Better Multiple-Choice

If I were a K-12 student right now, I’d want to live in San Diego. In 2020, San Diego Unified School District introduced a new district-wide math test that contained no multiple-choice questions. The district was allowed to use their own internal test instead of the state test last year, due to the pandemic, and they’re apparently allowed to use it again this year. Supposedly, the test moves away from a reliance on computational ability and instead measures three dimensions: students’ knowledge of mathematics (concepts and formulas); their application of that knowledge; and, their ability to communicate mathematically.

The optimist in me says, “It’s about time!” But the pessimist in me thinks, “Don’t they know that it’s a lot more expensive, and harder to ensure reliable and replicable results, when using humans to do the scoring instead of machines?” I’m old enough to remember the controversy and eventual dissolution of the Maryland State Performance Assessment Program (MSPAP) exams, which required extended answers and contained no multiple-choice questions. FairTest called the MSPAP test “perhaps the single best state exam,” but it was criticized for providing school-level but not individual student scores. Though generally agreed to have been a catalyst for improved teaching, it was replaced by an entirely multiple-choice test to meet the requirements of the Elementary and Secondary Education Act (ESEA).

Ah, the good old days. Reminiscing sure ain’t what it used to be. But, I digress.

To determine if multiple-choice questions are valid tools, I made a list of pros and cons regarding their use in educational assessment. 

Pros	Cons
They can be scored quickly.	The correct answer can be guessed.
They can be scored objectively and without bias.	The correct answer can be found by process of elimination.
	They encourage students to think like the test creators instead of like themselves.
	They provide no information about the student’s solution strategy.
	They are required to have only one answer.
	They exacerbate test anxiety.
	They don’t prepare students for college or the work force.
	Incorrect answer choices expose students to misinformation, which can influence future recall and thinking.

Seems a bit lopsided.

In recent years, multiple-choice questions have gotten a bit of a makeover. Those in the educational assessment industry now call them “selected-response items” because, well, students get to select a response.

But this is just semantics. Referring to a pig as a mud wrestler may sound nicer, but the pig won’t be any less dirty.

It’s the advertising trope of…

New look, same great taste!

Or as a pretentious coffee brand said when they changed the label…

Innovative presentation, but consistent quality.

Truth is, selected-response items look like they’ve always looked, typically with a really boring prompt and even more boring answer choices. As one example, the following item is from a PACE (Packet of Accelerated Christian Education), which “integrate Godly character-building lessons into the academic content.”

Mr. Louis Pasteur did experiments with milk. Mr. Louis Pasteur was…

1. a glass bottle
2. an airplane
3. a scientist

Despite your religious beliefs, you have to admit that this question is rather absurd. Would any student ever think that a glass bottle or an airplane would be referred to as “mister”? To be fair, this question appeared in a PACE packet in 2013, so it’s quite possible that it’s since been updated. Still, 2013 wasn’t that long ago, and there’s no time in history when those answer choices wouldn’t have been ridiculous.

And here’s one that was presented during a session at an NCTM regional conference:

To convert to radians, multiply by…

1. π/180
2. 180/π
3. 225π/180
4. π/40,500

Ignoring the fact that this question attempts to assess something that your calculator knows so you don’t have to, this question is fine. But in the reading passage directly above the question, it stated, “To convert an angle from degrees to radians, multiply by π/180.”

Well, that will just never do.

I’m not convinced that a great multiple-choice question actually exists. That said, some are better than others, so I offer you the following seven multiple-choice — or selected-response, or objective-response, or whatever-you-want-to-call-them — items.

What is the probability that you will randomly choose the correct answer to this question?

1. 25%
2. 50%
3. 0%
4. 25%

At any given time, the number of people in the air — that is, those who are flying in motorized aircraft, and not counting those who were recently launched by catapults or who have bounced on a trampoline — is closest to the population of…

1. Flint, Michigan
2. Seattle, Washington
3. New York, New York

The approximate volume of an average chicken egg is…

1. 7 cm³
2. 70 cm³
3. 700 cm³
4. 7,000 cm³

The polar (north-to-south) diameter of the Earth is about…

1. 1,000,000 inches
2. 20,000,000 inches
3. 500,000,000 inches
4. 1,000,000,000 inches

One million one-dollar bills weigh about as much as…

1. a three-toed sloth
2. a giant panda
3. Chris Christie
4. a grizzly bear
5. a black rhinoceros

The total number of calories in all the hot dogs consumed at Yankee Stadium during one season of Major League Baseball is closest to…

1. the number of five-card poker hands
2. the number of possible license plates in Indiana
3. the number of combinations in the Powerball lottery
4. the number of humans on Earth
5. the number of stars in the Milky Way

If the residents of New Mexico joined hands and stood in a straight line, they could reach from one side to the other of…

1. New Mexico
2. Rhode Island
3. Texas
4. Alaska

The answers to these questions will not be provided, though each question absolutely has a best answer among the choices. In lieu of an answer key, enjoy the following joke:

How do you keep a fool in suspense?