One of the persistent complaints about mathematics and science textbooks, especially high-school textbooks, is that the questions tend to involve formula manipulation in a way that is not very meaningful. Such questions tend to be artificial.

A case in point is the following question, taken from a chapter on special relativity in a high-school physics textbook:

A cellphone has a rest energy of 2.25 × 10^{16} J. Calculate its rest mass. [Ans: 0.25 kg]

Really? A quarter of a kilogram? And how exactly was the rest energy determined?

Honestly, I wouldn’t blame a student for being ticked off by a question such as this one. If you really want to know the mass of a cell phone, I don’t think any excursions into special relativity are needed. Just put it on a scale.

If a textbook author wants to illustrate the idea of using the formula *E* = *mc*^{2}, then why not do it with an example in which the use of the formula actually provides some insight into the world that can’t be obtained in a more elementary way. Otherwise there is a danger that readers will think that this relativity business is just mindless manipulation of dumb formulas.

In the past few decades there has been a trend of placing more and more advanced material in high-school textbooks. The problem is that most high-school students are not ready to learn quantum mechanics, special relativity, and other high-level subjects, and so their presentation in high-school textbooks tends to be watered down, oversimplified, and in general dumbed down. There are lots of examples of outright mistakes in such textbooks, too. But another big problem with cramming material that is at too high a level into high-school curriculum before students are ready for it is that the questions end up being of the overly-simplistic, artificial, non-insightful, formula-manipulation type.

(Fairness compels me to note that the question above was the first of a batch of four questions. The second question was a reasonable one involving a proton in an accelerator, the third question involved a nuclear reactor, and the fourth one was another absurd question giving the rest mass and total energy of an asteroid and asking for its speed. Oh well, two out of four ain’t bad, I guess. Sigh.)

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## About Santo D'Agostino

I have taught mathematics and physics since the mid 1980s. I have also been a textbook writer/editor since then. Currently I am working independently on a number of writing and education projects while teaching physics at my local university.
I love math and physics, and love teaching and writing about them. My blog also discusses education, science, environment, etc. https://qedinsight.wordpress.com
Further resources, and online tutoring, can be found at my other site
http://www.qedinfinity.com

Dan Meyer calls this Pseudocontext http://blog.mrmeyer.com/?cat=89

I think “pseudocontext” captures it really well!

Thanks for the visit, Peter. I note that you have some epub posts on your site … they look interesting, and I plan to read them.

All the best,

Santo

Recently found in a calculus textbook in the section on antiderivatives: “What constant acceleration is needed for a car to go from 30mph to 50mph in 5 seconds?” Based on the section it was in, and on the surrounding exercises, we can infer that the intended solution is to set f”(t)=k, antidifferentiate, and use f'(0)=30 and f'(5/60^2)=50 to solve for k and the constant of antidifferentiation. Intelligent students, however, will note that the same result can be obtained far more easily and intuitively by simply dividing the difference, 20mph, by the time 5sec.

Nice example, Sam!