AP Stat Test Today

I am sneaking this in before the 48 hour moratorium on discussing anything AP Statistics test goes in to effect.  Hopefully the gentleman in dark suits and sunglasses from the college board that I see lurking outside of my window will understand.

Today my students will take the AP Stat exam.  I have no idea how well they will do.  I'm fairly certain that the students that this test wants to get a "5" will get a "5".  I've told my students that they are much more important to me than a test score.  After all the amazing things we they do in class, it seems rather anti-climactic to summarize them with a number between 1-5.

One of the worries that I have is that I spend most of my year allowing my students to demonstrate what they've learned in whichever way they wish.  Some like to create videos, some create Prezi's, others are content to write a report.  At the bottom of it all is my belief in giving kids a choice in what they wish to do, so that they can enjoy a learning experience other than "listen-do this-receive grade".

But the AP Stat test will not take in to account the freedom of choice and "uber-differentiation" that has made my classroom something everybody enjoys.  I do think that the students who have chosen the most in-depth learning experiences will translate their knowledge to any medium, even if it's some boring old test.  What about the kids that chose to write a report, or chose a learning experience that wasn't all that in-depth?  If I told them to choose something else that would be better in terms of test preparation, then I wouldn't really be giving them their choice at all.

With such a push for meeting individual student needs, how can we only give students 40 questions with 5 different answer choices to show what they know?  On the free response section, how come they have to answer parts (a), (b), and (c) when the most enjoyable part would be to explore option (d) that doesn't exist?

Next year, I'm going to suggest that none of my students take the AP exam.  There...I said it.  Our reasoning will be that we are going to do something better than answer someone else's questions, we're going to answer our own.

Why Schools Do Not Innovate

This post is in response to Scott Swindells' post of "Where's the Innovation?".

A recent blog post by Seth Godin really resonated with me as to a school district's reluctance to innovate.  He writes:

It's impossible to have a coin with only one side. You can't have heads without tails.

Innovation is like that. Initiative is like that. Art is like that.

You can't have success unless you're prepared to have failure.

As soon as you say, "failure is not an option," you've just said, "innovation is not an option."

This is precisely why most schools systems are institutes of non-innovation. Innovation within a school system(okay, within all systems) frequently involves money.  A district doesn't want any money they spend to result in a failure, since taxpayers demand a constant "positive return on investment" (that phrase mixed with education makes me cringe, so I'll only use it once).  Nobody wants to anger our taxpayers by spending money on something that fails.  

This is the failure is not an option approach.

Who decides what kids should learn?

Stop me if you've heard these before...
"Kids these days can't do simple math without a calculator!"
"Kids these days can't write well at all!"
"Kids these days are lazy!"

So what?  What gives you the right to tell students today what they should learn?  You've never met my students, so in my view you have zero authority to tell them what they should be learning.  On the flip side, if you've never met my students, why is it okay to tell them what they don't need? (as you begin making those budget cuts to eliminate foreign languages and the arts)

Ultimately our kids should have the freedom to learn whatever they want.  There should be no reason that every student should have to take Algebra II before they graduate high school.  If they're interested in it or would like to try mathematics, then go for it.  If they have an interest in art, why would we then tell them that they can only take one art course this semester since they have to take 6 other subjects they don't care about?

Imagine if we required every student to take a painting and drawing class every year from 7th grade to 12th grade.  Why does that sound so blasphemous, yet we can easily require them to take a math class (or two) every year from 7th grade to 12th grade?

Don't get me wrong, I see the great benefits in students taking any mathematics courses.  I'm a math teacher.  I want kids to discover their own interest in learning mathematics on their own schedule, not on some mandated timetable. 

AP Stat Lesson: Type I and Type II Errors

THE EXCEL SPREADSHEET
Type I and Type II Errors (housed on Box.net...is there a better way to do this?)
Directions for the activity contained in the spreadsheet.

SKILLS ADDRESSED
Statistical significance, Confidence Intervals related to hypothesis tests, Type I Error, Type II Error, Power, Alpha, Beta

THE CONTEXT
A factory is producing pharmaceutical grade glass vials.  Quality control engineers are employed to see if the factory is producing items at or below the industry standard of 5% defects.  They conduct a sample of size 100 (Mistake #1: I know this violates np>10, but it turns out that you wind up failing to reject a lot and it leads to a good understanding of Type II error) and determine the proportion of their sample that is defective. (Mistake #2: sampling 100 items and getting a proportion defective of 0.063 defective is impossible.  They will need to round to a whole number of successes when using the graphing calculator.)  Based on the results of this hypothesis test, they will decide if the factory must undergo a quality control review or continue with business as usual.


THE ACTIVITY
1ST PART - CONDUCT THE TEST, DECIDE WHETHER TO REJECT OR FAIL TO REJECT
It's dynamic.  Each kid will receive a randomly generated proportion.  They may do this up to 50 times.
First part of the activity: conduct the one proportion z-test using your graphing calculator.

2ND PART - DECIDE IF YOU MADE THE RIGHT DECISION
Unlock the spreadsheet (password: apstat5).  Have them change the fill color of the "True Proportion" column to reveal the true proportion of items that are actually defective.  They then evaluate their decision as to whether it was correct or incorrect.  Cue a whole class discussion on the 4 different scenarios of errors, then slap the AP Stat vocabulary on.

REFLECTION
Two huge mistakes that led to an amazing understanding of errors.  An overly planned lesson would have avoided these mistakes.  It also would not have generated a discussion on appropriate assumptions and conditions for inference.  An overly planned lesson would have also not brought up the question of "How come I'm failing to reject so much when it's false?"  An awesome comment: "I would not have learned this that well if I didn't have to think about those things."

This was 3 days worth of 46-minute classes.  Let's see how they do on the assessment of these skills.

THE SLIDESHOW

10-11 Errors

View more presentations from christjt.

Coming soon to this post...
The Google Form Assessment
A better version of the spreadsheet that allows any null hypothesis and any sample size.
100 comments on how to make this even better (hopefully)

Good Teachers are Worth their Weight in Gold

The popular line from those that wish to criticize teachers is that "Good teachers are worth their weight in gold".

Every person that says this follows it up with a list of excuses for why we should pay them in dirt.

Treat teachers like they're providing your students with an education.  Treat teachers like people that are developing children into citizens.  They're not being asked to peddle some wares, manufacture something, or generate more money.  They're being asked to nurture and develop citizenship.

A teacher can make one child a great citizen, and in doing so they would outshine all the salesmen in the world.

AP Stat Lesson: Confidence Intervals (Graduation Party)

The Excel file: Graduation Party simulation.

What this Excel file does is simulates a student sending out 1500 invitations to a graduation party.  There is a true proportion of people that will attend, but it is unknown (see the "Population" tab of the Excel spreadsheet is completely blacked and password protected).  If you'd like the unlocked version, feel free to get in touch with me and I can send it along.  Students will conduct samples of 20, 50, and 100 to estimate the true proportion, and once they've generated a sufficient number of each sample size, they'll take a guess as to what the true proportion is.  Discussion follows as to which sample was most helpful to make the guess from.  Most guesses are that the true proportion is between 0.2 and 0.3.

They choose one of their sample proportions for sample size 100 and create a confidence interval for 4 different confidence levels: 68%, 90%, 95%, 99.7% (not randomly thought up by any means).  I chose these confidence levels because in the past I've seen students not associate confidence intervals with a middle percentage.

Collect students intervals using this form: One-Proportion Z-intervals Data Collection Form 
Display their responses here: One-Proportion Z-Intervals Raw Data (pay attention to both tabs, one has intervals and one has whether or not the interval captures the true proportion)

Once they've done some thinking, they will open this Excel file(One-Proportion Z-intervals Displays of Each Interval), providing a visual of each confidence interval.

We follow with having students lead their own discussion.  They'll begin by posting comments to a specific page of the class wiki, in order to get them to jot down an initial reaction to see if what they thought still holds up, or if their thinking needs revision.  A whole class discussion follows, and I challenge them to not allow me to speak for 10 minutes.  This can be difficult for me, but it is extremely difficult for them.

AP Stat Lesson: Unstructured Investigation

Give kids this: Hank Aaron - Home Runs by Pitcher

Let all hell break loose.

I've become quite a fan of "unstructured time" as of late, and I think this is perfect for an AP Statistics class.  I can see my baseball fans in class leaping at this opportunity to explore some baseball stats.  Whatever they wish to investigate, they are free to do so.  For the non-baseball fans, it may be just an opportunity to learn something about baseball.  I owe them some data on what they're interested in.  I look forward to hearing what a student that knows very little about baseball has to say.

Possible investigations:
1.  Comparison of Barry Bonds(or any other great home run hitter) to Hank Aaron. 
2.  Are pitchers today better (as a whole) than the ones Hank Aaron faced? (this comes from listening to Colin Cowherd say that Babe Ruth hit his home runs against guys who drove a milk truck in the off-season)
3.  Just how biased is this website?

Let them come up with how they're going to do any of the above.