CAREER: L-MAP: Pre-service Middle School Teachers' Knowledge of Mathematical Argumentation and Proving

数学教师教育领域需要对职前教师关于数学论证和证明实践的知识有深刻的理解，包括这种知识的发展，以有效地推动职前教师对他们自己的学生的这种实践有更复杂的理解和制定。综合研究和教育活动将有助于教师教育计划所需的知识基础，有效地准备中学教师应对如何使推理和证明成为教学实践的一个组成部分的挑战。研究结果有可能指导教师教育工作者和教育研究人员加强职前教师的能力，使推理和证明成为学校数学的一个组成部分。因此，职前教师将更好地培养他们未来学生的数学推理技能，并支持他们的学生用理解来学习数学。鉴于这个国家对有能力的STEM劳动力的需求日益增长，帮助所有学生以一种支持更深入理解的方式学习数学是一个优先事项。此外，早期职业学者在数学教育方面的支持将增加国家解决未来数学教育问题的能力。本研究计划的目的是考察中学职前教师的数学论证和证明知识如何在教师准备计划中发展。该项目探讨了一个研究问题：当中学职前教师进入他们的教师准备计划的数学课程序列时，在培养关于变化、比例性和比例关系的推理的情况下，他们持有什么样的数学推理和证明概念，以及这些概念如何在整个计划中发展？这一发展将从三个方面进行研究：(a)职前教师自己制定数学论证的能力，(b)他们分析数学论证的能力，以及(c)他们分析学生参与数学论证和证明的情况的能力。对60名职前教师的模型或解释系统的横断面和纵向研究，在课程背景下，数学论证和证明，促进对变化的推理，比例和比例关系将提供一个轨迹的理解，捕捉职前教师如何发展他们的数学论证和证明的知识，通过他们的大学数学准备计划和他们的学生教学。

The field of mathematics teacher education needs a strong understanding of pre-service teachers' knowledge about the practice of mathematical argumentation and proof, including the development of this knowledge, to effectively move pre-service teachers toward a more sophisticated understanding and enactment of this practice with their own students. The integrated research and educational activities will contribute to the knowledge base teacher education programs need to effectively prepare middle school teachers for meeting the challenges of how to make reasoning and proof an integral aspect of instructional practice. The research results have the potential to guide teacher educators and educational researchers concerned with strengthening pre-service teachers' ability to make reasoning and proving an integral aspect of school mathematics. Consequently, pre-service teachers will be better equipped to develop mathematical reasoning skills in their future students and to support their students in learning mathematics with understanding. Given this country's growing need for a competent STEM workforce, helping all students learn mathematics in a way that supports deeper understanding is a priority. Additionally, the support of early CAREER scholars in mathematics education will add to the capacity of the country to address issues in mathematics education in the future.The objective of this program of research is to examine how middle school pre-service teachers' knowledge of mathematical argumentation and proving develops in teacher preparation programs. The project explores the research question: What conceptions of mathematical reasoning and proving do middle school preservice teachers hold in situations that foster reasoning about change, proportionality, and proportional relationships, as they enter their mathematics course sequence in their teacher preparation program, and how do these conceptions evolve throughout the program? This development will be studied along three dimensions: (a) pre-service teachers' own ability to formulate mathematical arguments, (b) their ability to analyze mathematical arguments, and (c) their ability to analyze situations that engage students in mathematical argumentation and proving. Cross-sectional and longitudinal studies of 60 pre-service teachers' models, or systems of interpretation, of mathematical argumentation and proof in curricular context that foster reasoning about change, proportionality and proportional relationships will be conducted to provide an understanding of the trajectory that captures how pre-service teachers develop their knowledge of mathematical argumentation and proving throughout their university mathematics preparation program and into their student teaching.