Review of Why Johnny Can't Add

Morri's Kline's Why Johnny Can't Add was written in 1973 as an attempt to change the direction of mathematics education. Mathematics went through a small upheaval at the turn of the century with the foundational "crisis", the Bourbaki program, and related developments.

These developments inspired pedagogical reform that Kline felt made little sense. The book is an extended polemic against the pedagogical reforms that came to be known as "the New Math".

His argument is essentially that the New Math involves teaching abstract mathematics and a whole bunch of other things like set theory, group theory, arbitrary bases, and clock arithmetic, . . . to schoolchildren, at the expense of the basics.

The reforms insisted on abstraction, Kline argued for a more concrete approach to the teaching of mathematics.

For the record I am not convinced that Kline or his opponents were correct. I have no idea how mathematics is taught today, and I am pretty convinced that there are few good theories of education. But he did make a good recommendation. Kline suggests that we really need to treat mathematics education like a real science. That is we have to do real research in to what works in education. This needs to be taken more seriously than it is.

Review of Capitalism and Arithmetic

Frank J. Swetz's Capitalism and Arithmetic is a translation of the Trevisio Arithmetic by an unknown Italian teacher of arithmetic. (The translation is by David Eugene Smith, and there is a thoughtful tribute to him in the book.)

The Trevisio was a rather ordinary book teaching students, mostly merchants how to compute using addition, subtraction, division, multiplication, basic fractions, and the like.

It is historically interesting because we find a lot of mathematical techniques whose import we may not have otherwise been aware. Granted, it makes dull reading if you already know arithmetic through long division, but it does give us a few interesting clues about the life and times of the book.

Mathematically, I never realized how important some of these computing rules, like "casting out nines", or "the rule of three" were. Culturally, we can see the influence on banking and trade on the style of arithmetic and other areas of life. By merely looking at the examples, we can tell what was important to the culture, and money was certainly important.

There is also a good chunk of analysis and historical background thrown in.

The book is probably of interest to people who study the history of mathematics education, and the history of old reckoning books.

Pi

New Hero.

Review of Wallace's Everything and More

David Foster Wallace is obviously a very smart and tallented guy. His book Everything and More: A Compact History of Infinity is just that, it is a very good history of infinity from Zeno's paradoxes to Cantor, and even through continuum hypothesis. He presents all the metaphysical issues,a nd all the discussions of infinitesmals, and everything else you always wanted to know about infinity but were too afraid that you weren't math-savvy enough to handle.

The book is not for the math-phobic. There are going to be times you might have to take it a bit slow, or read something twice, but it'll be worth it.

Wallace's style is quirky and idiosyncratic, but it works. It does not read like any other book I've ever read, but it gets the point across, and does it with a sense of humor. I loved the book, and would recommend it to anyone, x, who: has some tiny bit of mathematical competence < x < is a professional mathematician.

last 4 books I read

Unfortunately I do not have the time I would like to write more detailed reviews, but I wanted to say something quick about the last four books I read before I forget that I have actually read them.

First is Charles Bukowski's Play the Piano Like a Percussion Instrument Until the Fingers Begin to Bleed a Bit. It is an interesting collection of peoms that were enjoyable, I presume for those who, unlike me, get poetry. The whole thing was a bit beyond me.

Second was Martin Gardner's The Numerology of Dr. Matrix. This is a collection of a few of his really old articles from the Mathematical Games column from Scientific American. They are all dated, though amusing. It is mostly a lot of these funny numerological thingies that dumb people find profound and smart people find cute, with real mathematical tidbits thrown in as questions that are pretty hard to figure out. He gives you all the answers in the back.

Third I read Douglas Adams' Last Chance to see. This is the story of Adams and Mark Carawdine's trip to some remote places to see some endangered animals. The story that is told is sentamental, as befitting an emotional tour through various places. Douglas Adams' style still comes out as clearly as in his other works, though less so. It is a quick read, and if you are a die-hard fan, it's a must.

Finally, I just finished Catherine Osborne's book Presocratic Philosophy: A Very Short Introduction. This is part of Oxford's Very Short Introduction series. The series is pretty good, though not always. This book really is good. I was pretty impressed. First I was impressed that Presocratic philosophy can be interesting, and second I was impressed that there is a solid methodological underpinning in this field of research that can be explained to simpletons like myself. And finally that someone actually did it. If you want a good introduction to the prsocratics, you would be well advised to start with this book.