The Problem With Math: Cheryl and Her Birthday
Recently the Singapore and Asian School Math Olympiads were met with a bit of notoriety when a word problem they had posed went viral via a Facebook post. The question is about Cheryl, who at first glance seems to be kind of a jerk.
In the math problem Cheryl is asked by two men for the date of her birthday.
She gives them ten possible options.
Then, proving she wants to further frustrate the men, she shares the day with one and the month with the other.
Here is the original problem:
"Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of ten possible dates.
- May 15
- May 16
- May 19
- June 17
- June 18
- July 14
- July 16
- August 14
- August 15
- August 17
Cheryl then tells Albert and Bernard separately the month and day of her birthday respectively.
Albert: I do not know when Cheryl's birthday is, but I know that Bernard does not know too.
Bernard: At first I don't know when Cheryl's birthday is but I know now.
Albert: Then I also know when Cheryl's birthday is.
So, when is Cheryl's birthday?"
So Many Problems With This Problem
First of all, Albert and Bernard need to just move on because Cheryl sounds like a needy woman who wants attention, and she thinks that playing games will get her that attention.
Second, in the real world, who does this? You either tell people your birthday or you don't.
In no way is this something that would happen in real life and it is little more than an exercise in frustration for most students who encounter it, not to mention poor maligned Bernard and Albert.
There does seem to be a proposed solution which curious minds can locate here.
But the solution, and the way to arrive at the solution, is longer than the problem itself.
I think we can safely assume that if Cheryl doesn't have her birthday on her Facebook profile, then she probably doesn't want you to know about it.
Most people that I know who like birthday attention tend to shout their birthdays from the mountaintops to ensure parties and gifts. Clearly Cheryl is not one of these people.
But what Cheryl is, is frustrating and it's problems like these that make math frustrating and make many people think that math itself is pretty useless.
I Don't Hate Math
Now, before you get all upset with me. I don't hate math. How could I? As an adult I use it every day from figuring out a recipe, to creating a household budget, to calculating the distance I'm going and the time it will take.
I wouldn't know what time I need to leave to get to the movie I want to see without not only figuring out how long it will take me to get to the theater in weekend traffic but also how long it might take to stand in line at the concession stand for snacks and how long the preview will likely run (in other words, what's the REAL start time of the movie).
And if you think about it, we all do those calculations and their pretty complicated and nuanced. And they are also not simple.
The Problem With Cheryl
The problem with Cheryl (besides her obvious dislike of Bernard and Albert) is that the problem doesn't really resemble real life and it's not likely to be something any real person runs into unless the girl at the bar is really trying to tell them, in a complicated way, to get lost.
The content is abstract and what it's trying to get us to do, eliminate other unlikely options, could be taught in a more practical way.
We will all run into problems where we have to eliminate some choices to find the right one. And sure there will be problems in life that will require critical thinking and reasoning.
But Cheryl's birthday and her silly word games won't be one of them.
And therein lies the problem about how we are choosing to teach math to our students.
The math problems in their workbooks are full of Cheryls with made up problems and have way less to do with practical use and application.
But it doesn't have to be that way.
In this TED talk by Dan Meyer, he looks at ways to make math problems practical and promote real world use and critical thinking.
Sure some of us are good at math and we relish these little word games and puzzles because they are fun for us. But for many of us, math education beyond the basics is really a waste of time---at least the way it's being taught now.
I mean nearly every one carries a little computer (also known as a smart phone) in their pocket that can add, subtract, multiply and divide in a split second. Beyond knowing what those numbers are and what function we need to use, (I have twenty dollars, and I want to buy this bag of fruit that costs $4.38. Will I still have enough for bus fare for the rest of the week?), our pocket computers can figure everything else out.
I remember when I was in school, teachers pointing out that you won't always have a calculator with you.
Do you remember the math you learned in school?
Towards More Specific Training
Consider Andrew Hacker's New York Times piece titled "Is Algebra Necessary?"
In it he makes the researched claim that Algebra is not only causing problems for many high school students, it very likely may not even be necessary for students to master in order to successful.
Hacker points out that many of the nuances of math and the math that needs to be applied on the job are taught on the job or through partnerships with universities.
He even suggests that we may be "wasting precious resources," our young people's minds, by taking the time to try to teach a subject that may have little practical use for most of the students struggling through it.
If You Don't Use It, You Lose It.
And what about all those who did take Algebra, Trigonometry and Calculus?
Unless you have a job that specifically relates to those skills or are a math teacher yourself, a Calculus problem handed to you today would look pretty much like a foreign language.
Why? Because you don't need it.
But what do you need? Fractions. Addition. Subtraction.
Pretty much what we learned in elementary school---back when math was more fun, more useful and way less frustrating. And most of this we learned through play, manipulatives and practical education.
Maybe Less Is More?
In a very non-logical conclusion, perhaps the answer to our math woes is that "less may actually be more" and that worrying less about endless worksheets of addition and subtraction and more about practical application---real world uses---would actually make for a strong, more math-able adult.
Consider the story of L.P. Benezet, a superintendent of schools in New Hampshire in the 1930s. According to Psychology Today (Peter Gray, "When Less Is More: The Case For Teaching Less Math In School), the schools had been challenged to find subjects that they could drop from school since so many had been added over the years.
Benezet, outrageously, decided to drop arithmetic from the school curriculum, favoring a later introduction. Benezet believed that early introduction of math actually was bad for the students. In a strange twist of events, he may have actually been right.
So in some schools in Benezet's district, math was not introduced until 6th grade. (Note that he actually chose some of the poorer schools in the district for the experiment.)
The teachers engaged a radical way of teaching that included talking "about topics that interested them" (Gray) and engaging in practical math such as counting and sorting.
A series of tests performed by a graduate student from Boston University showed that the students who were not taught math "performed much better...on story problems that could be solved by common sense and a general understanding of numbers and measurement... those in the experimental classes performed worse on the standard school arithmetic tests, where the problems were set up in the usual school manner and could be solved simply by applying the rote-learned algorithms" (Gray).
Furthermore, those students were able to catch up on the rote memorization in a very short time.
Practical application and delayed instruction actually made stronger math students.
Later Is Better.
Gray uses this story to help build his case that teaching math, specifically the way we teach it, at young ages, may be doing more harm in good.
We are teaching the opposite of critical thinking, and also teaching kids that math is a dull and segmented subject. If they can get the answers to a neat row of problems on a worksheet, they believe that they have mastered the task.
Conversely, Gray points out that in some cultures where there is "little to no math instruction" many students can still learn and apply math concepts.
In a follow up piece titled "Kids Learn Math Easily When They Control Their Own Learning," Grey also advocates for more practical and useful applications for math.
He gives many examples of children, who even without curriculum, learn and explore math and develop useful understandings of it.
Because in reality, math is intuitive, it is a part of us and it isn't actually hard once we learn the critical thinking skills that will help us solve the problem rather than rote memorization of formulas that we don't actually know how to apply outside of the math test for that week.
Let's Teach Our Kids To Give Cheryl The Boot.
So let's worry less about Cheryl and her coy birthday tactics and more about everyday math, the kind of math that helps us to live our lives and run our homes.
Cheryl can spend her birthday by herself.