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，是美国大学生第一次参加微积分课程人数的三倍。高中微积分的入学人数仍在以每年约6%的速度增长，最有利的学生面临的压力越来越大，他们不得不更早地学习微积分。现在有超过10万人在11年级结束前参加大学理事会的AP微积分考试。高中的微积分老师们发现，他们面临着来自家长和管理人员越来越大的压力，要让他们知道没有充分准备的学生进入他们的班级。《大学微积分成功课程的特征》（NSF DRL 0910240）的研究发现，在高中学习微积分的学生中，有25万人在中学后会重新学习主流的微积分I，而这25万人中有40%的人无法获得表明他们准备继续学习数学的a或B。对于剩下的50万，人们知之甚少。与此同时，全国一半的高中甚至不开设微积分课程，而来自代表性不足群体的学生，即使在开设微积分课程的高中，也经常被劝阻选修这门课程。结果是，如果他们渴望学习工程学或物理科学等数学密集型专业，那么他们会发现自己在与那些准备更丰富的学生竞争。本次研讨会项目将汇集研究人员和专家从高中到大学数学的过渡问题：(1)调查与此情况相关的知识状况；(2)确定最迫切和最有希望探索的问题；(3)对今后的工作进行规划。该项目将把研究这些问题的不同方面的研究人员聚集在一起，包括那些在大学理事会的支持下工作的人，以及那些独立工作的人。该项目将使人们更深入地了解微积分热潮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）领域的途径。它还将有助于阐明来自弱势高中的学生所面临的障碍。美国数学协会（Mathematical Association of America）将出版和传播白皮书以及研讨会提出的进一步研究建议摘要。研讨会的成果将在以下方面提供未来的调查方向：(a)跨学术水平的一般过渡和(b)提高国家对扩大STEM领域参与的需求的方法。

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.