# First reflections on Further Maths

Originally there were 7 students doing FM, all male. It took one question, literally one question, “Would you like to do Further Maths?”, for four girls to leap at the opportunity to do it. They just hadn’t considered the possibility. Great reminder to ensure everyone knows they are welcome to join the Maths Clique, especially those from groups that have historically been under-represented.

Highlight of the first week – exploring complex numbers.

1. I introduced complex numbers as natural next step in progression (x + 2 = 0, 3x – 2 = 0, x^2 – 2 = 0, x^2 + 1 = 0).
2. Students generated a whole load of really excellent questions

3. “Trust your intuition, and follow all the rules you already know”. The group were able to solve quadratic equations with complex solutions, manipulate expressions involving complex numbers, mess about with fractions using their knowledge of surds as analogy.
4. When looking at powers of i (remember, all I have given the students is the definition of i)
• “We are trapped in a loop!” yells Wintana
• “It’s like a circle” chips in Ifte
• Noemi draws the circle, notices that it looks like the real number line goes through horizontally
• “I guess the y-axis is the imaginary number line” jokes Igoris sarcastically

What beautiful and constructive conversation from the students. Replicating the discovery of the complex plane, inventing it for themselves. Obviously discovery-based learning has its pitfalls (“Now class, you will discover the trigonometric ratios”), but once you give the students the initial seed they can run very far indeed! I am very excited.

BTW, reminds me of a recent podcast by Ben, Ben and Blue about how lecturing is doing worse than doing nothing at all. Inspired by the work of Carl Wieman, physicist turned educationalist. An expert teacher has comfort in chaos, is able to move agilely in response to the class. Lecturing, in comparison is comfortable, easy, reliable.