FOOK: Oh Deep Thought, your task is this. We want you to tell us — the Answer.
Long pause. Deep Thought bleeps and bloops.
LUNKWILL: You know. The answer. To Life…the Universe…Everything.
FOOK: We’d really like an answer. Something simple. Can you do it?

The Hitchhikers Guide To The Galaxy

The above conversation reminds me of the many teachers, especially math teachers, when it comes to homework problems, test questions and questions asked in the classroom. “What is the answer?” The question posed may be an ambiguous question where there is no specific query, could have more than one meaning, may ask for several responses, or may not clearly define the subject/object. The problem with an ambiguous question is that the answer from the student can be equally as ambiguous, or not what you expected. The below image represents such a question, and the response is priceless!

Laziness on the part of the person asking the question? Maybe. But the conversation between the teacher (FOOK) and the student (DEEP THOUGHT) may be similar to the following conversation.

FOOK: Deep Thought. Do you have …
DEEP THOUGHT: An answer for you? Yes. I have.
FOOK: There really is an answer?
DEEP THOUGHT: Yes. There really is one.
FOOK: (almost strangled with emotion) Oh!
LUNKWILL: Can you tell us what it is?
DEEP THOUGHT: Yes. Though I don’t think you’re going to like it.
FOOK: Doesn’t matter! We must know it!
DEEP THOUGHT: You’re really not going to like it.
FOOK: Tell us!
DEEP THOUGHT: Alright. The answer to the ultimate question …
LUNKWILL: Yes …
DEEP THOUGHT: … of Life, the Universe, and Everything …
FOOK: Yes!
DEEP THOUGHT: … is …
CROWD: Yes … !
DEEP THOUGHT: (longest pause yet) Forty two.

The Hitchhikers Guide To The Galaxy

The question must be asked in a way to show that the student understands the concept and can apply it to the given problem. Otherwise, the student may provide an answer without showing the work, e.g., 5 is the answer to Find x in the Find x image above.

Now the student is perplexed and the conversation between the student (DEEP THOUGHT) and the teacher (LUNKWILL) may go as follows.

DEEP THOUGHT: I checked it thoroughly. It would have been simpler, of course, to have known what the actual question was.
LUNKWILL: But it was the Question. The Ultimate Question!
DEEP THOUGHT: Yes, but what actually is it?
FOOK: Everything! You know … just EVERYTHING!
DEEP THOUGHT: That’s not a question. Only when you know what the actual question will you know what the answer means.
LUNKWILL: Give us the Ultimate Question then!!

Later, when Benjy and Franky Mouse (i.e., Lunkwill and Fook) want to remove Arthur’s (student) brain to obtain the Ultimate Question, Arthur Dent then proposes the following.

ARTHUR: You want the question that goes with the answer “42” How about “What’s six times seven?” Or “How many Vogons does it take to screw in a lightbulb?” Or here’s one, “How many roads must a man walk down?”

The Hitchhikers Guide To The Galaxy

Some better questions to ask concerning the Find x image above may be as follows.

• What theorem would you use to find the value of x given the type of triangle in the image?
• Why can this theorem be used given the information provided in the image?
• Use that theorem to calculate the value of x based on the measurement of the two sides and angles as shown in the image. (Show your work.)

Teachers, and those who author books, just need to ask better questions.

Over time, I realized how little my students seemed to “get it.” They stumbled whenever a problem’s context shifted, and they struggled to justify their answers. Many ended up forgetting the process they had used to find the correct answer in the first place. Framing my teaching around answers was not helping my students learn mathematics.