Relating Mental Computation, Number Sense, and ComputationalEstimation

心理计算和计算估计正在接受 作为小学和高中的课程主题， 中学数学，主要是因为他们服务重要 在一个计算机文明的社会中发挥作用。仔细研究 这些主题在课程中的作用是基于以下方面的 最近的一项研究表明， 估计与心理发展密切相关 计算技能和数量概念。 为了探索心理计算的相互关系， 计算估计和数字感，纵向 研究项目涉及四年级，五年级，六年级， 七是计划。 长期心理辅导 计算和数量级将在四年级给出， 五这一指令对数感发展的影响 将在教学期间和 次年 心算与数的教学 六年级将提供量级，并提供有关 七年级的计算估计。 的影响 六年级计算机学习指导 估计技能将通过比较性能的研究， 七年级的学生和没有六年级的学生 指导。将效果转移到相关主题，如rational 数字也将被研究。 该研究具有挑战性，并具有潜在价值， 研究者和实践者。 我们一直在小心地 设计合理的开发和实施 schedule. 私家侦探备受尊敬， 相关的工作人员和顾问代表了一些顶级的 该领域的学者。所有的评论者都对 项目和建议的资金。 该项目计划为一个 为期33个月（33个月）。254，559美元的奖金是 建议如下：87财年109,467美元，88财年98,862美元， 从89财年起为46,230美元。

Mental computation and computational estimation are receiving considerable attention as curricular topics for elementary and middle school mathematics, mainly because they serve important functions in a calculator literate society. A careful study of the role of these topics in the curriculum is warranted based on recent research which shows that the development of computational estimation is closely related to the development of mental computation skills and number magnitude concepts. To explore the interrelationships of mental computation, computational estimation, and number sense, a longitudinal research project involving students in grades four, five, six, and seven is planned. Long-term instruction on mental computation and number magnitude will be given in grades four and five. The effects of this instruction on number sense development will be evaluated both during the instructional period and the following year. Instruction on mental computational and number magnitude will be provided in grade six, and instruction on computational estimation in grade seven. The influence of the grade six instruction on the acquisition of computational estimation skills will be studied by comparing performances of seventh grade students with and without the sixth grade instruction. Transfer effects to related topics such as rational numbers will also be studied. The proposed research is challenging and has potential value for both researchers and practitioners. It has been carefully designed with a reasonable development and implementation schedule. The P.I. is highly respected and the list of associated staff and consultants represents some of the top scholars in the field. All reviewers were enthusiastic about the project and recommended funding. The project is planned for a period of thirty-three (33) months. An award of $254,559 is recommended as follows: $109,467 from FY87, $98,862 from FY88, and $46,230 from FY89.