| Computational estimation, the process of converting from exact to approximate numbers and then of mentally computing those numbers to obtain an answer, has received renewed interest in the mathematics curriculum. To assess preservice elementary teachers' conceptual understanding of the computational estimation strategies, the researcher developed the Computational Estimation Instrument, comprised of sixteen situational problems (eight addition and eight subtraction) with dialogues to elicit the use of specific strategies.;The study compared the conceptual understanding of computational estimation strategies of incoming preservice elementary teachers and those preservice elementary teachers near the completion of the teacher education program. Within the part-whole relationships of the operations of addition and subtraction, the study explored the conditions of explanations and the quantitative mathematics ability (QMA) as related to four computational estimation strategies (front-end, rounding, compensation, and compensation-clustering).;The 60 subjects were from the following categories: 15 freshmen/high QMA, 15 freshmen/low QMA, 15 seniors/high QMA, and 15 seniors/low QMA. After the responses were transcribed and scored, the four-way analysis of variance analyzed the four factors of year, ability, condition, and strategy. The results indicated that for both operations, senior preservice elementary teachers had not acquired more conceptual understanding than those of freshmen. For the operation of addition, there was no significant difference for ability; however, for subtraction, the high QMA seniors conceptually understood the strategies better than the low QMA seniors. Within addition, the subjects conceptually understood all of the strategies better with the justify-correct, rather than the finish-partial condition. Within subtraction, the subjects better understood compensation, the least understood strategy, with the justify-correct, rather than the finish-partial condition. Within addition, the front-end, rounding, and compensation-clustering strategies were understood approximately the same. Within subtraction, the rounding and front-end strategies were understood approximately the same. The results of the dialogues indicated that rounding was the only strategy that many of the preservice elementary teachers mentioned by name. |
