Tag Archives: AP Statistics

Nix the Tricks – AP Stats Edition

For AP Stats teachers, this is the time of year where we move from innocent ideas like scatterplots and experimental design, and into uncharted waters; those topics which require sharper focus, and more time and reflection to develop properly. Sampling distributions, the Central Limit Theorem, confidence intervals and hypothesis testing…new and scary ideas.  With the crush to cover content before May, it’s easy to fall into traps where we shortchange discovery and real meaning and replace them with quick tricks.  Here I present one of my least favorite Statistics “tricks”, and hope you “Nix this Trick”!


Nix Header“Nix The Tricks” is a powerful, free document for math teachers of all grades; a crowdsourced collection of math shortcuts and well-intentioned devices teachers employ to assist students with math mechanics; devices which ultimately under-cut student understanding of mathematics.  Along with the tricks are suggestions for developing math concepts in your classroom without tricks; encouraging communication of ideas and language.  It’s a labor of love, compiled and edited by Tina Cardone, who I admire for her dedication to this project.  Some of my ideas from a blog post last year on phrases from math class which need to be expunged have been absorbed into Nix The Tricks, and I am thrilled to have had even a small part in building this document.  Share it with your math friends, and let the debates begin!


Back to Stats-world, and a phrase we need to Nix.  It’s time for hypothesis testing, a new world of strange symbols for the null and alternate hypothesis, lots of conditions and tests to think about, and making logical connections between computed values and real-life consequences.  Writing tight, meaningful conclusions takes practice, revision, and patience. But why struggle, when we have a cute shortcut?

When the P is low, reject the Ho!

This is the short version of the general argument that when we have a sufficiently low P-vale (below alpha), we have evidence against the null hypothesis, and in favor of the alternate. But why go through all of this meaning, when we can talk about Hos in math class!

 Snoop

So, what’s wrong with this catchy phrase?  Well, first, and probably most importantly, it’s damn offensive.  For teachers, talking about Hos in class, or even providing a “giggle” momnent about the idea, is out of bounds.  We all get that, right?  Good.

In stats-world, the problem with this phraise is that it provides students an excuse to not develop real understanding about the connection between P-Values, Alpha, and the null hypothesis.  As an AP Reader, I enjoy the opportunity to see how students craft their conclusions to a hypothesis test. In 2012, I read question 4, which was a full 2-proportion z-test.  It was fascinating to observe the clear differences between the written approaches to conclusions; which textbook they probably used, what mnemonic devices did their teacher push, how much attention was paid to written practice.  In addition, while many approaches relied upon a canned template, where students simply fill in blanks (with mixed success), I also enjoyed well-developed explanations which demonstrate clear evidence of understanding of the logic of hypothesis testing.

At last year’s AP Stats Reading “Best Practices Night” Luke Wilcox did a wonderful job explaining how he challenges his students to become clear communicators from day 1. You can download his presentation, and many other “best practices” resources, at the famous APStatsMonkey page.  Here’s a fantastic example from Luke’s class, which demonstrates clear understanding of the process:

Conclusion

In AP Stats, communication is essential.  Here are some thoughts and ideas to keep in mind:

  • A strong conclusion has linkage between a computed P-value and a defined significance level (alpha).  This is the computation piece.  The art of statistical writing is taking this numerical result and using it to reach a conclusion about our population.
  • My students write, write and write, and my boards are covered with samples, which we critique and revise.  I like to randomly assign students to work together (I often use playing cards for this), so that “group think” does not set in. I want students to debate language, and I can see from afar which groups are on-point by having them on boards around my room
  • My document camera is also a valuable resource here. As an opener, I’ll have students examine a homework problem, and write their conclusion on an index card. Random cards are selected and critiqued.

As many Stats teachers head toward their hypothesis testing units, let work together to Nix this Trick, and improve student writing!

My Favorite Teacher Circle: PASTA

Just got back from the fall meeting of my favorite local teacher circle, PASTA.  The Philadelphia-Area Statistics Teachers Association meets a few times each year to share best-practices in statistics teaching.  Many of this month’s presenters are AP Statistics readers, and the ideas are not specific only to stats…we just share great classroom action.  I gave a recap of our last meeting in the winter; enjoy the great ideas from our Fall meeting, and visit Beth Benzing’s website for materials from the meeting!

Daren Starnes, famous in the Stats-world as author of The Practice of Statistics, shared his first experience with Team Quizzes.  I have tried team quizzes before, mostly for quizzes where I knew students were having the most difficulties with material.  But Daren added some features I had not before considered:

  • Students are assigned to their teams at random.
  • Each team member received a copy of the quiz, and must complete the quiz.
  • In a quiz, one question is chosen randomly to be graded from each paper.  A student’s grade is a combination of the score they receive on the question, along with the average of the scores from the other papers in the team.

Daren also commented on the roles of introverts and extroverts in the teams, and how this method could empower introverted students to self-advocate.  He suggest the book Quiet: The Power of Introverts as a resource.

AdamAdam Shrager, famous as the social director and man-about-town at the AP readings, shared his movie-correlations activity.  This has become one of my favorite activities during the stats year.  Students are asked to fill out a movie-preference survey, which Adam then uses to compute peer-to-peer correltations in Excel.  (look for “correlation” in excel…you may need to activate the Stat Pack) Discussions regarding the interpretation of positive and negative correlations then occur.  Most importantly, mis-conceptions of the meaning of low or zero r-values are discussed with a context easily understood by students.

Table

Leigh Nataro shared her “Pacing a Normal Distance” activity, where students walked between 3 different campus buildings using “meter-long” steps.  The data is then entered into Fathom, and is used to discuss variability, the 68-95 rule, and normal probability plots.  Fun discussions of outliers and error as well!

Leigh

Our host, Beth Benzing from Strath Haven High School, shared a family income Fathom file which draws samples of various sizes from a clearly skewed distribution.  In addition to to having students record observations and work towards generalizations, Beth has worked to increase the rigor in her associated questions, using past AP items as her framework.  Some examples:

  • What is the probability that a sample of 5 families will have a combined income of over $500,000?
  • What is more likely: a sample of size 5 having a mean income of over $80,000, or a sample of size 25 having a mean income over $80,000?  You may recall a similar AP question from a few years ago regarding samples of fish.

Beth

Brian Forney shared ideas for bringing concepts from Sustainability to the AP Stats classroom.  In one example, Brian shared data on depths of ice sheets over time, with excellent opportunities to discuss cause and effect from scatterplots.  Check out Brian’s presentation on Beth’s website.

Finally, I was happy to share my recent lesson on Rock, Paper, Scissors and two-way tables.

The meeting concluded with some great ideas for making multiple-choice assessments more fair and effective.  There were a number of excellent ideas here, but I think I’ll look up some more info on alternate assessment methods and save it for another post…so stay tuned!

A Bowl of PASTA with Stats Friends

Today I attended the winter meeting for one of my favorite organizations: PASTA, the Philadelphia Area Statistics Teachers Association.  This group meets a few times a year to discuss best practices in statistics education, and includes a number of AP teachers, many of whom are AP exam readers.  As always, lots of interesting ideas today:

Joel Evans, from my home school, spoke on his first attempts to “flip” his AP Statistics class.  Based on feedback from his students, Joel realized that Powerpoints often dominate his classroom culture.  By flipping, Joel hoped to have students review material before class, then use class time to practice and discuss.   Follow Joel’s flipping story in the slides below.

It is always a pleasure to have Daren Starnes at our meetings.  Daren, one of the co-authors of the ubiquitous The Practice of Statistics textbooks, joins our group often to discuss his ideas for teaching statistics.  Today, Daren shared a presentation, “50 Shades of Independence”.

Daren asked us to think about all of the places where we encounter “independence” in AP Statistics:

  • probability of independent events
  • independent trials
  • independent random variables
  • independent observations
  • independent samples
  • independent categorical variables (chi-squared)

Man, that’s a lot of independence!

Which items from the list above deal with summarizing data?  Which are needed for inference?  How are they related?  How do we help our students understand the varied, and often misunderstood, meanings of independence.

Daren has a knack for leading conversations which invite participants to express and discuss their math beliefs. Daren   Many of the arguments concerning independence, according to Daren, are “overblown”, in that teaching them in a cursory manner often causes us to lose focus on the big picture. That’s not to say that we should discard them, but that, when teaching inference, we should have students focus on items which would cause a hypothesis test to be “dead wrong” if we didn’t mention them, i.e. randomness, justifying normality conditions.

penniesRuth Carver continued the presentations with some new tech twists on a lesson used by many stats teachers: analyzing sampling distributions by looking at the age of pennies.  A population graph of the ages of 1000 pennies hangs proudly in Ruth’s classroom.

After agreeing that the population is clearly skewed right, we move to the main event – drawing random samples from the population and analyzing the data we get from repeated samples of the same size.  Ruth has developed a lesson for the TI Nspire which generates the samples, and challenges students to think about the behavior of the sampling distributions, now considering the effects of sample size.  Ruth’s presentation allows students to experience and express the differences between:

  • Standard deviation of a population
  • Sample standard deviation
  • Standard deviation of a sampling distribution

Ruth

Great job Ruth!  Looking forward to more PASTA with my stats friends!