Comparing In-School and Out-of-School Mathematics Practice.

Researchers have noticed a gap between mathematics practice in school and mathematics practice in out-of-school situations. This study compares the out-of-school practice involving measurement of on-the-job carpet layers with the problem-solving strategies of ninth-grade students while engaged in measurement problems from the typical mathematics textbook. Data collection in the carpet-laying field work included participant observation, ethnographic interviewing, artifact examination, and researcher introspection. Data from the seventh- and eighth-grade textbooks were collected through content analysis of examples, exercises, and problems in the textbooks related to the concept of measurement. Data from the students included observation, informal interviewing, and researcher introspection. The carpet layers made use of four categories of mathematical concepts--measurement, computational algorithms, geometry, and ratio and proportion--and two categories of mathematical processes--measuring and problem solving. Analysis of the textbook problems indicated that students were involved in computational exercises whereas carpet layers were involved in measurement. Differences between students and carpet layers included a lack of deep understanding of the concept of area on the part of the students and more problem-solving skills and strategies on the part of the carpet layers. Contains 26 references. (MDH)