A physicist, a mathematician and a logician were travelling through the British Isles together.
Just after they had crossed the border into Scotland, they saw a black sheep in profile on the top of a hill.
The physicist remarked, “Look at that! All the sheep in Scotland must be black!”
The mathematician corrected him, “Not necessarily … all we can conclude is that at least one sheep in Scotland is black.”
The logician, however, had the last say. “You are both quite wrong,” he observed, “All we can really conclude is that at least one sheep in Scotland is black on at least one side!”
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.
This website and its associated FaceBook page and YouTube channel were all launched on Tuesday 20 November 2012.
I enjoyed your presentation and no it wasn’t too long. Each subtraction algorithm has its merit as you demostrated, but after learning the “one up and one down” method, I’m employing it because of its speed and ease of usage. Even my wife, who hates mathematics with a passion, thinks it’s too easy. I look forward to your future presentations on both multiplication and number theory. I read an introduction text book some twenty five years ago on number theory by Oystein Ore who taught at Yale for better than twenty years. So in closing, please produce these lectures and the longer the better. Thanks.
Dennis Bell (on a CCM YouTube video about How to Subtract (Large) Numbers Easily)
