We all have lived through a quick transition to the distant learning. In this situation, embodied aspects of student-teacher communication that usually ground understanding in a classroom are severely cut. Natural gestures and guidance of students’ attention are hardly available in a speaking-head setup without a whiteboard. Immediate feedback is also lacking, as teachers do not have all the students available for visual examination.

 In teaching from a distance, embodied design could help to preserve learning-with-understanding direction and provide a rare opportunity to keep embodied engagement with mathematics. Immediate feedback to sensory-motor actions support students’ learning process second to second and facilitate conceptual understanding.

Trigonometry learning: From a unit circle to a sine graph.

We offer two versions of e-learning materials prepared in Numworx environment:

• for students who have a multi-touch technology available (a tablet or a touch screen)
• for students who have a computer with a mouse available

E-learning materials consist of an introduction with a short test of prior knowledge and four interactive learning sequences.

Multi-touch technology	Mouse-based technology
Introduction: an angle measurement on a circle and sine relations in a right triangle Dutch version         English version	Introduction: an angle measurement on a circle and sine relations in a right triangle Dutch version         English version
Part 1. Sine on a unit circle       Dutch version            English version	Part 1. Sine on a unit circle Dutch version         English version
Part 2. X-coordinate of a sine graph Dutch version           English version	Part 2. X-coordinate of a sine graph Dutch version         English version
Part 3. Y-coordinate of a sine graph Dutch version          English version	Part 3. Y-coordinate of a sine graph Dutch version          English version
Part 4. Constructing a sine graph Dutch version          English version	Part 4. Constructing a sine graph Dutch version          English version

Using e-learning materials

Learning sequences are freely available for the use with your students. They can be used as a homework or as additional exercises.

Research Publications:

Shvarts, A., van Helden, G. (2023) Embodied learning at a distance: from sensory-motor experience to constructing and understanding a sine graph Mathematical Thinking and Learning, 25(4), 409–437, DOI: 10.1080/10986065.2021.1983691

Shvarts, A., Zenger, L. (2023) Dynamic visualization and embodied design for trigonometry learning: looking or doing? In M. Ayalon, B. Koichu, R. Leikin, L. Rubel., & M. Tabach (Eds.). . Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 211–219). University of Haifa.

Shvarts, A., van Helden, G. (2021) Embodied design versus dynamic visualization: Benefits for a far transfer problem solving in trigonometry. In Reflecting the Past and Embracing the Future. Proceedings of ISLS Annual Meeting on Learning Sciences, 7-11^th of of June, 2021, Bochum, Germany. (link)