CAREER: Designing and Enacting Mathematically Captivating Learning Experiences for High School Mathematics

这个设计和开发项目探讨了中学数学教师如何规划和制定学习经验，以激发学生的好奇心，用复杂的数学内容吸引学生，并迫使学生参与和坚持（称为“数学吸引学习经验”或“mcle”）。这项研究很重要，因为美国中学生对数学一直不感兴趣。本研究将探讨高中教师如何设计课程，使数学内容本身成为学生兴趣、追求和热情的来源。为了做到这一点，数学课程中的内容（包括计划的和制定的）被框定为数学故事，随着数学故事的展开，学生如何揭示和隐瞒信息之间的紧张关系被框定为数学情节。数学故事框架（Dietiker, 2013, 2015）突出了数学课程的连贯性（故事有意义吗？）和美学（它是否刺激了对即将发生的事情的预期，如果有，如何？）两个维度。该项目将产生可供教师在其他环境中使用的课程设计原则和可共享的范例课程。DRK-12计划中的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，为拟议的项目提供了理论和实证依据。具体而言，本项目借鉴了先前的课程研究和设计，以(a)发展一套教师MCLE设计和制定数学故事框架的理论，(b)增加研究人员和教师对数学课程美学本质的理解，以及(c)生成详细的MCLE范例，展示课程一致性、认知需求和数学课程的美学维度。该项目以设计为基础的教育研究框架为基础。一个由经验丰富的高中教师组成的团队将与研究人员一起设计和测试mcl（每名教师四个），周期为三年。在第一个周期之前，将收集数据（访谈，观察）来记录教师关于学生对数学倾向的初步课程策略。然后，专业发展经验将引入数学故事框架，以及其他课程框架，以支持课程的规划和实施（即认知需求和连贯性）。在设计周期内，将收集MCLE和非MCLE（随机选择作为MCLE之前或之后的课程）的视频观察和学生审美测量（调查和访谈），以便进行比较。此外，在每个周期的开始和结束时收集的学生性格测量将用于了解学生对数学的态度是否以及如何随时间变化。在设计和测试的mcle中，将选择一个样本（基于美学和数学差异）并开发成模型，并完成美学维度的基本原理和描述。

This design and development project explores how secondary mathematics teachers can plan and enact learning experiences that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere (referred to as "mathematically captivating learning experiences" or "MCLEs"). This study is important because of persistent disinterest by secondary students in mathematics in the United States. This study will examine how high school teachers can design lessons so that mathematical content itself is the source of student intrigue, pursuit, and passion. To do this, the content within mathematical lessons (both planned and enacted) is framed as mathematical stories and the felt tension between how information is revealed and withheld from students as the mathematical story unfolds is framed as its mathematical plot. The Mathematical Story Framework (Dietiker, 2013, 2015) foregrounds both the coherence (does the story make sense?) and aesthetic (does it stimulate anticipation for what is to come, and if so, how?) dimensions of mathematics lessons. The project will generate principles for lesson design usable by teachers in other settings and exemplar lessons that can be shared. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.Specifically, this project draws from prior curriculum research and design to (a) develop a theory of teacher MCLE design and enactment with the Mathematical Story Framework, (b) increase the understanding(s) of the aesthetic nature of mathematics curriculum by both researchers and teachers, and (c) generate detailed MCLE exemplars that demonstrate curricular coherence, cognitive demand, and aesthetic dimensions of mathematical lessons. The project is grounded in a design-based research framework for education research. A team of experienced high school teachers will design and test MCLEs (four per teacher) with researchers through three year-long cycles. Prior to the first cycle, data will be collected (interview, observations) to record initial teacher curricular strategies regarding student dispositions toward mathematics. Then, a professional development experience will introduce the Mathematical Story Framework, along with other curricular frameworks to support the planning and enacting of lessons (i.e., cognitive demand and coherence). During the design cycles, videotaped observations and student aesthetic measures (surveys and interviews) for both MCLEs and a non-MCLEs (randomly selected to be the lesson before or after the MCLE) will be collected to enable comparison. Also, student dispositional measures, collected at the beginning and end of each cycle, will be used to learn whether and how student attitudes in mathematics change over time. Of the MCLEs designed and tested, a sample will be selected (based on aesthetic and mathematical differences) and developed into models, complete with the rationale for and description of aesthetic dimensions.