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The Journey of Tangent from Geometry to Calculus

The Australian Curriculum is saturated and often we feel as if there isn’t enough time to explore the ‘how’ and ‘why’ responsible for our understanding of mathematics today. The two one-hour workshops will focus on conceptual understanding and use of dynamic mathematical software tools in visualising mathematical patterns and making sense of them. Our journey from Geometry and Trigonometry to Calculus will follow the enigmatic term, 'Tangent'. Tangents have appeared in many areas of mathematics - triangles, unit circles, functions, derivatives - each time appearing under a new topic. Is this a coincidence? Which meanings prepare the students best for the next occurrence? Let's unpack this once and for all using dynamic digital tools to visualise our journey. 

Date: Thursday 22 October 2020

Time: 4-6pm (AEST)

Workshop 1: (4-5pm),
 Thomas Sprenger will begin with the Unit Circle and use it to establish the Tangent Function (and more) in Trigonometric Ratios. By exploring the interconnected nature of Trig Ratios and grounding their meaning in Unit Circle, we will observe the profound consequence this has on students’ later work in Calculus. 

Workshop 2: (5-6pm)Fiona Vo will ask questions about tangents when these appear once again years later in derivatives. What are the similarities? What are the differences? How do our students need to reason about trigonometric ratios by this point to benefit from bringing the ‘old’ notions into this ‘new’ mathematical domain?

Technology: Throughout the workshop, we will use dynamic software Graphing Calculator by Pacific Tech and a free online textbook, which includes dynamic illustrations created in Graphing Calculator. Participants will not need to have the software installed on their computers, but if you are curious and interested (or will become so after the workshop), please click here The organisers, UQ, and QAMT are not affiliated with Pacific Tech.

Registration: As the workshop will be held online via zoom, please register so we can send you the zoom link details.




Zoom: As the workshop will be held online via zoom, please register so we can send you the zoom link details.