Month: December 2014

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Class Opener – Day 62 – When Good Questions Go Bad

Today is our last day in the experimental design unit in AP Statistics, and students started class today with an actual problem (or at least part of one) from the 2013 AP exam. This is a question I read during the 2013 reading, meaning I saw about a thousand different responses to this question. It’s quite an experience to be able to share the good, bad and ugly of responses I saw.

For this question, which was number 5 of 6, I only gave out part (a) of the question as this is the portion of interest to us in our experimental design unit. Here’s the question, with some symbols changed for online convenience…

  • Psychologists interested in the relationship between meditation and health conducted a study with a random sample of 28 men who live in a large retirement community. Of the men in the sample, 11 reported that they participate in daily meditation and 17 reported that they do not participate in daily meditation.
    The researchers wanted to perform a hypothesis test [compare the proportion of men with high blood pressure among all the men in the retirement community who participate in daily meditation and against the proportion of men with high blood pressure among all the men in the retirement community who do not participate in daily meditation.]
    (a) If the study were to provide significant evidence against the null hypothesis in favor of the alternate , would it be reasonable for the psychologists to conclude that daily meditation causes a reduction in blood pressure for men in the retirement community? Explain why or why not.

In additonal to providing a response, I asked students to circle the most important words in the question – which words or phrases are most important when considering part a) of this question.

There’s was a hidden agenda behind having students circle some words and phrases.  The average score nationally on this question in 2013 was 0.57 points (out of 4). Most questions usually have an average around 1.2-1.6…with some creeping below 1 occasionally, and some venturing above 2.  In my memory, this question was BY FAR the lowest-scoring question in recent AP Stats history. And while part (a) was the best opportunity to score points, many students still missed its intent.

After students completed the question, I asked each group to provide me a “top 3” list, and we compiled responses on the board. Here are some words which made our list:

  • STUDY
  • CAUSES
  • RANDOM SAMPLE
  • MEDITATION
  • SIGNIFICANT
  • HYPOTHESIS

It’s not a bad list. And, in looking back, my instructions arern’t totally helpful, as there is one (and ONLY one) word which is important here – CAUSES!

In Statistics, there are big ideas, and then there are BIG IDEAS:

A well-designed experiment can allow us to infer cause-effect relationships. Observational studies cannot.

In this problem, students who tended to write more probably dug themselves deeper into a hole. It’s not easy to tell kids to “write less” as details often matter, but in this question saying “this was an observational study, and not an experiment” was all that was really needed.  In reading this question in Kansas City, I found many students who appealed to the small sample size or to perceived confounding variables, and many who simply seemed to gloss over the word “cause” as important. Note: you can find more details about student errors in the Chief Reader’s summary.

Sometimes the simple questions which assess big ideas become the toughest, especially when there are lots of scary-sounding words surrounding the concept. Having students identify the meaningful words can help facilitate these discussions.

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Class Openers

Class Opener – Day 61 – Slicing the Cake

Today’s class started with a review of laws of exponents, including negative exponents. I like to send students up to boards often in class, and sometimes use a deck of cards to have students determine their fate. There are 3 large boards in my room, and those who drew Aces, twos and threes were each directed to a board – 3 at each board. Before I began to bark out problems, it’s time to claim our space –

Split the board into 3 parts so that each person has an equitable space.

This was no problem for most teams, as there is always someone willing to take control and draw big, vertical lines down the board. But you can easily determine the trios which had more than one “type A” personality, as erasing sabotage, arguing, and even boxing-out occurred to just split up the board….they’re freshmen….

After the first group of students had completed their problems, the fours, fives and sixes then went to the board. Remembering some lessons from a Contemporary Math class I had taught at Rowan University a few years back, this seemed like a great time to expose students to the divider-chooser method for fair division. And while we are splitting up a board, this would be ideal for splitting up a cake, land, or other assets.  Here are the instructions:

  • In your team of 3, assign roles of player 1, player 2 and player 3.
  • Player 1 – approach the board and divide it into 2 “fair” pieces, without help from the others.
  • Player 2 – choose one of the 2 pieces to claim as your own. Player 1 now owns the other piece. Both players should stand in fron of their pieces.
  • Players 1 and 2 – divide your area into 3 “fair” pieces.
  • Player 3 – choose 1 slice from the areas of players 1 and 2 to claim as yours.
  • Each player now has 2 “equitable” pieces.

Sometimes it’s fun to do 5 minutes of a math nugget they may never see again, but it’s worth the discussion it generates. It was interesting to see how some players chose to work horizontally, rather than vertically – and we even had a triangular arrangement (seen below). But these aren’t really practical for doing exponent problems, so we eventually went back to a traditional division.

North Carolina State provides a helpful file which summarizes a number of fair-division methods, including the Lone Chooser method for 3 people, and you can also easily search “Fair Division Methods” to find more interesting ways to divide assets.

boards

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Class Openers Statistics

Class Opener – Day 60 – Herding the Cats

After a wonderful Thanksgiving break (made more wonderful by the Eagles win over the Cowboys!), it’s the 3-week sprint to the holidays, followed by 2 full weeks before final exams.  There’s a lot of stopping and starting going on, which doesn’t help continuity when thinking about class content.  In my AP Stats class, we are deep into our unit on experimental design, which is filled with ideas, terms and arguments must different than a traditional math class. Groups are working through their “Old Wives’ Tales” project, and after grading some student responses this weekend I need an opener which brings the whole class back into the Stats circle. My friend Glenn Waddell has some awesome resources for statistics on his website, which provided inspiration for today’s opener – a short video from ABC News featuring the placebo effect.

http://abcnews.go.com/video/embed?id=19850208
More ABC US news | ABC World News

For today’s opener, I asked students to design an experiment which could prove (or disprove) the efficacy of the WYFFT “energy drink”.  This gave groups much to talk about, and a thorough discussion of elements of experimental design, including:

  • Treatments: WYFFT is not a “real” drink, it’s just soda. Students conjectured that the labeling and associated signage were the actual treatment. We can compare this vs a plain bottle, or against no drink at all.
  • Matched-Pairs: could subjects plausibly participate in both treatments? Is this reasionable?
  • Blocking: could the implied reaction be different in men than in women? Perhaps we should have two different experiments?
  • Response: what exactly are we measuring? What would be a suitable activity to measure a change in energy?
  • Randomization: how will subects be selected for the treatments?

And we are off and running after a long turkey-induced rest!