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What is mathematics#

See also: teaching-mathematics, what-do-mathematicians-do

Boaler (2015) sees the "the heart of the math problems we face in education" as being "the wide gulf between real mathematics and school mathematics"

Mathematics and Numeracy#

Definitions offered by the maths-in-schools course - Mathematics

"...is the study and science of numbers, shapes, space, patterns and symbols and the ways of manipulating them"

  • Numeracy

    "...is the ability to understand, recognise and apply mathematics concepts and skills to everyday life"

  • Connection between the two

    "Numeracy development is supported by mathematical understanding as students make connections between the real-world and mathematical concepts"

Roger Antonsen - Hidden secret to understanding the world#

TED Talk which suggests mathematics is

  • Finding patterns
  • Representing patterns
  • Making assumptions
  • Doing cool stuff

Which translates into mathematics helps you change perspectives to deepen understanding

Mathematics is a language that helps use represent things and helps us understand patterns.

Understanding something really deeply has to do with the ability to change your perspective

An equation is showing two different perspectives of the same thing.

every mathematical equation where you see the equality sign, it's an analogy between two things dn you're expressing that in a language

Uses many visual and aural example to illustrate.

Views to explore#

Thanheiser & Melhuish (2023) offer numerous possible definitions

  • apprenticeship into the discipline of mathematics - the one they use.
  • mathematics as contextual, every present, as a language to make sense of the world (Ani, 2021)
  • as a verb, a human activity, part of one's identity (Aguirre et al, 2013; Gutierrez, 2018)

Hersh (1999)#

In a book titled What is Mathematics Really (1999) suggests that it is

questions that drive mathematics. Solving problems and making up new ones is the essence of mathematical life. If mathematics is conceived apart from mathematical life, of course it seems - dead.

Boaler (2015)#

But mathematics, is a subject full of uncertainty; it is about explorations, conjectures and interpretations, not definitive answers

Devlin (1997)#

As the science of abstract patterns, there is scarcely any aspect of our lives that is not affected, to a greater or lesser extent, by mathematics; for abstract patterns are the very essence of thought, of communication, of computation, of society, and of life itself.

Mathematics is a cultural phenomenon; a set of ideas, connections, and relationships that we can use to make sense of the world. At its core, mathematics is about patterns. We can lay a mathematical lens upon the world, and when we do, we see patterns everywhere; and it is through our understanding of the patterns, developed through mathematical study, that new and powerful knowledge is created.

References#

Boaler, J. (2015). Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. John Wiley & Sons, Incorporated.

Thanheiser, E., & Melhuish, K. (2023). Teaching routines and student-centered mathematics instruction: The essential role of conferring to understand student thinking and reasoning. The Journal of Mathematical Behavior, 70, 101032. https://doi.org/10.1016/j.jmathb.2023.101032