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Sweep Equations Under the Textbook Rug

In his text A Brief History of Time (1988), Stephen Hawking noted someone had told him that "each equation included in the book would halve the sales."

And, in the preface to her "comic book" The Einstein Theory of Relativity (1936), Lillian Lieber wrote: "... just enough mathematics to HELP and NOT to HINDER the lay reader."

What is it about this downplaying of mathematics to avoid scaring away readers? Is it true?

A University of Bristol research study concluded that even scientists (in this case, biologists) tended to overlook (i.e. ignore) "their colleagues' research if it is packed full of mathematical equations."

The researcher's criteria: the idea of cross-citing in rersearch articles. That is, "scientific articles presenting many equations on each page are seldom referred to by other scientists. The most maths-heavy articles are referenced 50 per cent less often than those with little or no maths."

One of the researchers, Tim Fawcett, added: "This is an important issue because nearly all areas of science rely on close links between mathematical theory and experimental work. If new theories are presented in a way that is off-putting to other scientists, then no one will perform the crucial experiments needed to test those theories. This presents a barrier to scientific progress."

What is the remedy? The researchers suggest improving the mathematical training of science graduates. Plus, co-reasearcher Andrew Higginson suggests: "Scientists need to think more carefully about how they present the mathematical details of their work. The ideal solution is not to hide the maths away, but to add more explanatory text to take the reader carefully through the assumptions and implications of the theory."

The barrier is that this second suggestion will be fought by scientific journals whose "page space is at a premium." BUT....Fawcett notes: "The top journals want articles to be extremely concise, with many of the technical details going in an online appendix...Fortunately, our study suggests that equations in an appendix have no effect on citation rates. So moving some of the equations to an appendix may be the most pragmatic solution."

So let's do that with our modern math textbooks as well...move all of the symbolic mathematics to the Appendix, and we might see students actually reading the texts. But wait...that seems to have already been done in many modern texts; in fact, this supposed "appendix" of the necessary mathematics seems to have even been removed!

Source: Adapted from ScienceDaily, June 25, 2012