Questions related to the teaching and learning of mathematics.

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8
votes
2answers
136 views

How to introduce category theory to a high school audience?

I am a mathematician with background in Category Theory. I have been asked to give a 20 minute talk about my area of research to an audience of talented high school students and school mathematicians ...
-1
votes
1answer
21 views

Get sides of triangle with only angle as given?

Can someone tell me how to get the sides of triangle(opposite,adjacent and hypotenuse) if i only have an angle as given? I got the angle by getting using atan2(y-y,x-x); Now i want to get the sides ...
5
votes
1answer
185 views

What pure mathematics foundations should an applied mathematician have?

I'm studying mathematics, with some statistics also, and I've always chosen applied courses. I'm getting to the point where I'm studying 3rd year undergraduate to graduate level material. My first ...
5
votes
4answers
290 views

Why study quadrilaterals?

My niece is in the 10th grade, and they have to do lot of theorems related to quadrilaterals. And, I was surprised to know that they have to learn by rote some theorems. This has made her feel that ...
8
votes
1answer
176 views

Darboux's Integral vs. the “High School” Integral

The definition of the integral below is what I usually call the "High School definition," because that's usually where I've seen it in use. Take a partition $\Delta = \{ x_0, x_1, x_2, \ldots, ...
0
votes
1answer
76 views

Should i continue trying or am i just not good enough [closed]

You've probably seen many of these, and i'm sorry to create another one but i'm at loss. I want to be a programmer at some point in my life (just finishing highschool) I want to go to university ...
6
votes
4answers
335 views

Teaching irrational numbers?

I'm interested in teaching the irrational numbers to high-school students, and I need your ideas on how to do in an 'optimal' and innovative way. And my question is: What should the teacher know ...
2
votes
0answers
64 views

Exercises or courses to improve logical rigor and reasoning skills

There is plenty of math that is beautiful without needing much explanation of theory, such as fractals, geometric patterns and the Game of Life, that may interest beginners in mathematics. However, if ...
0
votes
0answers
23 views

What does typed and character mean?

Sometimes while I'm on the website I see stuff like simply typed lambda calculus, or "characters". What does this mean and where can I learn about that stuff? Thanks in advance
-1
votes
2answers
122 views

Is Math like a Language? [closed]

This is a sincere question, Is math like a language where after a certain period in one's life, he or she can't get good at it? I feel once someone reaches a particular age, he just loses to ability ...
0
votes
2answers
58 views

Question about secant and cosecant.

Ok so if we take a right triangle and consider an angle $\alpha$ we get the following: From here we can define the fundamental trigonometric functions sine and cosine where ...
2
votes
0answers
41 views

What is a sound curriculum for exponent rules in freshman algebra in high school?

We all know the the rules of exponents covered in freshman algebra. The question is, what is the best way to approach these topics as most 9th graders struggle in this area? I work as an after school ...
2
votes
2answers
78 views

Explaining how to simplify a quotient with negative exponents?

I work as an after school tutor at my high school. I've had kids come up to me asking how to do these types of problems: $\left(\displaystyle \frac{5xy^{-2}}{3z^{-1}} \right)^{-2}$ My approach is ...
0
votes
0answers
29 views

Different fields of work in different fields of mathematics?

I'd like to get some insight into what sorts of jobs one can expect from the different branches of mathematics degrees. The B.sc. degrees I am familiar with are: Pure mathematics. Applied ...
44
votes
8answers
1k views

How to maintain enthusiasm and joy in teaching when the material grows stale

I recently finished my third semester of teaching calculus to freshman college students. This means I was drawing the same pictures, solving the same example problems, and discussing the same ...
0
votes
1answer
81 views

Line Drawing Using Bresenham Algorithm

Indicate which raster locations would be chosen by Bersenham’s algorithm when scan converting a line from screen co-ordinates (1,1) to (8,5). First the straight values (initial values) must be found ...
0
votes
1answer
126 views

Puzzle of Probability Can give an idea …

A bird keeper has got $P$ pigeon, $M$ mynas and $S$ sparrows. The keeper goes for lunch leaving his assistant to watch the birds. Suppose $p=10, m=5, s=8$. When the bird keeper comes ...
-1
votes
1answer
128 views

Become a mathematician… again! [closed]

After reading the book "The 5 elements of effective thinking", I decided to start learning mathematics over again, just as I were a very beginner. This must help me to fill some gaps I have from my ...
2
votes
1answer
78 views

Philosophical side of MATH. knowing the path then walk it. [closed]

Can I find a book that gives me the purpose of theorems and definitions without going deep into proofs. It's just like knowing the path then walk it. That's will me the understanding reach the next ...
0
votes
1answer
120 views

Can any one help solving this puzzle of digits (Puzzle : Strike off any digit from each number in seven rows … )

Q) Strike off any digit from each number in seven rows (need not be at same place) and combine the same operations with 3 digit numbers to get the same addition. After this strike off another digit ...
0
votes
1answer
35 views

Standard deviation: When to use which sum-coefficient?

I'm wondering when to use $\sigma = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ and when to use $\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ which I have both seen in ...
0
votes
1answer
46 views

Relative Percentage vs Percentage Change

If I have a number say "500" and I say that it spiked 4 times (400%) of the original value i.e. "2,000". Does that make sense mathematically and grammatically because I'm talking about relative ...
0
votes
0answers
25 views

What do you want your children to learn? [closed]

Very unusual question here. Do those of you who have children in elementary school (age 6-10) think that memorization of mathematical facts is over-emphasized compared to concepts? It seems like math ...
6
votes
2answers
123 views

Teaching algebra in a culturally relevant way while fitting Common Core standards

I've been assigning algebra textbook and worksheet problems (from the publishers and my own) that look like this: Simplify the following expressions. $x^{- 3} y^2$ $c^2 d^{-5}$ ...
17
votes
5answers
477 views

$\epsilon, \delta$…So what?

Over the course of my studies I often encounter phrases in reference material of the type "and this avoids the need for using $\epsilon$, $\delta$ definitions" or "by this we can omit those ...
4
votes
2answers
377 views

Examples of open ended calculus “class project” ideas

I have instructed calculus I an II, each once, at the college level and would like to emphasize that math is not just about memorizing formulas and concepts for a test and that applied math is not a ...
2
votes
2answers
101 views

Examples of groups in the real world

I'm looking for some examples of groups in the real world to show students in a liberal arts math course. For example the Rubik's cube. Keep in mind these students have only a college algebra ...
114
votes
31answers
11k views

Stopping the “Will I need this for the test” question [closed]

I am a college professor in the American education system and find that the major concern of my students is trying to determine the specific techniques or problems which I will ask on the exam. This ...
6
votes
1answer
135 views

How to combat memorization

As a student in high school, I never bothered to memorize equations or methods of solving, rather I would try to identify the logic behind the operations and apply them. However, now that I've begun ...
7
votes
6answers
584 views

What we're never taught explicitly

I would like to make a complaint really. School math(s) can be the most boring way to learn: sitting down and rote learning binomial expansion or the volume of a cylinder is just not interesting. It ...
5
votes
3answers
84 views

Swapping Theorems with definitions

My question is motivated from the following passage of Gian-Carlo Rota's Indiscrete Thoughts, 'Suppose you are given two formal presentations of the same mathematical theory. The definitions of the ...
2
votes
1answer
46 views

Storytelling and Applied Narrative as a Teaching Tool

Is anyone integrating storytelling or applied narrative as a technique/methodology to help teach undergraduate mathematics-based course work? If so, how are you using it and from which sources are you ...
3
votes
4answers
465 views

Math is too hard for me. How can I make it easier?

I am trying to study, and I keep finding that math is hard (any kind), and it doesn't get easier(only harder). I am trying to learn these things all in progression (asynchronously): 1.Math for all ...
1
vote
2answers
98 views

Explaining the concept of $z$-scores in high school statistics

The students have so far studied the uniform probability distribution and have a working familiarity with relative frequency histograms and the 68-95-99.7 empirical rule. They still have trouble with ...
209
votes
32answers
30k views

Pedagogy: How to cure students of the “law of universal linearity”?

One of the commonest mistakes made by students, appearing at every level of maths education up to about early undergraduate, is the so-called “Law of Universal Linearity”: $$ \frac{1}{a+b} ...
1
vote
0answers
71 views

PERCENTAGE Problem

Q: Paulson spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%.Find the percentage increase in his savings . Sol: Let the original ...
3
votes
1answer
193 views

Math Shock in graduate program

People call it Culture shock but I call it Math Shock... let me explain my Problem... First I am graduate student in a good university in USA ( I get scholarship from my country). Before I lived in ...
55
votes
23answers
10k views

How would you explain to a 9th grader the negative exponent rule?

Let us assume that the students haven't been exposed to these two rules: $a^{x+y} = a^{x}a^{y}$ and $\frac{a^x}{a^y} = a^{x-y}$. They have just been introduced to the generalization: $a^{-x} = ...
4
votes
2answers
202 views

How can I explain my 9 years old brother that $8a\cdot4a \neq 64a$

My youngest brother had a pre-algebra test yesterday and he was asked to tell if two expressions are equal or not. We agreed on most of the things but on this one I find it hard to make him accept my ...
3
votes
0answers
64 views

Is there a link between level of abstraction and use of numbers?

One of my friend who stopped studying maths in high school told me once You study maths, can you help me fill my tax forms? In her mind, advancing in maths studies implied manipulating an ...
2
votes
1answer
40 views

Proving that there exists $w$ such that $4x < 6w < 6x$ and $\gcd(w,\frac{x\#}{6})=1$ where $x \ge 7$ and $x\#$ is the primorial

I am trying to show that for any integer $x \ge 7$, there exists $w$ with the following properties: $4x < 6w < 6x$ $\gcd\left(6w,\frac{x\#}{6}\right)=1$ I thought that this would be pretty ...
-1
votes
1answer
42 views

Learning way and Resource for Complete math Subject. [closed]

I want to learn [self learning] Mathematics from basic.What is the order [like 1) arithmetic,2) Geometry,Etc..] to learn the maths? and what is the best resource to that particular subject?
6
votes
2answers
81 views

Information on crucial results concealed as exercises or neglected in a textbook

First, where can students find lists, information, or resources on the crucial results, inequalities, theorems, etc... which a textbook might not explictly feature or even bring up at all? Second, ...
13
votes
2answers
509 views

A problem V.I. Arnold solved as a primary school student

According to a 1995 interview that Vladimir I. Arnold gave to the Notices of the AMS, his primary school teacher I.V. Morozkin gave in 1949 (when Vladimir I. Arnold was 12 years old) to a Soviet ...
12
votes
4answers
182 views

Scholarly work on the beauty of math

When reading mathematical books written for a general audience, or even searching questions on this site, the adjective beautiful is often used to describe mathematics. My question is whether there ...
3
votes
3answers
125 views

Learning math for physics

I am very interested in physics and am planning to self studying it. But for this I need to be mature in various areas of math. So I want to know what is the order in which I need to learn the math ...
3
votes
2answers
160 views

What's the right moment to learn Set Theory?

I've seen a question in which the OP asked when is the right moment to learn Category Theory, it seems this moment comes a little after a course of algebra, and indeed some books on abstract algebra ...
6
votes
1answer
119 views

Soft Question: Suggestions on mathematics resources for problem solving.

I'm doing my final year of under graduation through distance education and would be appearing for entrance tests for various graduate schools in a few weeks. I am looking for a database of ...
2
votes
3answers
102 views

On the nature of a first derivative

This is a very, very basic question. Never been very involved in math but I've been learning calculus in my free time, so here goes. I have observed some various things that happen with derivatives, ...
2
votes
2answers
98 views

Mclaurin on $\arccos(\frac{n^2-1}{n^2+1})$

I have expanded $\lim_{n\to \infty} \arccos(\frac{n^2-1}{n^2+1})$ to $\arccos(1-\frac{2}{n^2})$ and now i dont know what to do. I wrote the function on walfram alpha and he told me that the result is ...