Estimation performance and strategy use of Mexican 5th and 8th grade student sample

Abstract

What computational estimation skills and strategies do Mexican students possess? Does the theoretical model based on interviews with a select United States sample accurately describe the Mexican sample?

These were questions studied based on interviews with 8 eighth graders (those scoring in the top 5%) out of a sample of 177 eighth graders from twelve different Mexican schools representing a range of social and economic backgrounds. Preliminary screening data collected by administering a computational estimation test revealed that estimation was very difficult for the Mexican students (mean 4.0, range of 0 to 18 on the 38-item open-ended test).

The interviews revealed that the Mexican students as a whole did employ the three general cognitive processes outlined in the theoretical model, namely reformulation, translation, and compensation. The most common strategy employed was the front-end technique. Similarly, a frequent strategy used to “estimate” was mentally applying a paper/pencil algorithm. In contrast to data collected under similar conditions in Japan and the United States, rounding was a strategy only occasionally used in the interviews. The use of benchmarks (key reference points used as bounds in forming an estimate) as a strategy for estimating problems involving percent was common and may reflect students' “out-of-school” experience with mathematical applications. Consistent with parallel investigations with Japanese and United States students, these Mexican strudents rarely reflected on their estimates through their own initiative and rarely recognized unreasonable estimates.