Questions tagged [education]

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

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“Reverse thinking” exam questions-reference request

I am interested in exam questions that are "backwards" from how they are usually asked. For example: Brian and Megan have the following question on their exam: Find the volume of the solid ...
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Non-traditional math concepts for early education

I am currently working on source material for a math-related software project with my mother, who has a PhD in Elementary Education and specializes in math education. While she has quite a strong ...
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1answer
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Considering math or computer science

Let me start by saying I graduated High School in 2002 and have worked as a technician, a systems administrator, and a part time web developer up till now. I have started taking courses at community ...
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No radical in the denominator — why? [duplicate]

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to $\sqrt{3}...
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Most important elementary math skills [closed]

Barring very elementary arithmetic, which skills from elementary school are essential for understanding the world better?
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1answer
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Accounting Question: Computing margin of Safety Ratio

Smith Company produces desk lamps. The information for June indicated that the selling price was $\$25$ per unit, variable costs were $\$15$ per unit, fixed costs totaled $\$6,000$, and the margin of ...
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14answers
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How to effectively and efficiently learn mathematics [closed]

How do you effectively study mathematics? How does one read a maths book instead or just staring at it for hours? (Apologies in advance if the question is ill-posed or too subjective in its current ...
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10answers
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What is the (mathematical) point of straightedge and compass constructions?

The ancient discipline of construction by straightedge and compass is both fascinating and entertaining. But what is its significance in a mathematical sense? It is still taught in high school ...
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2answers
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Is there a online reference that chains mathematical knowledge from simple to complex?

I'm a very, very logical person -- but I've never taken any math classes; really, I know. So, on that note -- how do I teach myself math? As my question might suggest, I see the answer as being an ...
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5answers
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How to pick a thesis advisor?

This sort of question is probably in bad taste for math.stackexchange, but is probably in high demand. (I tried to start a site on Area 51 to house questions like this, but my request was closed due ...
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Popular general-interest math courses

I'm hoping the userbase here doesn't mind if I do a little crowd-sourcing. I'm curious to find out about popular general-interest mathematics or statistics classes that are offered universities that ...
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6answers
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How Do You Actually Do Your Mathematics?

Better yet, what I'm asking is how do you actually write your mathematics? I think I need to give brief background: Through most of my childhood, I'd considered myself pretty good at math, up ...
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Elementary Papers at ArXiv

Inspired by this question, at MO i am asking this question. Can anyone list some elementary articles at ArXiv which can be understood by High-School/Undergrad Students. I am asking this because, i ...
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When to learn category theory?

I'm a undergraduate who wishes to learn category theory but I only have basic knowledge of linear algebra and set theory, I've also had a short course on number theory which used some basic concepts ...
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3answers
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The elementary coordinate geometry of polynomials? Of rational expressions? Of radicals?

With a few colleagues, we're trying to design an (intermediate) algebra course (US terminology) where we stress the interplay between algebra and geometry. The algebraic topics we would like to cover ...
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21answers
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Mathematics problems for very young children?

This is a tall order, but since this site is for everything mathematical, here goes: What are some nice games/puzzles/problems/problem-like activities that would be appropriate for a three-five year ...
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3answers
571 views

Is there any physical analogy to explain multiplication by zero?

This is targeted for elementary kids. One way to think is that add any number to itself zero times... Just wondering if there is a better way...
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5answers
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Guidelines for learning about Ramanujan's work?

It is well known that one of the first books Ramanujan studied was "Synopsis of Pure and Applied Mathematics" and that it shaped the way Ramanujan thought and wrote about mathematics. Being interested ...
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how to explain that Prob[heads, tails] = 2 * Prob[heads, heads] to a student?

I throw two coins (simultaneously). A student (very much a beginner in both math and probability theory) thought that the following 3 outcomes are equally likely: "two heads", "two tails", "a head and ...
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4answers
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Preparing for the Mathematical Contest in Modeling

The Mathematical Contest in Modeling (MCM) is coming up in a couple of weeks. With the idea that the competition is ultimately about teaching students to become better at mathematical modeling, I was ...
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3answers
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Can a rule be formulated to explain this to 7 year old?

I'm trying to teach math to my 7 year old daughter. I'm teaching following type of equations. $$\cdots - x = y$$ I'm able to explain her the rule that: when $\cdots- x = y$, we can always take ...
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What is an intermediate definition for a tangent to a curve?

Most students come to calculus with an intuitive sense of what a tangent line should be for a curve. It is easy enough to give a definition of a tangent to a circle that is both elementary and ...
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2answers
483 views

For teaching: Combinatorial Construction Riddles

Can you give examples of combinatorial construction riddles, approachable by gifted high school students? Examples: Find a finite set $A$ and $B \subset 2^A$ such that any element of $A$ is covered ...
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1answer
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Best Practices for Learning Mathematics (especially in the classroom)

What study practices have led you to the best success in learning mathematics (or applied math, or theoretical CS) in the classroom (undergraduate/lower graduate level), especially in courses that ...
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5answers
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Fun math outreach/social activities

What are some great math social activities for students? I'm looking for things that bring people together with a "light" mathematical touch. The goal is to create a stronger mathematical community in ...
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1answer
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Some maps of the land of mathematics?

This question is motivated by a little anecdote. I was at home teaching some secondary school math to a relative. At some relax time, he glanced at a book I had over the table - it was some text about ...
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Differential Geometry of curves and surfaces: bibliography?

Dear all, next year, I will probably teach a one-semester course of Differential Geomtry of curves and surfaces. Its content must be something along the lines of the first four chapters of Do Carmo's ...
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Why do we need to prove $e^{u+v} = e^ue^v$?

In this book I'm using the author seems to feel a need to prove $e^{u+v} = e^ue^v$ By $\ln(e^{u+v}) = u + v = \ln(e^u) + \ln(e^v) = \ln(e^u e^v)$ Hence $e^{u+v} = e^u e^v$ But we know from basic ...
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Why is $\pi $ equal to $3.14159…$?

Wait before you dismiss this as a crank question :) A friend of mine teaches school kids, and the book she uses states something to the following effect: If you divide the circumference of any ...
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7answers
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Topic for a high school-level math elective?

I'm looking for ideas for a 15-hour mathematical enrichment course in a Chinese high school. What (fairly) elementary subject would you suggest as a topic for such a course? Background/considerations:...
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Need good material on multifractal analysis

I'm searching for some good reading material on multifractal analysis. Preferably something accessible that doesn't put the stress too much on mathematical proofs but rather on applications. As long ...
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1answer
669 views

How do you generate mathematical formulas programmatically using a server side language [closed]

We would like to generate simple mathematical formulas on the fly (e.g. $\sin^2 \theta$). The above function seems to be a MathJaX representation. Most of the solutions depend on writing mathematical ...
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3answers
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Research Experience for Undergraduates: Summer Programs (that accept non-American applicants)

There are many summer research programs in the United States, targeted at good motivated undergraduate students majoring in mathematics. The main aspects that characterize such programs are: (a) a ...
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What is the meaning of the third derivative of a function at a point

(Originally asked on MO by AJAY.) What is the geometric, physical, or other meaning of the third derivative of a function at a point? If you have interesting things to say about the meaning of the ...
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4answers
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What are or where can I find style guidelines for writing math?

I am a scientist writing my first manuscript with a substantial amount of mathematical methodological documentation. I am using LaTeX, but this is not my question. I would like to find a list of ...
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1answer
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Geometry or Topology

So, I am a graduate student who is certain that he does not want to do analysis (I think...). What are the most exciting fields in mathematics right now? It seems to me that very generally, they are ...
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9answers
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Motivating implications of the axiom of choice?

What are some motivating consequences of the axiom of choice (or its omission)? I know that weak forms of choice are sometimes required for interesting results like Banach-Tarski; what are some ...
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2answers
532 views

about math in general

I wanted to ask these questions here, feeling that this place place is without doubt is better than anywhere else, feeling hesitant and shy to ask such question. For several reasons, the environment ...
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3answers
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I would like to buy references in order to review and study mathematics [closed]

I am an ESL learner and most of the time I am able to understand English but In my courses, we don't study mathematics, and I think that it is a mistake or wrong. 1-What are really the best sources (...
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1answer
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Mathematics Graduate Student Summer Opportunities

I am currently a mathematics graduate student at Western Kentucky University in Bowling Green, KY. I am looking for some kind of summer opportunity to participate in during summer 2011. Does anyone ...
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Quotient geometries known in popular culture, such as “flat torus = Asteroids video game”

In answering a question I mentioned the Asteroids video game as an example -- at one time, the canonical example -- of a locally flat geometry that is globally different from the Euclidean plane. It ...
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Common misconceptions about math

YARFMO (Yet another reposting from Mathoverflow) ;-) The more you know about math the more you find conceptions previously thought correct to be false: 1.) math is not as exact as many believe - in ...
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Books that develop interest & critical thinking among high school students

I heard about Yakov Perelman and his books. I just finished reading his two volumes of Physics for Entertainment. What a delightful read! What a splendid author. This is the exact book I've been ...
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4answers
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Which discussion board is good for homework questions? [closed]

I'm a CompSci university student and i want some help for my math questions. Therefore i am looking for a good discussion board for math homework questions. I don't know any (good), because I come ...
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40answers
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Why is negative times negative = positive?

Someone recently asked me why a negative $\times$ a negative is positive, and why a negative $\times$ a positive is negative, etc. I went ahead and gave them a proof by contradiction like so: Assume ...
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How do I explain 2 to the power of zero equals 1 to a child

My daughter is stuck on the concept that $$2^0 = 1,$$ having the intuitive expectation that it be equal to zero. I have tried explaining it, but I guess not well enough. How would you explain the ...
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10answers
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Motivating infinite series

What are some good ways to motivate the material on infinite series that appears at the end of a typical American Calculus II course? My students in this course are generally from biochemistry, ...
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6answers
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Why Doesn't This Series Converge?

I am teaching a Calc II course and came across the following series when finding the interval of convergence for the Taylor series of $f(x)=\sqrt{x}$ centered at $x=1$: $$ \sum_{n=2}^\infty \frac{1\...
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7answers
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Best Cities for Mathematical Study

This may sound silly, but... Suppose an aspiring amateur mathematician wanted to plan to move to another city... What are some cities that are home to some of the largest number of the brightest ...
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14answers
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False beliefs in mathematics (conceptual errors made despite, or because of, mathematical education)

Over on mathoverflow, there is a popular CW question titled: Examples of common false beliefs in mathematics. I thought it would be nice to have a parallel question on this site to serve as a ...