# Mathematics and Art

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Mathematics and art are two areas of knowledge that demonstrate different degrees of interaction between critical and creative thinking. Whether considering mathematics or art, creative thinking evaluates a new or original idea containing some degree of value. Critical thinking examines assumptions and challenges a current belief or theory that has previously assumed to be true. Although general assumptions and creativity may be considered separately when considering extreme examples of concrete ideas and abstract ideas, the interplay of critical and creative thinking is one method in which new and validated knowledge is attained.

Mathematics is an area of knowledge that may seemingly appear to be concrete, utilizing reason as its source of knowledge. On one hand, mathematics represents learned concepts using a repetitive procedure and logic that will rarely deviate. Beginning concepts of mathematics taught in schools are concrete with fixed steps and formulas for solving problems. For example, the properties of addition, subtraction, multiplication, and division yield fixed answers. Students only have to use the steps previously taught and accept them to be true to attain the correct response. Therefore, concrete concepts can only be accepted as true by using learned skills to process and generate information and belief. However, without some degree of understanding or context, the use of the skills as a repetitive “exercise” is not critical thinking because it has no meaning.

It is accepted that the area of a right triangle is one half the base times the height. Reasoning can be used through the drawing of a grid and counting the squares to verify this formula. In this way, mathematics uses critical thinking to guid...

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...ture, for example, buildings, bridges, and structures are taller, more energy efficient, and able to utilize previously impossible designs because the interplay of critical thinking and creative thinking has yielded new techniques. These three fields each utilize mathematics and art to generate the latest knowledge.

Knowledge can be generated through the interaction of critical and creative thinking. Critical and creative thinking are both needed in different ways to create new ideas that are verifiable and credible. Ideas and interpretations that have been generated through advancements in math and the arts demonstrate that both critical thinking and creative thinking are needed to generate new knowledge. As a result, the questioning of established beliefs along with the creation of new ideas will yield beneficial knowledge to the world and its learners.