Archive for May, 2011

Antivenin? For Real?

May 23, 2011

I can’t read through my local daily newspaper without running across more than one misspelling, typo, or grammar error. I guess the copy editor was fired and not replaced some time ago. Anyway, this morning I was reading an article about the recent flooding in Louisiana and came across what I thought was a misspelling of antivenom – the word I saw was antivenin. Couldn’t be right – could it?

So, I consulted my handy Dictionary.com and was really surprised to learn that I had been doing it wrong all my life! (Sidenote: I should get partial credit for only having 2 letters wrong out of 9 – let’s call it a C+.)

My students do the same thing – well, not all of them, but there is a sizable number who express surprise at being told that they are misapplying a concept, and swear that’s how they were told to do it. They stubbornly cling to their false knowledge, and I spend a lot of time unteaching them things they have mislearned!

I think about what motivated me to consult the dictionary – after all, my experience told me to expect the newspaper to be wrong, so why did I doubt myself in this case? I remembered another time when I was in a similar situation – that time the word was temblor and it was referring to an earthquake. I thought it should have been tremor – so I looked it up and was surprised to find that I was wrong. If I was wrong once, I could be wrong again – so now I know the correct word for snakebite antitoxin.

I want my students to consult their mathematical dictionary – I want them to be curious about their process and question themselves if something they are doing doesn’t make sense – after all, it could be right but it could also be wrong. Either way, what they learn will more likely become part of their permanent mathematical memory.

Four Door Monty

May 12, 2011

OK, so in my regular Monty post I promised an answer to the 4 door Monty question and here it is.

Simply put, the only way you can win if you decide to use the switching strategy is if you first select the wrong door. Selecting the right door on your first choice will guarantee that you lose because you are switching after the host reveals one of the three doors you did not select. So, the first probability is just the probability of selecting a losing door from the four original doors,  3/4. Assuming you have selected a losing door, when the host opens one of the remaining doors, offering you the opportunity to switch, there are now two doors remaining, and only one is a winner. Your probability of selecting the winner now is 1/2. Thus, the combined probability is (3/4)(1/2)=3/8.

This is better than the probability of selecting a winner if you stick to your original choice – that probability is 2/8, clearly less than 3/8!

So, the interesting part of this is that it seems like the advantage gained by switching decreases as the number of doors increases – more on this later. I’m too lazy to do any more on this today!

Bucket

May 12, 2011

Check out this little guy – it took him a few minutes to figure out exactly how to maneuver the shovel and get a little sand into the bucket. First he struggled with which hand to use, then he found a fork and started using both hands – ambidextrous?

Is this one for the anyqs