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

这一设计和开发项目探索了中学数学教师如何计划和创造学习经验，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(被称为“数学迷人的学习体验”或“MCLEs”)。这项研究之所以重要，是因为美国中学生对数学一直不感兴趣。这项研究将考察高中教师如何设计课程，使数学内容本身成为学生兴趣、追求和激情的来源。为此，数学课中的内容(无论是计划的还是实施的)被框定为数学故事，而随着数学故事的展开，信息如何被揭示和被隐瞒之间的感觉紧张被框定为其数学情节。《数学故事框架》(Dietiker，2013,2015)突出了两者的连贯性(这个故事有意义吗？)和美感(它是否激发了对即将到来的东西的预期，如果是的话，是如何激发的？)数学课的维度。该项目将生成可供其他环境中的教师使用的课程设计原则和可共享的示范课程。DRK-12计划的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，为建议的项目提供了理论和经验上的证明。具体地说，该项目借鉴了先前的课程研究和设计，以(A)根据数学故事框架发展教师MCLE设计和实施的理论，(B)增加研究人员和教师对数学课程审美本质的理解(S)，以及(C)生成详细的MCLE范例，展示课程的连贯性、认知需求和数学课的审美维度。该项目以教育研究的设计型研究框架为基础。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MCLEs(每位教师四个)，历时三年。在第一个周期之前，将收集数据(访谈、观察)，以记录关于学生对数学的倾向的初始教师课程策略。然后，专业发展经验将介绍数学故事框架，以及支持课程计划和实施的其他课程框架(即认知需求和连贯性)。在设计周期中，将收集对MCLE和非MCLE(随机选择作为MCLE之前或之后的课程)的录像观察和学生审美测量(调查和访谈)，以便进行比较。此外，在每个周期开始和结束时收集的学生倾向测量将被用来了解学生对数学的态度是否以及如何随着时间的推移而改变。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，包括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.