Playing on a calculator, I multiplied the constant pi times a random large number. The strange thing that happened was that I didn't see a decimal. I quickly checked the settings on my calculator and found the missing decimal places, due to rounding up from four decimals. The thing that dawned on me is that I knew there should never be an integer answer to multiplying any rational constant by pi, (except zero).
It was at this time I realized the beauty of understanding a concept and the depth of how understanding changes your perception of the world. Funny how such a simple happening can have such a profound impact when you are paying attention.
(NCTM, Professional Standards for Teaching Mathematics, 1991, pp 3-4.)
The thing that stands out most for me is that every question is "helping students" to achieve some relevant goal. None of the examples have anything to do with the "answer" and none are "yes or no" questions.
By: Mr. Woodford
I will reflect on ideas and practices I learn through my formative years as a classroom math teacher.