Math: Conference: Collaborations Between Academic Levels to Promote Successful Student Transitions from Secondary to Post-Secondary Mathematics

发展数学课程的高失败率和不断增加的入学人数是本科生经常与中学到中学后数学过渡斗争的关键指标。 虽然在中学一级作出了很大努力，通过提供资源和支持帮助学生取得成功，改善学生对大学数学的准备，但中学和中学后机构之间似乎很少合作。 特别是，这两个级别的教师很少有机会讨论学生的优势和劣势，学习成果，教师的期望，评估策略和共同的教学实践。 因此，除了面临具有挑战性的数学内容，就读于数学入门课程的中学后学生也面临着在两个学术水平之间进行文化转变的挑战。本次会议的目的是通过鼓励两个学术水平的教师之间的交流，并通过聘请一组研究人员描述影响学生成功的两种学术文化的特征，来解决中学到中学后数学过渡的问题。 作为这种合作的结果，将制定关于如何更好地融合学生在不同学术水平的数学经验的建议。虽然为学生准备大学数学的责任往往落在中学，但两个学术水平在促进从中学到中学后数学的顺利和成功过渡方面发挥着重要作用。 该项目有三个主要组成部分：（1）一名中学数学教师和一名专上数学教师之间的专业发展伙伴关系，（2）研究小组（一个微积分和一个代数重点小组），及（3）举办工作坊及会议，以促进专业发展及传播研究结果。这项建议的主要目的，是促进中学及大专数学教师之间的合作，在中学阶段，交流最佳做法，并就促进学术水平之间的平稳过渡进行讨论。 这一目标将通过两种方式实现。 首先，中学和中学后数学教师之间的专业发展伙伴关系将允许平等分享最佳做法和机会，以更好地了解其他学术水平的期望。 其次，将成立两个研究小组，让调查人员沉浸在高中和大学课程中，目的是比较学术文化。 这将为两个级别的数学期望和课堂规范的研究提供信息。 由一名中学数学教师和一名中学后数学教师组成的专业发展伙伴关系将制定一份最佳做法清单，帮助学生做好准备，并促进学业水平之间的平稳过渡。 这些最佳做法将在该项目的组成部分之一-数学教与学最佳做法会议上分享。还打算提出适合在教学期刊上发表的建议。 研究小组将通过两个镜头进行正式的研究，比较中学和中学后的数学文化：代数和微积分。 研究结果将导致对数学界的智力贡献，关于如何特定的主题（例如，坡度和限制），以及对可能影响学生在学术水平之间成功过渡的能力的课堂规范的更广泛描述。

High failure rates and increasing enrollments in developmental mathematics courses are key indicators that undergraduate students often struggle with the secondary to post-secondary mathematics transition. Although great efforts have been undertaken at the secondary level to improve the preparation of students for college-level mathematics by providing resources and support to help students be successful, there seems to be little collaborative effort between secondary and post-secondary institutions. In particular, instructors at the two levels rarely have opportunities to discuss students' strengths and weaknesses, learning outcomes, teacher expectations, assessment strategies, and common instructional practices. Thus, in addition to facing challenging mathematical content, post-secondary students enrolled in introductory mathematics courses also are challenged with navigating a cultural shift between the two academic levels. The purpose of this conference is to address the issue of secondary to post-secondary transitions in mathematics by encouraging communication between instructors at both academic levels and by engaging a team of researchers in describing features of both academic cultures which influence students' success. As a result of this collaboration, suggestions for how to better merge students' experiences in mathematics across academic levels will be developed. Although responsibility for students' preparedness for college-level mathematics tends to fall on secondary schools, both academic levels play an important role in facilitating a smooth and successful transition from secondary to post-secondary mathematics. There are three main components to this project: (1) professional development partnerships between one secondary and one post-secondary mathematics instructor, (2) research groups (one calculus and one algebra-focused group), and (3) workshops and a conference to facilitate professional development and dissemination of findings.The primary goal of this proposal is to foster collaboration between mathematics instructors at the secondary and post-secondary level to share best practices and engage in discussions about facilitating a smoother transition between academic levels. This goal will be met in two ways. First, professional development partnerships between a secondary and post-secondary mathematics instructor will allow for equal sharing of best practices and opportunities to better understand expectations at the other academic level. Second, two research teams will be formed to allow the investigators to immerse themselves in a high school and college course with the intent of comparing the academic cultures. This will inform the body of research on mathematical expectations and classroom norms at both levels. The professional development partnerships consisting of one secondary and one post-secondary mathematics instructor will develope a list of best practices for preparing students for and facilitating a smooth transition between academic levels. These best practices will be shared at the Best Practices in Teaching and Learning Mathematics Conference--one of the components of the project. It is also the intention to develop recommendations suitable for publication in pedagogical journals. The research teams will be conducting formal research by comparing the secondary and post-secondary mathematics culture through two lenses: algebra and calculus. The research findings will lead to intellectual contributions to the mathematics community regarding how particular topics (e.g., slope and limits) are conveyed at each academic level as well as a broader description of classroom norms which may impact students' abilities to successfully navigate the transition between academic levels.