Mathematical maturity often refers to the mastery of the way
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
s think, operate and communicate. It pertains to a mixture of mathematical experience and insight that cannot be directly taught. Instead, it comes from repeated exposure to mathematical concepts. It is a gauge of mathematics students' erudition in
mathematical structure
In mathematics, a structure on a set (or on some sets) refers to providing or endowing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the ...
s and methods, and can overlap with other related concepts such as mathematical intuition and mathematical competence. The topic is occasionally also addressed in literature in its own right.
Definitions
Mathematical maturity has been defined in several different ways by various authors, and is often tied to other related concepts such as comfort and competence with mathematics, mathematical intuition and mathematical beliefs.
One definition has been given as follows:
A broader list of characteristics of mathematical maturity has been given as follows:
Finally, mathematical maturity has also been defined as an ability to do the following:
[A Set of Mathematical Equivoques](_blank)
Ken Suman, Department of Mathematics and Statistics, Winona State University
It is sometimes said that the development of mathematical maturity requires a deep reflection on the subject matter for a prolonged period of time, along with a guiding spirit which encourages exploration.
Progression
Mathematician
Terence Tao has proposed a three-stage model of
mathematics education
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out Scholarly method, scholarly research into the transfer of mathematical know ...
that can be interpreted as a general framework of mathematical maturity progression. The stages are summarized in the following table:
[Numberphile2. (2017, March 18). Terry Tao and “Cheating Strategically” (extra footage) - Numberphile ideo YouTube. https://www.youtube.com/watch?v=48Hr3CT5Tpk]
See also
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Logical intuition
*
Four stages of competence
References
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Mathematics and culture
Skills
Literacy