The visual arts are art forms that create works that are primarily visual in nature, such as ceramics, drawing, painting, sculpture, printmaking, design, crafts, photography, video, filmmaking and architecture. These definitions should not be taken too strictly as many artistic disciplines (performing arts, conceptual art, textile arts) involve aspects of the visual arts as well as arts of other types. Also included within the visual arts are the applied arts such as industrial design, graphic design, fashion design, interior design and decorative art.
The current usage of the term "visual arts" includes fine art as well as the applied, decorative arts and crafts, but this was not always the case. Before the Arts and Crafts Movement in Britain and elsewhere at the turn of the 20th century, the term 'artist' was often restricted to a person working in the fine arts (such as painting, sculpture, or printmaking) and not the handicraft, craft, or applied art media. The distinction was emphasized by artists of the Arts and Crafts Movement who valued vernacular art forms as much as high forms. Art schools made a distinction between the fine arts and the crafts maintaining that a craftsperson could not be considered a practitioner of the arts. The increasing tendency to privilege painting, and to a lesser degree sculpture, above other arts has been a feature of Western art as well as East Asian art. In both regions painting has been seen as relying to the highest degree on the imagination of the artist, and the furthest removed from manual labour - in Chinese painting the most highly valued styles were those of "scholar-painting", at least in theory practiced by gentleman amateurs. The Western hierarchy of genres reflected similar attitudes.
Recreational mathematics is an umbrella term for mathematics carried out for recreation, self-education and self-entertainment, rather than as a fully serious professional activity. It often involves mathematical puzzles and games.
Many problems in this field require no knowledge of advanced mathematics and recreational mathematics often attracts the curiosity of amateur mathematicians, inspiring their further study of the subject.
In mathematics, the look-and-say sequence is the sequence of integers beginning as follows:
To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. For example:
In mathematics, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts in a developmentally appropriate, hands-on and an experiencing way. Mathematical manipulatives are used in the first step of teaching mathematical concepts, that of concrete representation. The second and third step are representational and abstract, respectively.
In the United States, prior to the late 1980s, manipulatives and student collaboration were nonexistent in elementary math classes. After 1989, due to a decision by the National Council of Teachers of Mathematics (NTCM), more creativity began to emerge in these elementary schools. This creativity took the form of manipulatives that modeled the addition, subtraction, multiplication, and division students used to have to memorize from practice.