You are here

Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research

Eric W. Hart and James Sandefur, editors
Publication Date: 
Number of Pages: 
ICME-13 Monographs
[Reviewed by
Karl-Dieter Crisman
, on

The International Commission on Mathematical Instruction (ICMI) is a commission of the International Mathematical Union, and every four years it holds a large congress on math education, called ICME. The most recent such meeting was in Hamburg, Germany, and yielded a lode of conference proceedings from Springer.

The volume under review is the outcome of the discrete mathematics subgroup of this conference. Given the increasing prominence of many of the topics in so-called discrete mathematics due to the computer/internet age, it is always great to see more literature surrounding this topic for new practitioners.

The authors span a range of mathematicians and math education researchers from Europe and the United States. Unfortunately, the content of the volume is quite uneven in terms of its applicability to the collegiate practitioner — or to the elementary and secondary levels of instruction, which is an emphasis of the collection — most likely due to the genre of conference proceedings. Hopefully some of these articles will find their way to expanded forms in some of the MAA journals or in PRIMUS. I will mention a few articles of broader interest which caught my attention.

Devaney’s report on the &ldquo:Chaos Game” is really just an introduction to resources available elsewhere, but thinking of it as a discrete mathematics topic was interesting. Sandefur et al. attempt to connect recursive thinking to traditional high school algebra via flow diagrams. Lockwood and Reed’s contribution is typical of many of the articles, as a more traditional qualitative math education research article (focusing in combinatorics, in this case) with reflection on challenges instructors and students will have.

Some articles, such as Colipan’s on the combinatorial &ldquo:Chocolate game”, are both fairly detailed and potentially of immediate use to instructors. Others have intriguing ideas more suitable to very open guided inquiry settings, such as Vancsó et al. on counting ice cream or Cozzens and Koirala on food webs. The most surprising article of all was Rougetet’s analysis of the many historical Nim-playing computers (including one called the &ldquo:Nimrod”) which students could try to emulate.

By the way, if you want to know more about ICME-13, don’t try the internet right now: &ldquo:Due to recent changes in the European Privacy Policy, we need to temporarily remove our website from the Internet.” No amount of discrete math education can fix political and ethical quandaries of the tools mathematics has enabled; this, however, is not addressed in the current volume.

Karl-Dieter Crisman teaches mathematics at Gordon College in Massachusetts, where he also gets to work on open source software, the mathematics of voting, and examining connections between all of these and issues of belief and faith.

See the table of contents in the publisher's webpage.