Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [education]

For math 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.

This tag is for questions that are primarily about mathematics, but are related to mathematics education. Also consider using the or the tag. On the other hand, questions that are primarily about teaching and learning mathematics would be a better fit for MathEducators.SE.

3357 questions
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Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain but are mathematically beautiful at the same time. Do you know…
RBS
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660
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164 answers

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's Lament," and found that I, too, lament the uninspiring…
Liz
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546
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37 answers

Do complex numbers really exist?

Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious and intuitive meaning. What's the best way to…
Neil Mayhew
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406
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33 answers

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”: $$ \frac{1}{a+b} \mathrel{\text{“=”}} \frac{1}{a} + \frac{1}{b} $$ $$ 2^{-3}…
Peter LeFanu Lumsdaine
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213
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15 answers

Identification of a quadrilateral as a trapezoid, rectangle, or square

Yesterday I was tutoring a student, and the following question arose (number 76): My student believed the answer to be J: square. I reasoned with her that the information given only allows us to conclude that the top and bottom sides are parallel,…
The Chaz 2.0
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207
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9 answers

"Advice to young mathematicians"

I have been suggested to read the Advice to a Young Mathematician section of the Princeton Companion to Mathematics, the short paper Ten Lessons I wish I had been Taught by Gian-Carlo Rota, and the Career Advice section of Terence Tao's blog, and I…
Dal
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205
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14 answers

How many sides does a circle have?

My son is in 2nd grade. His math teacher gave the class a quiz, and one question was this: If a triangle has 3 sides, and a rectangle has 4 sides, how many sides does a circle have? My first reaction was "0" or "undefined". But my son wrote…
Fixee
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185
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6 answers

What were some major mathematical breakthroughs in 2016?

As the year is slowly coming to an end, I was wondering which great advances have there been in mathematics in the past 12 months. As researchers usually work in only a limited number of fields in mathematics, one often does not hear a lot of news…
YukiJ
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185
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8 answers

Why is Euler's Gamma function the "best" extension of the factorial function to the reals?

There are lots (an infinitude) of smooth functions that coincide with $f(n)=n!$ on the integers. Is there a simple reason why Euler's Gamma function $\Gamma (z) = \int_0^\infty t^{z-1} e^{-t} dt$ is the "best"? In particular, I'm looking for…
pbrooks
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161
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31 answers

Stopping the "Will I need this for the test" question

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 is the typical "will this be on the test?"…
Wintermute
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160
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7 answers

Is Apple ipad / tablet good for mathematics students?

I am a math student. I'd like to find out if tablets (iPads, Galaxy Note 10.1) are worth the cost. How good are tablets for the purposes of reading textbooks as PDF and writing mathematics with a stylus? For writing math in TeX, it looked like the…
T. Webster
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155
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41 answers

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 this: Assume $(-x) \cdot (-y) = -xy$ Then divide both sides…
Sev
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151
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7 answers

Apparently sometimes $1/2 < 1/4$?

My son brought this home today from his 3rd-grade class. It is from an official Montgomery County, Maryland mathematics assessment test: True or false? $1/2$ is always greater than $1/4$. Official answer: false Where has he gone wrong? Addendum,…
SDiv
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148
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23 answers

The Best of Dover Books (a.k.a the best cheap mathematical texts)

Perhaps this is a repeat question -- let me know if it is -- but I am interested in knowing the best of Dover mathematics books. The reason is because Dover books are very cheap and most other books are not: For example, while something like…
Three
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147
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14 answers

Why do units (from physics) behave like numbers?

What are units (like meters $m$, seconds $s$, kilogram $kg$, …) from a mathematical point of view? I've made the observation that units "behave like numbers". For example, we can divide them (as in $m/s$, which is a unit of speed), and also square…
user377104
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