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PLEASE NOTE: If a candidate gives a layman's talk, the livestream will start fifteen minutes earlier.

Understanding how things change together is an important skill in both math and everyday life, from personal finance to public health. Learning about these relationships, in mathematics usually modeled as functions, can be challenging for students because the ideas may feel abstract and disconnected from their experience. Regular teaching with static formulas and graphs often fails to help students make sense of how the values of variables dynamically co-vary.

This thesis explores an innovative way to make the learning of functional thinking, and of covariation in particular, more concrete and interactive. To do so, we designed a digital learning environment that uses a visual representation called a nomogram. Our key innovation was to get students to use both hands to explore these mathematical relationships. By moving points on two parallel lines on a screen, students directly experience how changes in one variable affect another variable, based on the function rule. The learning environment provides real-time feedback: a green arrow appears for a correct pairing, and a red one for an incorrect match. This feedback helps students adjust their movement and develop an understanding of covariation.

Through a series of studies, from initial design pilots to trials in regular classrooms, we found this hands-on approach helped students grasp complex mathematical ideas in an embodied way. The action of moving the two hands and the perception of the feedback allowed students to develop a strong feeling for how functions work. By connecting physical action with abstract thinking through the use of digital technology, this research demonstrates that sometimes the best way to understand an abstract concept is to get your hands on it.