Actually, I don't because I haven't been teaching at the high school or college level. I am not 'qualified' to teach at the college level because I only have a Masters in Applied Statistics not a Masters in Math and I am not qualified to teach at the high school level because I don't have teaching certification. But whoever posted the statstics problem about how many tosses of coin would you need to quarentee with 90% probability at least 100 heads should have a pretty good idea. I will tell you, for what it is worth, that a copy of the design of experiments book by Box, Hunter, and Hunter is worth its weight in gold for someone who has to do real world experiments in industry. I also keep a Schaum's Outline Series on Probability around. I like the problems and they all come with solutions. I use a 1965 addition.

-- AnneDwyer - 11 Jun 2005

Another horror story,

We've got to get a dedicated page of Math Horror Stories up. We need to have all these things in one place, where we can all find them.

Anne, do you have a recommendation or recommendations for decent statistics texts at high school & college level?

And in particular, do you have a recommendation for books a parent or student could use on his/her own?

Thanks!

-- CatherineJohnson - 10 Jun 2005

I actually had an error in my post. This is her second time taking it after failing it the first time at her university. Now, she is trying to take it in the summer at a community college. She failed her first test, then came to me. She got a 92 on her second test!! But the book she is using is absolutely terrible. We are now working on Hypothesis testing. Without getting too technical, this is a way to compare two things to tell if there is a statistically significant difference. The student has to calculate a test statistic and compate it to a standard statistic that you look up in a table. In order to look it up, the student has to calculate the degrees of freedom. But the book uses the wrong degrees of freedom. Instead of using n1+n2-2, it uses n1-1 or n2-2. It was really difficult for me to find this information. It is buried in a paragraph with a lame explanation as to why.The teacher had never actually given them the degrees of freedom to use or explained the difference. And this was supposed to be an actual statistic class for math majors!!!! And, even worse, the answer in the back of the book listed the answer that you get from the TI-83 calculator which, of course, uses the correct degrees of freedom - so the answers are different!!

-- AnneDwyer - 10 Jun 2005

*AnneDwyer*--

How is your student doing?

-- CatherineJohnson - 09 Jun 2005

Hey!

This is the time to unveil our Berenson Family Motto!

No Common Sense-y

I originally came up with No Common Sense-y as it pertained to, say, stopping dead in the middle of a busy street to bend over and fiddle around with your shoe.

I didn't realize I could apply it to math, too.

-- CatherineJohnson - 09 Jun 2005

The point is, you can't possibly flip a coin 100.00001 times, no matter what the calculator tells you. Only a whole number greater than 100 would even make sense as an answer to this problem.

Sigh.

I have a long ways to go.

I'm trying to take notes on all my many, many, MANY errors & fragmented knowledge pieces . . . so I'm gonna be writing this one down, too.

Here's what got me hopscotching down the fragmented knowledge pathway inside my brain.

When Bernie told the girl that she'd set the problem up correctly, I jumped from that to thinking that her answer was right, except obviously it couldn't be less than 100.

This is an obvious example of the literal-mindedness of the novice that Willingham talks about: I didn't look past the 'surface features' of the post.

Then I missed the joke at the end, because I was still focusing on the '100'-----completely surface.

Here's the Willingham article, for anyone reading comments: Inflexible Knowledge: The First Step to Expertise

It's invaluable---and now I'm realizing it's going to be invaluable for me, in terms of assessing my own progress.

-- CatherineJohnson - 09 Jun 2005

Hi Anne, I'm glad you can comment now!

Re the education student -- I don't see how you can tutor a kid for a class that's being taught like that. What do you suppose they are actually learning?

-- CarolynJohnston - 09 Jun 2005

Ok, here's are real comment, now that I can see all the comments. I am tutoring a college student in statistics. She is an education major and only needs one statistics class. She is taking it for the first time. As we sat down to do problems, she told me that a graphing calculator is required. The teacher shows them the steps to use the calculator for each type of problem. Unfortunately, she doesn't explain how to use the actual formula. When we sat down to do some Binomial problems, she read the problem and started to put the numbers in the calculator. I asked her to write out the formula first and substitute. She says, "We never actually learned how to use the formula. We're just supposed to put it in our calculators."

-- AnneDwyer - 09 Jun 2005

test for Carolyn

-- AnneDwyer - 09 Jun 2005

test for Carolyn

-- AnneDwyer - 09 Jun 2005

The point is, you can't possibly flip a coin 100.00001 times, no matter what the calculator tells you. Only a whole number greater than 100 would even make sense as an answer to this problem.

So even when you have a calculator, you still have to think.

-- CarolynJohnston - 08 Jun 2005

One of my Assessment Measures for Have Become Competent At Math is going to be: immediately gets the joke.

As opposed to: looks it up on Math Forum and then gets the joke.

-- CatherineJohnson - 08 Jun 2005

Thank you.

I feel better now.

-- CatherineJohnson - 08 Jun 2005

The solution involves the binomial distribution (which, you're right, is related to Pascal's triangle)... which isn't covered in Saxon 6/5, you're right. It's a bit tricky -- I'll post it later if you like, but it wasn't the main point of this post!

-- CarolynJohnston - 08 Jun 2005

Uh-oh.

I'm afraid the solution to this problem involves Pascal's triangle.

That wasn't covered in Saxon Math 6/5.

-- CatherineJohnson - 08 Jun 2005

OK, we SO don't get this problem.

Help!

100.00001 isn't the right answer------????

Hey!

Are you being ironic!

I'm afraid you're gonna have to spell it out for us still-learnings---

-- CatherineJohnson - 08 Jun 2005

GirlVsCalculator

Calculators aren't actually so reliable. Actually, if you were to compare calculations done with calculators to those done by humans one to one, I'd bet that calculators produce a much higher error rate; it's so easy to mess up and hit the wrong button, or to get a complex sequence of operations in the wrong order.

My husband has a story that illustrates one of the consequences of overreliance on calculators in math classes.

He was teaching a probability unit in a freshman college course in finite math, and most of the kids were struggling with it. These kids came into class every day clutching their calculators fearfully, as though they were talismans to ward off math demons (embodied by their professors, I guess).

The unit test in probability happened, and one of the problems was as follows:

John flips a penny repeatedly. If the probability of its turning up heads is .5, then how many times must John flip the penny in order to have a 90% chance of its coming up heads 100 times?

One girl in the class -- a bright girl -- set up the problem, banged on her calculator for a while, and came up with an answer of .00001. When she went in to get help with the problem, my husband told her that she'd basically set up the problem correctly; the problem was with the calculator -- she wasn't getting the keystrokes in the right order.

"You need to use your common sense to check your answer," he told her. "Think about it. In order to have ANY chance of the penny coming up heads 100 times, how many times does he have to flip the coin at least?"

"Oh, yeah!" she said. "At least 100!"

A couple of days later, the class took a retest, and the exact same problem was on the test again. This time, the student performed the same calculation in the same way, and came up with .00001 again. Frustrated, she showed that she had absorbed my husband's lesson about common sense, and put down: 100.00001.

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• Posted by: CarolynJohnston
• LogDate: Jun 08, 2005 @ 00:18

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