In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal (e.g., mental construct) and external (e.g., graph).
Multiple representations include graphs and diagrams, tables and grids, formulas, symbols, words, gestures, software code, videos, concrete models, physical and virtual manipulatives, pictures, and sounds.
[citation needed] Some representations, such as pictures, videos and manipulatives, can motivate because of their richness, possibilities of play, use of technologies, or connections with interesting areas of life.
[4] Tasks that involve multiple representations can sustain intrinsic motivation in mathematics, by supporting higher-order thinking and problem solving.
[1] These multiple representations arise when each student uses their knowledge base and experience—to create a visualization of the problem domain on the way toward a solution.
Instead of only emphasizing computational skills, multiple representations can help students make the conceptual shift to the meaning and use of, and to develop algebraic thinking.
In part, it reads [10] "Instructional programs should enable all students to do the following: While there are many representations used in mathematics, the secondary curricula heavily favor numbers (often in tables), formulas, graphs and words.
Spreadsheet software such as Excel, LibreOffice Calc, Google Sheets, is widely used in many industries, and showing students the use of applications can make math more realistic.
There are currently 159 different activities available, in many areas of math, including numbers and operations, probability, geometry, algebra, statistics and modeling.
There are concerns that technology for working with multiple representations can become an end in itself, thereby distracting the students from the actual mathematical content.
[citation needed] Additionally, it is also objected that care should be taken, so that informal representations do not prevent students from progressing toward formal, symbolic mathematics.