# MyOpenMath/Pulling loose threads

If you pull on a small loose thread on your sweater you might turn it into a pile of yarn. It all started because I was uncomfortable with how OpenStax University Physics deals with electromotive force. They say textbooks are like rivers that are a mile wide and an inch deep. That is true, but it is also true that textbooks need to be that way. What started as an attempt to clarify the use of ill-defined terms in physics morphed into a question that attempts to highlight the interplay between experimental observation and theoretical speculation that lead to the development of electromagnetism in the 19th and 20th centuries.

I spend days struggling with this question because we need to adopt a game theory strategy regarding homework and exam questions in an era where virtually all information is available on the internet. In other words, we need to fight the Chegg effect by flooding the market with so many questions that students will find it difficult to use such websites to cheat on an exam. And ... we need to recognize that since solutions to all homework problems are available on the internet, homework questions should be accompanied by freely available answers.

This question does have merit. It shows how physics in the 20th century was dominated by gedanken experiments that uncovered paradoxical behavior unless the accepted theory is modified. Two famous examples are Maxwell's "missing" term and Einstein's special relativity.

It is not possible to teach introductory physics and the history of physics at the same time. So ... this problem made no effort to follow the true history. Instead we follow the sequence of ideas presented in the textbook and develop a thought experiment that supports the proposition that an emf can be produced by flux changes associated with changing the conducting loop's shape. As I wrote and thought about the question, its flaws soon emerged.

So we keep the question in the bank for two reasons: First, we want to flood the market so students will have difficulty finding potential exam questions by searching the internet. Second, __a few__ students will benefit from this exercise. This ability to serve both the average and exceptional student with the same quizbank is exactly why education based on AI is so valuable: We can serve ```all``` students at a fraction of the cost of cramming all of them into one lecture hall.

### On the use of true-false questions Edit

There are a number of ways we can compensate for the inherent inferiority of true-false questions:

- Permit a fraction of the answers to be wrong with no penalty
- Place the questions within the context of a discussion or expository prose
- Permit alternative assessments, for example, when used in undergraduate prelims. One advantage of the of the undergraduate prelim is that they are pass-fail. This automatically satisfies the first of these compensations.

#### "Flooding the market" Edit

We need a large number of exam questions if we are to create so many that students won't just study the answers. True-false questions are the simplest to write. I remember in the 1960s that teachers would just write them on the board, so students would write the answers on a blank page in the form: 1T, 2F, 3F, 4T, ...

The questions in the sample pdf file ensure that each question has a 50% chance of being true. And to make it more difficult to memorize answers, the code makes it possible to include even more questions with slightly different wording. While the pdf file shows only six questions, there are actually seven true-false pairs because there are two variations of the first pair, as shown in the following code fragment:

```
$n=0 // First question comes in two true/false pairs
if $temprand==1{
$isTrue="Within the context of this essay, the <strong>predictions</strong> made by an equation are <strong>more important</strong> than knowing the exact definitions of the terms used."
$isFalse="Within the context of this essay, the <strong>precise meaning of the the terms</strong> used in an equation is <strong>just as important as</strong> the predictions made by the equation."
}else{
$isTrue="The spirit of this essay is that in physics, equations can be <u>useful</u> <strong>even if the terms used are poorly defined</strong>."
$isFalse="The spirit of this essay is that in physics, equations are <u>useless</u> whenever the terms used are <strong>
poorly defined</strong>."
}
$questions[$n]=ifthen($TFs[$n]==1, $isTrue, $isFalse)
$n=$n+1 // This an the rest have only one true/false pair (randomly selected each time)
$isTrue ="The formula, `dA//dt=vl,` used for a rectangle <strong>also applies </strong>to the rate at which a circle's area expands, where `l` is the circumfrence and `v` is the rate at which the radius increases."
$isFalse="The formula, `dA//dt=vl,` used for a rectangle <strong>does not apply</strong> to the rate at which a circle's area expands, where `l` is the circumfrence and `v` is the rate at which the radius increases."
$questions[$n]=ifthen($TFs[$n]==1, $isTrue, $isFalse)
$n=$n+1 //
$isTrue ="In Fig. 4 the magnetic field is an <strong>external</strong> field (i.e., not caused by the current flowing through the parallel rails.)"
$isFalse="In Fig. 4 the magnetic field is an <strong>internal</strong> field (i.e., caused by the current flowing through the parallel rails.)"
$questions[$n]=ifthen($TFs[$n]==1, $isTrue, $isFalse)
$n=$n+1 //
$isTrue ="In the gedanken experiment using Fig. 4 to postulate that an observer moving through a magnetic field experiences an electric field, the resistance `R` in the circuit was set to <strong>infinity</strong>."
$isFalse="In the gedanken experiment using Fig. 4 to postulate that an observer moving through a magnetic field experiences an electric field, the resistance `R` in the circuit was set to <strong>zero</strong>."
$questions[$n]=ifthen($TFs[$n]==1, $isTrue, $isFalse)
$n=$n+1 //
$isTrue ="In the gedanken experiment using Fig. 4 to postulate that an observer moving through a magnetic field experiences an electric field, the electric field is <strong>perpendicular</strong> to the rails."
$isFalse="In the gedanken experiment using Fig. 4 to postulate that an observer moving through a magnetic field experiences an electric field, the electric field is <strong>parallel</strong> to the rails."
$questions[$n]=ifthen($TFs[$n]==1, $isTrue, $isFalse)
$n=$n+1 //
$isTrue ="The magnetic field in the rail gun of Fig. 5 is <strong>inhomogeneous</strong>."
$isFalse="The magnetic field in the rail gun of Fig. 5 is <strong>homogeneous</strong>."
$questions[$n]=ifthen($TFs[$n]==1, $isTrue, $isFalse)
```