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I'm wondering about the use of word problems on exams which are "cute": they have a slightly funny story, or some sort of pop culture reference, or tie into a running theme of some kind. (As an example of the last category, I recall hearing about a professor who was, or at least professed to be, obsessed with some animal, perhaps a porcupine, and routinely gave word problems in which porcupines were the main actors.)

Some advantages are:

  • Many students seem to enjoy them (I know I did when I was a student).
  • They can provide a small break from the monotony and stress of an exam.
  • They can make a problem more memorable and get students to read it more carefully. (For instance, the one time I did this in a class, students asked about the "Indiana Jones problem" from the rest of the quarter.)

Some concerns are:

  • They may unfairly disadvantage students who aren't native speakers
  • They may distract students (especially weaker students) from the essential information (for instance, a sufficiently nervous student might not realize an unfamiliar pop culture reference is purely fluff)
  • Students who dislike the class may be further annoyed by the apparent frivolity

Some questions (closely related enough, I hope, to count as a single question):

  1. Is there any actual research on the effect of such questions on student performance?
  2. Am I missing important benefits/problems?
  3. Does anyone have useful anecdotal evidence in favor of or against such questions?
  4. Does anyone have tips for using such questions in a way which avoids those concerns? (In particular, I don't think kinds of problems I'm talking about are equally problematic.)
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    $\begingroup$ I have done things like this with homework and exam problems, giving them punny titles. This is a great question! $\endgroup$ – Brendan W. Sullivan Apr 4 '14 at 19:19
  • $\begingroup$ I'm interested in hearing people's answers; I had trigonometry students find the height of the Mother Russua statue in Volgograd on the final, with an image attached. I thought it was fun, but maybe they didnt, maybe they did. $\endgroup$ – Brian Rushton Apr 4 '14 at 22:43
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    $\begingroup$ One related idea I just remembered: A former student remarked on the prevalence of gender partition in combinatorics problems, i.e. "We have 2n people, n boys and n girls. How many ways...?" They said if there were only one thing I would change about my course, it would be that. Since then, I've always avoided those, and gone with "Suppose we have n CMU students and n Pitt students (and no one goes to both schools). How many...?" $\endgroup$ – Brendan W. Sullivan Apr 6 '14 at 17:26
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    $\begingroup$ I can't believe nobody mentioned this: xkcd.com/135 ! $\endgroup$ – mbork Apr 6 '14 at 18:18
  • $\begingroup$ I like to ask questions about ninjas. Or, Ron Swanson. Sometimes, I'll throw in Dwight Schrute and a Naruto reference. Those who know like it, those who don't, don't seem to care. $\endgroup$ – James S. Cook Apr 7 '14 at 1:18
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A related example that comes to mind at the (strong) secondary level is Yellow Pigs Day at Hampshire College; this includes David Kelly's focus on the number 17.

At the (undergraduate) tertiary level, I am reminded of Frank Morgan's focus on soap bubbles.

Earlier in school mathematics, teachers often use sports questions (e.g., ones related to baseball) to teach various courses in mathematics (e.g., Statistics). I don't think "baseball" lends itself to "cute word problems" the same way that, e.g., yellow pigs, soap bubbles, and porcupines do, but there is a similar issue insofar as some students may simply be disinterested in the recurring theme that you choose.

With regard to research, I am not aware of anyone exploring the notion of a "cute" problem. (Probably you would need to be more precise with regard to what you mean...) I will say, though, that there is some relation to my answer to your earlier question (on the chain rule): namely, novice problem solvers (here, students - much of the time) differ from expert problem solvers (here, math teachers - much of the time) in how they think of related problems.

More precisely, there is a tendency among the novices to associate problems based on superficial features, such as grouping together animal problems as being mathematically similar instead of, say, chain rule problems. (See my linked answer for relevant references.) From this perspective, it may be that disentangling the cuteness from the mathematics is not entirely straightforward. This worry is captured somewhat by your second concern; indeed, it is a reasonable consideration.

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  • $\begingroup$ Of course, one could argue that observing "animal problems" for wildly different applications is itself integral in breaking that erroneous mental grouping. Such a thing is probably better left to homework and examples than practice tests, but... $\endgroup$ – LinearZoetrope Apr 6 '14 at 8:30
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You are missing two important benefits:

  • These problems visualize, that the theory has many and diverse applications and it's up to us humans to find even more applications. Anything can be modelled mathematically.
  • If this kind of question becomes a routine, you can use it to make your students use some routine (way of solving, heuristic, think outside of the box, …)

One anecdote here:

During a math course for 11th and 12th graders at the German school in Egypt, I work for, I repeatedly used the same person in my word problems: Mahmoud. Whenever the students read a problem involving Mahmoud, they knew it's gonna be about practical applications and they should think practically as well as purely mathematically. Of course, these problems were harder than purely formal tasks. They even told the students of the other German schools, who did the same exams: "If there is a task involving Mahmoud, forget about it, you won't solve it."

I regard this as evidence in favour but have the ambiguity of it in mind.

My regard of your concerns: They are invalid.

  • Non-native speakers have the same problem with "cute word problems" as with "normal word problems". If you connect the "cute word problems" with some routine, you can even help non-native speakers. Besides, it's part of the challenge of math.
  • Distraction from essential information: This is a reason for this kind of problems. It's part of the challenge of math to extract mathematical information from non-mathematical. This is the very essence of modelling.
  • Students, who dislike the class: Forget about them. They won't like the class because of "normal word problems" instead of "cute word problems". You cannot help these students, except offering different approaches to math. This is only a concern against only using cute word problems.

Concerning research on students' performances:

This would be rather difficult, as "cute word problems" are a wanted difficulty in itself. Solving a "cute word problem" may be a greater performance than solving a "normal word problem".

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    $\begingroup$ I don't quite understand the third concerns point. Language like forget about student who dislike the class and you cannot help these students worries me. $\endgroup$ – Benjamin Dickman Apr 5 '14 at 11:18
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    $\begingroup$ @BenjaminDickman If a student latently dislikes a math course (which happens in all the time in high school) he may or may not be further annoyed by "cute word problems". What's the difference? Every approach to math may be cause of annoyance to some students in the course. Consequently, you don't use any approach? It's not about approaches who might annoy students, it's all about approaches who might attract or engange students. And the sentence "you cannot help these students" has a big exception. $\endgroup$ – Toscho Apr 5 '14 at 13:50
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Please consider whether your examples typically favor one gender. For example, questions about sports (@BenjaminDickman mentioned baseball) will turn off some students, more females than males.

I agree with @Toscho, that making up memorable situations helps students learn to visualize better. During a unit on exponential functions (and logarithms), I use a murder mystery that my students must solve. I think they learn a lot from it. Ironically, I've also seen evidence that their learning hasn't transferred well - they often do better on murder problems on the exam than the easier population growth problems.

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