Recent developments in cognitive and educational science highlight the role of the body in learning. Novel digital technologies increasingly facilitate bodily interaction. Aiming for understanding of the body’s role in learning mathematics with technology, we reconsider the instrumental approach from a radical embodied cognitive science perspective. We highlight the complexity of any action regulation, which is performed by a complex dynamic functional system of the body and brain in perception-action loops driven by multilevel intentionality. Unlike mental schemes, functional systems are decentralized and can be extended by artifacts. We introduce the notion of a body-artifact functional system, pointing to the fact that artifacts are included in the perception-action loops of instrumented actions. The theoretical statements of this radical embodied reconsideration of the instrumental approach are illustrated by an empirical example, in which embodied activities led a student to the development of instrumented actions with a unit circle as an instrument to construct a sine graph. Supplementing videography of the student’s embodied actions and gestures with eye-tracking data, we show how new functional systems can be formed. Educational means to facilitate the development of body-artifact functional systems are discussed.

认知和教育科学的最新发展突出了身体在学习中的作用。新型数字技术越来越促进身体互动。为了理解身体在使用技术学习数学中的作用，我们从激进的具身认知科学的角度重新考虑工具方法。我们强调了任何动作调节的复杂性，这是由身体和大脑的复杂动态功能系统在多层次意向驱动的感知-动作循环中执行的。与心理计划不同，功能系统是分散的，可以通过工件进行扩展。我们引入了身体-人工制品功能系统的概念，指出人工制品包含在仪器化动作的感知-动作循环中的事实。对工具方法的这种激进的具体化重新考虑的理论陈述通过一个经验示例来说明，在该案例中，具体的活动引导学生开发工具化的动作，并以单位圆作为构建正弦图的工具。 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 用眼动追踪数据补充学生具体动作和手势的录像，我们展示了如何形成新的功能系统。讨论了促进身体人工制品功能系统发展的教育手段。用眼动追踪数据补充学生具体动作和手势的录像，我们展示了如何形成新的功能系统。讨论了促进身体人工制品功能系统发展的教育手段。用眼动追踪数据补充学生具体动作和手势的录像，我们展示了如何形成新的功能系统。讨论了促进身体人工制品功能系统发展的教育手段。