An International Perspective on the Role of Algebra in Elementary School Mathematics

国际视角看待代数在小学数学中的作用

• 批准号: 0140104
• 负责人: James Kaput
• 金额: $ 6.19万
• 依托单位: University of Massachusetts, Dartmouth
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-12-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0140104&HistoricalAwards=false
• 关键词: International; Perspective; Role; Algebra; Elementary

The Algebra Problem: US Mathematics Education has an increasingly difficult in AlgebraProblems to solve. The standard indicators of student achievements international comparisons, NAEPand other national measures, as well as state test results all point in the direction of lower achievementas grade levels increase. Well-known TIMSS analyses of US curricula point in the direction of repetitionof elementary skill building and superficiality of topic coverage as important contributors to the problem,combined with tell-and-drill pedagogy that puts students in overly passive position as learners. And, ofcourse, high failure rates in first year algebra courses contribute to alienation on the part of students andlow morale among teachers. Responses involve a wide variety, but largely ineffective tactics involvingmiddle and early high school curricula: pre-algebra courses of various kinds, screening and diagnostictests, district and state mandates that all students take Algebra I, lengthened courses, modifying thedefinition of if algebra, creating different versions of if algebra, end-of-course exams, among others.Each adjustment produces small improvements, although, since the tactics tend to be ad hoc andimplemented independently, improvements do not accumulate or multiply. NCTM recommendations forintegrating the development of algebraic reasoning across K-12 are implemented only in a few of thestandards-based curricula, and these mainly at the middle school level.Research Towards Solutions: Several research teams studying the development of algebraicreasoning in the early (K-5) grades, who are represented in this proposal, have formed an informalresearch collaborative, renewing a prior collaboration funded by the US DoE OERI in the early/mid1990. These researchers share broad hypotheses regarding the large positive potential of buildingalgebraic reasoning in the context of elementary mathematics, the need to exploit untapped studentlearning capacities among younger students, the powerful role of generalization and formalization indeepening students experience and understanding of elementary mathematics especially arithmeticand the potential for using changes in the curricular relationships between algebra and elementarymathematics as a catalyst and vehicle for faculty development of elementary teachers. These researchersare engaged in several complementary lines of work focusing on different aspects of the challengesstudent learning, classroom practice, curriculum development, professional development, capacitybuilding, and so on.Proposed Combination of Travel, Conferences and Monograph: The collaborating researchershave all been invited to present papers to an important conference to be held December 8-15, 2001, inMelbourne, Australia on The Future of the Teaching and Learning of Algebra which is being sponsoredby the International Commission on Mathematics Instruction. Professor Kaput has been designated toCo-Chair the Early Algebra Group at the conference. We request funds to exploit, in 3 ways, this uniqueopportunity to bring an intensely international perspective to bear upon our active research program: (1)To support travel to the international conference. (2) To hold two meetings in the US, one prior to andone following the Melbourne conference, involving a slightly larger group of mathematics educatorsworking in this area. (3) To write and publish a monograph expressing our findings in order to informpolicy makers, curriculum developers and assessment builders of the latest developments in this rapidlychanging field. Hence we also request a small amount of funding for editorial work to pull together andpublicize the monograph, which in turn will point to additional web resources illustrating relevantresearch.

代数问题：美国数学教育中越来越难解决的代数问题。学生成绩国际比较的标准指标，naep和其他国家措施，以及州测试结果都指向随着年级水平的提高而降低的方向。著名的TIMSS对美国课程的分析指出，重复基本技能培养和肤浅的主题覆盖是造成问题的重要原因，再加上“告诉-练习”教学法，使学生处于过于被动的学习者地位。当然，第一年代数课程的高不及格率导致了学生的疏离和教师的士气低落。回应包括各种各样的，但基本上无效的策略，包括初中和高中早期的课程：各种代数预科课程，筛选和诊断测试，地区和州强制所有学生学习代数I，延长课程，修改代数的定义，创建不同版本的代数，期末考试等等。每次调整都会产生小的改进，但是，由于战术往往是特别的和独立实施的，改进不会累积或倍增。NCTM关于在K-12阶段整合代数推理发展的建议仅在少数基于标准的课程中实施，而这些课程主要是在中学阶段。研究解决方案：本提案中有几个研究早期（K-5）年级代数推理发展的研究团队，他们已经形成了一个非正式的研究合作，延续了1990年代早期/中期由美国能源部OERI资助的先前合作。这些研究人员分享了关于在小学数学背景下建立代数推理的巨大积极潜力的广泛假设，需要开发低年级学生未开发的学习能力，概括和形式化的强大作用加深了学生对小学数学特别是算术的经验和理解，以及利用代数和小学数学之间课程关系的变化作为小学教师教师发展的催化剂和载体的潜力。这些研究人员从事几个互补的工作，重点关注挑战的不同方面：学生学习、课堂实践、课程开发、专业发展、能力建设等等。旅行、会议和专著的建议结合：合作研究人员都被邀请在2001年12月8日至15日在澳大利亚墨尔本举行的一次重要会议上发表论文，该会议是由国际数学教学委员会主办的，主题是“代数教学的未来”。Kaput教授被指定为会议早期代数小组的联合主席。我们要求资金以三种方式利用这一独特的机会，为我们正在进行的研究项目带来强烈的国际视野：(1)支持参加国际会议的旅费。(2)在美国召开两次会议，一次在墨尔本会议之前，一次在会议之后，让在这一领域工作的数学教育工作者人数稍大一些。(3)撰写并出版一篇专著，表达我们的研究结果，以便为政策制定者、课程开发者和评估创建者提供这个快速变化领域的最新发展信息。因此，我们也要求少量资金用于编辑工作，以汇集和宣传专著，这反过来将指向额外的网络资源，说明相关的研究。