Friday, December 19, 2014

MAA Books Beat: Knowing vs. Measuring: Doing the Scholarship

Written by Steve Kennedy, MAA Acquisitions Editor, Knowing vs. Measuring: Doing the Scholarship appears in the December 2014/January 2015 issue of MAA FOCUS.

Last winter I participated in the tenure review of a junior colleague, watched with interest as Miguel Cabrera defeated Mike Trout in a close American League Most Valuable Player contest, and read a draft version of Curtis Bennett’s and Jackie Dewar’s Doingthe Scholarship of Teaching and Learning in Mathematics. It could just have been the temporal proximity of these experiences that led me to see analogies between them, but I think there are real connections.

Measuring

First, and most frivolously, the baseball: There is a huge, fascinating, and contentious debate going on in baseball these days that we might characterize as traditionalists versus statheads. Even if you are not a baseball fan, you might know about this from the movie and book Moneyball.

Baseball players have traditionally been measured by their batting averages, home runs, and runs batted in. All of these are easy to count, have obvious meaning, and have value that is clear to even the most casual baseball fan. All are limited as a measure of what they ostensibly represent: the player’s contribution to his team winning the game.

For example, batting average is a rough proxy for the frequency at which a batter gets on base, but it does not count walks, or reaching base on an error; it values a single and a triple identically; and it ignores certain outs that achieve other (good) outcomes, such as advancing another baserunner.

None of these three stats cited even tries to measure baserunning skill, or the ability to reach base by walk or error, or defensive prowess.

A number of more advanced statistical measures of a baseball player’s performance are in use today. WAR, Wins Above Replacement, is one such. It attempts to measure the total (batting, defensive, baserunning) contribution of a player to his team’s success.

In 2012 Mike Trout, the young centerfielder for the Los Angeles Angels, posted a WAR score that was among the two dozen highest in modern baseball history. That is out of tens of thousands of individual seasons.

In the same season, Miguel Cabrera led the league in all three of the traditional statistics: batting average, home runs, and runs batted in. This is, in baseball lingo, called winning the Triple Crown. It had happened only 15 times previously in baseball history and not since 1967. Cabrera had a batting season among the best of all time, but he is a slow runner and not a very good fielder.

WAR (and other advanced statistical metrics that include baserunning and defense) rated Trout’s season as very strongly more valuable than Cabrera’s. The debate over the MVP award was widely portrayed as a battle between crusty, tradition-bound baseball old-timers against basement-dwelling, smart-aleck nerds.

Essentially the same thing happened in 2013. Cabrera dominated the old-fashioned offensive categories; Trout lead the league in WAR, again by a wide margin.

Friday, December 5, 2014

New: How Euler Did Even More


How Euler Did Even More

By C. Edward Sandifer
Spectrum Series

"Read Euler, read Euler, he is master of us all," LaPlace exhorted us. And it is true, Euler writes with unerring grace and ease. He is exceptionally clear thinking and clear speaking. It is a joy and a pleasure to follow him. It is especially so with Ed Sandifer as your guide. Sandifer has been studying Euler for decades and is one of the world's leading experts on his work. This volume is the second collection of Sandifer's "How Euler Did It" columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler's clever inventiveness and Sandifer's wonderful ability to explicate and put it all in context.

Pick up your copy today at the MAA Store!

Prefer an ebook? Visit the MAA eBooks Store.

Monday, December 1, 2014

MAA Cyber Monday Sale: 35% off Books, 15% off eBooks


Treat Yourself to a New MAA Book


For one day only, receive 35% off MAA books! Visit the MAA Store and enter the code CYBMON14 during checkout.



Prefer an ebook? Visit the MAA eBooks Store and enter the code 356839621 to receive 15% off your ebooks purchase.

Hurry! Sales end at Midnight PST.

Friday, November 7, 2014

New: Doing the Scholarship of Teaching and Learning in Mathematics

Doing the Scholarship of Teaching and Learning in Mathematics

Jacqueline M. Dewar and Curtis D. Bennett, Editors

The Scholarship of Teaching and Learning (SoTL) movement encourages faculty to view teaching “problems” as invitations to conduct scholarly investigations. In this growing field of inquiry faculty bring their disciplinary knowledge and teaching experience to bear on questions of teaching and learning. They systematically gather evidence to develop and support their conclusions. The results are to be peer reviewed and made public for others to build on.

This Notes volume is written expressly for collegiate mathematics faculty who want to know more about conducting scholarly investigations into their teaching and their students’ learning. Conceived and edited by two mathematics faculty, the volume serves as a how-to guide for doing SoTL in mathematics.

The four chapters in Part I provide background on this form of scholarship and specific instructions for undertaking a SoTL investigation in mathematics. Part II contains fifteen examples of SoTL projects in mathematics from fourteen different institutions, both public and private, spanning the spectrum of higher educational institutions from community colleges to research universities. These chapters “reveal the process of doing SoTL” by illustrating many of the concepts, issues, methods and procedures discussed in Part I. An Editors’ Commentary opens each contributed chapter to highlight one or more aspects of the process of doing SoTL revealed within. Toward the end of each chapter the contributing authors describe the benefits that accrued to them and their careers from participating in SoTL.

The final chapter in the volume, the Epilogue, represents a synthesis by the editors of the contributing authors’ perceptions of the value of SoTL. This volume has two goals: to assist mathematics faculty interested in undertaking a scholarly study of their teaching practice and to promote a greater understanding of this work and its value to the mathematics community.



Purchase your copy today at the MAA eBooks Store.

Friday, October 17, 2014

MAA Books Beat: Stories at the Heart of Teaching

Written by Steve Kennedy, MAA Acquisitions Editor, Stories at the Heart of Teaching appears in the October/November 2014 issue of MAA FOCUS.


Steve Willoughby taught mathematics for 59 years at every level from elementary school to graduate school. He is a keen and perceptive observer and a witty and talented storyteller. And, man, after 59 years does he have some stories to tell in Textbooks, Testing, Training: How We Discourage Thinking. 

From a fourth-grade book on a page titled “Divided By 6”:

Twelve turkeys. Six turkeys in each cage. How many cages?

There was a picture on the page with the right number of cages so that exactly six turkeys could be, and were, placed into each with no leftover turkeys. The teachers’ guide directed that any student who wrote the answer without writing “12 ÷ 6 = 2” was to be marked wrong. Fortunately, because of the title at the top of the page and four years of intensive schooling, no child would have an urge to read the problem. There are two numbers. One is 6. Certainly 12 must be divided by 6 and the problem is solved to the satisfaction of all concerned without a single thought passing through the head of anyone involved or of any child making the heinous error of counting the cages depicted.

Did the authors really suppose that if somebody wanted to know how many cages there were, he would count the turkeys, count how many are in each cage, and, upon discovering the unlikely fact that the same number were in each cage, would divide the first number by the second?