What is Mathematics? A Pedagogical Answer to a Philosophical Question

By Guershon Harel, B. Gold, Roger A. Simons. 2009

151 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Experimental and Cognitive Psychology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5f7dbccaa85a33ef6a7d4a37e23e23a9ec436738

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Guershon Harel

In Experimental and Cognitive Psychology

1. Guershon Harel
2. Annie Selden
3. Todd D. Cadwalladerolsker

In Mathematical Physics

1. Guershon Harel
2. Todd D. Cadwalladerolsker

Citations in the corpus

• A DNR perspective on mathematics curriculum and instruction. Part II: with reference to teacher’s knowledge base (2008, background): “Seldom do students see an intellectual purpose for the latter method—to solve quadratic equations and to derive a formula for their solutions—rendering completing the square problems alien to most students (see Harel, 2008a for a discussion on a related way of thinking: algebraic invariance).”
• What Do We Mean by Mathematical Proof (2011, background): “Harel [24] describes proving as an example of a mental act, and defines the result of a mental act as a way of understanding.”
• MATHEMATICAL HABITS OF MIND (2009, background): “institutionalized ways of understanding, which is a collection of established definitions, axioms, theorems, proofs, problems, and solutions that have been accepted by the mathematical community; and (b) the second is a collection of ways of thinking, which are conceptual tools that are useful for t”