85 votes
Accepted

What's a replacement for "married couples" in combinatorics problems?

I've been using "pets" and "owners" (as in: possible pet-shelter adoptees) in recent years.
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82 votes

What's a replacement for "married couples" in combinatorics problems?

In the stable marriage problem, you can introduce the problem as it is. But then you ask your students how things change if you assume there are not only heterosexual but also gay and lesbian people (...
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  • 1,143
66 votes

What's a replacement for "married couples" in combinatorics problems?

A few possibilities off the top of my head: Students and chairs. How many ways are there for $n$ students to sit in $k$ chairs. The game of musical chairs might be fun to play around with. One can ...
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59 votes

Impressive common misleading interpretations in statistics to make students aware of

Anscombe's quartet is pretty good: All four of these sets have almost identical mean and variance for both x and y coordinates, correlation, and best-fit linear regression. But they're obviously very ...
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  • 691
58 votes
Accepted

Impressive common misleading interpretations in statistics to make students aware of

Here are two well known examples: If someone tests positive for a rare disease (say its prevalence is 1 out of 100,000) with a test that has a 1% false positive rate, it is tempting to say that we ...
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  • 966
49 votes

Impressive common misleading interpretations in statistics to make students aware of

A book I remember has the title "the egg-laying dog". The titular dog enters a room where we placed 10 sausages and 10 eggs. After a while the dog leaves the room, and we observe, that the ...
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  • 587
43 votes

Impressive common misleading interpretations in statistics to make students aware of

Sally Clark (http://en.wikipedia.org/wiki/Sally_Clark) was convicted in the UK of murdering both her infant sons, when in fact it is much more likely that they died of natural causes. The case ...
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37 votes

What's a replacement for "married couples" in combinatorics problems?

The issue is not making problems about heterosexual married couples. The issues are: Implicitly making the assumption that all married couples are heterosexual. Making problems about heterosexual ...
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  • 707
34 votes

Impressive common misleading interpretations in statistics to make students aware of

Simpson's paradox: see http://en.wikipedia.org/wiki/Simpson%27s_paradox. To summarize the Berkeley Admissions example: in 1973, 43% of men applying to graduate school at Berkeley were admitted, but ...
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34 votes

What's a replacement for "married couples" in combinatorics problems?

Try objects that often occur in pairs but are distinct from each other: forks and spoons (or forks and knives), left and right shoes, salt and pepper shakers, and so on (where each fork has an ...
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26 votes

What's a replacement for "married couples" in combinatorics problems?

When I taught a class about the stable marriage problem last week, I replaced "men" and "women" with "medical students" and "hospitals": the classical instance in which the Gale-Shapley algorithm is ...
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24 votes

Impressive common misleading interpretations in statistics to make students aware of

Multiple hypothesis testing is a common one. Let's say you run a study where you try to link some genetic marker to cancer rates. You look at perhaps 80 different genes and see if any of them have a ...
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  • 341
23 votes

Impressive common misleading interpretations in statistics to make students aware of

Percentages are a source of many, many, many common mistakes. One that is very common is believing that percentages can be added. An example: one of our presidents increased its salary by 172%; the ...
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22 votes

Impressive common misleading interpretations in statistics to make students aware of

Just two (now three, see below), to whet the appetite. Stating the mistakes: "Correlation implies Causation": it doesn't. The finding of statistical correlation between two variables may strengthen ...
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17 votes

How can we handle grocery store/bus stop conversations better?

This happened to me two days ago! The "What is it that you teach then?" conversation. I first said everyone's different and has different brains, and that a bunch of us who did PhDs together decided ...
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  • 1,912
17 votes

Impressive common misleading interpretations in statistics to make students aware of

Sometimes extreme sample bias. Here is an example (numbers made up, but realistic): In some country with a population of 100 million people, every year 100 people are bitten by poisonous snakes and 50 ...
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17 votes

Examples of arithmetic and geometric sequences and series in daily life

I tutored a student who came with a kind of problem I had never seen before and found quite refreshing. It was something like: A child is being pushed on a swing by their father, reaching a maximum ...
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  • 583
14 votes

What's a replacement for "married couples" in combinatorics problems?

Protons and electrons (form hydrogen atoms) Or cations and anions (form salts), e.g. Na+ and Cl- Pens and pen-caps Bottles and bottle caps, etc. Textbooks (for the course being taught) and ...
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  • 319
14 votes

Nice examples of limits to infinity in real life

If you are willing to take some time to explain the model and do some simulation, I really like to show students a logistic growth model (in discrete time). The basic setup is something like the ...
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12 votes

What's a replacement for "married couples" in combinatorics problems?

An idea I find interesting is to use abstract objects: "given X squares and Y circles, in how many ways it's possible to pair one circle with one square?" If the students are at kindergarten or ...
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11 votes

Impressive common misleading interpretations in statistics to make students aware of

If you succumb to the temptation of ejecting, say, a 5-sigma outlier from a n=10 sample taken from what you believe to be a normally distributed source, then you are discarding 50% of the sample's ...
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  • 209
11 votes

Inspirational Mathematics Books for Teenager

If you looked at those other topics, you saw the links to the books page at my blog, Math Mama Writes. There are a number of books there that would work for a teen. One of my favorites is Carry On, Mr....
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  • 17k
10 votes
Accepted

Examples of arithmetic and geometric sequences and series in daily life

Here are a few more examples: the amount on your savings account ; the amount of money in your piggy bank if you deposit the same amount each week (a bank account with regular deposits leads you to ...
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10 votes

Electronic devices to replace pencil and paper

Taking a break from a convoluted computation... To me the key limiting factor is space. I can spread out several sheets over the table and have various bits and pieces directly visible. I cannot do ...
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  • 7,572
10 votes

What's a replacement for "married couples" in combinatorics problems?

I like several of the answers which found clever sets that avoid assumptions about genders and sexes. Just to provide an alternative, what about keeping the assumption about sexes, but changing ...
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  • 1,101
9 votes

Impressive common misleading interpretations in statistics to make students aware of

If a coin is biased to land heads with probability $p$ and $(a,b)$ is a $95\%$ confidence interval for $p$ then $p$ is in $(a,b)$ with probability $95\%$. Added in edit - While it is often argued ...
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9 votes

Impressive common misleading interpretations in statistics to make students aware of

Unfortunately, it is in German, but the book Angewandte Statistik: Eine Einführung für Wirtschaftswissenschaftler und Informatiker by Kröpfl, Peschek and Schneider contains many typical mistakes that ...
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9 votes

Why do we prove things we already know?

You've touched on why it's problematic for educators to only talk about proving in the context of formal proofs. Students need to be accustomed to mathematical reasoning and justification well before ...
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  • 7,375
9 votes
Accepted

How can we handle grocery store/bus stop conversations better?

My go-to response is: I used to be "not a math person" as well, but I stuck with it, and eventually I learned what math was all about and I fell in love. My response may make me seem like a bit ...
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