55 votes

How to explain Monty Hall problem when they just don't get it

For some reason, the 'extend it to 100 doors and eliminate 98' explanation doesn't make it any clearer for me. Rather than talk about probabilities as fractions, I explain it this way: "If you ...
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  • 1,214
29 votes
Accepted

How to explain Monty Hall problem when they just don't get it

Your explanation, by the way, is very elegant. As an experienced mathematician, I see immediately that it cuts right to the heart of the matter and admits no ambiguity. Unfortunately, this is ...
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  • 1,083
20 votes

How to explain Monty Hall problem when they just don't get it

There isn't any sure-fire method of explaining anything, and especially in math. But specifically in the case of the Monty Hall problem it has been proven by extensive experience that many individuals ...
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19 votes

How to explain Monty Hall problem when they just don't get it

Perhaps it's not the explanation that's the problem. I suggest you have them explain to you their understanding of the problem. Listening to their justification might reveal why your explanation is ...
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  • 7,405
14 votes

How to explain Monty Hall problem when they just don't get it

I've had best luck by simplifying the problem to asking whether you want to pick one door or two doors. Everyone understands they'd be better off picking two doors. At that point I tell them to just ...
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  • 241
13 votes

How to explain Monty Hall problem when they just don't get it

I found the most helpful way to think about the problem is to expand it to a larger number of doors. For example, if you have them select from 100 doors, where 99 are losers and 1 is a winner. Then ...
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11 votes

Challenge questions for extremely bright kids

Here are some suggestions for problem sources in English. Some of them are appropriate for very bright students studying geometry or Algebra II, but might nonetheless prove too difficult for students ...
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  • 587
9 votes

Explaining the "siblings" paradox

I think there are a few independent questions here that can be considered teaching mathematics (I will not broach the subject of how to solve the problem). First, there is: How can you state this ...
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  • 1,083
9 votes

How to explain Monty Hall problem when they just don't get it

The best sure-fire method for teaching this to people who don't want to learn it is to set up a Monty Hall style game for small stakes of real money. When they start losing 2/3 of the time, they will ...
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9 votes

How to explain Monty Hall problem when they just don't get it

I never understood it until my Maths lecturer explained it to me. Unfortunately I can't remember the exact way he explained it, but I'll try my best to remember. I really like your own explanation, so ...
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7 votes

How to explain Monty Hall problem when they just don't get it

While your explanation is correct, and easily understood by people like us, it's a bit too terse (a quality we like) for a lay person to understand. You can simply expand on it. And most importantly ...
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7 votes

Tricks for computing things in your head

I devised a trick in 8th grade for converting repeating decimals to fractions. They were teaching a very long drawn-out process. My trick basically does the same thing but for some reason they ...
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6 votes

Tricks for computing things in your head

Because of an exercise we ran every year, I accidentally memorised $\log_{10}2=0.301$, and I could find many logarithms quickly in my head using the log laws. One holiday I decided to take it a little ...
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  • 1,912
6 votes

How to explain Monty Hall problem when they just don't get it

Speaking from my own experience, a stage I had to go through before understanding any explanations of the logic and math involved was indignation at being baffled by a cheap fairground trick that ...
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6 votes

How to explain Monty Hall problem when they just don't get it

I find that most people who THINK they understand the Monty Hall Problem, actually don't. For about 5 years I was one of them, until a further insight made me understand it better. More of that at the ...
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6 votes

How to explain Monty Hall problem when they just don't get it

Here's my take on explaining it. (And it usually involves a drawing for me :-) ) Assuming the host opens a door the odds of making the right choice without switching the door is 1/3 because it was ...
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  • 161
6 votes

Challenge questions for extremely bright kids

I work with gifted elementary school students, but one of my favorite sites, nrich has challenging problems that you could use for older gifted students. Try looking at secondary problems for stages ...
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5 votes

How to explain Monty Hall problem when they just don't get it

The big problem with the "Monty Hall" problem is that there are many problems that sound superficially the same, but have different solutions. The terms of the game have to be stated very precisely. ...
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5 votes

Explaining the "siblings" paradox

I see three issues: the limitations of the English language, information leakage, sampling. Issue 1 was addressed by Ryan Reich. In brief, there is no natural English phrase corresponding to the ...
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5 votes
Accepted

Does solving crosswords help with recall of definitions?

I had a teacher friend who learned in college that word searches were worthless in most respects, but crosswords should have some intrinsic value because it requires you to read the definition and ...
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4 votes

How to explain Monty Hall problem when they just don't get it

The best way I came up with is to draw all 9 possible outcomes. Prize is in A, you pick A; Prize is in B, you pick A; Prize is in C, you pick A; Prize is in A, you pick B; and so on. Each outcome is ...
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4 votes

How to convince parents that Mathematical puzzles/games help students in their academics too

Oh this is subtle and tough, in my opinion. It seems to me (and forgive the appalling over-generalizations I am about to present) ... In some vague but emotionally potent sense, math is seen as vital ...
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3 votes

How to explain Monty Hall problem when they just don't get it

The problem is most of the time something in the line of that a switch isn't believed to be helpful, because nothing has changed in the eyes of the person you are explaining the problem to: they ...
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3 votes

Explaining the "siblings" paradox

As with the Monty Hall problem, it is important to know exactly what information you have. Let's say I offer a parent a present of 100 dollars if they have two girls, and 10 dollars if they have at ...
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  • 1,141
3 votes

Challenge questions for extremely bright kids

The website mathschallenge.net has pdfs of tiered problems with solutions. They are nicely posed problems, often with some humour, and are based on different stages of mathematical maturity. To begin ...
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  • 541
3 votes

Easy and good book on combinatorial problems

This book is unfortunately out of print, but it is still accessible: The Penguin Book of Curious and Interesting Puzzles by David Wells. A majority of the problems are of a discrete or combinatorial ...
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  • 131
3 votes
Accepted

Suggestion and advices

I'd put my money on: Mathematics and the Imagination by Edward Kasner and James Newman The four-volume set The World of Mathematics that Newman edited. These books appeal to people in all subject ...
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3 votes

Suggestion and advices

It seems that your main concern is cost. I therefore suggest you look for sources of free textbooks. If you're looking for books for undergraduate students, then you might want to take a look at the ...
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  • 10.2k
2 votes

Tricks for computing things in your head

Squaring natural numbers around 50 Let n be an integer "around 50" (which can be anywhere from 30 to 70). If we write $n$ as $n = 50+m$ then $n^2= 2500+100m+m^2$. So just multiply $m$ by 100, square ...
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2 votes

Tricks for computing things in your head

Multiplying whole numbers times $25$ is counting quarters. Many American students find this easy. Getting a better that whole number approximation of square roots is possible using $$\left( a+\frac{...
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