Hello all- Here's Dick Shaffer's excellent case for using computers in the AP Stat course, which first appeared on this list last April. Since the qeustion has come up again (I asked it last time), nodoubt there are people out there who ought to see it.
Tim Brown Lawrenceville School Lawrenceville NJ Received: by cln.etc.bc.ca for firstname.lastname@example.org (4.1/1.39) id AA23154; Fri, 26 Apr 96 13:23:23 PDT Received: from stat.ufl.edu by cln.etc.bc.ca for /spool2/majordomo/wrapper resend -l apstat-l -h cln.etc.bc.ca apstat-l-outgoing (4.1/1.39) id AA23135; Fri, 26 Apr 96 13:23:18 PDT Received: from squid (squid [184.108.40.206]) by stat.ufl.edu (8.6.10/8.6.9) with ESMTP id QAA13997 for <email@example.com>; Fri, 26 Apr 1996 16:22:23 -0400 Received: (scheaffe@localhost) by squid (8.6.10/8.6.4) id QAA01163 for firstname.lastname@example.org; Fri, 26 Apr 1996 16:23:10 -0400 Date: Fri, 26 Apr 1996 16:23:10 -0400 From: Richard Scheaffer <email@example.com> Message-Id: <199604262023.QAA01163@squid> To: firstname.lastname@example.org Subject: Computers and AP X-Sun-Charset: US-ASCII Sender: email@example.com Precedence: bulk
WHY COMPUTERS IN INTRODUCTORY STATISTICS?
Richard L. Scheaffer University of Florida Chief Faculty Consultant, AP Statistics
In recent years, much discussion has take place around the role of computers in teaching introductory (pre-calculus) statistics. Since the AP Statistics Course Description has been out, this discussion has broadened to include a new audience of high school teachers. I have an abiding interest in teaching introductory statistics and had something to do with that Course Description, and so I will add my thoughts and opinions to this discussion.
In recent times the argument has moved from "some technology v. no technology" to "computer technology v. graphing calculator technology." This is a positive step, for those of us who have been around awhile, for we still have colleagues who insist on students remembering the "short- cut" formulas for calculations of certain statistics, and make them work through numerous examples by hand. These hand calculation skills will be of little help on an AP exam. All formulas used on the exam are given in the form that was thought to be most meaningful for understanding the underlying concept, not for simplifying calculations.
Can a student do well in introductory statistics without ever touching a computer? Yes. Can a student perform well on the AP Statistics exam without having computer experience? Yes. In fact, a student who understands statistics can do well on an AP exam with just a scientific calculator and may do OK with NO calculator. Calculation is not the key to success here! The policy is, though, that students are expected to have a graphing calculator for the exam.
The AP Statistics Course Description recommends, however, that students get some experience with modern statistical software sometime during the course. Why do I think this is a sound and reasonable policy for a course of the type we are promoting here?
The AP course emphasizes data collection, summarization and analysis as the basis for decision making under uncertainty. It is designed to be a course about the practice of modern statistics, but taught so that the practitioners understand the underlying concepts that are at work. Since we are not going to prove any theorems, the only way for students to understand these concepts is to provide them with empirical evidence. That empirical evidence comes about most efficiently and effectively through the use of a computer. I will embellish this general comment in just two areas, exploratory data analysis and simulation in inference.
Exploratory data analysis is much more than drawing a boxplot or two, which can be done on a graphing calculator (albeit without scales on the axes). It is sometimes defined as the art of seeing into the data through revelation, residuals, re-expression, and resistance. Revelation comes about first by looking at various plots of the data (stemplots, boxplots, dotplots, scatterplots, matrix scatterplots, three-dimensional plots, etc.). Modern software has a host of plots most students have never seen before and allows for the tailoring of these plots to emphasize certain features of the data. Also, the plots might be linked so that a potential influential observation highlighted in a scatterplot will show up on a histogram or a stemplot, or in the data set itself, allowing connections to be made. Exploration is only of interest, however, on real data sets, many of which are too large to be entered into a graphing calculator (although this is only a temporary problem).
Residuals have to do withFrom owner-majordomo Thu Sep 12 09:03:21 1996 Received: (from daemon@localhost) by cln.etc.bc.ca (8.7.5/8.7.3) id JAA23679 for apstat-l-outgoing; Thu, 12 Sep 1996 09:03:21 -0700 (PDT) Received: from lville.pvt.k12.nj.us (ls_smtp.lville.pvt.k12.nj.us [220.127.116.11]) by cln.etc.bc.ca (8.7.5/8.7.3) with SMTP id JAA23673 for <firstname.lastname@example.org>; Thu, 12 Sep 1996 09:03:19 -0700 (PDT) Received: from Lawrenceville-Message_Server by lville.pvt.k12.nj.us with Novell_GroupWise; Thu, 12 Sep 1996 12:07:06 -0400 Message-Id: <email@example.com> X-Mailer: Novell GroupWise 4.1 Date: Thu, 12 Sep 1996 12:03:26 -0400 From: Timothy Brown <firstname.lastname@example.org> To: email@example.com Subject: M&M's Sender: owner-apstat-l Precedence: bulk
I'm sorry that I'm so late getting in on the m&m discussion, but the beginning of the year always swamps me.
I haven't used m & ms at the beginning of the year, but last year I used them when we began hypothesis-testing, first to test whether the proportion of blue ones was the same as the proportion of the tan ones they replaced (using the proportion of tans given by Mars and published in Moore and McCabe), then to introduce Chi-Square goodness-of-fit tests (for the distribution of all colors). We found that there was *enormous* variation in proportions of each color between manufacturing lots. So if you buy all your bags from the same carton in the same store, you might get tons of yellows and almost no greens. The same goes for buying one 2-pound bag. So you have to get your students to spread out over town and buy bags of m & ms from a "random" selection of stores!