Cute Word Problems

Question

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.)

Answer 1

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.

Answer 2

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".

Answer 3

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.