Questions tagged [intuition]
The intuition tag has no summary.
53 questions
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How should we address students’ persistent misconceptions that conflict with their explicit mathematical reasoning?
In a recent philosophical paper, Michiel Esseling critiques the view that desires are simply beliefs about reasons for action by pointing to recalcitrant desires desires that persist even when someone ...
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Translating Intuition Into Rigor: Motivating The Proof Of A Result From Topological Vector Spaces
I have seen many students struggling with the concept of topological vector spaces. They get stuck with the proofs of quite trivial results even though they feel it is true. However, the main problem ...
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Is there an intuitive explanation for the properties of Pascal's triangle?
Pascal's triangle has two properties which are very interesting, but for which I have no "intuitive" explanation. If we list out Pascal's triangle by computing "n choose k" for ...
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Literature on mathematical intutiion
Is there any literature on mathematical intuition?
I would like to read the following, for example.
How to train intuition?
How to test intuition?
user24421
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Overcoming Dyslexia and Building Intuition
I am 25 and have been studying mathematics on my own for several years, but I am still between the middle and high school levels.
My main weakness is my dyslexia. I sometimes forget words or confuse ...
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How can we explain intuitively the convergence and divergence of these two series?
It is known that $\displaystyle\sum_1^{\infty} \frac{1}{n^{1.000001}}$ converges while $\displaystyle\sum_{n\text{ is a prime number}}\frac{1}{n}$ diverges. Though we can logically prove these results,...
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Are these explanations of variance and covariance intuitive?
When tutoring, I try to simplify concepts. I came up with these examples to explain the intention behind variance and covariance. Could you please help me find conceptual, pedagogical or mathematical ...
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What are some ways that one can progress from stage 2 to stage 3 of the rigor stages that Terry Tao has described?
Terry Tao describes 3 stages of one's mathematics education on his web blog.
1: Pre-rigorous
2: Rigorous
3. Post-rigorous
I know how one can progress from stage 1 to stage 2 (this simply can be done ...
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"Rough subitising / estimation" for better intuition and ability to apply arithmetic
tl;dr: Why do so many students have poor intuition of numbers, and
what can be done about it?
$$$$
I've always been good with numbers. As a maths tutor, one of the things I notice is how poor the ...
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How do we explain to a little child that a date in 2020 and a date in 2021 are not necessarily a year apart?
I talked with my friend on December 29 2020. Then I talked with him again on January 03, 2021.
Q: What was the year when you last talked with your friend?
A: 2021.
Q: And what was the year the ...
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Replacement for the Pac-Man grid analogy
To most people, a torus is a donut-like shape. Topologists like to describe the torus differently: you start with a square, and "identify opposite sides". We can imagine gluing together one ...
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Intuition explanation about Lebesgue measure zero of the rational numbers [closed]
This is a question about the intuition of the rational number having measure zero. Let us consider followng proof:
Let $I = [0,1]$ and $Q = \mathbb Q \cap I$ and let $\lambda$ be the Lebesgue measure. ...
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Intuition or geometry for Partial Fractions
When teaching partial fractions, there's probably no way to escape the heavy algebra necessary for partial fractions, but I'm wondering how to introduce the idea in a way that is intuitive or ...
user13544
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How to naturally encounter the properties of identity, commutativity, associativity, and distributivity (to define rings)?
(Cross posted at MSE: https://math.stackexchange.com/questions/3742948/how-did-we-isolate-the-properties-of-identity-commutativity-associativity-and)
In elementary school, I remember learning about ...
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How to intuitively understand how the trig ratios are calculated
I've asked a question on Math Stack Exchange, but it was suggested it might be a better idea to post it on this Educators instead.
Here's the question link:
https://math.stackexchange.com/questions/...
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