Mathematical representations are visible or tangible productions such as diagrams, number lines, graphs, arrangements of concrete objects or manipulatives, physical models, mathematical expressions, formulas, and equations, or depictions on the screen of a computer or calculator (Goldin, Volume 14 Number 1, 2021 2014, p. 409).
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What does representation mean in math?
representation but also to construct, refine, and use their own representations as tools to support learning and doing mathematics. Through the middle grades, children's mathematical representations usually are about objects and actions from their direct experience. Primary school students might use objects to represent the number of wheels on
What is a mathematical representation of the physical world?
- Use of mathematics to model situations or events in the world;
- Explanations of how the complexity and interrelatedness of situations or events in the world are reflected in the model;
- Data generated by the model to make and defend a decision; and
- A decision or conclusion supported by the mathematics within the context of a global community.
What are representations in math?
Over time, they will work toward developing Common Core Standards for Mathematical Practice:
- CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
- CCSS.Math.Practice.MP4 Model with mathematics.
- CCSS.Math.Practice.MP5 Use appropriate tools strategically.
What is the theory of representation?
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example ...
What are examples of mathematical representations?
Examples of such conventional mathematical representations include base ten numerals, abaci, number lines, Cartesian graphs, and algebraic equations written using standard notation. In contrast, mathematical representations created on specific occasions by students are frequently idiosyncratic.
What is the meaning of mathematical representation?
Abstract. Mathematical representation is students' ability in expressing mathematical ideas in the form of drawings, mathematical equations, and words/written text. Mathematical representation is needed in solving mathematical problems.
What are the five mathematical representations?
The authors presented 5 types of representation: (1) representation of numerical forms; (2) graph representation; (3) verbal representation; (4) representation by symbols, including equations, expressions, algebraic formulas; (5) dual representation, consisting of two types of representation in the previous four forms.
Why is mathematical representation important?
Students' use of representations can help make mathematical ideas more concrete and available for reflection. In the lower grades, for example, children can use representations to provide a record for their teachers and their peers of their efforts to understand mathematics.