The New STEM Math Challenge: “Advanced-Think” Word Problems
From Richard C. Larson
Math: Those dreaded "word problems." Remember them? When we were in school they seemed to be the hardest thing to do in math.

But wait, they're baaa...ck, and this time in a much more powerful form! We're speaking about the new Common Core State Standards, put forward by the National Governors Association and about to be implemented across much of the United States. While those old dreaded word problems seemed difficult, in fact they tended to be formulaic. To solve one you had to recognize the type of problem it is -- by doing some pattern matching with topics taught recently by your teacher, then recall the recipe or algorithm for solving that type of problem, then plug in the given numbers, and turn the crank. Presto, you're done. Not so bad after all.

Now come the Common Core Standards. These will require elevating the student's understanding of math to a higher level. Simple pattern matching will not suffice. Many of the new word problems that will be tested will be non-formulaic. A student who plans to excel using only pattern matching will be surprised: he’ll do poorly. New emphasis will be placed on problem framing and formulation, modeling and determining which aspects of mathematics to apply to the given novel problem. According to the web site of the new Standards http://bit.ly/l9tMGS.

“The high school standards call on students to practice applying mathematical ways of thinking to real world issues and challenges; they prepare students to think and reason mathematically.”

This could be fun or scary, and certainly challenging. Those students who do well— assuming the written questions achieve the current high expectations—will certainly be STEM-literate in math. That's good for them and for their country!

In thinking about this, I'd like to see some word problems that are brief, like Tweets (140 characters maximum) and then ask for a mathematical interpretation. Here's an example from Garrison Keillor's Lake Wobegon radio program:

"Lake Wobegon, where all the children are above average."

Lake Wobegon is a fictional town in Minnesota, USA. I'd like to see this quoted and then have an accompanying question with parts (a), (b) and (c).

(a) Explain in words and using whatever math you need, how this statement is not possible for the residents of Lake Wobegon.

(b) Explain in words and using whatever math you need, how this statement might in fact depict correctly the excellence of the children of Lake Wobegon.

(c) Describe how each of the two interpretations (parts (a) and (b)) can be correct and relate that to the mathematical assumptions underpinning the arguments.

How did you do on this question? If you want to see my answers, please email me at <rclarson@mit.edu>. But I’ll only respond if you send me your answers, too!

Then I have another one for you. Yogi Berra, the famous Hall-of-Fame New York Yankees baseball player and coach, is well known for his "Yogi'isms." Here is one that he said when speaking to friends about a famous restaurant:

"Nobody goes there anymore, it's too crowded."

Question to the students:

Explain in words what Yogi really meant to say. Does the quote have a plausible and mathematically possible explanation? Or does the quote simply say something that is impossible?

Ask me for my solution, again by email!

These two questions share a common theme in approach: What is the base population against which you are making a statement? Being able to elucidate the correct logic not only unravels these two apparent contradictions but also develops within the student the ability to address similar situations in everyday life when “population base” puzzles may appear in daily news, in business dealings and even in personal conversations.

Are these types of questions too obscure for the new Standardized tests? I'd like to hear from you.

Dick Larson rclarson@mit.edu

Richard Larson is the Mitsui Professor of Engineering Systems at MIT. He is also the Director of MIT LINC and the Principal Investigator of MIT BLOSSOMS.

Back to newsletter