Office hours (until further notice)
Tuesdays: 10:55-11:55 in my office
Tuesdays: 2:45-4:00 at Steep and Brew (544 State St.)
Wednesday: 1:30-3:30 at Steep and Brew
Thursdays: 10:55-11:55
Also available by appointment.
You never need to ask "Can I come to your office hour?"
The answer is YES.
If you can't make it to my office hour, and we can't settle your question by email, we can try to make an appointment for some other time.
Show “Paper Moon” (first scene)
How much money is Moses Pray stealing?
Show “Paper Moon” (second scene)
How much money is Addie stealing?
Announce exam dates: Feb. 23 and Apr. 6
Ask about Daphne's office hours
Give students time to discuss problem #3 in groups and then report on sources of error.
"I won't always do it, but I hope this gives you a sense of the benefits of working with other people"
Sources of error:
Not understanding the problem YET
Misreading the problem
Careless thinking
sign errors (adding instead of subtracting
or vice versa)
fencepost errors
Miscopying a number
Misreading your own writing
Fencepost errors
Calculation mistakes
Tips for clear thinking:
Using reference points
Mental subtraction (someone mentioned this in the cards I had you fill out last week as something she wanted to get better at): 6'1" minus 5'4", etc.
Another source of error: “Externalities”, aka “Forgetting to take all the relevant factors into account”
[Show Supermarket.doc]
What does he mean, “YOU should buy the large one?”
Why is this part right? What can you buy for $6?
If double-cents-off coupons exist in such abundance that, each time Morris uses one to buy a product, he can be fairly sure of having another one in hand before it’s time to replenish his supply of the product, Morris' conclusion is correct: he will indeed, paradoxically, save money buying the smaller, “less economical” 10-ounce size for $1.00.
But what if double-cents-off coupons are rare?
What Tim Morris’ analysis fails to take into account is that, having passed up the 15-ounce product in favor of the 10-ounce product, he will have to restock sooner (and he probably won't have another double-cents-off coupon when he does).
Take an extreme case: What if Tim has only one double-cents-off coupon and the supermarket has decided to stop giving double-cents-off coupons? Which size should Tim buy?
NONQUANTITATIVE REASONING
Your book gives some examples in chapter 1.
This fun little book (“Tools of Criticial Thinking: Metathoughts for Psychology”) gives others.
I’ll just do one example of fallacious thinking from this book today: “Tautologous reasoning,” more commonly known as “circular reasoning”.
How to detect circular reasoning: When someone says to you “A because B”, ask yourself if they could have said “B because A” and it would’ve sounded just as good. If so, then they may well be engaging in circular reasoning!
“Why does she firmly cling to her false beliefs, despite obvious evidence to the contrary?”
“Because she’s got Delusional Disorder.”
“How do you know that she’s got Delusional Disorder?”
“______.”
“Why does the patient have a persistent, irrational fear of train travel?”
“Because she’s got Siderodromophobia.”
“______?”
“______.”
“Why does the patient have a persistent, irrational fear of the number 13?”
“Because she’s got Triskaidekaphobia.”
“______?”
“______.”
NONQUANTITATIVE REASONING
What’s good about math is that one can follow certain formalized procedures that prevent one from making mistakes.
What’s bad about math is that these procedures can become a substitute for reasoning, so you turn off your reasoning faculty and get wildly wrong answers.
It’s kind of like the difference between walking and riding a train. The train will take you wherever you want to go, faster. It’ll also take you over a cliff faster.
The trick is that when you’re solving a problem, you should use both formulas and procedures (on the one hand) AND estimation and reasoning (on the other).
Read Section 1A for Thursday!