Categories
High School Middle School Statistics

Estimation and Anchoring

A recent post by my Stats-teacher friend Anthony, “Wisdom of the Crowd“, reminded me of an estimation activity I have used many times in my 9th grade Stats class.  The activity is based on a chapter from John Allen Paulos’ book A Mathematician Reads the Newspaper.

You’ll need two groups of students; 2 different classes will do.  Each student uses an index card or a scrap of paper to write responses to 2 survey questions. I warn the students beforehand that the questions may seem strange: just do your best to answer as best you can.

  • Question 1: Do you believe the population of Argentina is MORE or LESS than 10 million people?
  • Question 2: Estimate the population of Argentina.

Allow a few moments between the questions for the inevitable blank stares and mumbling.  Then collect the responses.

For the second group, you will ask the same two questions, except that the first question will replace 10 million with 50 million.  After you have data from both groups, write it on the board or print it and hand it out. It’s time to analyze and compare. Challenge students to communicate thoughts about center and spread. Also, which group’s data do they feel does a better job of estimating question 2?  It’s a neat activity, and while you will receive some strange responses as estimates, and students will generally guess higher on question 2 if they have been anchored to the 50 million number.  Some guidelines for this activity are avilable.  Have fun!

According to Google, the actual population of Argentina is around 41 million.

 

 

Categories
High School Statistics

When Student Choice is a Struggle

Like most of the East Coast, schools here still have quite a ways to go before enjoying summer. I see my students for one more full week before final exam review begins and finals are given; a time which becomes more crazy as I travel to Kansas City for the AP Stats reading (or…Stats Christmas in June!)

It’s a starange time of year for AP Stats.  The College Board exam was given on May 9, and students took a final exam in my class before then, so we have been done with new material for some time now.  With a full 3 weeks (or more) between the exam and the end of the school year, it’s a time to take my foot off the gas from day-to-day material, but I still need to see my kids engaged in statistics.  Our culminating event, Stats Fair, provides a chance to highlight our program and keep the statistical ball rolling.  There’s really only one requirement for Stat Fair: design a project of your choosing which serves as evidence of your statistical learning. At the Fair, students show off their work to invited guests and fellow students (you can see pictures from previous fairs on my school website).  Teams must also provide printed documentation of their project to me.  It’s a great opportunity to be creative, study something you are passionate about, and explore something new.  There’s just one little problem…

Most student project ideas suck

Yep.  After a year of learning about experimental design, the role of randomness, and all sorts of nifty confidence intervals, many of my 17 year-old students will revert back to their 6th grade dopplegangers; proposing scientific studies of their peers’ favorite colors or chocolate chip cookie preference or how much honors’ kids backpacks weigh. Sigh….

Maybe I’m just jaded.  I warn the students early-on that it is likely I will reject their first 5 stats fair ideas.  It’s not that I am intentionally trying to be mean, rather I want my students to pick something memorable, something they could speak passionately about in front of others.  Working with students to develop their concepts could be the most frustrating part of my academic year.  Why is it so difficult for students to develop a “good” concept?

  • Despite a year full of examples and articles, it’s still a tough leap to the “real world” of teenagers.
  • Developing a good concept takes deep thought, revision, patience and reflection; not always teenage qualities.
  • The best concepts often contain a high dose of creativity – not something we are always accustomed to in math class.
  • It’s the end of the year, and the beach awaits

But all is not lost!  Today’s class started with a rousing success: a student, who had earlier proposed a study of NBA player ages (which was going nowhere), finally moved towards one of his passions – music. Using an app on his iphone, he tested the ability of peers to detect high and low pitches in mHz.  This led him today to some independent study online of the human ear, and reflection on the data he had gathered.

Another group is using their passion for fashion to see just how “skinny” jeans are these days, comparing waist sizes from different stores.  Some interesting data coming from this.  Another group is testing the “locally grown produce” claim of supermarkets…neat stuff!  And I’m looking forward to the random study of our school’s wireless device access – just how slow is it?  It’s the interesting projects which keep me coming back, and make this class memorable – like the team a few years back who entered and won the American Stats Association poster competition with their Bacterial Soap review.

Stats Fair is next Friday.  Look forward to sharing pictures and reflections!

Categories
High School Middle School

Your Official Guide to Math Classroom Decorations

null_zps9fabad2bThe most recent challenge by the MTBOS (Math-Twitter-Blog-oSphere) is to share what’s on your classroom walls.  (Follow the action on twitter, #MTBoS30)

This post will go beyond my own classroom, and take you on a tour of many classrooms of my colleagues.  Here I present to you the Official Guide to Math Classroom Decoration.

To rank these items, I will be using the “Justin Scale”, an internationally-accepted scale of math beauty.  It is based on the works of Justin Aion, who is an expert on classroom decoration.  Seriously, you should be following Justin’s Blog for his daily classroom obsessions.

Here’s how the “Justin Scale” works

  • 1 Justin = an insult to scotch tape
  • 2 Justins = better than having a blank wall; marginally stimulating mathematically
  • 3 Justins = setting the tone for an engaging math experience
  • 4 Justins = cool beans!

You can see it’s pretty scientific.  Now, on to the decor!


PROCEDURE POSTERS

null_zpsc7a23222In the history of math posters, has any student ever looked at one of these and thought “hey, so THAT’S how you add fractions”…seriously?  Sure, these posters are well-intentioned, but they are boring as heck and suck any imagination out of math class.  Also, I have to cover them up anytime the SAT comes around.

VERDICT:

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MATH T-SHIRTS

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I like to have items around my room which tell a story. Maybe they are stories of past students or experiences; other times they remind me of math nuggets I pull out once a semester. These shirts are from a number of Muhlenberg College Math Contests from the past few years, each with a neat math concept from the year of the contest.  On the left, the 28th year celebrated 28, a perfect number. 27 is a cubic formula, and the 31st features the Towers of Hanoi.   Full disclosure, I designed the 16th shirt as an undergrad.

VERDICT:

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TI CALCULATOR POSTER

null_zpsbff2ac29Go to any math conference and you’ll find gaggles of math teachers walking around the vendor area with swag bags, free stuff the many companies have for you. TI posters are one of the most popular items, and you’ll find many math classrooms sporting these artifacts of math boredom.  “It was free, therefore I must place it on my wall”

These posters fill lots of space and give your room the right dose of geekiness.  And a reminder of the vast machine TI is.  Have any english teachers ever placed a large photo of a typewriter on their wall?  Nope.

VERDICT:

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INFOGRAPHICS

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A338E759-516A-4B97-8AAE-EB7C225B9AB1_zpsxravcheaSo many cool infographics to choose from, so little toner. Love posting these guys all over my room; love it even more when I find kids checking them out just before the bell.  But they are a pain to print, and they age badly.

 

 

 

 

 

 

VERDICT:

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ASSORTED MATH HUMOR / INSPIRATIONAL POSTERS

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Usually purchased by rookie teachers, you will find these posters at your local teacher supply store.  Hunting season for these posters is short, running from early August to mid-September, so get yours while they last.  “Is that a cat hanging from a tree”….why yes, yes it is….

VERDICT:

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PICTURES OF INTERESTING THINGSnull_zpsb74b0de6

You don’t need to try hard to find neat stuff for your classroom.  A colleague of mine, who often teaches geometry, has pictures of neat things above his board.  Here’s your challenge: find your favorite items from 101qs.com, print them, and post them all over the place. The conversations start themselves.

VERDICT:

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 STUFF KIDS MADE AND DID

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Anytime you can post, share and provide inspiration through student work, it’s bonus time.  Here, I share pictures from many past years of our AP Statistics Fair.  These often lead to stories of projects past, and where many of these students are now in their colleges and careers.  As we get later in the year, student work will take over many of the empty spaces on the walls. Also, I have a John McClane action figure on this board….and you can’t blaspeheme Nakatomi Plaza….never forget!

VERDICT:

4justins_zpsf824160c.JPG