The Role of Calculus in the Transition from High School to College Mathematics

2014年，大约75万美国高中生参加了微积分课程，是大学第一次上微积分课程的美国学生数量的三倍。高中微积分的入学人数仍在以每年约6%的速度增长，最有优势的学生面临着越来越大的压力，要求他们更早地学习微积分。现在有超过10万人在11年级结束前参加大学理事会AP微积分考试。高中微积分老师发现他们面临着越来越大的压力，要求他们让他们知道没有做好充分准备的学生进入他们的班级。《关于大学微积分成功课程特点的研究》(NSF DRL 0910240)发现，在高中学习微积分的学生中，有25万人将在大专阶段重修主流微积分I，这25万人中有40%的人将无法获得A或B，这表明他们准备继续学习数学。关于剩下的50万人，人们知之甚少。与此同时，全美有一半的高中甚至不开设微积分课程，来自代表人数较少的群体的学生，即使是在开设微积分的高中，也经常被劝阻学习这门课程。结果是，如果他们渴望数学密集型专业，如工程或物理科学，那么他们将发现自己与准备更丰富的学生竞争。这个研讨会项目将聚集高中到大学数学过渡问题的研究人员和专家：(1)调查与这种情况有关的知识状况；(2)确定最紧迫和最有希望探索的问题；(3)为未来的工作制定议程。该项目将把致力于了解这些问题的不同方面的研究人员聚集在一起，包括那些在大学委员会的支持下工作的人，以及那些独立于大学委员会工作的人。该项目将使学生更好地理解对微积分的狂热如何影响学生最终走向依赖数学的领域，特别是科学、技术、工程和数学(STEM)领域。它还将有助于阐明贫困高中学生面临的障碍。白皮书以及讲习班提出的进一步研究建议的摘要将由美国数学协会出版和传播。讲习班的成果将在以下方面为今后的调查提供方向：(A)学术水平之间的一般过渡和(B)加强国家扩大参与科技、经济、技术和经济领域的需要的方法。

In 2014, approximately 750,000 United States high school students were enrolled in a calculus class, three times the number of U.S. students who took their first calculus class in college. High school calculus enrollments are still growing at roughly 6% per year, with increasing pressure on the most advantaged students to take calculus ever earlier. Over 100,000 now take a College Board AP Calculus exam by the end of grade 11. High school calculus teachers find themselves under increasing pressure from parents and administrators to admit into their classes students they know are not adequately prepared. The study of Characteristics of Successful Programs in College Calculus (NSF DRL 0910240) found that a quarter million of the students who study calculus in high school will retake mainstream Calculus I at the post-secondary level, and 40% of these quarter million will fail to get the A or B that signals they are prepared to continue in mathematics. There is very little known about the remaining half million. At the same time, half of all nation's high schools do not even offer calculus, and students from underrepresented groups, even when they are in a high school that offers calculus, are often discouraged from enrolling in this course. The result is that, if they aspire to a mathematically intensive major such as engineering or a physical science, then they will find themselves in competition against students with a much richer preparation.This workshop project will bring together researchers and experts in the issue of the transition from high school to college mathematics to: (1) survey the state of knowledge related to this situation; (2) identify the most pressing and promising questions for exploration; and (3) lay out an agenda for future work. The project will bring together researchers who have worked to understand different aspects of these issues, including both those who have worked under the aegis of the College Board and those who have worked independently of it. The project will produce a greater understanding of how the rush to calculus affects the pathways that students ultimately take toward fields that depend on mathematics, especially science, technology, engineering, and mathematics (STEM)fields. It also will help to illuminate the obstacles faced by students from disadvantaged high schools. White papers, together with a summary of the recommendations for further study that come out of the workshop, will be published and disseminated by the Mathematical Association of America. The outcomes of the workshop will provide future directions for investigation in terms of (a) general transition across academic levels and (b) approaches that enhance the national need of broadening participation in STEM areas.