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Questions tagged [philosophy-of-maths]

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votes
3answers
316 views

Why's math more complicated to understand than philosophy? [closed]

Why's math more abstruse, perplexing than philosophy? This feels true, as intelligent laypeople can understand unsolved philosophy problems and competing possible solutions, but can't understand or ...
7
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1answer
156 views

Native language, writing, and mathematical problem solving

This question is meant to explore the intuition that mathematical thought does not most naturally proceed from writing in one's native language. The hackneyed and not entirely satisfying slogan that ...
11
votes
3answers
418 views

Why is modulo not an elementary operation?

Like it is just as primitive as makes intuitive sense in a way similar to division. I feel like teaching 4th graders the modulo function would complement learning division extremely well, as it helps ...
15
votes
0answers
785 views

Is metacognition ever bad?

Metacognition seems pretty universally positive. I'm wary of viewing it as such. Aside from the obvious criticisms like "you can't learn to ride a bicycle by thinking about and writing a 200 page ...
14
votes
1answer
227 views

Impact of philosophy of mathematics upon effectiveness of instructor

Is there any research out there on how an instructor's philosophical beliefs about mathematics might affect some aspect of his or her impact as a teacher? My intended meaning of 'impact' is broad, ...
9
votes
3answers
327 views

Why is Distribution Prioritized Over Combining?

In every algebra (or basic analysis) book that I've seen, three properties of real numbers are taken as axiomatic: commutativity, association, and distribution of multiplication over addition [$a(b + ...
12
votes
2answers
331 views

Mathematics and the hermeneutic circle

Many students, teachers and parents view problems as confrontational. Many students develop a self concept in mathematics based on failed attempts to easily win such confrontations. This leads me to ...
14
votes
3answers
395 views

Calculation versus writing in mathematics

Writing mathematics is an important activity of the mathematician. In trying to write one's mathematics, one finds ways to balance intuition and rigor and to efficiently communicate concepts and ideas ...
7
votes
1answer
185 views

Answering the Diversity Question for Mathematics Instructor Applications

As I apply for several other colleges who are hiring part time math teachers, I find myself wondering about this question as it is asked on ALL college instruction applications. Some of the questions ...
17
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6answers
656 views

What is a number?

In a set theoretic point of view all mathematical objects are sets. We "call" some of them as numbers (e.g. sets in $\mathbb{N}$, $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, $Ord$, $Card$) but what is ...