[Maths Education] Mathematical Journalling

     Nowadays, I see some schools / textbooks asking students to search the internet and to write on a certain problem on their “mathematics journal”.  It's so very guided.  It's so artificial.  The questions should come from the learners themselves, out of their own curiosity.  The learn then seeks to answer their own questions.  The journal can serve as to document and summarise their process of learning.

     The best maths journals are self-initiated.  Great mathematician Karl Friedrich Gauss and renowned scientist Richard Feynman kept math journals on their own accord, not because some teacher told them to do it. 

     When I was a student, I borrowed books from the National Library on things out of the normal curriculum.  I kept notes of things I learned.  I also did my own investigations.  I accidently discovered quadratic equations when I was in Primary 4.  I read guidebooks, asked my friend's elder brothers and sisters, my Chinese teacher (!) and other people to find out more.  I did not like factorisation by trial-and-error.  Neither did I like completing the square nor using the quadratic formula.  So I did my own research to find a sure-fire way to factorise without trial-and-error.  I finally managed to find a way, but my method had an uncanny similarity to the quadratic formula.  It was a Pyrrhic victory, but it was fun!  I thoroughly enjoyed it.

     If students need to be told or goaded to write mathematics journals, then we as educators need to ask ourselves:  Why?  What is their conception of mathematics and education?  What experiences have they gone through that lead them to these beliefs?

     Some food for thought, eh?