Jay Warner wrote: > I find these references very interesting from like, a 'pedagogical' > viewpoint. My typical Business & MBA students, who are by no means > mathematically / analytically / statistically inclined, frequently > insist on seeing and using the equations, as a means of 'understanding' > what they are doing. I can go along with the gag once, but after that, > let's have the machines do the work, OK? > > As a means of 'understanding,' I think grinding through some examples > 'by hand' is a good thing. Whether it really helps those who are > seriously math impaired, could be debatable. But I'm willing to try it. > Does anyone have experience with a strictly 'pull down menu' approach? > > Jay
Hi Jay. As anyone who teaches introductory stats knows, textbooks have indeed been moving away from presentation computational formulae, and instead tend to concentrate more on the concepts. I don't have a problem with that. However, when I stand back and look at what actually happens in introductory stats classes today, it seems to me that things are not really all that different than they were when I was taking stats (for a psychology degree) in the 80s. In classes I took, a textbook author or lecturer would proceed roughly as follows: 1) Present the conceptual formula for some statistic (e.g., the conceptual formula for the variance). 2) Point out that if you used the conceptual formula to calculate the statistic in question, you would often end up with an inaccurate answer due to rounding area. 3) Give you a computational formula for the same statistic that allowed you to avoid the rounding error, but provided little or no conceputal insight into the statistic. PCs with stats packages were not available to us, so we did all the calcuations on hand calculators, using computational formulae. It should come as no surprise, therefore, that we knew the computational formulae inside out and backwards, but could hardly recognize some of the conceptual formulae. Fast forward to today's stats classes, with their emphasis on presentation of conceputal formulae, and "letting the computer do the computations". This sounds like a great idea. But, it seems to me that all we have done to the old sequence of events is replace use a computational formula on a hand calculator with use of a computer. The point is that /neither/ of these activities provides any great conceputal insight into the statistic you are calculating. What lecturers and textbook authors /ought/ to be doing instead, it seems to me, is this: 1) Ask students to perform the calculations using the conceptual formula, not with a hand calculator, but on the computer, where they can carry enough decimal places to avoid rounding error. (I sometimes refer to this as using the computer to do the calcuations "by hand".) 2) Then, after students have had some practice with the conceputal formula (which should promote conceptual understanding), show them how to obtain the same results using the standard functions and procedures provided in the stats package of choice. Point number 1 has obvious limitations (i.e., it works for something simple like variance, but perhaps not for multiple regression). But the principle can be extended--i.e., use the building blocks you have already learned to compute something in a conceputal fashion BEFORE you click on a button that does it all for you. For example, ask students generate all of the sums of squares needed for a one-way ANCOVA model by running the appropriate series of linear regresion models BEFORE they are allowed to click on an ANCOVA button in the stats package. (Dave Howell's book Statistical Methods for Psychology gives a good example of this approach.) As one regular in these groups often says... FWIW, Bruce -- Bruce Weaver [EMAIL PROTECTED] www.angelfire.com/wv/bwhomedir/ . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
