OFFICE MEMO: Dick Pilgrim Date: Tue, 5 May 1998 13:34:56 -0700 To: firstname.lastname@example.org From: email@example.com (Dick Pilgrim) Subject: re: Math Word Problems
* Date: 2 May 98 14:14:04 -0400 (EDT) * From: Hal Schneider <firstname.lastname@example.org> * Subject: Math Word Problems * * As the author of the book, Solving Math Word Problems: * URL: http://home.earthlink.net/~mathaid/mathbook.htm * * I would like to share ideas and opinions on this subject with the goal * of finding valid common reasons why a very high percentage of students * continue to have difficulty with MWP ! * cut * Please, please only respond with specific answers to the questions * below and, when applicable, reasons for your position. Let's try to * limit it to key elements that apply to most situations. Here goes... * * 1. In your experience, do a significant percentage of students with * good reading ability and good math operational skills also have * difficulty with MWP ? If yes, any opinions as to why ?
Yes, just ask anyone in the school of engineering or physics department. Seriously, I think it does stem from artificiallity of the math textbook problems. On the other hand, I don't have time to teach Newton's Laws from physics, Quantitative Microeconomics, Qualitative Analysis from chemistry, Cell biology, etc., etc. prior to trying to introduce students to some potential applications. I do, however, now think that my students learn more from tackling a few general problems - i.e. general constants, some extraneous information - over a longer time than the common formulaic textbook problems.
Often it seems that the better the operational skills the more time the student spends looking for the appropriate formula to use than thinking about the problem. --- * 2. Is the use of MWP earlier than 5th grade a helpful approach or does * difficulties that are experienced dilute the math operation education?
I only have the experience of my own children and the volunteer time I spent in elementary classrooms during their youth. On that background, I found my time most profitably spent with using the math to model their world rather than MWPs or "operations" worksheets. --- * * 3. Most MWP can be solved by first developing an equation. However, it * can also be solved without the equation by doing the proper math in * steps (e.g. add 'this' to 'that' ..then divide 'this' by 'that'.... * then multiply the answer by 'that' ... etc.). * Should the equation be developed prior to doing the math ?
I equate "doing the math" to the generalization process. This frequently happens when several computations have been done with different parameters to identify some generalization which can then be put into a symbolic model. Often, students don't actually understand the problem until they have done some arithmetic to solve a particular example - the infamous "Twice as many X as Y" translation problem is a good example of the need to compute first.
----- * * 4. Have you heard the term: 'dimensional analysis' ? If so, do you use * it ? If yes, how ?
I agree with Karl Casper here: * It leads to a student trying to * reach an answer by guessing. I can get to a mass by taking a force * unit and multiplying it by the square of the time and dividing by the * distance. Which doesn't work at all if the force is varying. It's * helpful only to check to see that you haven't left something out. ---- * 5. If you have developed specific MWP techniques that have been really * successful for even the poorer students, please share then with us.
Even better, bottle it and sell it, you'll make a fortune. * * 6. I consider my 'Word/Fraction' technique to be a generic solution * for MWP. Do you think there can be a detailed generic solution that is * usable even for poorer students ? * * Let's here it from out there ! ! * * Hal Schneider
- - - - - - - - - - - - - - - - - - - - - - - - - - - reply to: Richard Pilgrim Director: Math Testing and Placement University of California, San Diego 9500 Gilman Drive #0423 La Jolla, CA 92093-0423 email@example.com (619) 534-3298 fax: (619) 534-1011 - - - - - - - - - - - - - - - - - - - - - - - - - - -