Johnson-Glenberg，2013 年;Nemirovsky et al.， 2014）。这些系统使用计算机视觉和其他进步（参见本卷第 15 章的 Johnson-Glenberg），跟踪和解释学习者的身体行为，通过提供有关学习者的运动和位置的反馈来指导参与。一些设计跟踪学习者的手和手臂运动，而另一些设计跟踪整个身体的运动（Abrahamson & Lindgren，2014 年）。迄今为止，已经开发了用于探索各种 STEM 现象的技术。例如，在科学教育中，有一些设计允许学习者使用他们的身体来预测流星的轨道（Lindgren & Johnson-Glenberg，2013），成为物质不同阶段的运动粒子（DeLiema et al.， 2016），并体验地形变化对动物运动的影响（Lyons et al.， 2012）。在数学教育中，具身学习技术支持基于具身手指的计数（Jackiw & Sinclair，2017），参数函数的探索（Nemirovsky等人，2014），以及学习者对比率和比例的调查（Abrahamson等人，2014），等等。 Johnson-Glenberg，2013 年;Nemirovsky et al.， 2014）。这些系统使用计算机视觉和其他进步（参见本卷第 15 章的 Johnson-Glenberg），跟踪和解释学习者的身体行为，通过提供有关学习者的运动和位置的反馈来指导参与。一些设计跟踪学习者的手和手臂运动，而另一些设计跟踪整个身体的运动（Abrahamson & Lindgren，2014 年）。迄今为止，已经开发了用于探索各种 STEM 现象的技术。例如，在科学教育中，有一些设计允许学习者使用他们的身体来预测流星的轨道（Lindgren & Johnson-Glenberg，2013），成为物质不同阶段的运动粒子（DeLiema et al.， 2016），并体验地形变化对动物运动的影响（Lyons et al.，2012）。在数学教育中，具身学习技术支持基于具身手指的计数（Jackiw & Sinclair，2017），参数函数的探索（Nemirovsky等人，2014），以及学习者对比率和比例的调查（Abrahamson等人，2014），等等。
当学习者使用具身学习技术时，他们会体验到构成具身思想的新移动和感知方式。这些感知运动体验 - 学习者注意到的模式和他们发展的运动曲目 - 是身体知识的形式，对大脑来说是不可简化的，也与在世界上行动的身体不可分割（Abrahamson & Lindgren，2014;Nemirovsky et al.， 2014）。学习者经常被邀请与同龄人和教育者一起反思和理解他们的具体想法，并在具体体验（例如，穿越空间和时间的感觉）和 STEM 中的文化形式（例如，速度的学科定义为每单位时间行驶的距离，外部表示，如距离与时间图;Abrahamson & Lindgren，2014 年）。然而，通过与具身学习技术交互而产生的具身见解可能难以用文字表达，并且经常使用界面、手势、身体表演、谈话和其他符号学资源的丰富示范动作配置进行多模态表达（Abrahamson et al.， 2014）。教育工作者要利用这些技术支持学习和发现，他们必须关注学习者的移动和感知方式，并且能够理解学习者对其具体体验的多模态表达。
我们的工作重点是经验丰富的导师用来支持学生使用两种不同的数学具体学习设计的实践：比例数学意象训练器（MIT-Proportion;Abrahamson et al.， 2014）和抛物线数学意象训练器（MIT-Parabola;Shvarts & Abrahamson，2019 年）。两个数学意象训练器都体现了具体设计的原则（Abrahamson，2014），其中学习者 我们的工作重点是研究经验丰富的辅导教师在支持学生使用两种不同的数学体现式学习设计时的做法：比例数学意象训练器（MIT-Proportion；Abrahamson等人，2014）和抛物线数学意象训练器（MIT-Parabola；Shvarts & Abrahamson，2019）。这两个数学意象训练器都体现了体现式设计的原则（Abrahamson，2014 年），其中学习者发展实现特定目标状态的物理策略。在导师的指导下，学习者被邀请分享他们的物理策略，并采用数学工件来描述和量化这些策略（例如，笛卡尔坐标系）。通过这种支持，学习者能够做出复杂的数学发现，并将他们所体现的思想与学科数学相协调（Abrahamson et al.， 2012）。
MIT-Proportion 为学习者提供了一个交互式环境，让他们使用双手运动来探索与比率和比例相关的概念。为了操作 MIT-Proportion，用户抬起和降低两个独立的手持式 Nintendo Wii 遥控器，这两个遥控器在计算机屏幕上垂直上下移动光标（图 12.1 a 和 b）。当光标高度包含固定的隐藏比率时（例如如图 12.1b 所示，以浅灰色显示）。当光标高度不满足该比率时，屏幕将变为红色（图 12.1a， "麻省理工学院比例 "为学习者提供了一个互动情境，让他们利用双臂运动来探索与比率和比例相关的想法。要操作 MIT-比例，用户需要抬起和放下两个独立的手持式任天堂 Wii 遥控器，在电脑屏幕上垂直上下移动光标（图 12.1 a 和 b）。当光标高度体现了设定的隐蔽比例时，屏幕会变成绿色（例如， 如图 12.1b 所示，显示为浅灰色）。当光标高度不符合比例要求时，屏幕将变为红色（图 12.1a.）、
图 12.1 图 12.1 （tcp） 当 Mathematics Imagery Trainer for Proportion （MIT-P） 设置为 图 12.1 （TCP）当数学图像比例训练器 （MIT-P）设置为比率，则仅当右侧遥控器的高度是左侧遥控器的两倍时，屏幕为绿色（B，以浅灰色显示）;否则屏幕为红色（ a ，以深灰色显示）。（下）在 Mathematics Imagery Trainer for Parabolas 中，点 C纵，点 A 是固定的（抛物线的“焦点”），点 B 沿水平线（抛物线的“准线”）运行。当点 C 位于抛物线上时，三角形变为绿色（d ，以浅灰色显示）;否则，它将为红色（ c ，以深灰色显示）。此图表中插入了线条和字母，但不向学生显示。 比，只有当右手遥控器的高度是左手遥控器的两倍时，屏幕才是绿色的（b ，显示为浅灰色）；否则，屏幕就是红色的（a ，显示为深灰色）。(下图）在抛物线数学图像训练器中，C 点被操作，A 点固定（抛物线的 "焦点"），B 点沿水平线运行（抛物线的 "直 线"）。当点 C 位于抛物线上时，三角形变为绿色（d ，显示为浅灰色）；反之，三角形变为红色（c ，显示为深灰色）。本图插入了线段和字母，但不显示给学生看。以深灰色显示）。询问学习者是否能弄清楚如何通过将光标从屏幕底部不断移动到顶部来使屏幕变为绿色，以及如何使屏幕保持绿色。通过开发和探索不同的 “绿色 ”方法，学习者发现了许多动态模式，并在他们的身体策略与具有挑战性的数学思想（如比率、比例、速度、协变、乘法关系和迭代加法等）之间建立联系（Abrahamson et al.， 2014）。 另一方面，麻省理工学院-抛物线（Shvarts和Abrahamson，2019）为学习者创造了一种互动体验，让他们发现抛物线的定义并探索其性质。学习者在触摸板上移动手指以操作屏幕上的三角形，移动其顶点（图 12.1 c 和 d 中的点 C），并指示尝试将三角形保持为绿色。为了保持三角形的绿色（图 12.1d，以浅灰色显示），学生们不知道，他们必须保持点 C 的位置，使其与固定点 A（抛物线的“焦点”）和点 B 的距离相等，B 点沿水平线移动（抛物线的“直线”）。这也意味着当顶点移动时，三角形将保持等腰（长度相等的两条边）。当点 C 与点 B 和 A 的距离不相等时，三角形变为红色（图 12.1 c 以深灰色显示）。移动点 C 以保持三角形为绿色意味着点 C（三角形的顶点）将沿着已预设到系统中的隐藏抛物线的路径移动。要求学习者确定在移动点 C 时保持三角形绿色的策略。使用该设计，学习者将抛物线曲线探索为一组等腰三角形的顶点，并表达出现曲线的公式。 麻省理工学院抛物线（Shvarts & Abrahamson, 2019）则为学习者创造了一种互动体验，让他们发现抛物线的定义并探索其特性。学习者在触摸板上移动手指，操作屏幕上的一个三角形，移动其顶点（图 12.1 c 和 d 中的 C 点），并被要求尝试将三角形保持为绿色。为了使三角形保持绿色（图 12.1d，浅灰色显示），学生们并不知道，他们必须保持 C 点的位置，使其与固定点 A（抛物线的 "焦点"）和沿水平线移动的点 B（抛物线的 "直角坐标系"）之间的距离相等。这也意味着随着顶点的移动，三角形将保持等腰（两边长度相等）。当点 C 与点 B 和点 A 的距离不相等时，三角形变为红色（图 12.1 c 中的深灰色）。移动 C 点使三角形保持绿色，意味着 C 点（三角形的顶点）将沿着系统中预设的隐蔽抛物线轨迹移动。学习者需要确定在移动 C 点的过程中保持三角形绿色的策略。学习者可以利用设计，探索作为一组等腰三角形顶点的抛物线曲线，并表达新出现的曲线的公式。
响应式教学：关注并参与学习者思想的学科内容 响应式教学：关注并参与学习者思想的学科实质
为了促进学习者的发现及其在具身经验和组织这些经验的学科方法之间的联系，教育工作者必须关注并参与学习者的具身想法。在 STEM 教育中，教育工作者用来关注和参与学习者想法的实践集合被称为响应式教学（Robertson et al.， 2016;另见 teacher noticing， Sherin et al.， 2011）。响应式教学包括 （1） 提取、关注和参与学习者想法中具有潜在学科价值或实质的方面，以及 （2） 参与持续的近端形成性评估（Erickson，2007）（即持续监控学生的想法以在当下调整教学支持）（Ball，1993;Coffey等人，2011 年;Pierson，2008 年）。学生在 STEM 课堂上学到更多， 为了促进学习者的发现及其体现性经验与组织这些经验的学科方式之间的联系，教育者必须关注并参与学习者的体现性想法。在 STEM 教育中，教育者用来关注和参与学习者想法的一系列做法被称为回应式教学（Robertson 等人，2016 年；另见教师注意，Sherin 等人，2011 年）。回应式教学包括：（1）引出、关注并参与学习者想法中具有潜在学科价值或实质内容的方面；（2）参与持续的近端形成性评估（Erickson，2007）（即持续监测学生的想法，以便及时调整教学支持）（Ball，1993；Coffey et al.，2011；Pierson，2008）。学生在 STEM 课堂中学得更多教师对学习者的想法做出回应（Pierson，2008 年;Robertson等人，2016 年;Saxe et al.， 1999）。
响应式教学的一个基本方面包括理解学习者的想法并监控这些想法，以寻找富有成效的学科理解的种子，这些知识可以用来将学习者的直觉与更正式的概念和实践联系起来（Robertson et al.，2016）。教育工作者必须能够识别这些种子，即使它们最初从数学或科学角度代表了不完整或不正确的想法。以前的研究考察了教育者如何通过口头解释和铭记来关注学习者分享的想法（例如，Pierson，2008 年），但很少有研究试图了解教育者如何监控和理解学习者，当他们使用具身学习技术时，他们是具身的想法。教育工作者不仅必须持续关注学习者所说的内容，还必须持续关注学习者的动作、他们独特的感知形式以及他们对具体体验的解释（Abrahamson et al.， 2014;洪水，2018 年;Shvarts & Abrahamson，2019 年）。这种身体间的协调（Sheets-Johnstone，2000）允许导师在关键时刻重新构建学习者对感知运动活动的注意力，以便导师可以建议文化形式（例如，描述现象的学科数学方式）作为学习者协调他们的活动和组织他们对具身体验的解释的有用方式（Shvarts & Abrahamson，正在出版;Flood，2018 年）。 响应式教学的一个基本方面包括理解学习者的想法并监控这些想法，以寻找富有成效的学科理解的种子，这些知识可以用来将学习者的直觉与更正式的概念和实践联系起来（Robertson et al.，2016）。教育工作者必须能够识别这些种子，即使它们最初从数学或科学角度代表了不完整或不正确的想法。以前的研究考察了教育者如何通过口头解释和铭记来关注学习者分享的想法（例如，Pierson，2008 年），但很少有研究试图了解教育者如何监控和理解学习者，当他们使用具身学习技术时，他们是具身的想法。教育工作者不仅必须持续关注学习者所说的内容，还必须持续关注学习者的动作、他们独特的感知形式以及他们对具体体验的解释（Abrahamson et al.， 2014;洪水，2018 年;Shvarts & Abrahamson，2019 年）。这种身体间的协调（Sheets-Johnstone，2000）允许导师在关键时刻重新构建学习者对感知运动活动的注意力，以便导师可以建议文化形式（例如，描述现象的学科数学方式）作为学习者协调他们的活动和组织他们对具身体验的解释的有用方式（Shvarts &Abrahamson，正在出版;Flood，2018 年）。 Shvarts 和 Abrahamson （2019） 使用双眼动追踪说明了一种身体间调和形式，其中导师和学生的感知系统在与具身学习技术一起工作时动态地出现紧密的空间耦合。在一个例子中，学生 Ada正在与一位导师合作，移动 MIT-Parabola 三角形的顶点，以寻找将三角形变为绿色的位置。起初，Ada 和导师的目光都沿着三角形的路径移动（图 12.2a）。然而，过了一会儿，Ada 发展出一种专门的方式来组织她的动作：她不再观察三角形在空间中的路径，而是开始在移动顶点时将目光保持在三角形的中线（从三角形的顶点延伸到另一侧的假想段，将其一分为二）（图 12.2c）。值得注意的是，导师能够预测 Ada 的感知运动开关。在 Ada 开始关注中位数之前，导师自己开始关注中位数（图 12.2b）。与学生的表现相结合，使导师能够检测到何时出现了有效的感知运动策略，并允许导师区分干预的关键时刻。在这个例子中，关注中位数是一种有用的感知运动策略，用于动态保持等腰三角形（两条边的长度相等），这将使三角形在顶点移动时保持绿色。这也将导致顶点沿着 “秘密” 抛物线的路径移动。在预料到 Ada 的切换后， 与学生的表现相结合，辅导教师就有可能发现有效的感知运动策略何时出现，并区分关键时刻进行干预。在本例中，关注中线是一种有助于动态保持等腰三角形（两边等长）的感知运动策略，当顶点移动时，这种策略将使三角形保持绿色。这也将导致顶点沿着 "秘密 "抛物线的轨迹移动。在预测到艾达的切换后
Figure 12.2 图 12.2
(a) Ada and the tutor's eye movements (Ada in white, the tutor in grey) synchronously follow the movement of the triangle as Ada moves the vertex. Later (b) the tutor attends to the median of the triangle before (c) Ada begins attending to the median of the triangle. In (a) the triangle is red (shown in dark grey) and in (b) and (c) the triangle is green (shown in light grey) (a) 当 Ada 移动顶点时，Ada 和导师的眼球运动（Ada 为白色，导师为灰色）同步跟随三角形的移动。之后（b），在（c）Ada 开始关注三角形的中值之前，导师开始关注三角形的中值。在 (a) 中，三角形为红色（显示为深灰色），在 (b) 和 (c) 中，三角形为绿色（显示为浅灰色）
tutor asks Ada to reflect on her strategy to keep the triangle green, reframing Ada's attention in this moment toward cultural forms of perceiving and expressing the strategy. In response, Ada is able to articulate the isosceles quality of the triangle she is manipulating. 导师要求艾达反思她让三角形保持绿色的策略，在这一时刻将艾达的注意力重构为感知和表达策略的文化形式。对此，艾达能够清楚地表达出她正在操作的三角形的等腰性质。
When educators recognize the disciplinary potential in learners' ways of moving, perceiving, and interpreting embodied experiences, opportunities arise to connect learners' embodied ideas with mathematical ways of organizing those ideas. Coupled as an intercorporeal system with students and the device, tutors seem to be able to vicariously experience learners' perceptuomotor experiences from the learners' point of view (Shvarts & Abrahamson, in press). 当教育者认识到学习者的运动、感知和解释具身经验的方式所蕴含的学科潜力时，就会有机会将学习者的具身思想与组织这些思想的数学方法联系起来。辅导教师作为学生与设备之间的体外系统，似乎可以从学习者的角度来体验学习者的感知运动经验（Shvarts 和 Abrahamson，出版中）。
Goodwin (2018) has argued that skilled actors (e.g., senior surgeons) are able to inhabit the actions of the newcomers with whom they work, perceiving as newcomers and being in a state of bodily readiness to anticipate what moves the newcomers will make next. However, such intercorporeal attunements are not always readily achieved and can require additional interactional work. In the next sections, we describe three additional practices educators use to elicit and engage with learners' multimodally expressed embodied ideas in order to help lead users of embodied learning technologies towards new discoveries. 古德温（2018）认为，熟练的行动者（如资深外科医生）能够栖息于与他们共事的新人的行动中，感知为新人，并处于身体准备状态，以预测新人接下来会做出什么动作。然而，这种身体间的契合并不总是那么容易实现，可能需要额外的互动工作。在接下来的章节中，我们将介绍教育者用来激发和参与学习者多模态表达的具身想法的三种额外做法，以帮助引导具身学习技术的使用者获得新发现。
Encouraging the Multimodal Expression of Learners' Embodied Ideas 鼓励以多种方式表达学习者的体现性想法
As part of responsive teaching, educators try to provide opportunities for learners to share and reflect on their reasoning (Robertson et al., 2016). Doing so makes it possible for learners to clarify and elaborate their ideas and also allows educators to better understand learners' ideas so they can effectively adapt their support in the moment (proximal formative assessment; Erickson, 2007). 作为回应式教学的一部分，教育者努力为学习者提供分享和反思其推理的机会（Robertson et al.）这样做可以让学习者澄清和阐述自己的想法，也可以让教育者更好地理解学习者的想法，从而有效地调整他们的支持（近端形成性评估；Erickson，2007）。
Learners, however, often know more than they can express in words, and sometimes the words they use to describe their ideas can mislead (Crowder, 1996; Flood et al., 2015; Roth & Lawless, 2002). Both in and outside of embodied learning environments, nonverbal aspects of learners' explanations can contain discrepant, "mismatched" information when compared with verbal aspects (e.g., Alibali & Goldin-Meadow, 1993). In technology-enabled embodied learning environments, embodied ideas-drawing on tactile and kinesthetic experiences, and containing complex, dynamic spatial information-are especially challenging for children to articulate. In addition, learners themselves may often still be making sense of and organizing their experiences as they try to express them multimodally (Crowder, 1996). As a result, a key approach for being responsive to learners' embodied ideas involves finding 然而，学习者知道的往往比他们能用语言表达的要多，有时他们用来描述自己想法的语言可能会误导学习者（Crowder，1996；Flood 等人，2015；Roth & Lawless，2002）。在具身学习环境内外，学习者的非语言解释与语言解释相比，可能包含不一致、"不匹配 "的信息（例如，Alibali & Goldin-Meadow, 1993）。在技术驱动的具身学习环境中，具身的想法--借鉴触觉和动觉经验，包含复杂、动态的空间信息--对儿童来说尤其具有表述的挑战性。此外，学习者在尝试以多模态方式表达自己的经验时，他们自己可能往往还在理解和组织自己的经验（Crowder，1996 年）。因此，对学习者的具象想法作出反应的一个关键方法是找到
ways to elicit these ideas in modalities beyond speech and being on the lookout for ways gesture is nonredundant to or mismatched with speech (Flood et al., 2015). 用语言以外的方式激发这些想法，并注意手势与语言的非冗余性或不匹配性（Flood 等人，2015 年）。
We present an example from previous work (Flood et al., 2020) to illustrate this embodied responsive technique. Ben, a middle school student, is working with two tutors to try to determine how to turn the MIT-Proportion's screen green. Unbeknownst to Ben, the MIT-Proportion is set to a ratio. Ben shares a theory for producing green feedback that is difficult to interpret. He says, "My right hand is sort of the pinpoint sort of thing, so . . . and then to keep it green you have to even them out, I would say." The tutor is responsive to Ben's ambiguous but potentially promising idea for how to make green, and he explicitly encourages Ben to use his hands, stretched out flat without the remotes, to explain what he means. 我们从之前的工作（Flood 等人，2020 年）中提出了一个例子来说明这种嵌入式响应技术。Ben 是一名中学生，他正与两名辅导员一起尝试确定如何将 MIT-Proportion 的屏幕变绿。本并不知道，MIT-比例被设置成了 比例。Ben 分享了一种难以解释的绿色反馈理论。他说："我的右手是那种精确定位的东西，所以......然后为了保持绿色，我认为你必须把它们拉平"。导师对本模棱两可但有可能产生绿色反馈的想法做出了回应，他明确鼓励本在没有遥控器的情况下平伸双手来解释他的意思。
When encouraged to gesture, Ben is able to provide a physically accurate demonstration of how his hands need to move to make the screen: his right hand rises approximately twice as fast and ends up twice as high (figure 12.3a). Verbally, however, Ben describes his hands as "even apaced" and "going at the same pace." The tutor is responsive to this mismatch between Ben's gestured demonstration and encourages him to elaborate. In response, Ben uses his hands again, but this time he evokes the analogy of two cars traveling a horizontal trajectory where one is going "twenty" and one is going "fifty." He describes this as going "the same speed limit" (figure 12.3b). 当鼓励他做手势时，本能够准确地演示出他的手需要如何移动才能做出屏幕的效果：他的右手上升的速度大约是屏幕的两倍，最后上升的高度也是屏幕的两倍（图 12.3a）。但在口头上，Ben 将他的双手描述为 "节奏均匀 "和 "步伐一致"。辅导员对本的手势演示之间的不匹配做出了反应，并鼓励他详细说明。作为回应，Ben 再次用手演示，但这次他打了个比方：两辆汽车在水平轨迹上行驶，一辆速度是 "20"，一辆速度是 "50"。他形容这是 "相同的速度极限"（图 12.3b）。
"you keep them going even apaced" "你让他们的节奏更快"
"If you wanted to do this with a car, it would sort of be the same speed limit" "如果你想用汽车来做这件事，速度限制也是一样的"
Figure 12.3 图 12.3
After being encouraged to use gesture to explain his idea, (a) Ben uses his hands to show how the remotes must move "even apaced" although he moves his hands at different speeds. When asked to elaborate, (b) he describes his hands as being like cars moving at the "same speed limit" going "twenty" and "fifty." Underlined speech corresponds with gesture. 在鼓励他用手势来解释自己的想法后，(a) 本用手来表示遥控器必须以 "均匀的速度 "移动，尽管他移动双手的速度不同。当被要求详细说明时，(b) 他说他的手就像以 "相同的速度 "行驶的汽车，速度分别为 "20 "和 "50"。下划线语言与手势相对应。
By only paying attention to Ben's initial verbal explanations ("even them out," "same pace") it would be easy to conclude that Ben believed (incorrectly) that the remotes have to go the same speed to make green. However, by encouraging Ben to use his hands to explain his idea further, the tutors created an opportunity to better understand Ben's embodied idea and let it evolve. With his continuing multimodal explanation, Ben explores a disciplinarily valuable idea: the remotes have to move at two ferent yet constant speeds. By eliciting and probing Ben's gesture, the tutors were able to make sense of the apparent mismatch between Ben's speech ("even apaced," "same pace," "same speed limit") and his gesture. Instead of correcting Ben, the tutors adjusted their instruction in the moment and made space for Ben to pursue the idea. Ben's new productive car analogy emerged from his exploration and reflection on his own gestured movements. These gestures, elicited by the tutors, became a substrate from which Ben could build. 如果只注意本最初的口头解释（"使它们均匀"、"相同的速度"），很容易得出这样的结论：本认为（不正确的）遥控器必须以相同的速度移动才能变绿。然而，通过鼓励 Ben 用手进一步解释他的想法，导师们创造了一个机会，让他们更好地理解 Ben 的体现性想法，并让它不断发展。通过持续的多模态解释，Ben 探索出了一个具有学科价值的想法：遥控器必须以两种 不同但恒定的速度移动。通过诱导和探究 Ben 的手势，导师们能够理解 Ben 的语言（"均匀的节奏"、"相同的速度"、"相同的速度限制"）和他的手势之间明显的不匹配。辅导教师没有纠正本的错误，而是及时调整了他们的教学，并为本提供了追求想法的空间。Ben 对自己手势动作的探索和反思，产生了新的有成效的汽车类比。这些由导师激发出来的手势动作成为了 Ben 可以进行构建的基础。
Encouraging students to "explain an idea in your own hands" provides productive opportunities for reflection on embodied ideas: Through this reflection, learners are able to reformulate and elaborate their initial utterances in ways that demonstrate new clarity or specificity, and sometimes they are able to make new discoveries/realizations like Ben's car analogy. 鼓励学生 "用自己的双手解释一个想法"，为他们提供了对体现的想法进行反思的机会：通过这种反思，学习者能够重新表述和阐述他们最初的表述，使其更加清晰或具体，有时他们还能有新的发现/认识，如本的汽车比喻。
Revoicing and Reformulating Learners' Multimodally Expressed Embodied Ideas 重新认识和重新表述学习者以多种方式表达的具象思想
In addition to eliciting students' contributions, another crucial aspect of responsive teaching is taking up and reformulating learners' ideas in order to help them extend and connect these ideas with new STEM disciplinary understandings. One way to achieve this is through the practice of revoicing or recasting learners' contributions. In revoicing, educators repeat (report or restate verbatim), reformulate (modify the content of), and/or elaborate (add new content to) ideas learners have shared ( Connor & Michaels, 1996). This practice can serve a number of purposes, including (1) highlighting particular elements of students' ideas while backgrounding others, (2) helping students adopt disciplinarily normative language and representations, and (3) extending and reshaping the content of students' contributions to resemble disciplinarily normative concepts (Forman & Ansell, 2002; O'Connor & Michaels, 1996). 除了激发学生的贡献之外，回应式教学的另一个重要方面是接受和重新表述学习者的想法，以帮助他们扩展这些想法并将其与新的科学、技术和工程学科理解联系起来。实现这一目标的方法之一是对学习者的贡献进行重述或重塑。在revoicing中，教育者会重复（逐字报告或重述）、重新表述（修改内容）和/或阐述（添加新内容）学习者分享的观点（ Connor & Michaels, 1996）。这种做法可以达到多种目的，包括：（1）突出学生想法中的特定要素，同时介绍其他要素的背景；（2）帮助学生采用学科规范的语言和表述方式；以及（3）扩展和重塑学生贡献的内容，使之与学科规范的概念相类似（Forman & Ansell, 2002; O'Connor & Michaels, 1996）。
Revoicing has been studied primarily as a verbal phenomenon. Yet, when working with embodied learning technologies, learners do not just share ideas with words, but do their best to capture and represent their embodied experiences of interacting with the system, drawing on multiple modalities like fullbody reenactments, gesture, and demonstrative action with the device. What 逆反主要是作为一种语言现象来研究的。然而，在使用具身学习技术时，学习者并不只是用语言来分享想法，而是尽力捕捉和表现他们与系统互动的具身体验，利用多种方式，如全身重现、手势和使用设备的示范动作。什么
Table 12.1 表 12.1
Repeat gesture 重复手势
Omit gesture 省略手势
Elaborate gesture 精心设计的手势
Modify gesture 修改手势
Repeat talk 重复谈话
Omit talk 省略谈话
Elaborate talk 详谈
Modify talk 修改对话
does responsive revoicing look like in this context? When learners share ideas in multiple modalities, there are a number of different ways educators can re"voice" what has been shared (Flood, 2018). They can repeat, elaborate, omit, or modify parts of learners' speech or gesture (table 12.1). For example, an educator might repeat a learner's gesture, but elaborate on their speech, adding a vocabulary word to describe what was represented in gesture (Shein, 2012). Gestures, like sentences, have different phrases or parts to them (Kendon, 2004), and educators also repeat and reformulate gestures by adding, omitting, or modifying gesture phrases (Flood, 2018). 在这种情况下，"响应式再发声 "是什么样的？当学习者以多种方式分享想法时，教育者可以通过多种不同的方式重新 "表达 "所分享的内容（Flood，2018）。他们可以重复、阐述、省略或修改学习者的部分语音或手势（表 12.1）。例如，教育者可以重复学习者的手势，但对他们的讲话进行阐述，添加一个词汇来描述手势所代表的内容（Shein，2012）。手势和句子一样，有不同的短语或部分（Kendon，2004），教育者也会通过添加、省略或修改手势短语来重复和重新表述手势（Flood，2018）。
We illustrate gesture reformulation with an example from Flood (2018) and demonstrate how revoicing gestures can help learners make connections between their multimodally expressed embodied ideas and disciplinary ideas. With the help of some tutors, Lilah and a peer are working with the MITProportions with the concealed ratio setting of 1:2. The children have already reported two strategies for "making green:" (1) ensure that the right hand is always double as high as the left hand; or (2) move the hands with the right hand rising double as fast as the left hand. One of the tutors asks whether there is any connection between these strategies. Lilah volunteers an answer, and her response is composed of talk and an elaborate multipart gesture that has a variety of distinct gesture phrases (figure 12.4a and b). 我们以 Flood（2018 年）的一个例子来说明手势重塑，并展示了手势重塑如何帮助学习者在他们以多模态表达的具身思想和学科思想之间建立联系。在一些辅导员的帮助下，莉拉和同伴正在使用 MITProportions，隐蔽比例设置为 1:2。孩子们已经报告了两种 "绿化 "策略：(1) 确保右手的高度始终是左手的两倍；或 (2) 移动双手时，右手上升的速度是左手的两倍。一位辅导员问这些策略之间是否有联系。Lilah 自告奋勇地回答，她的回答由谈话和一个精心设计的多部分手势组成，其中包含各种不同的手势短语（图 12.4a 和 b）。
As Lilah says "that one" she points to the right hand remote. Then, as she continues to speak, she holds her hands out in front of her as if holding phantom remotes. When she says "same time" she holds her hands level at chest height (figure 12.4a), and when she says "would have to go faster" and "lift higher," she raises her hands so that the right hand travels approximately twice as fast and ends up approximately twice as high (figure 12.4b). Overall, Lilah's embodied performance accomplishes the idea that the right hand remote is going faster because it must go higher at the same time. 莉拉一边说 "那个"，一边指向右手的遥控器。然后，当她继续说话时，她将双手伸向前方，就像拿着幻影遥控器一样。当她说 "同一时间 "时，她将双手举到与胸部齐平的高度（图 12.4a），而当她说 "必须走得更快 "和 "举得更高 "时，她举起双手，使右手以大约两倍的速度移动，并最终举到大约两倍的高度（图 12.4b）。总的来说，莉拉的具体表现实现了右手遥控器速度更快的想法，因为它必须同时举得更高。
One of the tutors uses gesture and speech to revoice and reformulate Lilah's idea, treating her initial utterance as a substrate and reusing and transforming 其中一位导师用手势和语言重新表达和表述了 Lilah 的想法，将她最初的话语作为一个基质，并对其进行了再利用和转换
"if you're going to do it like, at the same time [a] that "如果你打算这样做，同时[a]那
"it has more ground to cover" [c] one would have to go faster [b] to like end at the same time [a] that one would have to [b] lift higher" "它有更多的地面要覆盖" [c] 人们必须走得更快 [b] 同时 [a] 人们必须 [b] 抬得更高"，"它有更多的地面要覆盖" [c] 人们必须走得更快 [b] 同时 [a] 抬得更高"。
Figure 12.4 图 12.4
Lilah's explanation of "faster" has two gestural phrases that she repeats twice: (a) she holds both her hands at the same height, and (b) then she pantomimes a motion with curled hands that would produce green feedback. (c) The tutor's revoicing turn reformulates Lilah's explanation by repeating only one of her gesture phrases, using flat hands, and co-timing it with a new verbal description. Underlined speech corresponds with gesture. 莉拉对 "更快 "的解释有两个手势短语，她重复了两次：(a) 她将双手举到同一高度，(b) 然后她用卷曲的双手做了一个动作，产生绿色反馈。(c) 导师在重新配音时，只重复了 Lilah 的一个手势短语，使用平举的双手，并与新的语言描述共同配音，从而重新表述了 Lilah 的解释。下划线语言与手势相对应。
it (Goodwin, 2018). The tutor reenacts Lilah's gesture moving his right hand so that it travels twice as fast as his left hand and ends up twice as high (figure 12.4c). However, he also reformulates Lilah's gesture: He changes the shape of his hands, flattening them instead of pantomiming the operation of the remotes. He also simplifies the hand movements, omitting gesture phrases where Lilah held her hands at the same height. Finally, he also modifies Lilah's speech, saying that the right hand has "more ground to cover" than the left, which could describe horizontal or vertical distance. 古德温，2018 年）。导师重演了莉拉的手势，移动他的右手，使其移动速度是左手的两倍，最终高度也是左手的两倍（图 12.4c）。不过，他也重新调整了莉拉的手势：他改变了双手的形状，使其扁平化，而不是模仿遥控器的操作。他还简化了手部动作，省略了莉拉双手保持同一高度的手势短语。最后，他还修改了莉拉的语言，说右手比左手 "有更多的地方要覆盖"，这可能是在描述水平距离，也可能是在描述垂直距离。
The tutor's reformulation decontextualizes Lilah's explanation in both gesture and speech to be less situated in the details of the device, and presents a more generalized disciplinary definition of "faster" as greater distance traveled during the same amount cf time. Although some aspects of Lilah's multimodal explanation were reformulated, the visible repetition of part of her gesture serves as bridge for Lilah to recognize the similarity between her idea and the tutor's reformulation. After the revoicing, Lilah adopts the tutor's reformulated version of what faster means into her explanation of how to make the screen green. 导师的重新表述将 Lilah 在手势和言语中的解释去语境化，使其不再局限于装置的细节，并提出了 "更快 "这一更为宽泛的学科定义，即在相同时间内行进的距离更远。虽然莉拉的多模态解释中的某些方面进行了重新表述，但她的手势中部分内容的明显重复为莉拉认识到自己的想法与导师的重新表述之间的相似性起到了桥梁作用。在重新发音后，莉拉在解释如何让屏幕变绿时采用了导师重新表述的 "更快 "的含义。
Overall, this example illustrates how reformulating learners' multimodally expressed embodied ideas can be a powerful responsive teaching strategy for highlighting what parts of learners' representations of embodied experiences are relevant to how scientists and mathematicians might think about representing the situation. 总之，这个例子说明，重新表述学习者以多模态表达的具身思想，可以成为一种强有力的响应式教学策略，突出学习者对具身体验的表述中哪些部分与科学家和数学家可能思考的表述情境相关。
Co-constructing Multimodally Expressed Embodied Ideas Together 共同构建多模态表达的体现式理念
Another way that educators can take up and build on learners' ideas is by directly interacting with the gestures that learners produce when describing their embodied experiences with embodied learning technologies. Educators and learners can contribute to the same gesture as part of co-constructing a multimodally expressed embodied idea together. As an embodied responsive teaching strategy, educators can interact with an unfolding student gesture by (1) highlighting aspects of the gesture (Flood et al., 2015) or (2) contributing new dynamic gestural imagery to the gesture (Flood et al., 2020). By coconstructing gestures, educators can help steer and formulate ideas in productive new directions, while at the same time keeping these new directions grounded in learners' initial observations and ideas. We present an example from Flood et al. (2020) of a tutor and learner co-constructing an embodied, dynamic representation together through gesture. 教育者接受和借鉴学习者想法的另一种方式，是直接与学习者在描述他们使用具身学习技术的具身体验时所做出的手势进行互动。教育者和学习者可以对同一手势做出贡献，共同构建多模态表达的具身理念。作为一种体现性响应教学策略，教育者可以通过以下方式与正在展开的学生手势进行互动：（1）强调手势的某些方面（Flood 等人，2015 年）或（2）为手势提供新的动态手势意象（Flood 等人，2020 年）。通过共同构建手势，教育者可以帮助引导和形成富有成效的新思路，同时使这些新思路立足于学习者最初的观察和想法。我们以 Flood 等人（2020 年）的研究为例，说明辅导教师和学习者通过手势共同构建了一个体现性的动态表征。
Ela and two tutors are working with the MIT-Proportion set to a 2:3 ratio. After being encouraged, Ela uses her hands to gesturally demonstrate her discovery of how to make the screen green: she raises her left hand one unit; then, to locate the right hand, she raises the right hand one and a half units. With her iterative 1-to-1.5 method, Ela is able to predict a number of height pairs that go together such as 1 and 1.5 units, 2 and 3 , and 3 and 4.5 , but she gets stuck predicting larger numbers and cannot predict where the right hand would be if the left were on 10 units. The tutor sees an opportunity to build on Ela's multimodally expressed embodied 1-per-1.5 idea and transform it into multiplicative understanding. He instructs Ela to keep her hands outstretched but instead of iteratively raising each hand by units, he suggests she try positioning the right hand one and half times as high as the left hand. He instructs her to lift her left hand about six inches off the desk, and then to put her right hand at a height that is the same height as the left hand plus another half of that height (figure 12.5) so the height of the right hand is one and a half times as much as the left hand. Ela 和两名辅导员正在将 MIT 比例设置为 2:3。在老师的鼓励下，Ela 用手演示了她发现的如何让屏幕变绿的方法：她将左手抬起一个单位；然后，为了确定右手的位置，她将右手抬起一个半单位。通过 1 到 1.5 的迭代法，Ela 能够预测出一些高度对，如 1 和 1.5 个单位、2 和 3 以及 3 和 4.5，但她在预测更大的数字时遇到了困难，无法预测出如果左手抬高 10 个单位，右手会在哪里。辅导老师发现了一个机会，可以在 Ela 多模态表达的 1-per-1.5 概念的基础上，将其转化为乘法理解。他让 Ela 继续伸出双手，但他建议 Ela 不要反复举起每只手，而是尝试将右手举到左手的 1.5 倍高处。他指示她将左手抬离桌面约六英寸，然后将右手放在与左手相同的高度上，再加上该高度的一半（图 12.5），这样右手的高度就是左手的 1.5 倍。
The tutor also uses his own hand to contribute additional dynamic imagery to co-construct a multimodal embodied representation with Ela when she struggles with the embodied multiplicative strategy. She gets stuck when the tutor asks her to predict where the right hand would be if the left hand is at two units. As she hesitates, the tutor reaches into Ela's gesture to lend an extra hand (both literally and figuratively). He makes a pinch shape with his hands to bracket the height under Ela's left hand, which she has raised to two units (figure 12.5a), then he decreases the height between his thumb and index 当 Ela 在体现乘法策略上遇到困难时，辅导员还用自己的手提供额外的动态图像，与 Ela 共同构建多模态体现表征。当辅导员要求她预测如果左手在两个单位处，右手会在哪里时，她被卡住了。 就在她犹豫不决的时候，辅导员把手伸进了 Ela 的手势中，伸出了一只额外的手（既是字面意义上的，也是比喻意义上的）。他用手捏成一个 "捏 "字形，括住 Ela 左手下方的高度，她已经将左手抬高到两个单位（图 12.5a），然后他又降低了拇指和食指之间的高度。 当 Ela 在体现乘法策略上遇到困难时，辅导员也会用自己的手提供额外的动态图像，与 Ela 共同构建多模态体现表征。当辅导员要求她预测如果左手在两个单位处，右手会在哪里时，她卡住了。 就在她犹豫不决的时候，辅导员向 Ela 的手势伸出了援助之手（既是字面意义上的，也是比喻意义上的）。他用手捏成一个 "捏 "字形，括住 Ela 左手下方的高度，她已经将左手抬高到了两个单位（图 12.5a），然后他将拇指和食指之间的高度减小
Tutor: "If you take two, and take half of two, which is one, so it's. . ." 老师"如果你拿两个，再拿两个的一半，也就是一个，那么它就是......."
Figure 12.5 图 12.5
The tutor reaches in to Ela's gesture to co-construct a multimodally expressed embodied idea about multiplication. (a) He makes a pinch shape under Ela's left hand, and then (b) shrinks it by half and moves his hand toward Ela's right hand. Underlined speech corresponds with gesture. 辅导员将手伸入 Ela 的手势中，共同构建了一个多模态表达的乘法概念。(a) 他在 Ela 的左手下捏出一个形状，然后 (b) 将其缩小一半，并将手移向 Ela 的右手。下划线语言与手势相对应。
finger by about half and slides his hand towards Ela's right hand (figure 12.5b), saying, "If you take two, and take half of two, which is one, so it's . . ." By contributing this dynamic imagery to Ela's gesture-in-progress, the tutor helps her find the correct one-and-a-half times position for her hand. Ela finishes the tutor's sentence, correctly answering "three." The tutor's interaction with Ela's gesture impacted her understanding, and she later applies the same shrinking pinch gesture to illustrate a new situation when she compares the relationship of the speeds of the two cursors. 辅导员将埃拉的手指比划了一半左右，然后将手滑向埃拉的右手（图 12.5b），说："如果你拿两根手指，再拿两根手指的一半，也就是一根手指，那么就是......"。通过对 Ela 正在做的手势进行动态想象，导师帮助她找到了正确的一倍半位置。埃拉完成了辅导员的句子，正确地回答了 "三"。辅导员与 Ela 手势的互动影响了她的理解，后来她在比较两个光标的速度关系时，也用了同样的缩小捏手势来说明新的情况。
Together Ela and the tutor have co-constructed a dynamic, embodied way of representing the relationship between the left- and right-hand heights, using iterative addition and then multiplication. Ela's initial gesture, demonstrating iterative addition, serves as a substrate that is taken up and simultaneously transformed by the tutor, allowing the tutor to instruct Ela on how to experience her gestured demonstration as a functional multiplicative relation between the heights of the left and right hand. Overall, co-constructing a gesture with learners is a useful responsive-teaching strategy to build from and elaborate learners' initial embodied ideas (e.g., Ela's additive scheme), thus connecting them with new disciplinary understandings (e.g., the functional multiplicative scheme the tutor and Ela co-construct). 埃拉和导师共同构建了一种动态的、体现性的方式，用迭代加法和乘法来表示左手和右手高度之间的关系。Ela 最初演示迭加法的手势是一个基底，导师在使用它的同时也对其进行了改造，使导师能够指导 Ela 如何将她的手势演示体验为左手和右手高度之间的功能性乘法关系。总之，与学习者共同建构手势是一种有用的响应式教学策略，可以从学习者最初的具象想法（如 Ela 的加法方案）出发并加以阐释，从而将其与新的学科理解（如辅导员和 Ela 共同建构的功能性乘法方案）联系起来。
Concluding Remarks 结束语
Embodied learning technologies pose unique challenges for instructional practice by embracing learners' hands and full bodies as the primary instruments of 嵌入式学习技术将学习者的双手和全身作为学习的主要工具，对教学实践提出了独特的挑战。
STEM learning. Educators must find ways to responsively guide learners toward disciplinary understandings, starting with the substrate of learners' spontaneous, embodied experiences of perceiving and moving as they operate the devices. In this chapter, we presented four ways that educators can attend to and engage with multimodally expressed embodied ideas to support learners' mathematical discoveries as they use embodied learning technologies. Drawing on EMCA, CoAF, and sociocultural studies, our fine-grained investigations contribute to filling current gaps in our understanding of how learning can be facilitated with digital technologies that deliberately incorporate the body into STEM learning. In addition, our work has implications for instructional practice by suggesting effective multimodal discursive moves instructors can adopt to facilitate meaning-making with embodied learning technologies. STEM 学习。教育者必须从学习者操作设备时自发的、体现性的感知和运动体验出发，找到引导学习者理解学科知识的方法。在本章中，我们介绍了教育者可以关注和参与多模态表达的具身思想的四种方法，以支持学习者在使用具身学习技术时的数学发现。我们的研究借鉴了EMCA、CoAF和社会文化研究，有助于填补我们目前对如何利用数字技术促进学习的认识空白，这些技术有意将身体融入STEM学习中。此外，我们的研究还对教学实践产生了影响，提出了教师可以采取的有效的多模态话语行动，以促进具身学习技术的意义生成。
Although we have discovered these embodied responsive teaching practices in the case of mathematics, we conjecture that these practices would also have utility in other STEM learning domains. Responsive teaching that attends to and engages with learners' embodied ideas is, itself, an embodied practice that involves recruiting one's own body to make sense of learners' perceptuomotor activity, to repeat and reformulate leaners' gestures, and to co-gesture. Future research could investigate teachers' embodied learning of responsiveness (i.e., how teachers come to adopt embodied practices of attending to and interpreting learners' multimodally expressed embodied ideas). For example, the role of mirror neurons (see Butera & Aziz Zadeh, chapter 16 in this volume) could be examined. In addition, the collection of practices we have presented here are not comprehensive, and we hope our work will open up additional investigation into the embodied dimensions of responsive teaching with educational technology. 虽然我们是在数学教学中发现这些体现性回应教学实践的，但我们猜想，这些实践在其他科学、技术、工程和数学学习领域也会有用。关注并参与学习者体现性想法的响应式教学本身就是一种体现性实践，它涉及运用自己的身体来理解学习者的感知运动活动，重复和重新表述学习者的手势，以及共同构思。未来的研究可以调查教师对反应能力的具身学习（即教师如何采用具身实践来关注和解释学习者多模态表达的具身想法）。例如，可以研究镜像神经元的作用（见布特拉和阿齐兹-扎德，本卷第 16 章）。此外，我们在此介绍的实践并不全面，我们希望我们的工作能为教育技术响应式教学的具身层面开启更多的研究。
Notes 说明
References 参考资料
Abrahamson, D., Gutiérrez, J., Charoenying, T., Negrete, A., & Bumbacher, E. (2012) Fostering hooks and shifts: Tutorial tactics for guided mathematical discovery. Technology, Knowledge and Learning, Abrahamson, D., Gutiérrez, J., Charoenying, T., Negrete, A., & Bumbacher, E. (2012) Fostering hooks and shifts：引导数学发现的教程策略。技术、知识与学习， 。
Abrahamson, D., Lee, R. G., Negrete, A. G., & Gutiérrez, J. F. (2014). Coordinating visualizations of polysemous action: Values added for grounding proportion. ZDM Mathematics Education, . Abrahamson, D., Lee, R. G., Negrete, A. G., & Gutiérrez, J. F. (2014).多义词动作的协调可视化：为接地比例添加数值。ZDM Mathematics Education, .
Abrahamson, D., & Lindgren, R. (2014). Embodiment and embodied design. In K. Sawyer (Ed.), Cambridge handbook of the learning sciences (pp. 358-376). Cambridge University Press Abrahamson, D., & Lindgren, R. (2014)。体现与体现式设计。In K. Sawyer (Ed.), Cambridge handbook of the learning sciences (pp. 358-376).剑桥大学出版社
Alibali, M. W., & Goldin-Meadow, S. (1993). Gesture-speech mismatch and mechanisms of learning: What the hands reveal about a child's state of mind. Cognitive Psychology, 25, 468-523. Alibali, M. W., & Goldin-Meadow, S. (1993).手势-言语不匹配与学习机制：手势揭示了儿童的心理状态。认知心理学》，25，468-523。
Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93(4), 373-397 Ball, D. L. (1993).With an eye on the mathematical horizon：Dilemmas of teaching elementary school mathematics.Elementary School Journal, 93(4), 373-397
Coffey, J. E., Hammer, D., Levin, D. M., & Grant, T. (2011). The missing disciplinary substance of formative assessment. Journal cf Research in Science Teaching, 48(10), 1109-1136. Coffey, J. E., Hammer, D., Levin, D. M., & Grant, T. (2011).形成性评估缺失的学科实质。Journal cf Research in Science Teaching, 48(10), 1109-1136.
Crowder, E. M. (1996). Gestures at work in sense-making science talk. Journal &f the Learning Sciences, 5(3), 173-208 Crowder, E. M. (1996).感性科学谈话中的手势。Journal &f the Learning Sciences, 5(3), 173-208
De Jaegher, H., Peräkylä, A., & Stevanovic, M. (2016). The co-creation of meaningful action: Bridging enaction and interactional sociology. Philosophical Transactions of the Royal Society B: Biological Sciences, 37l(1693), Article 20150378. De Jaegher, H., Peräkylä, A., & Stevanovic, M. (2016)。The co-creation of meaningful action：衔接行动学和互动社会学。英国皇家学会哲学论文集 B：生物科学》，37l(1693)，第 20150378 条。https://doi.org/10.1098/rstb. 2015.0378
DeLiema, D., Saleh, A., Lee, C., Enyedy, N., Danish, J., Illum, R., Dahn, M., Humburg, M., & Mahoney, C. (2016). Blending play and inquiry in augmented reality: A comparison of playing a video game to playing within a participatory model. In Looi, C. K., Polman, J. L., Cress, U., and Reimann, P. (Eds.), Transforming learning, empowering learners: The International Cor ference (f the Learning Sciences (ICLS) 2016, Volume 1 (pp. 450-457). International Society of the Learning Sciences. DeLiema, D., Saleh, A., Lee, C., Enyedy, N., Danish, J., Illum, R., Dahn, M., Humburg, M., & Mahoney, C. (2016)。增强现实中游戏与探究的融合：玩电子游戏与在参与式模型中玩游戏的比较。In Looi, C. K., Polman, J. L., Cress, U., and Reimann, P. (Eds.), Transforming learning, empowering learners：The International Cor ference (f the Learning Sciences (ICLS) 2016, Volume 1 (pp. 450-457).国际学习科学学会。
Erickson, F. (2007). Some thoughts on "proximal" formative assessment of student learning. In Moss, P (Ed.), Evidence and decision making (pp. 186-216). Blackwell Publishing Erickson, F. (2007).关于学生学习的 "近距离 "形成性评价的一些想法。In Moss, P (Ed.), Evidence and decision making (pp. 186-216).布莱克威尔出版社
Flood, V. J. (2018). Multimodal revoicing as an interactional mechanism for connecting scientific and everyday concepts. Human Develcpment, 61, 145-173. Flood, V. J. (2018).多模态再认知作为连接科学概念和日常概念的互动机制。人类发展》，61，145-173。
Flood, V. J. (2021). The secret multimodal life of IREs: Looking more closely at representational gestures in a familiar questioning sequence. Linguistics and Education, 63, 100913. Flood, V. J. (2021).IREs 的秘密多模态生活：更仔细地观察熟悉的提问序列中的表征手势。语言学与教育》，63，100913。
Flood, V. J., Amar, F. G., Nemirovsky, R., Harrer, B. W., Bruce, M. R. M., & Wittmann, M. C. (2015). Paying attention to gesture when students talk chemistry: Interactional resources for responsive teaching. Journal cf Chemical Education, 92(1), 11-22. Flood, V. J., Amar, F. G., Nemirovsky, R., Harrer, B. W., Bruce, M. R. M., & Wittmann, M. C. (2015)。关注学生谈论化学时的手势：响应式教学的互动资源。化学教育杂志》，92（1），11-22。
Flood, V. J., Shvarts, A., & Abrahamson, D. (2020). Teaching with embodied learning technologies for mathematics: Responsive teaching for embodied learning. ZDM Mathematics Education, 52, Flood, V. J., Shvarts, A., & Abrahamson, D. (2020).使用具身学习技术进行数学教学：用具身学习技术进行数学教学：具身学习的响应式教学。ZDM Mathematics Education, 52、. Flood, V. J., Shvarts, A., & Abrahamson, D. (2020).使用具身学习技术进行数学教学：用具身学习技术进行数学教学：具身学习的响应式教学。ZDM Mathematics Education, 52, .
Forman, E. A., & Ansell, E. (2002). Orchestrating the multiple voices and inscriptions of a mathematics classrooms. Journal of the Learning Sciences, 11(2-3), 251-274 Forman, E. A., & Ansell, E. (2002).Orchestrating the multiple voices and inscriptions of a mathematics classrooms.学习科学杂志》，11（2-3），251-274 页。
Goodwin, C. (2018). Co-cperative action. Cambridge University Press Goodwin, C. (2018).合作行动》。剑桥大学出版社
Jackiw, N., & Sinclair, N. (2017). TouchCounts and gesture design. In T. Hammond (Ed.), Frontiers in pen and touch (pp. 51-62). Springer Jackiw, N., & Sinclair, N. (2017)。TouchCounts 和手势设计。In T. Hammond (Ed.), Frontiers in pen and touch (pp. 51-62).斯普林格出版社
Jacobs, V. R., & Empson, S. B. (2016). Responding to children's mathematical thinking in the moment: An emerging framework of teaching moves. ZDM Mathematics Education, 48(1-2), Jacobs, V. R., & Empson, S. B. (2016)。当下回应儿童的数学思维：一个新兴的教学行动框架。ZDM Mathematics Education, 48(1-2)、. Jacobs, V. R., & Empson, S. B. (2016)。当下回应儿童的数学思维：一个新兴的教学行动框架。ZDM Mathematics Education, 48(1-2), .
Kendon, A. (2004). Gesture: Visible action as utterance. Cambridge University Press. Kendon, A. (2004).Gesture：Gesture: Visible action as utterance.剑桥大学出版社。
Lindgren, R., & Johnson-Glenberg, M. (2013). Emboldened by embodiment: Six precepts for research on embodied learning and mixed reality. Educational Researcher, 42(8), 445-452. Lindgren, R., & Johnson-Glenberg, M. (2013)。化身的力量：关于具身学习和混合现实研究的六条戒律》，《教育研究者》，42(8), 445-452.Educational Researcher, 42(8), 445-452.
Lineback, J. E. (2015). The redirection: An indicator of how teachers respond to student thinking. Journal cf the Learning Sciences, 24(3), 419-460. Lineback, J. E. (2015).重定向：教师如何应对学生思维的指标。参阅《学习科学杂志》，24（3），419-460。
Lyons, L., Slattery, B., Jimenez, P., Lopez, B., & Moher, T. (2012). Don't forget about the sweat: Effortful embodied interaction in support of learning. In TEI 'I2: Proceedings of the Sixth International Cor ference on Tangible, Embedded and Embodied Interaction (pp. 77-84). ACM Digital Library. Lyons, L., Slattery, B., Jimenez, P., Lopez, B., & Moher, T. (2012)。别忘了流汗：支持学习的努力型体现互动。In TEI 'I2: Proceedings of the Sixth International Cor ference on Tangible, Embedded and Embodied Interaction (pp. 77-84).ACM 数字图书馆。https://doi.org/10.1145/2148131.2148149 Lyons, L., Slattery, B., Jimenez, P., Lopez, B., & Moher, T. (2012)。别忘了流汗：支持学习的努力型体现互动。In TEI 'I2: Proceedings of the Sixth International Cor ference on Tangible, Embedded and Embodied Interaction (pp. 77-84).ACM 数字图书馆。https://doi.org/10.1145/2148131.2148149
Mondada, L. (2019). Contemporary issues in conversation analysis: Embodiment and materiality, multimodality and multisensoriality in social interaction. Journal of Pragmatics, 145, 47-62. Mondada, L. (2019).对话分析中的当代问题：社会互动中的体现与物质性、多模态和多感官性。语用学杂志》，145，47-62。
Nemirovsky, R., Kelton, M. L., & Rhodehamel, B. (2014). Playing mathematical instruments: Emerging perceptuomotor integration with an interactive mathematics exhibit. Journal for Research in Mathematics Education, 44(2), 372-415 Nemirovsky, R., Kelton, M. L., & Rhodehamel, B. (2014)。玩数学乐器：与互动数学展品的感知运动整合。数学教育研究期刊》，44（2），372-415 页
O'Connor, M. C., & Michaels, S. (1996). Shifting participant frameworks: Orchestrating thinking practices in group discussion. In D. Hicks (Ed.), Discourse, learning and schooling (pp. 63-103). Cambridge University Press. O'Connor, M. C., & Michaels, S. (1996).Shifting participant frameworks：Orchestrating thinking practices in group discussion.In D. Hicks (Ed.), Discourse, learning and schooling (pp. 63-103).剑桥大学出版社。
Pierson, J. L. (2008). The relationship between patterns cf classroom discourse and mathematics learning [Doctoral dissertation, University of Texas at Austin]. Pierson, J. L. (2008).课堂话语模式与数学学习之间的关系[德克萨斯大学奥斯汀分校博士论文]。https://repositories.lib.utexas.edu /bitstream/handle/2152/17898/piersonj.pdf
Robertson, A. D., Scherr, R. E., & Hammer, D. (2016). Responsive teaching in science and mathematics. Routledge Robertson, A. D., Scherr, R. E., & Hammer, D. (2016).Responsive teaching in science and mathematics.Routledge
Roth, W.-M., & Lawless, D. (2002). Scientific investigations, metaphorical gestures, and the emergence of abstract scientific concepts. Learning and Instruction, 12(3), 285-304. Roth, W.-M., & Lawless, D. (2002)。科学调查、隐喻手势和抽象科学概念的出现。Learning and Instruction, 12(3), 285-304.
Saxe, G. B., Gearhart, M., & Seltzer, M. (1999). Relations between classroom practices and student learning in the domain of fractions. Cognition and Instruction, 17(1), 1-24. Saxe, G. B., Gearhart, M., & Seltzer, M. (1999).分数领域中课堂练习与学生学习之间的关系。Cognition and Instruction, 17(1), 1-24.
Schegloff, E. A. (1991). Conversation analysis and socially shared cognition. In L. B. Resnick, J. M. Levine, & S. D. Teasley (Eds.), Perspectives on socially shared cognition (pp. 150-170). American Psychological Association. Schegloff, E. A. (1991).Conversation analysis and socially shared cognition.In L. B. Resnick, J. M. Levine, & S. D. Teasley (Eds.), Perspectives on socially shared cognition (pp. 150-170).美国心理学会。
Sheets-Johnstone, M. (2000). Kinetic tactile-kinesthetic bodies: Ontogenetical foundations of apprenticeship learning. Human Studies, 23(4), 343-370 Sheets-Johnstone, M. (2000).运动触觉-动觉体：学徒学习的本体论基础。人类研究》，23（4），343-370 页
Shein, P. (2012). Seeing with two eyes: A teacher's use of gestures in questioning and revoicing to engage English Language Learners in the repair of mathematical errors. Journal for Research in Mathematics Education, 43(2), 182-222. Shein, P. (2012).用两只眼睛看：教师在提问和再提问中使用手势让英语学习者参与修复数学错误。数学教育研究期刊》，43（2），182-222。
Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2011). Mathematics teacher noticing: Seeing through teachers' eyes. Routledge. Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2011).Mathematics teacher noticing：Mathematics teacher noticing: Seeing through teachers' eyes.Routledge.
Shvarts, A., & Abrahamson, D. (in press). Dual-eye-tracking Vygotsky: A microgenetic account of a mathematics-tutorial case study as a teaching/learning collaboration. In Edwards, L. D., & Krause, C. M. (Eds.), The body in mathematics: Theoretical and methodological lenses. Brill. Shvarts, A., & Abrahamson, D. (in press).双目追踪维果茨基：数学教学案例研究作为教与学合作的微观遗传学论述。In Edwards, L. D., & Krause, C. M. (Eds.), The body in mathematics：Theoretical and methodological lenses.Brill.
Shvarts, A., & Abrahamson, D. (2019). Dual-eye-tracking Vygotsky: A microgenetic account of a teaching/learning collaboration in an embodied-interaction technological tutorial for mathematics. Learning, Culture, and Social Interaction, 22, Article 100316. https://doi.org/10.1016/j.lcsi.2019.05.003 Shvarts, A., & Abrahamson, D. (2019).双目追踪维果茨基：体现式互动数学技术教程中教与学合作的微观遗传论述。学习、文化与社会互动》，第 22 期，第 100316 条。https://doi.org/10.1016/j.lcsi.2019.05.003
Skulmowski, A., & Rey, G. D. (2018). Embodied learning: Introducing a taxonomy based on bodily engagement and task integration. Cognitive Research: Principles and Implications, 3(1), Article 6. https://doi.org/10.1186/s41235-018-0092-9 Skulmowski, A., & Rey, G. D. (2018).体现式学习：基于身体参与和任务整合的分类法介绍。认知研究：原理与意义》，3（1），第 6 条。https://doi.org/10.1186/s41235-018-0092-9
Vygotsky, L. S. (1986). Thought and language (rev. ed.). MIT Press. Vygotsky, L. S. (1986).Thought and language (rev. ed.).麻省理工学院出版社。
Wertsch, J. V. (1985). Vigotsky and the social formation of mind. Harvard University Press. Wertsch, J. V. (1985).Vigotsky and the social formation of mind.哈佛大学出版社。
Sociocultural theory, developed by Lev Vygotsky, is widely used in the fields of psychology and education. It is an approach to understanding learning and development as fundamentally entwined with and emerging from social interactions embedded in particular cultures, places, and times. Ethnomethodology and conversation analysis (EMCA), on the other hand, come from sociology and investigate the systematic practices people use to create social order as part of everyday life. Ethnomethodology (which means "people's methods") originated with the sociologist Harold Garfinkel; conversation analysis, an offshoot that focuses specifically on conversational practices, was introduced by the sociologists Harvey Sacks, Gail Jefferson, and Emmanuel Schegloff. Drawing on both of these approaches, the co-operative action framework ( CoAF ), developed by linguistic anthropologist Charles Goodwin (who trained with Gail Jefferson), synthesizes sociocultural theory, EMCA, and semiotics to explain how meaning-making, coordinated social activities, and human artifacts are all made possible through human beings' propensity to decompose, reuse, and transform the resources others have introduced into public arenas across multiple scales of time Lev Vygotsky 提出的社会文化理论被广泛应用于心理学和教育学领域。它是一种理解学习和发展的方法，认为学习和发展从根本上说是与特定文化、地点和时代的社会互动相联系的，并且是从社会互动中产生的。另一方面，民族方法学和会话分析（EMCA）来自社会学，研究人们在日常生活中用来创造社会秩序的系统实践。人种方法学（意为 "人们的方法"）起源于社会学家哈罗德-加芬克尔（Harold Garfinkel）；会话分析是社会学家哈维-萨克斯（Harvey Sacks）、盖尔-杰斐逊（Gail Jefferson）和埃马纽埃尔-谢格洛夫（Emmanuel Schegloff）提出的一个分支，专门关注会话实践。语言人类学家查尔斯-古德温（Charles Goodwin，曾与盖尔-杰斐逊一起接受培训）借鉴了这两种方法，提出了合作行动框架（CoAF），该框架综合了社会文化理论、EMCA 和符号学，解释了意义生成、协调的社会活动和人类手工艺品是如何通过人类分解、再利用和转化他人引入公共领域的资源的倾向，在多个时间尺度上得以实现的。
All student names are pseudonyms. 所有学生姓名均为化名。
This is good evidence that Ela is earnestly trying to understand Dor's proposal, since earlier predicting 3 from 2 was no problem with her original iterative strategy (raising the left hand one unit and the right unit one and half units). 这很好地证明了埃拉在认真地尝试理解多尔的提议，因为之前用她最初的迭代策略（左手提高一个单位，右手提高一个半单位）从 2 中预测出 3 是没有问题的。
