# All Questions

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398 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 ...
115 views

### Should the limits of one system of elementary set theory be the limits of a student's mathematical world? [closed]

In teaching elementary set theory, suppose we refrain from emphasizing historical decisions that were made in theory construction. Is there a danger that students may see the mathematical language ...
192 views

### Kid, 8 years old, developed a new calculation algorithm [closed]

I have a kid, 8 years old. The boy has phenomenal math skills. When he was 6 he was solving fractions with roots, writing Fibonacci series and much more. Now he developed a new calculation algorithm ...
313 views

### Proving basic Theorems and properties in high school [closed]

Why high school teachers do not emphasize knowing the proofs of properties and theorems in math. In my 40 years of teaching prospective high school teachers, I rarely found students who can derive ...
105 views

### Finding an error in a partial integration [closed]

There must be an error in this partial integration but I do not see it. Do you see it?
74 views

### Where can I find the partial order relation of prerequisites of undergraduate courses in the United States?

Let $A$ be the set of all undergraduate mathematical courses in the US and define a binary relation $\leq$ on $A$ such that for elements $a,b\in A$ (that is, $a$, $b$ are undergraduate mathematical ...
156 views

### Could students be taught the concept of rational numbers the same way as in the Formal construction section of the Wikipedia article rational number?

Link to article cited in title, Wikipedia rational number. According to this answer, some students 14-18 are still struggling to understand fractions. Maybe some students know how to perform the ...
102 views

### When a geometrical figure a special case of another [closed]

Squares are special types of rectangles. Are circles special types of ellipses/ovals? Are cones special types of pyramids? I guess the answer is no because of the 2D basis: circles are not special ...
119 views

### symmetry of a square - is it possible pure geometric approach in didactics? [closed]

Consider a square : four points in a plane constructed with classical means (compass and straightedge). Since no point is different from others (no coordinates, no labels...) it seems that we can not ...
102 views

### What are the uses of calculus in every day life? [closed]

Can anybody say me what is differentiation and integration and what is the use of these ?
82 views

### How do I solve this ratio problem? [closed]

Here is the problem: If Bill takes 3 hours to paint a room and James takes 5 hours to paint a room, how long will it take to paint a room if they work together? Show your working. Thank You.
299 views

### Inefficient methods

I see many teachers use slow methods to solve a given problem where there's another faster methods that doesn't demand much more effort. I'm not looking for mistakes like saying that $a$ is the slope ...
60 views

### Relational understanding for a specific topic

I want to aproach the undertanding of the trigonometric function based on the concept of relacional undertanding, but I have problems to came up with and problemic situation for it. I mean I don´t ...
180 views

### What is the best way of introducing set theory? [closed]

The students are aware of mathematical logic and proof but have not come across any of the notions of a set. What is the most natural and motivating way to introduce set theory?
619 views

### How can I convince my brightest student of Cantor's theory?

At the end of the mathematical high-school education I usually introduce the easiest facts of set theory: counbtability and Cantor's proof as the basis of modern mathematics. Now my brightest student ...
171 views

### Why focus on GCD and LCM, not LCD or GCM? [closed]

Introductory Number Theory courses, and even in high school, focus on GCD and LCM. Why don't we learn more about Lowest Common Divisor and Greatest Common Multiple?
172 views

### A role for a non-symmetric equality relation in teaching mathematics? [closed]

First, I will simply observe that it seems to be standard practice, in elementary set theory, to define relations to be sets of ordered pairs. If we had the option of introducing a "symmetric ...
281 views

### Missing Step in Most Proofs of the Irrationality of $\sqrt{2}$ [closed]

Numerous online resources parrot the usual proof by contradiction of the irrationality of $\sqrt{2}$. These all rely upon the assumption that the rational form (say, $a/b$) is in its simplest ...
247 views

Has learning through doing repetitive exercises and mechanical non-creative exercises been researched and analysed sufficiently for College and University level courses? Have there been surveys and ...