The Cumulative Final Exam

Please excuse the use of quotations, and please treat all quotations as if I'm using my hands to give the quotations signal.

Scenario A: Teacher speeds through all course material and is "done teaching" for the year by May.  They spend the remaining 1.5 months "reviewing" for the final.

Scenario B: Teacher spends time on each concept, working at the student pace to ensure everybody has a good understanding of each concept, differentiating when appropriate.  By the time June rolls around, there are 2 whole chapters (when did learning take place in chapters) that were not "covered". 

Since they both teach the same course, each teacher's students will be taking the same final exam.  After all, what better way to achieve a standardized curriculum than to make the final exam the same for everybody.  What will these final exam scores look like?

The teacher from Scenario A looks like a superstar.  An expert teacher whose students excel on the final exam.  A true veteran.  The teacher from Scenario B looks like a bumbling fool, a novice who can't even "cover their entire curriculum".  This is the teacher that others look at and say "They move too slow." (not sarcasm quotes)

The students from Scenario A look like the best and brightest, and are rewarded by high scores on a final exam that counts for 20% of their final grade.  Yes, 20%!!!  90 minutes of a school year equates to 20% of a student's grade.  The students of Scenario B are punished for having a teacher who cares about everybody learning, and a teacher that is following a district model of formative assessment and differentiated instruction.  They will not have high scores on their final exam, the same final exam that Scenario A's students beasted.

How does it make sense to give the same final exam, knowing that every teacher employs a different teaching style?  Why can't we have some freedom to develop our own final evaluation of what a student knows?  Something that is not necessarily a multiple choice exam.  Here's what I'd do: My End of Year Projects

Card Game: AP Stat Ideas

Below are 4 hands from the game "13" that my students now play all the time now that projects are getting finished and school is ending.  Apparently 2's are the best.  I don't know the rules, and I'm not certain they do either.  I believe you can play straights, multiple pairs of multiple numbers, I don't even know.  Do people besides students at my school play this game(i.e. do you know what a "cutup" is)?  An interesting way to analyze probability anyhow.  Here are 4 real hands dealt during a resource period.  Ideas...who will win?  who has the "best" hand

End of Year Project Topics

This is an incredibly interesting list of project ideas that my students have generated.  I thought I'd share what they're capable of when they have zero restrictions...

10-11 End of Year Project Ideas 

Some highlights if you don't feel like reading through the whole thing...

1. Mythbusters: Mac vs PC
2. Value of a Power Hitter or Contact Hitter in Fantasy Baseball
3. Developing software that is usable exclusively in an AP Stat class
4. Using a test vs. a qualitative measure to assess learning
5. Profiles of countries in a state of unrest to predict revolt (the wiki for this project)
6. Price differences between Ebay and craigslist
7. The chance of finding a 15 to 64 year old male in Luxembourg that is a noble compared to a similar-aged male in Denmark being a noble.  (easily the most unique project ever done)
8. Using Wikipedia, how long it takes for random words using the formula of always clicking the first blue, unbolded and unitalicized word, lead to the end word of Philosophy. On the theory that every word in Wikipedia will eventually lead to Philosphy. Words will be chosen via randomized dictionary words. (based on the fact that clicking the first blue, unbolded, unitalicized word of every page eventually leads to Philosophy)

With a little bit of freedom (okay, a lot of freedom) they come up with some awesome topics and they really enjoy their work in class during these couple of weeks.

How will I grade them?  By writing a list of what the student did well and what the student did not do well. 

A Farewell to Teaching

I'm writing this post to inform everyone that reads this (who knows how many) that at the end of this school year I will be making a career change.  I will be starting down the career path to becoming an actuary, which is a unique opportunity that I am extremely excited about.

I'd like to thank anyone that has taken the time to read this blog for allowing me to share some ideas about education that are unique.  I've continued to blog this year due to the amazing conversations that I've had with colleagues nation wide.  Most of you I've never met face to face, but I enjoyed having an audience to bounce some AP Stat and just general education reform ideas off of.  This is something I would not have done with anybody but my personal learning network on the internet.  Again, thank you.

Feel free to use any of my ideas in any capacity that you wish.  No need to be proprietary, as I'm all about moving education forward.  I encourage you to consult with and contribute to the class wiki that we've started this year, that will hopefully evolve into an online statistics resource for any and every statistics student that would be in need.

The Class Wiki: http://statknowledge.wikispaces.com

Will the blog continue?  Probably.  Just in a much different capacity and probably be more math nerd related than anything.  Again, to my PLN, thank you so much for contributing so much to my professional development. 

School Reform through the Eyes of Albus Dumbledore

"No spell can reawaken the dead, Harry. I trust you know that. Dark and difficult times lie ahead. Soon we must all face the choice between what is right and what is easy." - Albus Dumbledore, Harry Potter and the Goblet of Fire.

I can't help but think of this quote when it comes to education reform, so I'm going to list how things are done the right way and how things are done the easy way in various realms of education.

Implementing Change in a School District
The Easy Way: Write a policy
The Right Way: Have your buildings/staff make the necessary changes they need to help students learn

Technology Integration
The Easy Way: Buy some Smartboards and show the community our commitment to technology
The Right Way: Invest in technology that changes a teaching practice, not technology that isn't much different from an overhead projector

Community Relations
The Easy Way: Cave to whatever demands are placed upon you by the community, tell them you'll do everything they want
The Right Way: Stand up for something and explain to the community how it benefits your district, even if it means spending some money

Instruction
The Easy Way: Hand out some worksheets from a textbook manual and have students follow and copy down what you've done
The Right Way: Find out what each learner needs, and provide them with as much support for those needs as you can

School Structure
The Easy Way: Force all students to assimilate in to one model of what a school is
The Right Way: Provide students with several different options to attend school (brick and mortar, cyber, blended, etc) and have them choose which one works best for them

Grading
The Easy Way: Give points, then slowly and methodically remove them for each successive mistake a student makes. 
The Right Way: Have a list of things that a student does well, and some things they must improve upon.  Constantly revise and add to this list throughout the year.

Grading II
The Easy Way: Use a formula to calculate some type of average to summarize what a student can do.
The Right Way: Students have portfolios, that you can go through and look at to see their strengths, weaknesses, and interests. 

Personnel
The Easy Way: Make decisions based upon tenure/seniority/contract status
The Right Way: Make decisions based upon who is best for your district

A Project per Unit: Understanding By Design in AP

Some project ideas for AP Statistics that are unit specific.  I'd begin each unit by asking these questions and having kids consider just what data they'll collect and how they'll answer these questions.  Then build all the statistics concepts around them as they come up, not as a series of "concepts".

Unit I: Displaying and Describing Data
1.  Market Research: design a product, determine the market for it, determine how much you should charge for it

• Create a coffee stand for your school building
• Pillow-pack: A backpack with a pillow built in to it

2.  Consumer Education: Choose a series of similar products and determine which one is the best for consumers

• I have a number of kids working on an end of the year project comparing all types of smartphones
• Mac vs PC?
• Tablet PC's

3.  What makes a song popular?

Unit II: Displaying and Describing Bivariate Data (probably my weakest ideas)
1.  Have them collect data that makes them think about what a correlation actually shows (not causation, only a relationship between two variables, etc)

• Caloric Intake vs Weight 
• Grams of Fat vs Grams of Protein consumed daily
• Income Level vs Achievement Level in Standardized tests (state tests, SAT's, AP, etc.)

Unit III: Collecting Data
1.  What's the best sample we can get to investigate one of these questions?  I want them to see just how poorly they collected data in Unit I and II

• What proportion of the school district has internet access?
• Revise their sampling methods from previous units

Unit IV: Probability
1.  Design a game of chance that is profitable (run them all together on a casino day complete with fake money to see how profitable it is in the short-run)

Unit V: Inference for Proportions
1.  Continue any of the data collections that were done in the beginning of the year, looking for significant differences (consumer education, market research) - introduces significance, might be boring.
2.  Is there equality that exists between schools/institutions?  What do "richer" schools have that "poorer" schools do not?  Why?
3.  Tell a joke and determine whether or not it is funny.  Possibly look at a comedian's standup routine to determine if they are funny
4.  Type I and Type II Error: Explore wrongful convictions.  Have them explore some court cases that are under contention (OJ Simpson, Mumia, etc) and some court cases that are open and shut (Bernie Madoff).

Unit VI: Inference for Means
1.  Is there an advantage to eating a raw vegan diet vs the traditional "Western" diet? Inspired by recent events as we have recently started a Raw Vegan diet (and have never felt better)
2.  Is there equality between schools/institutions?

Unit VII: Inference when Variables are Related (T-tests for Slope and Chi-Squared Tests)
1.  Should you choose one letter over another when taking a multiple choice test? (sorry for so many testing heavy examples)
2.  Do a t-test for slope on any of the bi-variate data collected in Unit II

Most of the inferential statistics can be applied to enhance the projects and work done in the beginning of the year.  See my post on Inferential Statistics Data Collection for others, and of course feel free to lend me your ideas.

Inferential Statistics: A Different Approach

For the longest time I've given thought to providing instruction on inferential statistics in a unique fashion.  If you're an AP Stat teacher, it means a departure from the One-Proportion Z-test, Two-Proportion Z-test, One Sample t-test, Two-Sample t-test, Matched Pair t-test, Chi-Squared Test(s), t-tests for slopes of regression lines.

So here's how I'd start...all data collection.  Spend a couple of days collecting data for each situation.  One of the essential questions I'd like my students to explore throughout the year is "Which model is the most appropriate for data you have collected?"  Here's where we go into depth about why certain models are more appropriate than others...

Data to Collect

1. Number of victories in 100(or so) games of Rock-Paper-Scissors
2. Toss a thumbtack and record proportion of "up" 
3. Drop a piece of buttered toast 50(or so) times and measure how many times it lands "buttered-side down"
4. Give a dummy homework assignment and measure the proportion in each class that complete the assignment
5. Compare batting averages of two baseball players
6. Time how long it will take kids to walk to the pool and back
7. Prices of items at clothing stores (found through browsing catalogs online)
8. Number of each type of animal cracker per box
9. How long it will take you to sort beans on to bulls-eyes with a dominant/non-dominant hand
10. Give the ol' Memory Experiment(groups rate sentence on how hard they are to pronounce/how easily they can form a vivid mental image) and compare number correct for each group
11. Count the number of each color of M&M you receive in a sample of M&M's
12. Change drop-height/rotor length of paper helicopters and record the time it takes to fall

After you spend about a week or so doing data collection, ask students to reflect on how data was collected. Notice also that some activities are done the same way (measuring proportions/means).  I'm fairly certain this has to be done to guide reflections, make kids confused, and ultimately learn something about making generalizations (mathematical modeling at its finest).

Ideas for Reflection:

1. What was measured in each data collection?  How does it compare with other types of data?
2. Which activities were useful for making comparisons?
3. If we're not making a comparison, what can we do with the data we collect?
4. Does it matter than some samples are smaller than others?  
5. Create a display for each activity with the raw data.  Which models tend to be the most appropriate?

I can see this being two weeks of AP Stat where kids think about collecting data and fitting similar models to similar methods of data collection.  Once they start fitting models to each situation for comparison, then you bring about some hypothesis testing procedures.

If you're a Stat teacher or not, provide your suggestions and ideas for data to collect.  It'd be great to get a new type of data to collect from somebody outside of the Stat realm.