Does Major League Baseball Need a Stats Lesson?

I saw this data in the St. Louis Post-Dispatch last week claiming that the Cardinals are the 6th most expensive team  to see at their home park. (the "FCI" averages all of the columns from this chart together to get an estimate of what a family of 4 would expect to spend at the ballpark.)

I have no problem with the FCI, but I wonder if this chart's reporting of "MLB LEAGUE AVERAGE" is a little off. That row looked suspiciously in the middle to me, and when I counted rows, it was indeed exactly in the middle.

So what's going on here? Is it a misrepresentation of "average," do MLB teams attempt to group themselves symmetrically around this figure, or is it pure coincidence?

Here's the MEAN of those FCI listings by team:

Could the difference between 211.68 (reported in the table as "average") and my calculation of 211.89 be the result of rounding error in the data they used that I don't have access to in this report? Are there 21 rogue cents floating around in their numbers? 

What's this mean for my students?

I think this graphic and table is a good conversation starter for both mean vs. median AND the role of rounding in getting "different" answers. What's the clue that this CAN'T POSSIBLY be the median? Its not listed in the data of course. 

NCAA Tourney Simulation 2015

Following a process similar to last year's, I used the fan picks on Yahoo Fantasy Pick 'Em as a "true proportion," assigned integers according to those percentages for each team, and then used the randInt( function on my TI-84 to generate a number.

As an example, in the 2nd round game of Butler vs Texas, I assigned the numbers 1-60 to Butler (as the higher seed), and 61-100 to Texas. The number generated was between 1 and 60, so I chose Butler.

This year's simulation had Arizona upsetting Kentucky in the Final Four and Duke taking the championship in the final.

Here's the whole simulated bracket. Click the image for a larger view.

Simulating the NCAA Tourney with a Random Number Generator

It's "Big College Basketball Tournament" time, everybody!

(When I remember to get it in on time) sharing your bracket for the NCAA tourney is always an easy way to get conversations going with a lot of my students, which is especially good because right before Spring Break is when some of my students want to talk to me the least. :)

I did some research on building a "probabilities of the NCAA tournament" project a few years back, but it seemed kind of impossible, and not totally worth it when weighed against other curricular demands.

So, I scaled back expectations and started with having fun with it myself. Using the probabilities from the user picks on CBSSports.com's bracket manager, I simulated the outcome with a random number generator (from mathgoodies.com), and chose the victor from there.

BRIEFLY, MY PROCESS

Had this been the number generated for the game above between Oklahoma and North Dakota, OU would have been the winner because 33 is between 1 and 76.

RESULTS
To my pleasant surprise, the method produced a rather conventional bracket, while still making some fun, plausible upsets. As I'm writing, the first day's games are about half done, and the bracket is holding its own against most anyone else's.

(Effective) Teacher Technology Use Is Growing (INFOGRAPHIC)

A friend of mine, +Dave Hallmon , forwarded this infographic from onlineuniversities.com today and it had some points that really grabbed my interest.

1. 68% of students reported in 2012 that their teachers used technology effectively.

It doesn't go into what technology proficiencies made for "effective," or at what level, but that seems like an encouraging number.

2. Of teachers surveyed, 90% have a laptop or PC in the classroom.

This astounds me that is NOT at least 99%, but good for perspective, I guess. Even on days you're upset that your favorite tech tool isn't behaving, it could be WORSE.

3. 3 in 4 teachers say that tech allows them to reinforce and expand on content, motivate students, and accommodate multiple learning styles.

Is it statistically appropriate, then to link my first point, and this one and assume that of the ~75% of teachers that report these benefits, only 7% aren't doing it well? (Probably not, but it would be an interesting test of significance to run)

4. In a study of AP Calc students, the half in a #flipclass model scored an average of more than half a point higher on the 5 point AP exam scale

I feel like my most effective days teaching in AP Stats are the days we clarify misconceptions and reinforce what is understood. Giving lectures, which is something my kids DID ask for more of, seems like a bit of a time waste for kids that I know can and will mostly read/watch when I tell them to.

I have a hunch that at least a segment of these higher AP scores are because the brighter kids benefited more from the self-paced learning afforded by the video model, but it's significant enough for me to give it a shot next week when we return from Spring Break.

Reading in Math Class: Think Alouds (Formative Reflection)

First, I wanted to celebrate the fact that I tried Think Alouds with this iMovie trailer. (I blogged about the lesson plan here on Tuesday.)

That being said, today felt like a train wreck. :)

I had originally intended to copy each handout on the same piece of paper so I could have a parallel notes kind of situation like this:

I didn't get my copies done, so my first thought was to just have the kids pull it up in our AP Stats shared Dropbox folder and annotate on their iPads with any of our note-taking apps (since they were already out to transcribe the whole experience with Dragon Dictation). The whole process was started to get overwhelmed with all of the tech layers I was throwing on top of the lesson, so I abandoned that and eventually just went old-school print out of the text from my Google Drive file, highlighting items of emphasis and writing their thoughts in the margins.

There's a lesson planning truth here: Always try out new stuff with your most resilient class. My AP Stats class is my smallest, and the students most agreeable to patiently working on something else for another class if/when I have to troubleshoot. They're also independent enough to do some extra work YouTubing or reading on their own later if necessary (which is crappy for a teacher to do when its unintentional, so of course, we try to limit that). :)

My Verdict:

Kelly Fisher-Bishop followed up to my comment on her post about Think Alouds and it seems to summarize my current thoughts on the strategy:

I think this strategy will take some time for it to work and run smoothly; students will have have trouble vocalizing their thoughts in the beginning, but after some practice and modeling (on your part) the students will eventually get the hang of it. If it becomes part of the class routine, then students will get better and better at using this new reading strategy.

 If you watched all of the trailer I shared at the beginning of the most, my kids really were "defying stereotypes" with the reading lesson. Part of the problem may have been the texts I ended up choosing, but I'm willing to rest right now on a level of discomfort they had a) reading aloud in class, b)reading in math class (although of any of the courses in our catalog, stats has the most reading as routine), and c) working in new groups (they usually just pair up with the person next to them. I truthfully may have thrown too many variables into this lesson to attribute the effect to any one of them).

Students' Verdict:

Here are some of their thoughts on the lesson (collected using Today's Meet).

"I liked that we worked in groups to figure out what the reading was talking about."

"Group work is nice, binomials are a little clear, could've gone over it as a class more. I learned more than if it would have been a ppt."

"I liked that we could use the iPads to help figure stuff out. If we had more time to talk about it afterward, that would have helped me more" 

"I like that we got to go over the material from two different websites n we reviewed it"

"Can we do a binomial problem in class together step by step?" 

They're usually nicer than I expect them to be. :) Two things I gather from these responses:

1. they liked talking it out with their partner/group 
2. a summary of the activity/application of what they learned was necessary to validate thoughts from the group and clear misconceptions that may have developed. 

Adaptations for YOUR class:

Using Dragon Dictation was a waste of time. The help in the app suggests that you speak directly into the microphone, which is unnatural and weird to do if you're trying to have a constructive conversation with a person. If I want to archive the audio next time, I would just use the recording utility in Noteability or SmartNote Free. As mentioned from the student comments, a summary of the learning and thinking that went across groups should have been compiled before we left - a couple ways to share could be Todaysmeet.com, a Google Doc that everyone edits as they wrap up their own conversations, or good ol' pieces of butcher paper for each group.

As far as choosing your text, its very important that the reading level is appropriate for your individual learners so they can get into the reading. A great opportunity for differentiation would be to group according to reading level and provide separate, approachable texts. My Stats class has been previously screened to make sure they could handle the reading required for the course, but when I try this with my Applied Math class next week, they will shut down if the reading is over the heads.

Have you tried Think Alouds before? Any other tips for my next attempt?

Reading in Math Class: Think Alouds

Here's an attempt to synthesize a more lit-comp/ social studies/ science geared strategy for use in the math class. (We get used to that, am I right, math teachers?) For more info on think alouds, here's a post from Kelly Fisher-Bishop, an instructional coach in my district.

The point of a Think Aloud is to get students verbalizing the text, engaging with vocabulary, and forming an understanding of the nonfiction text. The "think aloud" part of the Think Aloud is a conversation between partners in which they explore meaning behind the words, connect concepts in the text to prior knowledge, define new words, and communicate their reasoning.

Archiving a think aloud could be done with Cornell Notes, a simple voice recorder, an app for notes and recording, and (what I'll be trying, the Dragon Dictation app, which would convert students' think aloud to text notes for later review, allowing them to focus on their dialogue.)

Math Class Adaptation:

My AP Stats kids did an introductory activity about binomial random variables (Lesson 8.1, TPS2e) today in class, played around with binomial coefficients and probability of discrete outcomes, and connected concepts (such as normal approximations) important in this lesson to material we've already mastered.

The purpose of this Think Aloud, then, will be to formalize the connections they made today by drawing definitions and concepts out of two different informational texts about binomial distributions, getting down definitions, and sorting out the reasoning behind the construction of formulas and when their use in appropriate.

I created a handout for them to read and annotate on, and I'm going to have them run the app the during step 2 of the Think Aloud, when most of the partner discussion will occur, and during their work on the practice exercise.
Handout 1, informational text 
Handout 2, Guiding Questions/Discussion Log

Although this is two pages, my plan is to print these on one sheet, side by side.

Here's a demo for the Dragon Dictation app

Adaptation for YOUR class:

Certainly if its common practice for your students to be reading informational texts, using Think Aloud with your students (and meta-cognitively modeling what you do most days anyway) should help your students construct sense and meaning. For instance, in math or science topics, I'd say most Wikipedia articles are very informative and could be very useful for students' understanding. A common problem I encounter, however, is that there is too much information in the article that becomes noise for what I want to be reading. Giving a tool to your students to sift out unnecessary information and methodically go through the text can make them more independent as learners and less dependent on you or only YouTube.

FacebookStories.com - Infographics Your Students Will Care About

Have you checked out your Facebook "Year in Review 2012" yet? If you're a blogger, you're probably  a pro at reflection, so maybe you did. What you may have skipped (because I very nearly did) were the "Facebook Trends."

What delightfully surprised me about the 2012 Trends was that it was a collection of culturally relevant infographics. (and even broken down by country. and analyzed.)

Background

I LOVE infographics. They're really just a 21st century repackaging of pie charts, line graphs, or histograms with words and associated images, but I love them because (good) ones are designed (instead of produced) and they're relevant. Pie charts live in boring budget proposals; line graphs on the ticker of Bloomberg TV or the Wall Street Journal. But infographics get shared on your Facebook timeline. Their pinned to your "Isn't That Clever" Pinterest board. They're so integral to the layout of USA Today, you probably didn't even notice.

To start off the year in AP Stats (and to ensure my students had appropriate degrees of tech proficiency before I unleashed wicked expectations upon them), I had everyone bring in infographics to share and then we discussed the ways graphs were represented and repackaged on them.

I think most of them just ended up doing a Google image search for "infographics," but here were the sites I suggested they try:

nerdgraphs.com
visual.ly
coolinfographics.com
Infographics - GOOD
flowingdata.com

The unintentional consequence of this assignment was that I also got to know my students' interest a little better through their infographic choices.

Here was my favorite; the controller pie charts opened up a discussion for me. Lost scaling opportunity in the bottom left corner about best-selling genres.

So What?

My Stats students did a good job grabbing infographics, and most of them took a clear interest to the assignment and made it meaningful, but what I like about Facebook Stories' Trends is that they're simply produced, yet relevant to their audience, and in an marketplace your students are frequenting.  Better than that, in the endless battle between what I want and what I can accomplish, these graphs represent to me an even more approachable example to have my students creating their own infographs. (When that finally happens.)

The one at right features songs that came up most in status updates. It's a pie chart.... but not really. Way to psych me out. I like these the slices were scaled by radial length rather than degrees because my eye tends to ignore tiny slices that have arrows pointed to them. (No offense, east coast, but this is kind of what I do when I look at maps of the US, too)

I mean, seriously. Can't you imagine this on a .PPT slide with the speaker saying, "As you can clearly see..."

There were a few that were slightly confusing, however, and strangely enough, looked very much like something I'd expect to see from a student who lazily wanted a easily scaled shape.

Bottom Line:

In my opinion, infographics are one of the least intimidating ways for students to begin publishing for the web and sharing on social media. Kids love poster projects - infographics are a digital extension of that (but they don't even HAVE to be digital). 

Infographics can introduce percentage problems, experimental design, discussions on statistical bias, geometric similarity, and even log scales in upper-level courses. Because they're all over the web and literally relevant to any interest, they're also convenient for enhancing engagement through choice and personalization.

Resources:

I went to a great infographic breakout session with +Kathy Schrock (@kathyschrock on twitter) at METC 2012. She's said it better than I can; here's her infographics page. If you're going to METC 2013 (after you see me) make sure you check out at least one of her sessions. 

The (Math Teacher's) Student Holiday Gift Guide

If I had my druthers, here's what I'd love for all of my Algebra 2 students to have under the tree on December 25th, (or some other time this holiday season) separated into categories:

STOCKING STUFFERS (Aunts, Uncles, Cousins, Friends)

• Highlighters
• Great for placing emphasis on steps, color coding elements of formulas, or triggering reminders of side-notes the student took during class
• Grid paper notebooks
• I had my students purchase grid paper composition books (or notebooks) this year, and it changed my teaching to be able to have them sketch (appropriately neat) graphs in their notes without having to have coordinate grid squares handy every day. Also, the students didn't have to tape/staple said squares into their "regular" notebook. Graphs, equations, and charts are all right next to each other, all in context.
• Personalized pencils
• My mom bought me 2 pencils when I went off to college that had "Charles" written on the side of them, and I cherished them so much I couldn't bear to sharpen one until this past summer. They sat in my desk waiting for that right moment for about 10 years. So.... having a lot of personalized pencils would have softened the blow of using them the first time. As far as my students, I've kept track of the pencils alright, and my students need some help in that department.
• Zebra mechanical pencils
• These metal pencils have a feel similar to using a pen, and for reasons similar to the pencils listed above, your student will probably keep track of this longer (and feel more important). I hunted a Zebra ballpoint down for a week once in high school.
• Erasers (Magic Rub)
• Mathematics and problem solving can be messy work - I always feel more ready to make mistakes and try a ton of different approaches when I'm working in pencil with a great eraser, than with ink. Finality is fantastic, but kids need to be okay with starting over sometimes.

---

UNDER THE TREE (Brother, Sister, Close Friends, Mom, Dad, Grandparents)

Books

If the only place my students ever read about math is in their textbook, they're always going to think no one really does anything with math.

• Freakonmics: A Rogue Economist Explores the Hidden Side of Everything (Levitt and Dubner) 
• Superfreakonomics: Global Cooling, Patriotic Prostitutes, and Why Suicide Bombers Should Buy Life Insurance (Levitt and Dubner)
• The Number Devil: A Mathematical Adventure (Hans Magnus Enzenberger)
• Euclid's Window: The Study of Geometry from Parallel Lines to Hyperspace (Leonard Mlodinow)
• Cartoon Guide to...
• Calculus (Gonick)
• Statistics (Gonick and Smith)
• The Manga Guide to...
• Calculus (Kojima and Togami)
• Linear Algebra (Takahashi)
• Statistics (Takahashi)
• How to Lie with Statistics (Darrell Huff)
• Math Doesn't Suck: How to Survive in Middle School Math Without Losing Your Mind or Breaking a Nail (Danica McKellar)
• Kiss My Math: Showing Pre-Algebra Who's Boss (Danica McKellar)
• Hot X: Algebra Exposed (Danica McKellar)
• Any sodoku

Electronics

• TI - 36X Pro ($18.97) or Casio FX-300ESPLUS ($12.99)
• These beefy scientific calculators are closer to what scientific calculators in 2012 should be. Can do most statistics, trigonometry, and functions work a graphing calculator can besides the graphing, yet comes in under $20, probably less than you might spend on some of those books.
• Casio Prizm FX-CG10 Color Graphing Calculator ($108.35)
• I've said before, I'd rather students not have to carry a dedicated calculator, but I beg of you, save $40 and buy the top of the line Casio graphing calculator instead of the Texas Instruments. This Prizm has the same functionality as the TI NSpire CX, at a fraction of the cost. 
• I would buy my own children a Casio for literacy reasons, as well. Most math teachers are still largely unfamiliar with how the menus on Casios function and are organized, so a student with a Casio has to be skilled at reading and following manuals. I've seen some kids sink because of this, but it wasn't because they couldn't, but because they wouldn't. I like knowing I'm nurturing young technical readers.
• Livescribe Echo Smartpen ($75.99)
• Not just a pen, the Livescribe will record audio, and track pen movements when used with the dedicated notebooks (yes, I know, another investment). 
• Livescribe pencasts are the selling point for me. You could use anything to record audio, but the pencasts can be replayed on a phone, tablet, laptop, or PC and students have their very own Khan Academy-style videos.
• Apple iPad Mini ($458) or Amazon Kindle Fire ($199)
• Everyone knows that tablets put learning in the palm of your hands. I may not be reading books all the time, but I'm definitely reading more content (blogs, professional websites) since my school district gave me an iPad last September, and students are going to need them in college, anyway.
• Moleskine Evernote Smart Notebook ($24.95)
• Evernote is fantastic for curate material and easily search text and notes later on, but not everyone wants to take notes on a tablet or laptop all the time. This notebook has special paper and tagging stickers that, when paired with a tablet or smartphone, allow you to upload those handwritten notes into your Evernote account and search/catalog however you please. 

AP Stats Teacher Advice (from a vet, not me)

As a part of my can't-believe-I'm-teaching-ap-stats preparations, I signed up for the electronic discussion group via the College Board's website. Following along with the discussion via my email inbox makes me feel oh-so 2002, but there have been a few helpful nuggets of advice, discussion, or desperation that have given me better perspective and preparedness.

Doug Tyson, of Central York High School in York, PA offered up this advice today on the EDG for me and my fellow first-years.

 Subject: Are you a new AP Stats teacher?

If no, then read no further.

If yes, I will break one of my long-standing rules in order

to write this message.  That rule is "Never offer un-asked-for

advice."  Although it has served me well over the years,

recent posts on this group have prompted me to offer 1 or 2

thoughts.  You are warned that these come from my very

own mind - read with eyes wide open...

1) Don't be afraid to admit to yourself, other AP teachers,

and your students that some of the material is subtle and

that you're still learning Statistics.

2) Real data are subtle and often break rules-of-thumb.  Be

wary of inviolate rules in Statistics, as they are often really

rules-of-thumb in disguise.

3) Think deeply about the ideas.  Get your students to do the

same.

4) Ask questions on this EDG. It's a safe place to learn.

There are lots of really knowledgable people here - I know

some of them, and they're really nice people.  And they

were all new Stats teachers at one point in their lives.

5) Read everything about Statistics you can get your hands on.

6) Develop a sense of wonder about the world around you.

Develop the same in your students.  Statistics (in one view)

is about understanding the world based on measurable evidence.

The world is your laboratory and playground.  Have fun!

Regards,

Doug

(former new AP Stats teacher) 

The EDG isn't as handy for me as Twitter, but I can't bring myself to unsubscribe.