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Curricula that support starting from conceptual understanding, then developing procedural fluency, for example, AIMS Foundation Activities, [6] frequently use multiple representations. Supporting student use of multiple representations may lead to more open-ended problems, or at least accepting multiple methods of solutions and forms of answers.
In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions. Usually instructors prepare students with worked examples: the exercise is stated, then a model answer is provided. Often several worked ...
In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of ...
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
All Kumon programs are pencil-and-worksheet-based, with a digital program that started in 2023. The worksheets increase in difficulty in small increments. [9] [10] Psychologist Kathy Hirsh-Pasek says that using such techniques for 2 to 12-year-olds "does not give your child a leg up on anything". [7] One study has observed a high percentage of ...
Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. [127]