JISHOU, HUNAN — It seems every few months or so the Internet is in turmoil about some silly “controversy” or another. The latest is the “Marty and Luis” pizza question.
An image of the question, supposedly marked in green by a teacher, ended up on reddit two months ago, apparently as a criticism of American education, or teachers, or math. Who knows?
Well, I’m a skeptic, so I went digging around the Internet trying to find the origin of the question and the image. The source of the question was easy to find: Pearson Education’s EnVision math series for 3rd Grade Common Core. The source of the image was a different matter.
Using TinEye.com, I used the image as a search parameter. It’s earliest appearance was, oddly enough, on a German image collection site, www.lachshon.de, and it was posted there in March 2015!
The account of the original poster, gelöscht-20111221-112645, has since been locked, and his new account, gelöscht-20120516-162657, is not visible to the public, though the images are searchable. Go figure.
After this mysterious German appearance, the same image ended up on imgur.com about a week later, where it began to attract the usual assortment of comments, ranging from “math is hard” to “teachers are dumb.”
I was trying to ascertain if the question was in fact marked by a teacher (who goofed, BTW) or whether it were some fake image created for political commentary. The reddit user who posted it, xtreme1461, appears to be a conservative of the alt-right ilk, judging from his reddit threads, so I was suspicious. I seriously doubt it was his own kid’s paper that was involved.
Well, that aspect of my research is as yet unanswered. The provenance of the image may forever be a mystery.
But the question itself is real. It’s included on a practice sheet published by Pearson Education, one of the biggest textbook publishers in the USA.
It’s for third grade math, and the students presumably would have learned enough about fractions by the time they did the exercises to answer the question correctly. The student who provided the answer in the image did.
Here’s my big complaint with the Internet commentators who are outraged that a teacher would get the question wrong and that third graders would be presented with such a tricky question — one which seems to baffle most Internet commentators.
This is a practice sheet, to be filled in AFTER the students have already been led through the lesson. It’s not something a teacher hands out cold, and tells the kids to complete while he or she surfs on Snapchat. It’s part of a unit covering several days.
Not knowing the origin of the image, I looked for a reasonably generic unit plan online, and found a draft scope and sequence scheme from 2011[PDF]. These are the documents school districts prepare to be ensure all teachers are on schedule and following the same game plan.
This paragraph on page 20 is the most pertinent to the Marty and Luis Pizza Dilemma. [NOTE: the draft plan here is coded to an earlier edition of the Pearson EnVision series, so the unit numbers are different from the one referenced above.]
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or < , and justify the conclusions, e.g., by using a visual fraction model.
I’ve highlighted the key concept here, which the Marty and Luis question is assessing. The practice question makes no statement about the size of the two boys’ pizzas, only the proportion of each pizza eaten. The student response in the viral image is correct: Marty ate more pizza than Luis, because Marty’s pizza was bigger.
Not having access to the student textbook or teacher’s edition, I don’t know how students would have been prepared to answer the question correctly, but I can make some educated guesses.
Common Core math focuses on manipulatives and models. So, I came up with an easy model. Rather than using area and pizza wedges for comparison (which could be challenging for third graders), I would use length. Students would have already plotted fractions on a number line, so my project here should be easy for them.
Student A (Marty) has a strip of construction paper 12 inches long and an inch wide. On it, the teacher has drawn lines every 2 inches across it. She asks him to fold over the strip so that he has 4/6 of its original length showing. (That’s 8 inches, BTW, grown-ups.)
Student B (Luis) has a strip of construction paper 6 inches long and an inch wide. On it, the teacher has drawn lines every 1 inch across it. She tells him to fold over the strip so that he has 5/6 of its original length showing. (IOW, 5 inches.)
Question: Who has the longer strip?
So, if the teacher had taught the lesson correctly, the Marty-Luis pizza question is fair. It gets to one of the objectives of the unit, that comparing fractions only makes sense when you have complete units of identical size. That’s an important concept for students to understand.
What’s more puzzling is how the grader got the question wrong. If the teacher had taught the lesson as it’s supposed to be taught, she (or he) would have known the correct answer. Plus, there are answer keys for teachers to use.
Unlike the many commenters who are quick to blame the anonymous teacher in this case, I can’t. It could have been an honest mistake, done because the teacher was trying to grade a stack of papers in a very short time. I would give the teacher the benefit of the doubt here.
If a teacher in fact really marked that paper. I still have my doubts.
[paypal_donation_button align=”center” price=”5.00″]