Relating Mental Computation, Number Sense, and ComputationalEstimation

心理计算和计算估计作为小学和中学数学的课程主题受到了相当大的关注，主要是因为它们在一个计算机文化社会中发挥着重要的作用。根据最近的研究，有必要仔细研究这些主题在课程中的作用，这些研究表明，计算估计的发展与心理计算技能和数量级概念的发展密切相关。为了探索心理计算、计算估计和数感之间的相互关系，计划了一个包括四年级、五年级、六年级和七年级学生的纵向研究项目。四年级和五年级将提供关于心算和数量级的长期教学。本教学对数感发展的影响将在教学期间和下一年进行评估。心理计算和数量级的教学将在六年级进行，计算估计的教学将在七年级进行。通过比较有无六年级教学的七年级学生的成绩，研究六年级教学对计算估计技能习得的影响。对有理数等相关主题的迁移效应也将被研究。这项拟议的研究具有挑战性，对研究人员和从业者都具有潜在的价值。它经过精心设计，并有合理的开发和实施时间表。P.I.非常受人尊敬，相关工作人员和顾问的名单代表了该领域的一些顶尖学者。所有的评审员都对该项目充满热情，并建议提供资金。该项目的计划期限为33个月。建议奖金为254,559美元：87财年为109,467美元，88财年为98,862美元，89财年为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.