id: 06609214
dt: b
an: 2016f.01107
au: Shell-Gellasch, Amy; Thoo, J. B.
ti: Algebra in context. Introductory algebra from origins to applications.
so: Baltimore, MD: Johns Hopkins University Press (ISBN 978-1-4214-1728-8/hbk;
978-1-4214-1729-5/ebook). xvi, 536~p. (2015).
py: 2015
pu: Baltimore, MD: Johns Hopkins University Press
la: EN
cc: H45 F60 A30
ut: history of mathematics; number systems; quadratic equations; cubic
equations; rule of three; logarithms
ci: Zbl 0419.01001; Zbl 1167.01012; Zbl 1318.01014; Zbl 1177.01004; Zbl
1225.01002; Zbl 0913.01001; Zbl 1066.01500; Zbl 1175.01004; Zbl
1183.01002
li:
ab: Although the mathematicians at the Schools of Education in Germany never
get tired of promoting the use of history of mathematics in class
rooms, the books currently used in the formation of future teachers
treat history at best as a collection of apocryphal anecdotes. This
decline of substance is dramatic given that there are excellent sources
on the history of elementary mathematics in German, in particular
Tropfke’s collection on the history of elementary mathematics ([Zbl
0419.01001] etc.) or the excellent series of textbooks for Bavarian
schools edited by Barth et al. (Algebra, Anschauliche Geometrie,
Anschauliche Analysis), not to mention the Hildesheim series on the
history of mathematics in the last 6000 years [Zbl 1167.01012; Zbl
1318.01014; Zbl 1177.01004; Zbl 1318.01014; Zbl 1225.01002]. The book
by Amy Shell-Gellasch and John Thoo discusses the history of elementary
high school algebra and proceeds from number systems to irrational
numbers, quadratic and cubic equations to logarithms. It is meant to be
read by high school and college teachers as well as by students in
general education courses. The historical claims are remarkably exact,
which is easily explained by quickly browsing the bibliography: there
you find references to quite a few editions of original sources
(Apollonius, Euclid, Fibonacci, Bombelli, Descartes) as well as of a
very broad selection of more recent books on the history of mathematics
such as {\it D. M. Burton} [The history of mathematics: an
introduction. 3rd ed. New York, NY: McGraw-Hill (1997; Zbl
0913.01001)], {\it V. J. Katz} [A history of mathematics. An
introduction. 2nd ed. Reading, MA: Addison-Wesley (1998; Zbl
1066.01500)], {\it K. Plofker} [Mathematics in India. Princeton, NJ:
Princeton University Press (2009; Zbl 1175.01004)], {\it E. Robson}
[Mathematics in ancient Iraq. A social history. Princeton, NJ:
Princeton University Press (2008; Zbl 1183.01002)] and many more. In
the last two chapters on the rule of the three and logarithms, the
authors included many “real life problems” that have become so
fashionable in recent years: this was an unfortunate decision in my
opinion, because the appearance of miles, gallons, ounces and dollars
and problems about buying motorcycles do not mix well with studying
e.g. a Babylonian cuneiform tablet or trying to understand Euclid. It
is probably no conincidence that one of the last examples in this book
is also by far the worst: the authors use logarithms to show that the
1906 earthquake in San Francisco with magnitude 8.3 was 199,526,232
times as intense as a standard earthquake, rounded to the nearest one
(!). Another problematic aspect is the decision to concentrate on
algebra alone, because it is difficult to separate algebra from
geometry during the long evolution from Babylonian mathematics to
Descartes. Coordinate systems appear when having to represent complex
numbers geometrically, but the history of coordinates is not properly
addressed even though Descartes’ geometry is mentioned in various
places. Although the book is not the answer to all of our prayers, it
is a step in the right direction, and I recommend it to all teachers of
mathematics. Teachers in Germany will be pleased to hear that there is
a section on addition and subtraction of numbers.
rv: Franz Lemmermeyer (Jagstzell)