Category: Statistics

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Statistics

Classroom Resources from the AP Stats Reading

Last week, I returned from 7 days in Kansas City where 650 of my closest friends and I successfully completed the “Million Question Challenge”.  This year, over 170,000 students took part in the AP Stats exam.  With each exam having 6 questions, this was the first year the readers had the million-question task.

In the evenings, there are lots of great learning and networking opportunities for teachers.  One of the highlights is “Best Practices” night, where this year 17 teachers shared their classroom action.  I presented my ideas and experiences with co-teaching in AP courses beyond stats (which I have featured on the blog before): what a fun and intimidating experience to present in front of so many people whose work I admire!  My slides, below, outline my experiences working with teachers an AP Psych and Chemistry, and some examples problems from Biology.

You can check out presentations and support materials for many of the Best Practice speakers at Jason Molesky’s Statsmonkey site.  Some of my favorites, things I am definitely looking forward to trying or exploring, include:

Kevin DiVizia’s “Scatterbrained Fathom”: to collect data to later use as an opening to the meaning of r-squared in scatterplots, Kevin takes his classes down to his football stadium’s turf field, “the world’s biggest ruler”, and has students launch stomp rockets.  A very cool data collection idea.  Does vertical height or participant weight make a difference ?  If the reaction of the room is any indication, the Stomp Rocket people will have many new customers this coming year!

Robin Lock – StatsKey.  This free online site has pre-loaded data you can use to explore topics from the AP Stats curriculum.  I enjoy the sampling distributions area, where samples can be drawn repeatedly from a large population and their means analyzed.  Check out this sampling distribution of samples of size 30 from 2011 movie budgets, a population which is skewed right.

StatsKey

ConclusionLuke Wilcox’s “Understanding and Visualizing Significance Level”. Do your students REALLY understand what they are saying when the write hypothesis test conclusions?  Stop using flippant phrases like “If the P is low, reject the Ho”.   and insist that your students write out specific language from day 1.

Check out the many great ideas on the Statsmonkey page.  Thanks to Adam Shrager and Jason for organizing the evening.  Looking forward to next year already!

Categories
Statistics

A.P. Co-Teaching: Stats Meets Psych

For seven years before becoming an instructional coach, I taught Advanced Placement statistics.  I loved this course, as every day brought a new applied situation,  a new set of data, and a new, rich classroom discussion.  While many of my math colleagues have an aversion to teaching statistics (one friend from another school said to me “you’ll become the loneliest person in your department”), I think teaching the course gives an appreciateion for how we should be approaching data analysis in ALL math courses.  But that’s a post for another day.

This week’s stats twitter chat (#statschat, 9PM on Tuesdays) started with a discussion of the recently released AP Stats items, but later moved to post-exam activities.  As part of this discussion, cross-curricular options came up, and I mentioned a co-taught lesson I have developed with my AP Psychology colleague.  For a number of years, this teacher and I had discussed co-teaching a unit on experimental design, as the AP Psych course outline actually includes a nice chunk of material AP Stats students come to understand.  One section of the description, Research Methods, is right in the AP Stats wheelhouse:

  • Describe how research design drives the reasonable conclusions that can be drawn (e.g., experiments are useful for determining cause and effect; the use of experimental controls reduces alternative explanations).
  • Identify independent, dependent, confounding, and control variables in experimental designs.
  • Distinguish between random assignment of participants to conditions in experiments and random selection of participants, primarily in correlational studies and surveys.
  • Apply basic descriptive statistical concepts, including interpreting and constructing graphs and calculating simple descriptive statistics (e.g., measures of central tendency, standard deviation).

Yey for math featured in non-math subjects!  What a natural fit for a handsome, fun math teacher and a respected social studies teacher to join forces in a class lesson!  Some students comments that it seemed so out of context to have the two of us in the same class together.  Worlds colliding!  Dogs and cats shaking hands!

For two days, we led a discussion on correlation and causation, based on a curriculum module provided by the College Board.  In the “Teaching Statistics and Research Methodology” module, the section “A Lesson on Correlation” by Amy Fineburg was used as a framework for discussion.  Students were provided with an article to read beforehand and was used to generate discussion regarding student ideas of correlation, causation and experimental design.  Our pesentation to the students is given below, and was completed over 2 days.

Ap psych stats methods revised 12 13 from bobloch
Looking forward to sharing this experience at the AP Stats reading next month, along with a similar co-taught experience developed with my school’s AP Chemistry teacher.
Categories
Statistics

The Case of “Too Many Powerball Winners”

Here’s a favorite activity of mine from prob/stat class.  I love bringing in real stories of statistical improbability from the media to get kids thinking about real-world applications of probability, and reinforce the fact that theoretical probability represents a long-term ratio.  In the short term, funky stuff happens sometimes.  In an earlier post, I gave some examples from the Amazing Race and the casino world.  Today’s example comes from another gambling example: Powerball.

First, some understanding of the game is required.  In Powerball, players attempt to guess the numbers that wil be drawn from ping-pong ball machines.  Two different machines are used for the game.  In the first machine, there are 59 white balls, while a second machine holds red balls numbered 1-35.

Powerball

Players select 5 numbers they believe will be drawn from the white-ball machine, and 1 number they believe will be drawn from the red-ball machine.  If you match all 6 numbers correctly, you win the grand prize, often in the 10’s of millions of dollars.  For more info on the game and how to play, the Powerball website provides lots of info, including a rather amusing FAQ area.  You can also use random.org to generate some draws, play the game with your class, and hopefully show them how difficult Powerball is to win, or even get 2 numbers correct.

THE TABLE HAS BEEN SET, NOW FOR THE MAIN COURSE

Print out the first page of this file, which is an article from the Washington Post, with key information removed.  Don’t give out the second page – it contains the secret to this probability anomoly.  You can read the article on your own, but here is a summary of the article:

  • If a player matches all 5 white balls in a Powerball drawing, but not the red ball, they win a prize of $100,000.
  • In a given week, there are “usually” 4 or 5 such winners.
  • On a drawing in 2005, there were 110 winners.
  • The Powerball police investigated.

What caused so many winners?  Cheating?  Luck?  Pure chance?  Are the winning numbers “special” in any way?  In Pennsylvania’s Daily Number, for example, the state pays has paid out more than 5 times the amount wagered when the 7-7-7 combination is drawn.

The second page of the article gives away the surprising twist, after students think about the situation, and make some conjectures.  So what’s the twist?

Spoiler space….if you want to think so more…do it now….

 

 

More spoiler space…..

 

 

Ready….it’s fortune cookies!

Fortune Cookies!

A company in Queens, NY produces fortune cookies for restaurants, and chooses numbers to go on the fortunes.  They seem to use the same numbers in a batch, and these numbers found their way into the hands of hungry Chinese-food lovers, who played the numbers.  They just happened to hit!

Hope you enjoy this tale of statistical improbability!