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.
Thursday, April 7, 2011
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.
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
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.
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
Friday, March 25, 2011
PA Education Budget...Am I reading this correctly?
To all my fellow educators in PA, readers in PA, and educators nationwide, please visit the link below and open the Excel file.
PA Dept of Education Budget
Check out line 10, the line for "PA Assessment". Yes, that 36, 590 is in thousands.
Compare with line 9, the line for "Information and Technology Improvement". 4,266.
Pick jaw up off floor.
A statewide system of standardized testing is costing us $36, 590,000, yet they are calling for teacher layoffs?
Am I reading this correctly? Please tell me if you have a different interpretation. If I am reading this correctly, then every person in the state of PA needs to see this.
Big props to Scott (Tuesday's With Swindy) for pointing me towards this.
PA Dept of Education Budget
Check out line 10, the line for "PA Assessment". Yes, that 36, 590 is in thousands.
Compare with line 9, the line for "Information and Technology Improvement". 4,266.
Pick jaw up off floor.
A statewide system of standardized testing is costing us $36, 590,000, yet they are calling for teacher layoffs?
Am I reading this correctly? Please tell me if you have a different interpretation. If I am reading this correctly, then every person in the state of PA needs to see this.
Big props to Scott (Tuesday's With Swindy) for pointing me towards this.
Wednesday, March 23, 2011
You Say It Best When You Say Nothing At All (about Hypothesis Testing)
I really like sharing things that work really well. I don't know if it's a good idea on it's own, but this worked great considering we've done a lot of remediation (for students that needed it) and a lot of projects that delve deeper into statistics. They are working with basics of statistics all the time, so tying it together into making statistical inferences is fairly easy when they have a good foundation. I'd also like to think it has something to do with the way we've interacted with hypothesis tests in class.
Thumbtacks - Introduction
It begins with this form (Inference for Proportions) and handing out one thumbtack. In their own brain, students decide what they think it is and what it would take to convince them it was wrong. Then they toss the tack to be able to compare their observations to a model they've developed. Sounds a lot like your entire hypothesis testing/inferential statistics unit.
The NCAA Basketball Tournament - A Basic Example
Kids then made predictions for the NCAA tournament and we tested just how good they were at doing so by comparing their proportion of correct first round picks to randomly guessing (p = 0.5). A big question that came up was "Are we just doing this for the first round?" and in true teacher fashion I said, "Yes. Now how come we're only doing it for the first round?" Cue a killer discussion about large enough sample sizes and the Success/Failure condition.
Back to Thumbtacks - Put it into practice
Fire up the laptops and open up what the rest of your classmates thought (What They Thought). Immediately they began to think "Why did this kid think they were incorrect when they got a lower proportion that what they thought they needed to be incorrect?"...a not so formalized way to think about a standard of proof and a low enough p-value to reject the null hypothesis. This was one of those points in class where I said nothing and let their brains piece together what they were looking at. I clarified what we were looking at, asked them to pick case that they thought was theirs and test the original hypothesis.
Conclusions
On the board, write your p-value and whether or not you rejected your original hypothesis. As a class we'll have a look at everyone's p-values and decisions, then decide who has correctly rejected/not rejected. They all argue about what p-value is considered "low enough" that you have to reject. One of those moments where again, I say nothing and they develop an understanding of alpha-levels. Not so formal...yet.
What's Left to Do?
Sit back, relax, and let the 5's on the AP exam roll in. Dress it up. Put all the formal AP Exam terms/vocab/stuff to what they've already understood. Then....
1. So what really is the true proportion (Confidence Intervals)
2. Is what we got really that different? (two proportions)
3. Repeat procedure for sample means instead of proportions
Feel free to go to our class wiki for any supplemental exercises/materials.
Thumbtacks - Introduction
It begins with this form (Inference for Proportions) and handing out one thumbtack. In their own brain, students decide what they think it is and what it would take to convince them it was wrong. Then they toss the tack to be able to compare their observations to a model they've developed. Sounds a lot like your entire hypothesis testing/inferential statistics unit.
The NCAA Basketball Tournament - A Basic Example
Kids then made predictions for the NCAA tournament and we tested just how good they were at doing so by comparing their proportion of correct first round picks to randomly guessing (p = 0.5). A big question that came up was "Are we just doing this for the first round?" and in true teacher fashion I said, "Yes. Now how come we're only doing it for the first round?" Cue a killer discussion about large enough sample sizes and the Success/Failure condition.
Back to Thumbtacks - Put it into practice
Fire up the laptops and open up what the rest of your classmates thought (What They Thought). Immediately they began to think "Why did this kid think they were incorrect when they got a lower proportion that what they thought they needed to be incorrect?"...a not so formalized way to think about a standard of proof and a low enough p-value to reject the null hypothesis. This was one of those points in class where I said nothing and let their brains piece together what they were looking at. I clarified what we were looking at, asked them to pick case that they thought was theirs and test the original hypothesis.
Conclusions
On the board, write your p-value and whether or not you rejected your original hypothesis. As a class we'll have a look at everyone's p-values and decisions, then decide who has correctly rejected/not rejected. They all argue about what p-value is considered "low enough" that you have to reject. One of those moments where again, I say nothing and they develop an understanding of alpha-levels. Not so formal...yet.
Projects/Practice
Pick another one of those contexts from the Inference for Proportions form and investigate it. I think I'm going to add some more situations/contexts. I'm also not sure that they ever need to fill out that form more than once...
What's Left to Do?
1. So what really is the true proportion (Confidence Intervals)
2. Is what we got really that different? (two proportions)
3. Repeat procedure for sample means instead of proportions
Feel free to go to our class wiki for any supplemental exercises/materials.
Wednesday, March 16, 2011
Homework? More like "1st Period"-work
At our school, the typical student will take 7 courses for the entire year. If that student has AP Stat with Mr. C on their schedule, this means that a student has 6 classes in which they will have homework. 6 other classes with one hour of homework assigned each night means approximately 6 hours of homework.
Some careful accounting as to how those 6 hours that could be spent working on homework are actually spent.
Hour 1: Facebook
Hour 2: Call of Duty
Hour 3: Facebook
Hour 4: Facebook
Hour 5: Facebook
Hour 6: Being a 17 year old....and throw in a little Facebook
I don't think that I"m very far off for the general population of high school students. Knowing that this is the truth, just why do we assign homework again?
Where do those hours get made up? During the 6 hours they are in school, simply because that is how you earn the points for homework completion. Do it in AP Stat, show it in Pre-Calc, consume points, repeat tomorrow morning in AP Stat. And it's Trigonometry Worksheets. Is my AP Stat class really less exciting than trig worksheets? Not a chance, but the homework "points" are more exciting as they appease the grade monger in all of us.
I'm all for allowing my students to make a choice about what they will be working on in class, as long as that choice involves learning. Consistently in my 1st period class (and each other class that I teach), the choice is made to fill in some unknown quantities for some triangles that nobody cares about (not even the teacher that assigned the homework) Why are you assigning homework if it's getting done in AP Stat? Can't they do that work in your class?
I don't assign homework. I don't plan on ever assigning homework again. I plan on assigning worthwhile assignments that students can make the choice to complete at home if they want to make it even more awesome. I plan on doing things that are valuable in class so that students do not need to work at home.
Imagine if your job gave you a minimal amount of time each day to complete everything for the next day for your 6 different classes and your boss told you, "Just do the rest of it at home." Oh, wait.....
Well, anyway, back to my 46 minute planning period :)
Some careful accounting as to how those 6 hours that could be spent working on homework are actually spent.
Hour 1: Facebook
Hour 2: Call of Duty
Hour 3: Facebook
Hour 4: Facebook
Hour 5: Facebook
Hour 6: Being a 17 year old....and throw in a little Facebook
I don't think that I"m very far off for the general population of high school students. Knowing that this is the truth, just why do we assign homework again?
Where do those hours get made up? During the 6 hours they are in school, simply because that is how you earn the points for homework completion. Do it in AP Stat, show it in Pre-Calc, consume points, repeat tomorrow morning in AP Stat. And it's Trigonometry Worksheets. Is my AP Stat class really less exciting than trig worksheets? Not a chance, but the homework "points" are more exciting as they appease the grade monger in all of us.
I'm all for allowing my students to make a choice about what they will be working on in class, as long as that choice involves learning. Consistently in my 1st period class (and each other class that I teach), the choice is made to fill in some unknown quantities for some triangles that nobody cares about (not even the teacher that assigned the homework) Why are you assigning homework if it's getting done in AP Stat? Can't they do that work in your class?
I don't assign homework. I don't plan on ever assigning homework again. I plan on assigning worthwhile assignments that students can make the choice to complete at home if they want to make it even more awesome. I plan on doing things that are valuable in class so that students do not need to work at home.
Imagine if your job gave you a minimal amount of time each day to complete everything for the next day for your 6 different classes and your boss told you, "Just do the rest of it at home." Oh, wait.....
Well, anyway, back to my 46 minute planning period :)
What defines "failure" in education?
This week is state testing week in our school district. Watching these kids go through this procedure, I can't help but feel bad for them. This is what their schooling career comes down to, in the eyes of the people giving out money and deciding whether or not they are a part of a failing school. Read that last sentence again. Really?
So you're telling me if the students in my class decide they want to solve the world hunger crisis using what they're learning and what they know, this won't be factored in to the final decision as to whether or not they fail? What if we decide to use our knowledge to assist those in need in Japan? Just how much of an impact do we need to make before this is acknowledged before test scores?
Those two outcomes get us a nice article in the newspaper, but we could still be considered "failures" without the right test scores. How is this right? How does it change?
So you're telling me if the students in my class decide they want to solve the world hunger crisis using what they're learning and what they know, this won't be factored in to the final decision as to whether or not they fail? What if we decide to use our knowledge to assist those in need in Japan? Just how much of an impact do we need to make before this is acknowledged before test scores?
Those two outcomes get us a nice article in the newspaper, but we could still be considered "failures" without the right test scores. How is this right? How does it change?
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