NCTM – Saturday

Much quieter here today, as the math folk move out and an antiques show moves in.  But still time for some sessions!

Essential Understandings in Grades 9 – 12 Statistics: Preparing for the Common Core.

Very excited for this session today, as one of the speakers is Roxy Peck, former Chief Reader of the AP Stats exam.  Also, looking for some ideas for our freshman year prob/stat course.

Big ideas –

1.  Data consists of structure + variability: look at math models but explore the big picture

2.  Hypothesis tests answer the question, “do I think this could have occurred by chance?” – what hypothesis is more plausible?

3.  To evaluate an estimator, you need to consider bias and the sampling method.

4.  Describe variability – distinguish different ways distributions are used (population, sample, sampling distributions) and be able to compare them. As more teachers are compelled to teach stats in HS, we need to train for the abstraction of sampling distributions.

How much do sample distributions tend to look like population distributions, and how can samples differ based on randomization?

5.  The way in which data are collected matters.  The is a risk of error that needs to be acknowledged and quantified.  Also, the collection method determines the type of inferential conclusions that can be made.  If the sample is not representative of the population, we should be suspicious of generalization.

“as statistics people, we are OK with being wrong 5% of the time” – Roxy Peck

All HS math teachers will find themselves in the dual role of being teachers of math and teachers of statistics. This is a bit scary to me.  While many resources are coming out which will assist teachers in presenting statistical ideas, I wonder how many math teachers are prepared to facilitate a discussion, perhaps over many class days, centering on one scenario and its many statistical concepts.  A colleague, at the end of the session ,offered that his department is “petrified” of the prospect of being made to teach stats courses.  Many great math teachers I know are like musicians playing classical music, adept and expert in the rhythm and complexity of math.  How many of my colleagues are prepared to become jazz musicians, and have conversations meander in new and exciting directions?

After attending 2 conference in the last month, and moving through meeting rooms, with various degrees of “fullness”, I have begin to develop the “Large Ballroom Theory”

Large ballroom theory:  given a large ballroom with many empty seats, people will

  • Find somebody familiar and sit with them
  • Sit in the back, for easy escapability from intolerable sessions
  • Sit in a location which will maximize the apparent fullness of the room, looking for bare spots

Philadelphia-20120428-00195, Uploaded by Photobucket Mobile for BlackBerry
It is the last bullet which I believe could be the start of a full-blown thesis.  In the photo above, think about where you would sit?  On the end?  Which row?  Someplace equidistant to others?  Or would you sidle up next to a stranger?


By Bob Lochel

HS Math Teacher. Hatboro-Horsham School District, Horsham, PA.

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