Chalk and Talk 2021

 When I began teaching Mathematics in high school in the mid-1960s, the teaching pedagogue was what was called "chalk and talk". There was little attempt by traditional Maths teachers to use any other teaching approach. I must admit that I was primary trained learning to teach the whole variety of subjects to my class. This continued with my transfer to a high school. There I taught a number of general subjects-English, Science, History, and Geography as well as Mathematics. So my range of teaching strategies was extensive. Mathematics in high school is normally a compulsory subject. Many Students can not see its relevance to their life or see it as too hard, especially when the "boogie man", Algebra, comes on the scene. So, in order to gains the attention of all my class, I used a variety of approaches including quizzes, radio and television as well as films. This brings me to the Walt Disney film, "Donald in Mathmagic Land". I discover it by chance look...

 My ever ongoing debating theist (MG) insists that if there is a past temporal infinity then it is impossible to reach the present since you have to participate in an infinite number of events before you can arrive at any current event. He introduced the analogy of "the infinite ladder" and how if you climb such a ladder you will never reach the top. However, he muddled his own analogy big time as the following series of exchanges made over many moons, and which I've cobbled together, demonstrate. My key distinction here is that if you have a finite lifespan and you started an infinite amount of time ago, then clearly you can't reach the present. However, if you happened to be blessed with an infinite lifespan, like say an up-quark (which can neither be created nor destroyed) then there's no problem. A finite lifespan can only travel through a finite time period; an infinite lifespan is under no such restrictions. [Note: previous to-and-fro discussions resulted i...

 Traditionally, the teaching of Mathematics in secondary schools rarely included the use of resources other than a text book. This was "satisfactory" because most of the student body was academically included. In today's jargon, using Gardener's learning styles; they were most likely maths-logic learners. The prevailing pedagogue was "Chalk and Talk". In simple terms it was lecture style approach followed by lots of worked exercises from simple to harder (more complex) examples. There was little or no attempt to teach problem solving skills needed to solve unfamiliar problems. With the introduction of all students into secondary education in the mid twentieth century, the steady raising of the school leaving age and the expectation of parents that their offspring get the opportunity to seek university qualifications mathematics teachers had to work with students who could not learn just with the "Chalk and Talk" approach. Many able learners found ...