For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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0
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2answers
183 views

How to calculate profit share for this example [closed]

How can we calculate a profit share for Rs. 100,000 that remained in an account for 5 days only. See this question illustration below I was confused about which tags were more appropriate for ...
5
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1answer
206 views

Explain/illustrate Goedel's theorems and possible implications to non-mathematicians

I am asked to give a talk about (a) mathematical practice, (b) axiomatization, (c) Gödel's theorems and (d) possible antimechanist arguments based on the incompleteness theorems (as mentioned in P ...
1
vote
1answer
179 views

Explain mathematical practice and axiomatization to non-mathematicians

I am asked to give a talk about (a) mathematical practice, (b) axiomatization, (c) Gödel's theorems and (d) possible antimechanist arguments based on the incompleteness theorems (as mentioned in P ...
6
votes
1answer
250 views

What is meant by “mathematical maturity”?

I have often heard people talk of "mathematical maturity", sometimes in the sense of the maturity required to understand an area of mathematics or in the approach to a problem or proof. However, it's ...
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4answers
264 views

Formality and mathematics

Why is it important to be formal in mathematics? Is formality beneficial for students? Or is it just to scare students away from mathematics?
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3answers
870 views

How do you validate that two math expressions are equal?

Let's say you have a few expressions like the following: $$\begin{array}((x+17)^2 \\ x^2 + 34x + 289 \end{array} \\ 288 + \frac{x^2}{2} + \frac{x^2}{2} + 34x + 1 \\ [...] $$ You get the idea: ...
3
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0answers
75 views

Math for kids with Cuisenaire rods

I work with kids and i am searching some cool stuff to do with Cuisenaire rods. Thinking about an application i thought that i can show to my students what will be the sum of first $N\in\mathbb{N}$ ...
4
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4answers
410 views

Showing How Prime Factorization Helps Solving Problems

I need some problems conceivable by middle school students, which are not easy to solve unless the prime factorization of some number is known. An example: It's not easy to know wheter $n$ can be ...
3
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2answers
102 views

Motivated and unmotivated mathematics courses [closed]

The standard calculus course does not acquaint the student with the reasons why calculus has been and continues to be important in the intellectual development of humankind. Rather, it attempts to ...
3
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1answer
237 views

What are the benefits or losses of learning real analysis through a constructivist approach instead of a standard apporach?

Recently I've found some courses on real analysis that use the constructivist approach and I got curious on some aspects: What are the benefits of learning through this approach? Is it ok to learn ...
1
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0answers
115 views

Convention on the order of scalar multiplication (Multiplier vs multiplicand)

Is there a convention on the order of scalar multiplication? I know there were questions before mine, but I would like to know if such distinction is culturally dependent. This came from a news in ...
0
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0answers
125 views

Question about limits [closed]

I am quite new on SE. I see a lot of question about integrals, series, limits. I am wondering if there is a limit to teachers (or textbooks) imagination in these areas.
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10answers
519 views

$2\times2$ matrices are not big enough

Olga Tausky-Todd had once said that "If an assertion about matrices is false, there is usually a 2x2 matrix that reveals this." There are, however, assertions about matrices that are true for ...
2
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0answers
60 views

Resources for Teaching High School Statistics

I am a student teacher looking for resources to teach high school Probability & Statistics (untracked). The second semester will be inferential statistics and will include these following topics: ...
6
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0answers
121 views

Educational software for graduate mathematics

Our university uses computer software to help automate and expedite the learning process for basic math classes (college algebra, trigonometry, precalculus, etc.). Software such as this provides ...
4
votes
1answer
133 views

Planning a mockup maths class for high school related to river reactivation

I have to plan a mockup maths lesson where the "main topic" should be river reactivation. The given suggestion is to focus on computing cross-sectional areas of rivers using basic geometry and for ...
2
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0answers
242 views

Dynamic Geometry Software for Straight-edge and Compass Constructions

Geogebra is a very good dynamic geometry software. It has so many default tools, e.g. parallel line, angle bisector, tangent to the circle, inscribed and circumscribed circles, etc. But I want the ...
2
votes
1answer
126 views

Describing the impossibility of trisecting the angle to high school students.

Does anyone have an idea on whether it would be possible to present the proof of the impossibility of trisecting the angle (or doubling the cube, for example) in order to demonstrate the power of ...
0
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3answers
352 views

Practical context for a quadratic equation with negative discriminant.

I'm looking for practical questions that lead to quadratic equations with negative discriminant. The pupils involved are 16 years old and technically educated. Abstract mathematic questions are ...
3
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1answer
107 views

Fair Division: Making the Differences in Players' Valuations Believable

When teaching basic fair division algorithms, the students always propose some simple and (at the first glance) correct solutions for $n$ players, which unfortunately are not correct! The only way I ...
4
votes
4answers
324 views

Hilbert's Hotel and Infinities for Pre-university Students

Hilbert's paradox of the grand hotel is a fun and exciting ground to base a talk on the set theoretic concept of infinity for interested students - even in middle- and high school. However, it does ...
8
votes
1answer
262 views

Learning Mathematics in a Second Language

My first language is English, and since all of my formal education has been undertaken in the USA, I have learned mathematics entirely in the English language. However, I have spent a fair amount of ...
4
votes
2answers
716 views

Prison problem: locking or unlocking every $n$th door for $ n=1,2,3,…$

I have a problem called "The Prison Problem" that I need to explain to my 9-year-old cousin. I would think that he has just started learning about divisors and perfect squares, and as such, I have a ...
8
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4answers
403 views

What's the deal with integration?

So at uni we learned tricks and techniques for integration until cows came home. But to what end? Any/All definite integrals can be evaluated using numerical methods. Most integrals in application can ...
0
votes
1answer
112 views

Are Parabolas similar intuitively?

All parabolas are similar, but are they all similar in that it is just a question of 'zooming in and out' intuitively speaking? It seems that there should therefore be on all parabolas a curve from ...
3
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2answers
472 views

Good at abstractions bad with numbers

Ever since I had an interest in math I was aware that what I'm good at and what really pulled me was the abstract thinking. My intuition for even the simplest number related concepts (modulo ...
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0answers
84 views

A question on mathematical writing.

One of the problems I am grading this week is as follows: Given a simply connected bounded domain $\Omega$ on $\mathbb{R}^{2}$, prove that there exist a line that separates it into two parts of equal ...
3
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1answer
314 views

Basic Fourier Series Question

Let $f$ be a $2π$ periodic function where $$f(x) = \frac{π - x}2$$ over $[0, π]$. It is known that the Fourier series of $f$ is $$\sum_{n=1}^{\infty}\frac{\sin nx}n$$ At which points in $[-π, π]$ ...
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3answers
97 views

Mean Value Theorem Motivation

I am currently practicing presenting mathematics to various audiences and am considering the example of the mean value theorem. I was wondering how would I be able to motivate this theorem to a ...
2
votes
1answer
205 views

Motivations for Prime Factorizaton

I'm at the beginning of some middle school math sessions on divisors, gcd, lcm, and prime numbers. It's the first place in the curriculum that the students encounter the three latter concepts ...
2
votes
2answers
121 views

Pre Algebra Text book or online

I have a kid who just started middle school. I would like to introduce them to pre algebra. I would like her to know the fundamental concepts. Just like "What is mathematics" book, if there is a book ...
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3answers
31 views

significant figure representation?

I was wondering: Why does $1.30 \times 10^3$ have $3$ significant figures while $1300$ has $2$ significant figures (they are both the same number) Why is that distinction ? When should I use ...
20
votes
1answer
626 views

Learning Math Efficienctly and Succeeding in Grad School

I'm currently a second year Ph.D. student studying pure math. I've recently come to the conclusion that I must be studying wrong. Actually, more to the point, I must be thinking about mathematics ...
3
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3answers
909 views

Minimizing perimeter given rectangle's area for 10-years-olds

I was recently in touch with some person from Russia how is busy with books for Russian elementary schools, in particularly I learned that now they give elementary set theory for the 2nd grade ...
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4answers
544 views

Is $\tan\theta\cos\theta=\sin\theta$ an identity?

A friend of mine, who is a high school teacher, called me today and asked the question above in the title. In an abstract setting, this boils down to asking whether an expression like "$f=g$" is ...
9
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2answers
358 views

Why do we want probabilities to be *countably* additive?

In probability theory, it is (as far as I am aware) universal to equate "probability" with a probabilistic measure in the sense of measure theory (possibly a particularly well behaved measure, but ...
7
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2answers
1k views

Explaining Hypercomplex numbers to Children.

Imagine a highschool freshman walks up to you and asks you what hypercomplex numbers are. Explain to her, in a fair amount of detail, the different types of hypercomplex numbers in a way that any ...
1
vote
3answers
292 views

Roadway and book recommendations to math study.

I had some calculus, linear algebra and complex analysis courses back in college. But it is not comprehensive. And I felt that my college math was not taught in a logical sequence (maybe because my ...
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0answers
441 views

What are some good ideas in teaching combinations and permutations

I am a student teacher trying to brainstorm some effective lesson plans for combinations and permutations for a high school statistics course. My master teacher has decided that he will introduce ...
2
votes
1answer
115 views

Why do we need primitive roots?

What is the most motivating way to introduce the order of a modulo n? Apart from simplifying powers of residues is there any other use of the order? Are there any examples which have a real impact on ...
1
vote
1answer
388 views

Parabola & Area Proving (Integral)

This is not a homework question. I am a new teacher (just graduated) and a student asked me this question. The points $A(3,9)$ and $B(-2,4)$ lie on the parabola $y=x^2.$ The line $y=x+6$ joins $A$ ...
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0answers
3k views

What are some strong algebraic number theory PhD programs? [closed]

I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...
1
vote
0answers
141 views

Help in mathematical combinatorics.

Hi guys I am studying for my exam which is in a few hours and I ran into two past exam problems. Questions: 1) how many 7 letter sequence you can make with a,b,c such that there is at least one b ...
2
votes
0answers
173 views

About the raised negative sign in some basic textbooks

In a math document recently (a UK A level test paper from the EdExcel board), I noticed that the negative/minus sign was raised and aligned to the top of the number. I'm interested to know whether ...
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0answers
61 views

Who made now part of the problem?

Who came up with the meme of putting the current year as a four digit number into exercise problems? Is there a known first historical account?
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20answers
3k views

Good math bed-time stories for children?

What are some good references/books/articles from which to derive some good bed-time math stories to pique a child's interest in math? I am fascinated by math (used to hate it as a kid) and want my ...
2
votes
0answers
571 views

The NES mathematics accreditation test

I have to take the NES mathematics test to get accreditation as a High School teacher to become highly qualified to teach mathematics. I have a PhD in physics so I thought that I wouldn't have to ...
2
votes
3answers
53 views

Commutativity or Distributivity - Which One to Use to DEFINE Multiplication of Negative Numbers?

It's easy to calculate $3 \times (-4)$, using the meaning of multiplication: $3 \times (-4)=(-4)+(-4)+(-4)=-12$. But it's not the case about $(-4)\times 3$! To DEFINE $(-4)\times 3$ we can choose ...
2
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1answer
233 views

Book about Tensor Product of Vector Spaces

This subject is very commun for any book about modules. However, some undergraduate majors have Linear Algebra course before the Abstract Algebra one (where we treat about modules) and it is not ...
76
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22answers
7k views

Is math built on assumptions?

I just came across this statement when I was lecturing a student on math and strictly speaking I used: Assuming that the value of $x$ equals <something>, ... One of my students just rose ...