Were Story Problems Ever Any Good?


I have been reading Mapping In Michigan and the Great Lakes Region, edited by David I Macleod, because — look, I understand that I have a problem. I just live with it. The book is about exactly what you might imagine from the title. And it features lots of those charming old maps where, you know, there wasn’t so very much hard data available and everyone did the best with what they had. So you get these maps with spot-on perfect Lake Eries and the eastern shore of Lake Huron looking like you pulled it off of Open Street Maps. And then Michigan looks like a kid’s drawing of a Thanksgiving turkey. Also sometimes they drop a mountain range in the middle of the state because I guess it seemed a little empty without.

The first chapter, by Mary Sponberg Pedley, is a biography and work-history of Louis Charles Karpinski, 1878-1956. Karpinski did a lot to bring scholastic attention to maps of the Great Lakes area. He was a professor of mathematics for the University of Michigan. And he commented a good bit about the problems of teaching mathematics. Pedley quoted this bit that I thought was too good not to share. It’s from Arithmetic For The Farm. It’s about the failure of textbooks to provide examples that actually reflected anything anyone might want to know. I quote here Pedley’s endnote:

Karpinski disparaged the typical “story problems” found in contemporary textbooks, such as the following: “How many sacks, holding 2 bushels, 3 pecks and 2 quarts each can be filled from a bin containing 366 bushels, 3 pecks, 4 quarts of what?” Karpinski comments: “How carefully would you have to fill a sack to make it hold 3 pecks 2 quarts of anything? And who filled the bin so marvelously that the capacity is known with an accuracy of one-25th of 1% of the total?” He recommended an easier, more practical means of doing such problems, noting that a bushel is about 1 & 1/4 or 5/4 cubic feet. Therefore the number of bushels in the bin is the length times width times 4/5; the easiest way to get 4/5 of anything is to take away one-fifth of it.

This does read to me like Pedley jumped a track somewhere. It seems to go from the demolition of the plausibility of one problem’s setup to demolishing the plausibility of how to answer a problem. Still, the core complaint is with us yet. It’s hard to frame problems that might actually come up in ways that clearly test specific mathematical skills.


And on another note. This is the 1,000th mathematical piece that I’ve published since I started in September of 2011. If I’m not misunderstanding this authorship statistic on WordPress, which is never a safe bet. I’m surprised that it has taken as long as this to get to a thousand posts. Also I’m surprised that I should be surprised. I know roughly how many days there are in a year. And I know I need special circumstances to post something more often than every other day. Still, I’m glad to reach this milestone, and gratified that there’s anyone interested in what I have to say. In my next thousand posts I hope to say something.

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

4 thoughts on “Were Story Problems Ever Any Good?”

  1. Happy 1,000th! I see someone let slip about the Love Bug tv series, well at least we managed to keep the secret this long,let me tell you it wasn’t easy restricting all Entertainment data flow to your computers for all this time but now it’s over and we can sit back to reflect upon a job well done.Just for our records, did you ever find out about the “Stir Crazy” and “George Burns Comedy Week” shows?

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    1. Thanks kindly! … I had not heard about either of these series, but I did just yesterday find out about Small and Frye, a sitcom about a pair of detectives, one of whom sometimes uncontrollably shrinks to six inches tall. Or grows back to normal. I could not understand how I missed this except it turns out it was on opposite That’s Incredible, and I was plainly so busy watching that idiocy I missed some perfectly good idiocy on CBS.

      I don’t suppose the current generation would believe that there was a time there were only three TV networks, and they all had a program that was showing bloopers from other TV shows.

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        1. I don’t know how future generations will understand that we used to find it extremely funny when a local news anchor couldn’t say someone’s name and then cracked up giggling and we didn’t even meme-caption a screenshot as, say, “NEILED IT”.

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