Generating a Research-Informed Transition to a Mathematical Proof Curriculum

该项目旨在为国家利益服务，为数学过渡到证明课程开发一个研究知情的课程。证明和逻辑推理是数学中用来解决高级问题的工具。许多STEM专业的学生，尤其是数学专业的学生，在学习如何阅读和制作数学证明方面需要支持。这种技能是学习和做数学在第三和第四年的大学数学课程的主要手段。与大多数现有课程不同，新课程将侧重于通过几个相互交织的项目活动引导学生阅读，理解和欣赏数学证明。植根于先前的研究，该项目的课程将支持学生学习数学逻辑通过阅读和比较证明文本。与此同时，项目团队将与几位数学家合作，为学生提供丰富的数学证明文本。由于学生通常通过阅读伟大的作品来学习文学，因此课程将帮助学生通过阅读丰富，具有挑战性和吸引力的证明来学习数学证明。课程将包括数学家作者的传记故事，以使数学人性化。项目团队成员将与有色人种数学家和女性数学家合作。该课程将为学生提供一个机会，让他们看到更广泛的数学科学代表性。三个基本组成部分--阅读、理解和欣赏--旨在使学生能够学习数学证明并从中学习。他们将支持学生体验数学作为一种人类活动，他们可以参与。这个项目将追求与提高学生的经验和成功过渡到证明（TTP）课程相关的几个目标。由于TTP课程的具体学习目标相对不明确，因此项目的主要目标是在先前研究的基础上为TTP课程建立更明确的学习目标。第二个目标是将学习目标的设计，开发，实施和完善的研究为基础的课程TTP数学课程的过程中。该项目旨在通过项目的研究成果产生新的知识并填补TPP文献中的空白。另一个目标是在全国范围内传播项目成果和课程资源，特别是数学科学部门，致力于提高学生在TTP课程以及依赖于解决问题，证明和证明的后续课程和场景中的学习和成功。研究人员将采用严格的研究设计，努力建立一个课程，同时开发一个关于学习如何在这个教学和学习空间发生的理论。 该项目的假设是：比较证明将支持学生学习抽象的逻辑概念和证明技术;分析和讨论非平凡索赔的复杂证明将支持学生从证明文本中学习;阅读来自不同专业数学家的故事将有助于使基于证明的数学人性化，同时设想他们参与该学科。该项目将采用基于研究的逻辑理解，证明理解和数学归属的措施，研究这些假设在课程中的实施。研究人员将这些结果与标准课程教授的TTP课程进行比较，并在此过程中，将研究课堂上培养的学习活动，以深入了解这些学习过程。课程材料将免费提供给教师和学生在线。这些资源也将通过讲习班，期刊出版物，专业会议和数学教师的专业社区传播。NSF IUSE：EHR计划支持研究和开发项目，以提高所有学生STEM教育的有效性。通过“学生参与学习”轨道，该计划支持创建、探索和实施有前途的实践和工具。该项目还得到了NSF IUSE：HSI计划的支持，该计划旨在加强本科STEM教育，扩大STEM的参与，并建立HSI的能力。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project aims to serve the national interest by developing a research-informed curriculum for mathematics transition to proof courses. Proofs and logical reasoning are tools used in mathematics to solve advanced problems. Many STEM majors, especially those in the mathematical sciences, need support in learning how to read and produce mathematical proofs. This skill is a primary means of learning and doing mathematics in third- and fourth-year college mathematics courses. Unlike most existing curricula, the new curriculum will focus on guiding students to read, understand, and appreciate mathematical proofs through several intertwined project activities. Rooted in prior research, the project's curriculum will support students in learning mathematical logic through reading and comparing proof texts. In conjunction with this, the project team will partner with several mathematicians to produce rich mathematical proof texts for students to study. As it is the case that students most often learn literature by reading great works, the curriculum will help students to learn about mathematical proofs by reading rich, challenging, and engaging proofs. The curriculum will include biographical stories of the mathematician authors to humanize mathematics. Project team members will collaborate with mathematicians of color and women mathematicians. The curriculum will provide an opportunity for students to see broader representation in the mathematical sciences. The three underlying components - reading, understanding, and appreciating - are designed to empower students to learn about and from mathematical proofs. They will support students in experiencing mathematics as a human activity in which they can participate.This project will pursue several goals related to enhancing student experiences and successes in transition to proof (TTP) courses. Because there has been relatively little clarity about the specific learning goals for TTP courses, a primary project goal is to build on prior research to establish clearer learning goals for TTP courses. A second goal is to incorporate the learning goals in the process of designing, developing, implementing, and refining a research-based curriculum for TTP courses in mathematics. The project aims to generate new knowledge and fill gaps in the TPP literature through the project’s research findings. An additional goal is to disseminate project outcomes and curriculum resources nationwide, particularly to mathematical sciences departments working to enhance student learning and success in TTP courses as well as subsequent courses and scenarios that rely on problem solving, proofs, and proving. The researchers will employ a rigorous research design to pursue efforts for establishing a curriculum while developing a theory regarding how learning occurs in this teaching and learning space. The project hypotheses is that: comparing proofs will support students in learning abstract logical concepts and proof techniques; analyzing and discussing complex proofs of non-trivial claims will support students in learning from proof texts; and reading stories from a diverse set of professional mathematicians will help humanize proof-based mathematics while envisioning their participation in the discipline. The project will employ research-based measures of understanding of logic, proof comprehension, and belonging in mathematics to study implementation of these hypotheses in the curriculum. The researchers will compare these outcomes to TTP courses taught with standard curricula, and, in the process, will study the learning activity fostered in the classroom to gain insight into these learning processes. Curriculum materials will be freely available to faculty and students online. These resources will also be disseminated through workshops, journal publications, professional conferences, and professional communities of mathematics instructors. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools. This project is also supported by the NSF IUSE:HSI program, which seeks to enhance undergraduate STEM education, broaden participation in STEM, and build capacity at HSIs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.