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Feb 1, 2022 · Based on a systematic literature review, we found that characterizations of definitions in the mathematics education literature can be classified into five main themes: requirements, preferred features, role and function, nature, and types of definition.
- Descriptive Accounts
- Normative Accounts
- Why Do Mathematicians Use Certain Definitions and Not Others?
In discussing how mathematics develops, metaphors are often used. Hacking (2014), for instance, discusses two metaphors that explain how mathematics grows and which concepts are studied: the butterfly model and the Latin model. According to the butterfly model, mathematics develops teleologically, like a caterpillar becoming a cocoon and then turni...
Several authors tacitly assume that valuable mathematics becomes part of the shared mathematical theories and mathematics with little to no value does not. Muntersbjorn (2003) discusses this relation explicitly. She argues that the history of mathematics is sometimes wrongfully portrayed as teleological: Earlier mathematics is developed to facilita...
An approach that addresses the value of definitions can be found in (Werndl 2009). Her main question is: “in what ways are definitions in mathematics justified, and are these kinds of justification reasonable?” (Werndl 2009, p. 313). Werndl argues that it is important to justify definitions, since unjustified ones are less meaningful to “us.” Note ...
Dec 17, 2023 · They reflect the understanding of mathematics at a particular time in history, by a particular community, and often by a single person. In this paper, 50 definitions are collected, classified,...
Apr 18, 2023 · Based on interviews with nine algebraists/category theorists, we characterize two mathematical values upheld through definitions: clarity in and for communication and freedom of choice in the use and writing of definitions.
Dec 1, 2014 · In the current work, we reviewed (1) how conceptual knowledge is defined in the mathematical thinking literature, and (2) how conceptual knowledge is defined, operationalized, and measured in three mathematical domains: equivalence, cardinality, and inversion. We uncovered three general issues.
- Noelle M. Crooks, Martha W. Alibali
- 2014
Nov 1, 2014 · In the current work, we reviewed (1) how conceptual knowledge is defined in the mathematical thinking literature, and (2) how conceptual knowledge is defined, operationalized, and measured in...
Jan 2, 2023 · What is a literature review? A literature review is a survey of scholarly sources on a specific topic. It provides an overview of current knowledge, allowing you to identify relevant theories, methods, and gaps in the existing research that you can later apply to your paper, thesis, or dissertation topic .
