Questions related to the teaching and learning of mathematics.

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0
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1answer
41 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 ...
45
votes
8answers
2k 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
313 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
152 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 ...
2
votes
1answer
83 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
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1answer
37 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
148 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
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0answers
29 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
186 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. $x^{- 3} y^2$ $c^2 d^{-5}$ ...
19
votes
5answers
590 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 ...
5
votes
2answers
613 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
141 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 ...
116
votes
31answers
12k 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
162 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 ...
8
votes
6answers
631 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
89 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
54 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 ...
4
votes
5answers
1k 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
119 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 ...
223
votes
33answers
31k 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
149 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
220 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 ...
56
votes
24answers
11k 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
220 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
69 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
43 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
45 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?
7
votes
2answers
98 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, ...
14
votes
2answers
619 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 Arnold was 12 years old) to a Soviet classroom, most ...
12
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5answers
207 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 ...
2
votes
3answers
161 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 ...
2
votes
2answers
186 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
135 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
104 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
111 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 ...
2
votes
3answers
127 views

Difference between school mathematics and university (real) mathematics [closed]

Several people I know were good in mathematics when they were in high school and they loved it but when they joined a university (specializing in mathematics) they felt mathematics is hard and that ...
2
votes
0answers
105 views

Book an undergraduate should read [closed]

I know this question is heavily opinion-based, but I'm not searching for one perfect answers, I just want some advice from people with some experience in maths (I hope the question will not be closed ...
3
votes
0answers
92 views

Learn enumerative combinatorics? [closed]

I am interested in becoming proficient in enumerative combinatorics relatively quickly. I want to be able to look at a problem briefly and think of multiple different useful approaches to it. Any ...
0
votes
2answers
989 views

How to learn calculus for beginners? [duplicate]

As a precalculus student interested in teaching myself calculus, where should I start and how should I go about learning? This question is different than past questions as I am not solely interested ...
13
votes
3answers
344 views

Being mathematically critical: how should a student approach statements that appear to be obvious?

Very occasionally, I will read or hear a theorem, and think: isn't that obvious? Not in a contemptuous "I can immediately see how to prove this" way, but rather in a "I would have thought this was ...
2
votes
4answers
294 views

How would you create a math class that centers on the cultural experiences of African American and Latino students [closed]

I need to write a paper on "Ethnocentric Mathematics" and I have no idea what kind of effective teaching strategies are available. We read an article from this scholar named Tate who explained that in ...
12
votes
1answer
341 views

How do you remember theorems?

I am currently a Master's student in math. I do very well in my classes, understand the material, can do the proofs w/o having to read the text, etc, but as time passes, I find that I will forget ...
8
votes
6answers
699 views

Up-to-date advice on the best way to take notes (maths)

I have read some old discussions about this topic and would like to get some up-to-date advice if possible. I'm going to start university next year (maths), and I know how important is to have a set ...
1
vote
1answer
117 views

Reform of math symbols for high school texts

I am looking for references to papers and resources related to reforming math symbols for introductory courses at middle or high school level. Pointers to other forums also welcome. Eidt: For ...
14
votes
11answers
689 views

Maths at university [closed]

Next year I'm going to start university (maths, obviously), and would like to ask you (I suppose you're mathematicians or, at least, people who studied maths somehow) some advice: what did you learn ...
11
votes
1answer
187 views

How can I raise my intuition in solving mathematical problem?

I am an undergraduate student studying some elementary calculus and statistics. In my honor calculus class, my professor gave one of final exam problem: $$\lim_{n \to \infty} \int_{[0,1]^{n}} ...
2
votes
2answers
489 views

Most effective order for learning different branches of mathematics. [closed]

So, I'm just a current student with a lot of interest in mathematics. Usually I am on the site looking at the questions and most of them are about things I can't currently comprehend. As I would like ...
9
votes
1answer
68 views

Education: Reading Proofs

I am finishing my undergraduate degree and one thing I've noticed is how little weight has been placed upon the ability to read proofs, in basically all of my math courses. In first year calculus you ...
3
votes
2answers
110 views

Motivation for abstractness

I'm seeking examples of concepts or theorems in school mathematics that are better understood when we generalize (when we deal with a more abstract concept where the former concept is a special case ...
5
votes
2answers
114 views

Books that develop ideas through tough problems?

I want examples of books that advance by first posting a hard problem, one that would be very difficult without a given idea and then proves this idea and the power of the idea by solving the problem. ...