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A Smoother Pebble: Mathematical Explorations
A Smoother Pebble: Mathematical Explorations
by Donald C. Benson
Edition: Hardcover
Price: $39.77
50 used & new from $0.01

5 of 5 people found the following review helpful
5.0 out of 5 stars An Interesting Guide to the History of Mathematics, September 29, 2004
This is definitely a very interesting book for anyone interested in Math. Most people, including myself, originally studied Math only to find out how to solve particular problems and never learned any of the interesting history associated with Math. A Smoother Pebble presents many interesting aspects of this history: for example, the horribly awkward use of Egyptian Unit Fractions and of Babylonian's Sexagesimal Number System. It also describes the mathematical ratios involved with the musical scales.

I also found it interesting how the early use of graphs developed and the connection between Algebra and Geometry and the history involved in trying to find the path of fastest decent. I'm sure that a reader will also find other areas of particular interest.


The Moment of Proof: Mathematical Epiphanies
The Moment of Proof: Mathematical Epiphanies
by Donald C. Benson
Edition: Hardcover
53 used & new from $0.01

8 of 8 people found the following review helpful
5.0 out of 5 stars An excellent and easy-to-read broad coverage of mathematics., November 5, 1999
I specifically commend the very broad coverage of the subject of Mathematics for readers who may even be struggling to recall some elementary algebra. Even most educated people do not realize that Mathematics includes such things as Probability Theory, Game Theory, Finding Optimal Strategies, The Study of Prime Numbers, Map Coloring with no more than four colors and designing and deciphering Secret Messages.
I specifically appreciated the many excellent comments in marginal boxes and the frequent marginal notations of a "Dangerous curve" in many key areas. I also appreciated the comment near the end of having "finished the main course, and even the dessert, of our mathematical banquet" and the comment on page 298 about there being no Nobel Prize in Mathematics.


The Moment of Proof: Mathematical Epiphanies
The Moment of Proof: Mathematical Epiphanies
by Donald C. Benson
Edition: Hardcover
53 used & new from $0.01

9 of 9 people found the following review helpful
5.0 out of 5 stars An excellent summary of the BROAD Field of Mathemetics, November 4, 1999
This is an EXCELLENT book on the broad subject of Mathematics - not just related to those topics that the general public understands as being Mathematics.
I specifically commend the very broad coverage of the subject of Mathematics for readers who may even be struggling to recall some elementary algebra.
Even most educated people do not realize that Mathematics includes such things as Probability Theory, Game Theory, Finding Optimal Strategies, The Study of Prime Numbers, Map Coloring with no more than four colors and designing and deciphering Secret Messages.
I specifically appreciated the many excellent comments in marginal boxes and the frequent marginal notations of a "Dangerous curve" in many key areas that may not be obvious to the general reader.
I also appreciated the comment near the end of the book of having "finished the main course, and even the dessert, of our mathematical banquet" and the comment on page 298 about there being no Nobel Prize in Mathematics.
Clearly a book to remember and one to make you think!


You Just Don't Understand: Women and Men in Conversation
You Just Don't Understand: Women and Men in Conversation
by Deborah Tannen
Edition: Paperback
1327 used & new from $0.01

79 of 84 people found the following review helpful
5.0 out of 5 stars An excellent book for anyone interested in communicating., October 29, 1997
Deborah Tannen has written an excellent book analyzing theverbal interaction between men and women. I highly recommend it toanyone. For many years I have been only generally aware of some of the symptoms she describes, mostly through personal communication problems that arose in my marriage. After reading her book, I now have a much better understanding of these challenging problems of differing perspective and I hope I can even change my reactions when these problems reoccur. I even note on pg. 201 (page numbers throughout refer to the Hardcover Edition) that the author herself, "as a result of doing this research, learned not to use machine-gun questions or cooperative overlapping with people who don't respond well -- a tangible benefit of understanding conversational style."
I don't believe her book is at all one-sided. It presents examples of how some people (often women) feel they are always being interrupted and not allowed to present their views. It also describes how a male speaker, through his style, fails to get a professional group's attention or credit for bringing up a major point -- that is then later repeated by another speaker, who refers to the earlier speaker but still gets all the credit.
In order for others to gain an appreciation of this book, I quote below from several selections.
WHO DOES MORE OF THE TALKING, AND UNDER WHAT CIRCUMSTANCES?
"Who talks more, then, women or men? The seemingly contradictory evidence is reconciled by the difference between what I call public and private speaking. More men feel comfortable doing `public speaking,' while more women feel comfortable doing `private' speaking. Another way of capturing these differences is by using the terms report-talk and rapport-talk.
"For most women, the language of conversation is primarily a language of rapport: a way of establishing connections and negotiating relationships. Emphasis is placed on displaying similarities and matching experiences. From childhood, girls criticize peers who try to stand out or appear better than others." (pg. 76, 77)
"From childhood, men learn to use talking as a way to get and keep attention. So they are more comfortable speaking in larger groups made up of people they know less well -- in the broadest sense, `public speaking.' But even the most private situations can be approached like public speaking, more like giving a report than establishing rapport." (pg. 77)
"Many men honestly do not know what women want, and women honestly do not know why men find what they wand so hard to comprehend and deliver." (pg. 81)
JUDGMENTS ABOUT WHY PEOPLE TALK AND DON'T TALK.
"For girls, talk is the glue that holds relationships together. Boys' relationships are held together primarily by activities: doing things together, or talking about activities such as sports or, later, politics." (pg. 85)
"Women and men are inclined to understand each other in terms of their own styles because we assume we all live in the same world. [A] young man in [Thomas Fox' college] writing class noticed that his female peers refused to speak with authority. He imagined the reason to be that they feared being wrong. For him, the point was knowledge, a matter of individual ability. It did not occur to him that what they feared was not being wrong, but being offensive. For them, the point was connection: their relation to the group." (pg. 179)
WHICH IS A BETTER LEARNING EXPERIENCE: BOYS PLAYING GAMES WITH COMPLEX RULES OR GIRLS HAVING VERY FEW, IF ANY, EXPLICIT RULES IN THEIR GAMES?
"[I]t is not that the boys' behavior is more complex in general. Rather, boys and girls are learning to handle complexity in different arenas -- boys in terms of complex rules and activities, girls in terms of [non explicit] complex networks of relationships, and complex ways of using language to mediate those relationships." (pg. 181)
WHEN DO WE LEARN TO BE DIFFERENT?
"If it is fascinating to see the source of adult patterns in second-graders, it boggles the mind to see them in three-year-olds. No wonder it is hard for men and women to understand each other's point of view: We have been looking at the view from different vantage points for as long as we have been looking." (pg. 257)
There is another quote on a page that I can't remember that goes something like "second-grade girls already have more in common with 10th grade girls than they do with second-grade boys."
INTERRUPTIONS AND NOT GETTING AN EQUAL CHANCE TO TALK.
"[I]nadvertent interruptions -- and the impression of domination -- came about because the friends had different conversational styles. I call these styles `high considerateness' and `high involvement,' because the former gave priority to being considerate to others by not imposing, and the latter gave priority to showing enthusiastic involvement. Some apparent interruptions occurred because high-considerateness speakers expected longer pauses between speaking turns. While they were waiting for the proper pause, the high involvement speakers got the impression they had nothing to say and filled in to avoid an uncomfortable silence." (pg. 196)
THE EFFECTS OF FOREIGN CULTURES.
"If cultural differences are likely to cause misjudgment in personal settings, they are certain to do so in international ones. I would wager that the much-publicized antipathy between Nancy Reagan and Raisa Gorbachev resulted from cultural differences in conversational style. According to Nancy Reagan, `From the moment we met, she talked and talked and talked -- so much that I could barely get a word in, edgewise or otherwise.' I suspect that if anyone asked Raisa Gorbachev, she would say she'd been wondering why her American counterpart never said anything." (pg. 207)
Another example of "foreign" cultures relates to Americans from different backgrounds, not only of obvious ethnic differences, but even, for example, simply from different parts of America. On page 201 Tannen points out the different backgrounds and conversational styles of Jewish New Yorkers (and many New Yorkers who are not Jewish), who "have high-involvement styles and are often perceived as interrupting in conversation with speakers from different backgrounds, such as Californians. But [on the other hand] many Californians expect shorter pauses than many midwesterners or New Englanders, so in conversations between them, the Californians end up interrupting. Just as [the author] was considered extremely polite when [she] lived in New York but was sometimes perceived as rude in California, a polite Californian was shocked and hurt to find herself accused of rudeness when she moved to Vermont."
Still another example of cultural difference is that of an American tourist in Turkey trying to refuse a street merchant. "She found herself holding a stone head, and when she told him politely that she did not want it, he would not take it back. Instead, he thrust forward another one, which she also automatically accepted. Since the man would not take either head back, the only path to escape she could envision was offering to buy them. She cut his price in half and hoped he'd refuse so she could move on. Instead, he agreed to drop the price and she dropped the two heads in her tote. But as she handed him the money, he handed her a third head. ... Seeing no alternative, she paid for the third head and stalked off -- shaken and angry. When ... she showed her purchases to custom officials [at the ship, they] had her arrested and thrown into jail for trying to smuggle out a national treasure. The third head was a genuine antiquity." (pg. 281)
THE BOTTOM LINE IN ALL OF TANNEN'S RESEARCH IS:
"We all want, above all, to be heard -- but not merely to be heard. We want to be understood -- heard for what we think we are saying, for what we know we mean. With increased understanding of the ways women and men use language should come a decrease in frequency of the complaint `You don't understand.' END
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