Friday, April 29, 2011

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.

Wednesday, April 27, 2011

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. 

Friday, April 15, 2011

AP Stat Lesson: Type I and Type II Errors

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

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

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.

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.

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.

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.


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)

Thursday, April 14, 2011

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.

Thursday, April 7, 2011

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.

Wednesday, April 6, 2011

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. 

Tuesday, April 5, 2011

How does change happen?

First of all, check out the new blog format.

Second of all, today we played the Making Change for School Improvement game with the fellow Montgomery County instructional coaches and it was awesome.  Our group successfully moved every teacher to becoming a routine user, but ran out of money to perform a complete curriculum revamp. .  Amazingly, we still had plenty of funding to give our kids standardized tests (kidding).

What I left my meeting with today is that I don't talk to nearly enough people in our district.  I have a great rapport with our teachers.  I am friendly with our administrators.  It's REALLY hard to have a conversation about things that need to change with administrators though.  As a whole, I feel like preservation of the status quo can sometimes be more important to them.  Or, the need for change is viewed as such a huge problem that mere mortals are powerless to do anything about it.

It's become necessary for me to provide data at every waking moment to support what we're doing as instructional coaches.  I'm the one responsible for providing it, when there's a real easy way to collect that data.

If you want to see the effect that an instructional coach is having, GO INTO A CLASSROOM  and see.  Look at what is happening in the classroom first, then decide what additional data (if any) that you need.  As a statistics teacher, my recommendation is to gather data to assist in making an informed decision.  Please try to avoid gathering data to support an argument for/against.  It turns litigious and confrontational.

I had the pleasure of speaking with @kenrodoff about how his administrative team walked through classrooms for 6 hours as part of an ISTE site visit and was amazed at what was happening with technology. Hopefully this leads to a continued and improved support for instructional technology within their district.  Honestly, I have no doubt about it.

My classroom door is wide open for anyone that would like to visit.  My students and I would love to share what we're doing with you.  I have no reservations and I don't get scared when an administrator walks in to my room.  I want you to come in.  I want to share.  I want to be seen because I believe what I'm doing is in my student's best interest.  I am proud of the fact that what happens in my classroom is different than every other classroom in the district.  I have no idea how well my students will do on an AP Exam, in fact, I don't really care.  I care that my students are producing something they genuinely care about and are interested in.

Here's some of the great things happening:
Probability presented through Penalty Kicks
Binomial vs Geometric Probability: A Jimmer Fredette Example
Experimental Design: Pokemon and Smash Bros