From: bruck@math.usc.edu (Ronald Bruck) Newsgroups: sci.math Subject: Re: Math Word Problems Date: 7 Nov 1998 21:30:52 -0800 In article <722f0b$f4a@b.stat.purdue.edu>, Herman Rubin wrote: >In article <721qok$b4o$1@nnrp1.dejanews.com>, wrote: >>Many science educators (including engineering in college) find a serious lack >>in the ability of students to readily do math word problems (MWP) > ... >The most important tool needed to "solve" word problems is to be >able to formulate them. The key tool here is to be able to use >the unlimited supply of variables, which are essentially nothing >more than pronouns, to translate the problem into a set of >formal expressions subject to analysis. Yes, but language can be tricky. Consider the following problem, which was popular around the turn of the century: "Mary is 24 years old. She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?" It's not that the mathematics is especially difficult; the problem is unravelling the convoluted ENGLISH. For non-native speakers this is a nightmare. I'd hate to have to solve a similar thought-twister in French or Russian. Actually, there is a famous "Professors and Students" phenomenon: "A certain university has five times as many students as professors. If P denotes the number of professors and S denotes the number of students, which of the following expresses the relation between S and P? (a) P = 5S (b) S = 5P" Apparently a MAJORITY of the people asked this will reply (a). (I don't know from which population they're drawn.) --Ron Bruck ============================================================================== From: hrubin@b.stat.purdue.edu (Herman Rubin) Newsgroups: sci.math Subject: Re: Math Word Problems Date: 8 Nov 1998 11:34:37 -0500 In article <723aac$qm3$1@math.usc.edu>, Ronald Bruck wrote: [see above -- djr] > "Mary is 24 years old. She is twice as old as Ann was when Mary was > as old as Ann is now. How old is Ann?" The most common pitfall people fall into is to try to minimize the number of variables. For the non-adept, I would suggest using three or four. For the non-mathematician, it is this translation step which is the important one, and no amount of manipulation will do much to get it understood. The use of variables should be taught early, with beginning reading, and not just for numerical quantities. >It's not that the mathematics is especially difficult; the problem is >unravelling the convoluted ENGLISH. For non-native speakers this is a >nightmare. I'd hate to have to solve a similar thought-twister in French >or Russian. Unravel it a piece at a time. Let M be Mary's age now, m her age at the time in the past. Let A be Ann's age now, and a her age at the time in the past. So we have: M = 24 M = 2a m = A M-m = A-a The time interval is the same for both Doing with fewer variables should not be considered for the one trying to learn. The mistake usually made is trying to do this with one variable. I doubt that I would have any more difficulty in any language for which I could even attempt to translate the problem; knowing the basic grammatical structure may be needed. However, it is now considered that the grammar of a language is unimportant. This might be part of the problem; mathematics is essentially grammar. >Actually, there is a famous "Professors and Students" phenomenon: > "A certain university has five times as many students as professors. > If P denotes the number of professors and S denotes the number of > students, which of the following expresses the relation between S > and P? > (a) P = 5S (b) S = 5P" >Apparently a MAJORITY of the people asked this will reply (a). (I don't >know from which population they're drawn.) With the refusal of the educationists to teach precise structure, I am not surprised. No amount of computation will do much to help understand what anything means. Too much is likely to hinder. The teachers could not learn the new math. Those who have taken the usual computational calculus course, and the computational linear algebra course, may even be less prepared to understand what it means than those who cannot compute at all. In the past, the high school geometry course, which was all proofs, at least got rid of some of this. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558