Category: pseudocontextsaturday

Total 36 Posts

[PS] The Progress We’ve Made In 34 Years

Christopher Danielson finds a text in his college library called How to Solve Word Problems in Algebra: A Solved Problem Approach (Johnson, 1976).

A sample problem:

Mrs. Mahoney went shopping for some canned goods which were on sale. She bought three times as many cans of tomatoes as cans of peaches. The number of cans of tuna was twice the number of cans of peaches. If Mrs. Mahoney purchased a total of 24 cans, how many of each did she buy? (p. 14)

From Johnson’s preface:

There is no area in algebra which causes students as much trouble as word problems…Emphasis [in this book] is on the mechanics of word-problem solving because it has been my experience that students having difficulty can learn basic procedures even if they are unable to reason out a problem.


And here is the crux of the matter. I have already argued that the very nature of word problems is such that people’s actual experience has no bearing on solving them. But in this preface is the rarely stated truism that we can train students to work these problems even when we cannot teach them to think mathematically. Entire sections of textbooks are devoted to the translation of word problems into algebraic symbols and Ms. Johnson has written the book on it.

2011 Mar 07: Christopher Danielson responds to some of our commentary at his blog.

Kate’s Urban Legend

Kate Nowak, on the grand finale of Pseudocontext Saturday:

I realize this is going to sound urban legendy, but I know someone who knows the teacher who wrote this question [..] And, the story goes she wrote this question as a joke. As in, as a lark she wrote something so bad and ridiculous that it would never be used. And then they put it on the exam.

Nope nope nope. No way. Not buying.

[PS] The End

This is completely subjective, but Peter Brouwer sent in the problem that I thought satisfied both halves of the working definition of pseudocontext in the most spectacular fashion. This is it. This is as bad as it gets.

From the June 2001 Math B New York Regents examination [PDF]:

Jo Boaler gets the last word:

Students do however become trained and skillful at engaging in the make-believe of school mathematics questions at exactly the “right” level. They believe what they are told within the confines of the task and do not question its distance from reality. This probably contributes to students’ dichotomous view of situations as requiring either school mathematics or their own methods. Contexts such as the above [pseudocontext], merely perpetuate the mysterious image of school mathematics.

That’s it. Thanks for pitching in.

[PS] Pseudorejects

These are submissions I received that didn’t seem to fit the criteria. This isn’t to say they’re great problems. This isn’t to say that I’d throw water on any of these problems if they were on fire. This isn’t to say that they’ve even represented or examined their context well, just that the context itself isn’t pseudocontext.

Breedeen Murray

McDougal Litell’s Math Course 1:


Barbara Panther

McGraw-Hill’s Total Math – Grade 6:

Bill goes to a farm and sees cows and chickens. He counts 6 heads and 18 legs. How many of each animal does he see?


Melissa Griffin

Haese and Harris Mathematics for the International Student.:


Jeff Bowlby

McGraw-Hill’s Algebra 1:


Phil Aldridge

EdExcel International’s Longman Mathematics for IGCSE Book 1:


Iain Mackenzie

Scotland National Examination:


Christine Lenghaus

Australian Year 12 Exam:


Amulya Iyer

Pearson’s Algebra 2:


Steve Bullock