relates each real number x to its square x 2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. The input variable(s) are sometimes referred to as the argument(s) of the function.
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