16 votes

Imbuing a six year old with a sense of mathematical wonder

I remember being excited about the following at a young age. If you add consecutive numbers you get triangle numbers. Triangle numbers are fun. If you put two consecutive triangle numbers together ...
  • 6,937
15 votes

Imbuing a six year old with a sense of mathematical wonder

How about: Numbers go the other way, too (negative) You can cut numbers in half, forever What if you cut a number into three pieces? 1 million is a thousand thousands (100 is ten tens) If you don't ...
  • 251
15 votes

Mnemonics for some properties in mathematics

Recently, a student in my beginning algebra course offered the following to the class, regarding signed number multiplication: Assuming positivity is like love, and negativity is like hate, then... "...
  • 7,703
11 votes

Mnemonics for some properties in mathematics

The minimax theorem states the following: Let $X\subset \mathbb{R}^{n}$ and $Y\subset \mathbb {R} ^{m}$ be compact convex sets. If $ f:X\times Y\rightarrow \mathbb {R} $ is a continuous ...
  • 702
11 votes

Mnemonics for some properties in mathematics

I tell students to visualize $<$ and $>$ as mouths. They always want to eat the bigger number.
10 votes

What are some great books for exploring mathematics? (not kids' books and not textbooks)

I highly recommend Paul Lockhart's Measurement
  • 895
10 votes

Mnemonics for some properties in mathematics

Fatou's Lemma states: for nonnegative measurable functions $f_n$, $$ \int_E \liminf_{n\to\infty} f_n\;d\mu \le \liminf_{n \to \infty}\int_E f_n\;d\mu $$ The mnemonic is $$ \text{ILLLLLI}, $$ meaning "...
  • 6,418
9 votes

The impact of dyslexia on learning mathematics, and available resources

I think the short answer to your question is that you are (like many people) confusing the arithmetic that you called 'mathematics' at school with the mathematics that mathematicians do. I very rarely ...
  • 5,576
7 votes

Imbuing a six year old with a sense of mathematical wonder

There is a great old Disney short called Donald Duck in Mathmagic Land. As well as being delightfully drawn in the traditional Disney style, it contains lots of useful and occasionally surprising ...
6 votes

Imbuing a six year old with a sense of mathematical wonder

Below are some great and inspiring books by an excellent mathematician. (In the Really Big Numbers book, on the page where counting by tens is discussed there is an inspiring error (?)…Big Bird is ...
  • 5,857
6 votes

Imbuing a six year old with a sense of mathematical wonder

The earlier question, "Teaching a very enthusiastic and bright 5 year old" could help. Building and manipulating shapes enhances geometric imagination. Consider polydrons, or snap-cubes:   ...
5 votes

Imbuing a six year old with a sense of mathematical wonder

Arranging counters into groups (multiplication and division), so arranging 12 counters into 6x2, 3x4 etc, and realising that there are some numbers that cant' be arranged, no matter how hard you try (...
5 votes

Imbuing a six year old with a sense of mathematical wonder

Another book, to add to @Jon Bannon's list, that my 4 year old daughter and I can recommend is Introductory Calculus For Infants. We also seem to discuss Graham's number a bit after watching the ...
  • 151
5 votes

What are some great books for exploring mathematics? (not kids' books and not textbooks)

For more mathematical philosophy try: "Godel, Escher Bach" by Douglas Hofstadter This is a great book for exploring mindset when approaching natural mathematical problems. Many problems are entirely ...
5 votes

Entertaining and fun books about mathematics for (basically) liberal arts students

I'll suggest the book Flatland by Edwin A. Abbott. It's an interesting read about geometry and thinking in a higher dimension. The downside is that this book is, well, antiquated to put it nicely. ...
  • 4,462
4 votes

What are some great books for inspiring children to explore mathematics?

In addition to your excellent list on your own site, I would add: The Grapes of Math by Greg Tang and illustrated by Harry Briggs Each page has a picture puzzle described in rhyme, where the goal is ...
4 votes

Imbuing a six year old with a sense of mathematical wonder

Just to complete the list of books. Some time ago I read The Number Devil and liked very much. I think it is the proper book for your needs as the argument shows how a "math devil" shows math concepts ...
4 votes

What are some great books for exploring mathematics? (not kids' books and not textbooks)

How to Lie with Statistics, by Darrell Huff. Pictures by Irving Geis. http://www.amazon.com/exec/obidos/ISBN=0393310728/ The World of Mathematics. I have Volume Four, which was edited by James R. ...
  • 3,041
4 votes

Mnemonics for some properties in mathematics

One I recently learned -- for the order of the signs in factoring a sum or difference of cubes, remember SOAP: Same sign, Opposite sign, Always a Plus. Sum of Cubes: $x^3 + a^3 = (x + a)(x^2 - ax + a^...
4 votes

Mnemonics for some properties in mathematics

This only makes sense in Spanish but it's pretty fun. For integration by parts, $$ \int u dv = u v - \int v du $$ Si un día vi una vaca menos sexy vestida de uniforme Which translates roughly to: ...
4 votes

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

After giving the book another look I have to expand on my comment above and make it stronger: no, this isn't a good book for a first-time learner, and in fact I think it's a terrible choice. I looked ...
  • 1,284
4 votes

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

The fact that the book uses infinitesimals (presented informally) rather than limits is definitely a big deal, and I think you will have to read the book for yourself to see if it works for you. When ...
3 votes

What are some great books for exploring mathematics? (not kids' books and not textbooks)

There is nothing even remotely close to T. Gowers Mathematics, A Very Short Introduction. (And less than $10 so that it can be really recommended to students.) From the preface: "It is possible to ...
  • 866
3 votes

Imbuing a six year old with a sense of mathematical wonder

Base 2 counting on fingers - gets you up to 1023. Base 12 counting - need two more numbers flip & flap. 1, 2, 3, 4, 5, 6, 7, 8, 9, flip, flap, flap-one, flap-2, flap-3, flap-4, flap-5, flap-6, ...
3 votes

Imbuing a six year old with a sense of mathematical wonder

Try folding a piece of paper in half, then in half again and see how many times you can do it. start with A4 then find larger pieces-newspaper then wallpaper perhaps.
3 votes

Entertaining and fun books about mathematics for (basically) liberal arts students

The Number Devil: A Mathematical Journey by Hans Magnus Enzensberger is an essential in the "fun math book" category. Very accessible, great illustrations and actually touches on pretty sophisticated ...
  • 4,860
3 votes

Mnemonics for some properties in mathematics

Here is my way of memorizing the three main trigonometric functions. An angle $\theta$ is in standard position locating a point $(x,y)$ on a circle with a radius $r$ centered at the origin. There is ...
  • 10.2k
3 votes

Mnemonics for some properties in mathematics

First heard it from a former classmate of mine, might be her own invention: When the second derivative is positive, the function is happy (i.e., its graph looks like a smile). When the second ...
3 votes

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

In a sense it is OK. In the sense that almost any book (except for one that is very difficult, and assigned to a weaker student and/or one without strong motivation to prevail) is OK. It's really ...
  • 39

Only top scored, non community-wiki answers of a minimum length are eligible