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.

learn more… | top users | synonyms (3)

2
votes
1answer
107 views

How to solve this Mystery with Mathematics

I read a mystery in a book but I can't solve it with Mathematics. The mystery is: "I have tripled my nephew's age, and 5 years ago I have 5 times from his twin brother age. What is my age now?" In ...
0
votes
3answers
111 views

Baloney detection kit for Math

There are folks who claim they proved Fermat's Last Theorem, Riemman Hypothesis offering no more than a half a dozen pages (sometimes one or two pages) of proof, very few if any citations of previous ...
16
votes
3answers
458 views

which exact integration techniques belong in a first year calculus/analysis course?

At our university we are now discussing changes to the course contents and there is some heated discussion regarding integration in the first year calculus courses. Currently, the techniques of exact ...
1
vote
1answer
63 views

How Should the First Sessions of an Undergrad. Course Be?

Form a teaching perspective, the first sessions of an undergraduate mathematics course are of a great importance. They can make clear the aims of the course, and point out to the main problems and ...
4
votes
1answer
91 views

Natural discontinuities

As I stare at a cube-shaped building whose side has length $100$ meters, while walking westward parallel to its north wall at a location $100$ meters north of the building, the distance to farthest ...
1
vote
2answers
828 views

Math Riddles #10 - Car Meter Riddle

Today my car meter reads as 72927 kms. I notes that this is a palindrome. How many minimum kms I need to travel so my car meter find another palindrome?
3
votes
1answer
73 views

Figuring out deficiencies in math education.

I'm mostly self-taught and while I know (and use) many advanced mathematical topics, I often enough find holes in my understanding of lower level math. Is there an exam (or series of exams) I could ...
2
votes
1answer
137 views

What is the contribution of group theory to topology?

An answer for a question on MathOverflow.net which asked for some recommendations on textbooks for books in topology received the following comment: "It's a great book to introduce applied ...
1
vote
1answer
64 views

What are some helpful pre-requisites/hints/encouragement for going through Theodore Frankel's “Geometry of Physics” in a self-study?

I plan on working through "Geometry of Physics" by Frankel. I keep on running into little snags here and there, and I am wondering if that's just part of the process, or whether I am ill-prepared. ...
1
vote
0answers
109 views

Why are hyperbolic trigonometric functions avoided in (my) high school and early post-secondary school?

I remember seeing hyperbolic trigonometric functions (sinh, cosh, tanh, etc.) in my precalculus textbook back in high school and see them today in my calculus textbook. However, I have not had a ...
10
votes
2answers
309 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
47 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 ...
8
votes
1answer
673 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 ...
7
votes
4answers
261 views

How do I convince someone that $\mathbb{R}^2$ and its copy inside $\mathbb{R}^3$ are different?

One of my friends is taking a first course in linear algebra now, and one of the problems on his latest homework was to explain why $\mathbb{R}^2$ and $\{(a_1,a_2,a_3) \in \mathbb{R}^3 \mid a_3 = 0\}$ ...
5
votes
4answers
8k 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 ...
9
votes
1answer
346 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, ...
-2
votes
3answers
143 views

What is trigonometry? [closed]

I am going to learn trigonometry next year. I am an advanced student and I like to get a head start on things. So, How do you describe and introduce Trigonometry to the advanced secondary school ...
10
votes
1answer
440 views

How often should math students take day breaks and longer breaks or vacations? Any research?

John Edensor Littlewood wrote in page 197 of Littlewood's Miscellany "For a week without teaching duties - and here I think I am preaching to the converted - I believe in on afternoon and the ...
58
votes
19answers
18k views

How do I convince my students that the choice of variable of integration is irrelevant?

I will be TA this semester for the second course on Calculus, which contains the definite integral. I have thought this since the time I took this course, so how do I convince my students that for a ...
5
votes
4answers
2k 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 this in an 'optimal' and innovative way. And my question is: What should the teacher know ...
2
votes
0answers
143 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
2answers
158 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
65 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
266 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 ...
49
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 ...
13
votes
6answers
2k views

Self studying math, how can I learn the most?

I am currently studying Pre-Calculus on my own. I have a few texts I am working with but feel like I could learning a lot more than I am. When people typically ask these kind of questions the common ...
0
votes
1answer
1k 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 ...
2
votes
1answer
89 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 ...
2
votes
2answers
942 views

Fundamental theorem of linear algebra

When I studied linear algebra we (our books, our professors) used to call Fundamental theorem of linear algebra the theorem that says: Fundamental theorem of linear algebra: A linear ...
0
votes
1answer
41 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
290 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 ...
12
votes
1answer
1k views

Teaching engineers mathematical thinking skills

In my experience, many introductory engineering mathematics textbooks these days tend to skip proofs and discuss logic only in the context of digital electronics. On the other hand, I can imagine that ...
6
votes
3answers
422 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. $x^{- 3} y^2$ $c^2 d^{-5}$ ...
20
votes
5answers
1k 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 ...
6
votes
2answers
3k 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
433 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 ...
130
votes
31answers
13k 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
216 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 ...
11
votes
3answers
1k views

Why study metric spaces?

Most universities have a 3rd year undergraduate analysis course in which metric spaces are studied in depth (compactness, completeness, connectedness, etc...). However, in practice it seems that most ...
8
votes
6answers
699 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
104 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
75 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 ...
1
vote
2answers
225 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 ...
269
votes
33answers
34k 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
1k 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 ...
1
vote
0answers
63 views

Studies on how the wording employed on the explanation of mathematical concepts helps students to learn?

I remember that I had to learn division in my childhood, I could handle all the other mathematical concepts that were presented until then but division was a real pain to learn, somehow the idea of ...
3
votes
1answer
324 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 ...
62
votes
24answers
13k 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
3answers
358 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
76 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 ...