Imaginary numbers are real!
A glimpse from some recent lessons in the DP Applications and Interpretation Higher Level Mathematics course. Let me tell you about our first adventure with complex numbers, great minds’ missed opportunities for more discoveries, and using technology to imagine the un-imaginary.
By Lilia Myszkowska, secondary mathematics teacher
To begin with, for the majority of time, the students have been working individually via the online platform Kognity. It has been a steep learning curve for developing self-management skills and I would like to compliments all students for the high level of independence and motivation!
Currently, the AI HL students are busy exploring the concept of complex numbers. We didn’t search for complex numbers; the need for them arose from a problem we couldn’t solve with the knowledge we currently had. This naturally led students to switch between the two thinking modes as described by Prof. B. Oakley: focused and diffused. While the focused mode is important for the learning process, learning to shift to the diffused mode, might help to see problems from different perspectives. It is all about finding the balance.
Can complex numbers exist?
Making connections to history of mathematics, students might be interested to read about the Greek mathematician Heron of Alexandria who missed the chance to explore a “brand new” area of mathematics. To bring some Theory Of Knowledge to the classroom, we planned to contemplate about the following question: “If imaginary numbers don’t actually ‘exist’ in the real world, and complex numbers are formed using imaginary numbers, can complex numbers be said to exist?” What do you think?
Finally, we looked at a common problem about functions from a 3D perspective using GeoGebra AR. Students sketched a 2D graph on a piece of paper and then used the app to visualize their drawing in 3D. There is so much more we can do. With a little imagination, students could also see how the topic connects to making movies. Check it out!
Thanks to Ella, Malak, Liv, Natasha, Adrian, Connor, Elias and Zachary for their contributions. (Note: It worked well for Apple users, unfortunately not so well for Android users)
After the long lock-down, students will get ready for looking at the displacement vectors. By engaging in the “Dancing Vectors Challenge”, we will try to visualize challenging concepts through movement and music. We aim to become more active, well-coordinated and develop further our communication skills though music and mathematics.