… mathematics has an aesthetic side. A conjecture can be “obvious” or “unexpected.” A result can be “trivial” or “beautiful.” A proof can be “messy,” “surprising,” or, as Erdős would say, “straight from the Book.” In a good proof, wrote Hardy, “there is a very high degree of unexpectedness, combined with inevitability and economy. The argument takes so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching consequences; but there is no escape from the conclusions.”
School classrooms can be exceedingly difficult places in which to learn mathematics well.
Teachers vary in passion and ability (as is natural); class behaviour and attitudes (and bullying) can alter the learning environment radically; learning in a large group at the same speed and with little opportunity to receive one-on-one help leads to boredom or frustration for many/most students; textbooks vary in quality and frequently lack stimulating material (because publishers restrict the size of the books); and sometimes students are negatively influenced by parents and peers who share their own bad experiences or attitudes.
Home educators, too, often feel that they lack sufficient understanding to teach their children mathematics … and the resources that they have access to can sometimes be bland, unstimulating, and even poorly explained or constructed.
My wife and I home educated our daughter and I have taught and tutored mathematics for many years. I am aware of the difficulties listed above and have often been asked by students and parents to create a website to share my understanding and resources with others. Crystal Clear Mathematics is the result.
Because this medium is not interactive (in the sense of allowing immediate interaction between you and me) I cannot provide the quality of tutition that I would like to offer you … but I hope you find the videos and the supporting files to be useful none-the-less.
My son isn’t rapt about attending tutoring but Graeme has taken the time find out the things my son is interested in and relate the maths topics to them. I can’t speak highly enough of his patient, calming manner. The maths resources provided have been helpful (and sometimes fun!) in my son’s learning and I have noticed a great improvement in his confidence and ability since starting tutoring.
Judee F (parent, 2012)