Dave Hewitt: in-class video reflection

      Once you got past the British accents and terminology changes, (take 2 vs. minus 2) watching Hewitt's atypical teaching style was very informative for aspiring mathematics teachers.
      The first lesson had the teacher use a meter stick to tap arbitrarily spaced areas on the walls of the classroom to teach the real number line in a far more effective manner (via repetition).  Even though the loud, repetitive sound appeared to be disruptive to learning, I found it to be conducive because it created an association between the number and its place in the room (relative to other ones).  As opposed to teaching the number line (and some basic binary operations) the traditional way, (a two-sided horizontal arrow) the meter stick method of using the classroom as a tangible I believe enables more students to 'picture' the concept.  Moreover, when the learners were asked to solve chains of binary operations (+/-) they were immediately able to not only solve the problems using their own 'meter' stick, but were able to construct multiple paths beginning at x and ending at y.  A few criticisms of this technique were: some students will be confused with the usage of ellipsis (...) - why is the distance from 1000 to 15 the same as from 15 to 1?  The choral approach can also mask certain students that may need help: if 90% of the class answers correctly, then those who are incorrect/unsure are drowned out and may be hesitant to voice their uncertainty.
      The second lesson was a creative approach to solving equations of one variable (I'm thinking of a number).  Starting with a simple example, having the students describe their thought patterns and repeat those results aloud draws the others into those patterns and helps everyone reinforce the connections between each operation and its inverse.  Without explicitly introducing the notion of "x" or parentheses, the students were (very quickly) able to extend their newfound knowledge to a much more difficult problem.  When converting the oral version of this more complex question to the board, (algebraic form) Dave used different and consistent sound cues when converting a word to its algebraic equivalent (parentheses, horizontal fraction, "x").  As in the previous lesson, creating an association in the student's mind can assist them when they attempt to recall a concept later on.