Today's AP Stat Lesson: EXCEL HEAVY - VLOOKUP(RANDBETWEEN(NERD, GEEK), STATGEEKS,2)

Today's(tomorrow's) plan for AP Statistics is a little Excel heavy,  something that I hope carries over for my students into college and beyond. Is there a standardized test that measures a student's increased proficiency at Microsoft Excel, or other computer apps for that matter?  Most commands involve looking up a value at random between zero and one hundred.

Each student has been keeping track of the number of sheets of paper received in each class, each day, over the span of about 2 months. The focus is on teacher created paper, so if a student uses a piece of their own notebook paper it doesn't count.  Incidentally, om pretty sure that AP Stat is dead last for every one of my students major subjects (AP Stat instructor pats himself on back).

Using this info, they are going to create a probability model for the number of sheets of paper received for a single class.

For AP Stat...

SHEETS OF PAPER    0     1      2 

PROBABILITY         0.90 0.05 0.05  

Now that the probability model is created the Excel fun can begin.  Number all cells in one column from 1-100 to represent a possible outcome. Place each possible outcome in the second column according to it's the probability you observed. Example: in the chart above, the probability of receiving 0 sheets of paper was 0.90, so spaces 1-90 would be 0. The probability of receiving 1 was 0.05, so 91-95 would be 1, and 96-100 would be 2.  Repeat for all other possible outcomes. Suggest to students that they choose a class that is at least manageable as far as different numbers of sheets of paper.  Yes, there is a way to make Excel do this, but that is a little too awesome for an AP Stat class.  

Create a new sheet for simulating new days of each class. For the first day, we are going to "lookup" random values from the previous sheet to see how many sheets of paper we will receive. The command for doing this... VLOOKUP(RANDINT(1,100),in the previous sheet, give the value in the second column in the row that the random number is in). 

Example:  =VLOOKUP(RANDBETWEEN(1,100),Sheet2!A$1:B$100,2)

Keep the dollar signs so that when you drag to autofill the formula they continue to look within the same array of cells. Autofill about 200 or 300 of these cells...or 500 :)

Next we're going to calculate the average number of sheets of paper we've received each day. AVERAGE(cell to the left and all cells above). 

Example: =AVERAGE(B2:B6)

Now we can look at the average over the long run (1000 days, or even more) and begin to build our definition of Expected Value.  Then, later, we'll do expected value the easy way in Microsoft Excel using the formula.  I wanted them to wrap their brains around the definition of Expected Value before they began using the formula: E(X) = SUM[X*p(X)].  It's pretty cool to see just how long of a run you need to make the simulation average approach the expected value.

The lesson is a bit like a cooking show, but it's the first time we are in Excel. The kids use their own data, so that's enjoyable/unique for most of them. The bigger idea of simulating outcomes is very powerful in learning statistics. I love nothing more than a student centered approach, but I would hate to say "discover how to use vlookup and randint functions in Excel. If anyone has a way to take a constructivist approach to learning Microsoft Excel, I'd love to hear it.

The Excel spreadsheet that students create

My Test with No Right Answers

At the slightly more than halfway point in the year, I decided to give my students an assessment on skills we would have learned previously this year.  In an AP Stat class, this type of exercise is meant to take the place of the 2 weeks of "review" that most educators wind up with at the end of the year before the AP Exam.

Here's the test: AP Statistics Mid-Year Assessment .  Using this link (and excusing the poor formatting that comes with inserting images into Google docs) they are to create a Google Doc and share it with me that is essentially their stream of consciousness  statistical reasoning.  They were permitted to use the class wiki, their Stat textbook (BVD - Stats: Modeling the World), and any other online resources available to them.  Big thanks to David Wees (@davidwees) for the data, graph, and the article!

They were not permitted to use each other as a resource, as this was an assessment to see what they know as individuals.  This makes me uncomfortable, since it doesn't necessary follow the cooperative model I've we've built the classroom on.  Next time I give an assessment, I'll allow them to use each other as a resource as well, but the task needs to be uber-authentic.  Suggestions?
I'll share a conversation I had with a student about this, since it made my day.

"Mr. C, can we use each other as a resource?" - Student
"I'd prefer not, since I want to see what you know." - Me
"But in 'real life' we'd be allowed to use each other." - Student
"Arrggghhh, why must you make that argument?" - Me
"Because you taught me to." - Student

First thing a Stat teacher, or anyone familiar with Statistics will notice is that for most of the questions there's not really one "right" answer.  The purpose behind this is to allow kids to think and write what they know, in regard to the skills being assessed.  I'm loving the thought that has gone into each response.  It feels like I've really touched on something here, something that does a little bit better than the strategy of "write everything you know about the topic" for the poor test taker/assessment do-er.

So what resource did kids use the most?  At quick glance, my class wiki comes in first, with the Stat textbook coming in second.  I'm hoping this spurs more content creation on the class wiki, so that it can develop into the ultimate online stat textbook.  Yes, I am still living that dream.

What to do When the Projector Bulb Breaks? Don't Use It...

I float between 3 different classrooms.  All of them equipped in pretty much the same way (laptops, Promethean board, etc).  Upon arrival at my last class of the day, the teacher who is primarily in that room asked me, "How are your punting skills?"  then informed me that the projector bulb blew right in the middle of one of his Calculus lessons.

Fortunately for me on this day, my students did not need to use the board (please note the use of "my students" instead of "I" in this sentence).  So what happens?  I made a few adjustments here and there, and I have one of the best AP Stat lessons I've ever had.

The Plan
Students were assigned three "drawing" tasks, of which they could use any drawing utility they wanted to use (Paint, a Drawing in Google Docs, old fashioned pencil and paper). 
1.  Construct a tree diagram labeled with proper notation to distinguish between P(A), P(A|B), and P(A and B)

2.  Construct a tree diagram for a two-card Texas Hold 'Em hand and for two rolls of a die (illustrate the difference between independent and non-independent events)
3.  Construct 2 Venn Diagrams for drawing one card and the event that it's an Ace or a Heart and also for the event that it's an Ace or a Ten (difference between disjoint and non-disjoint events)

What Happened
I found myself sitting with each individual student, having a conversation about at least one of the topics mentioned above.  None of these conversations began with a student asking "Did I do this right?"  Most of the conversations led to one or more of the skills I had targeted with my original plan.  The students I wasn't actively talking to were talking with others, having discussions about the likelihood of getting two aces in a hand.  Another pair discussed the difference between independence and non-independence through other examples than the ones they created a tree from.

Where I'm going with this
Gradebook revamp...again...slightly.  I've been wondering how I can give more feedback and guide instruction.  After a few classes of these one-to-one(or 3) conversations, I'd like to have an accurate reflection of where each student stands with regard to the skill set we're currently learning.  I see this as a continuously updated Google doc to reflect upon conversations I've had, and students' demonstration of mastery during class.

After I put together my assessment of a student's body of work, I want to share it with them, and place something in my gradebook after I see how it fits in the scale of 1(minimal) to 5(advanced).  I've decided that this has to be done not just after an assessment, but after a consideration of a student's entire body of work.  I don't want to give a test, and have that be the lone summary of what a kid can do.  That's the old way.  I want to consider an entire body of work (tests, quizzes, projects, formative assessment, etc) then place a numeric score in my gradebook.  Yes, the last part of that sentence makes me just sigh and agree that I'm going along with the establishment, at least just a little bit.

Resources
My Probability Skills List (SBG)
Rethinking Assessment (Spencer's Scratch Pad)
What is "Bad" Teaching (Steve J. Moore)
Slideshow of the Lesson Itself

10-11 Probability Wrapup

View more presentations from christjt.

"AP Kids" are not the only ones who need quality learning experiences

After hitting the Google Reader hard while at Subway the other day (probably should've been eating lunch and relaxing instead of working) I was inspired by @InnovativeEdu's post on asking kids to design their own learning. Having just switched to the project-based learning format for my classroom, I love to share what my students are doing at these professional development sessions we conduct.

The question that always comes up is "Yeah, but what level do you teach?"  When my response is AP Statistics, it's immediately dismissed since "they are AP kids."  So what if I said, "I had this great lesson where I stood and lectured for 46 minutes with zero audience participation!"  I can almost guarantee to have the same response, "Well, your lecture worked so well because they're AP kids, no way that would work with my 4.0's!"

As an educator in a professional development workshop, why not spend that time to think of ways to reach the kids that are not "AP kids".  It seems like that would be a better use of time than to confirm your suspicions that there just isn't anything that works to educate those that are not taking Advanced Placement courses.

The students in 4.0 classes are the ones that have been most vocal about being not interested in what you have to say.  They are students that are completely unwilling/unmotivated to work unless it interests them.  Know what is especially uninteresting...x's, y's, and slopes of lines.  But these lower level courses cover basic equation solving and "find the slope" the exact same way, over and over again from the time the student is in 9th grade until 12th grade.

Great lessons, quality education, and interesting projects shouldn't be reserved for the best and brightest students.  The 4.0 students don't need more lectures and more basic junk that they don't care about.  They need to be interested, first and foremost.  They don't need more discipline or a rigid classroom structure.  They've told you 100 times that they hate that environment, so stop imposing it on them.

When I see my "AP kids" work on a project that they're excited about (sampling teachers in the school to see if they have tattoos, experiment on whether or not people can walk and text, see how often radio stations repeat certain songs) they aren't excited about it because they're "AP kids".  They aren't excited about it because I threatened them with detention if they showed a lack of enthusiasm.  They're excited about it because they had the choice in what they wanted to do.  They're students, there is no way they are so drastically different than their peers that just so happened to not do well in one math class so they were forced to slide down the ladder and be stuck in "4.0 world".

Oh, and they learn way more from me doing their own projects than they ever could from answering some multiple choice and some free response questions for me.

Reading through state standards(PA), going "mental"

I am spending my snow day planning for a presentation on technology integrated K-6 math instruction.  The focus of my session is on generating student inquiry and keeping technology completely transparent.  I am keeping this presentation aligned to state standards and vision, and doing so makes me very uncomfortable.  These standards/essential questions/competencies seem to all center around being able to generate a correct answer for a test.  This elementary math curriculum framework can be found at the Pennsylvania Standards Aligned System Website.  Here's a few phrases I don't particularly care for:

Taken from the 2nd Grade Mathematics list of Big Ideas and Essential Questions:
1.  "How do we know when it is appropriate to estimate or when it is appropriate to use mental math for an exact answer?"
The person that included the phrase "mental math" is clueless in the area of mathematics.  Estimation and approximation are (in my view) much more "mental" than development of an "exact" answer, yet they are projected here as completely non-cerebral tasks.

2.  "Develop extended understanding of multiple models, and properties of addition and subtraction, leading to fluency with efficient, accurate and generalizable methods to add and subtract multi-digit whole numbers and develop quick recall of addition and related subtraction facts. Select and apply appropriate methods to estimate sums and differences or to calculate them mentally."
Again, here they reference calculation as being done "mentally" and estimation as something that's done as an alternative to thinking.  I also don't like the use of the words "efficient" and "quick recall" as they imply that the student that adds two numbers in 10 seconds is somehow better than a student that adds two numbers in 10 minutes.

As we move towards common core standards and the like, is this the language that is to be used?  If so, mathematics instruction will never be more than an instruction of process.  A focus on efficiency over a focus on an understanding of mathematics keeps us at this procedural level.  Maintaining that estimation is done non-mentally, now we're completely missing the boat.  Right answers are not the most important part of learning mathematics.  Isn't it time we start asking our students to experiment and create in their math classes, instead of simply generate the same right answer that 25 other classmates generated?

Reassessment Fridays (SBG): A Love Story

“Every student did their own thing in class today.”
How often is that the summary of a mathematics class?  How about an art class? 


Today was the standard reassessment day for my AP Stat classes.  I wasn’t sure how I was going to let students reassess when I started Standards Based Grading.  I’ve come up with using every Friday as a reassessment day.



I let students pick 2 skills to reassess on.  They pick them Wednesday, I create reassessments Thursday, they take them on Friday.  The reassessors are given a mail merged document that is their assignment for that day’s reassessment.  Should they choose not to formally reassess in class, they always have the option to do a project on their own to show their mastery of any of the skills they have learned.  This has been a system that works for the students that want to reassess, but it works even better for those not reassessing.


Today about a third of each class was reassessing.  So what do the other students in class do?  They play.  They learn.  They collaborate:

1. One student began conducting simulations to simulate random clicks in Minesweeper.  Two others quickly became interested and a Minesweeper collaborative was born.
2. About 10 different students were editing 10 different pages of the class wiki to make it an online textbook.  
3. They were gathering data for different projects they hope to complete later in the year
1. a project where they wish to determine the proportion of teachers at school that have tattoos
2. simulating hands for various different card games
3. the true proportion of dives by a diver that are “ripped”

I look forward to my “Reassessment Fridays” because of the classroom vibe.  I’ll provide a few ideas for what can be worked on, then they get started doing things that they want to do.  Today’s ideas: Conduct a simulation, finish an old project, start a new project, edit the class wiki, create models of data collected this week.  I’m immediately working on making this the classroom activity for every day, not just Friday.  


My favorite part about it is that I am providing them time to be as smart as they want to be in class.  I’m not tricking them into learning with some gimmick.  I’m not having them finish a worksheet for points.  I’m not asking 26 of them to answer the same question.

Dares for the 21st Century Teacher

I dare ya to...
...teach math without using "x" and "y"
...throw out all of your worksheets
...let students decide what's important to learn in history class
...teach English without assignments of "write a paper"
...(for high school teachers) do activities that you get from Elementary school teachers
...make your students say more than you do during a class period
...let your students design the science experiment
...never give a student the correct answer
...design an activity where every student generates a unique product
...let your kids use their cell phones to learn
...teach Geometry(high school) using Euclid's "The Elements"
...let your students pick what they want to read
...not assign homework
...have students research a topic strictly through Twitter
...involve creative writing in every topic of your course
...let kids decide if they need a desk or not
...never teach the same lesson twice
...teach phys ed. using nothing but multimedia

Other suggestions?